| Line 10: |
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| | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o | | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o |
| | | | |
| − | Version : May-Jun 2004 | + | Version : May-Jun 2004 [Draft 11.00] |
| | | | |
| | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o | | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o |
| Line 21: |
Line 21: |
| | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o | | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o |
| | </pre> | | </pre> |
| | + | |
| | + | <div class="nonumtoc">__TOC__</div> |
| | | | |
| | ==1. Introduction== | | ==1. Introduction== |
| Line 385: |
Line 387: |
| | </pre> | | </pre> |
| | | | |
| − | ====1.3.1. Initial Analysis of Inquiry -- Allegro Aperto==== | + | ====1.3.1. Initial Analysis of Inquiry — Allegro Aperto==== |
| | | | |
| | <pre> | | <pre> |
| Line 4,221: |
Line 4,223: |
| | </pre> | | </pre> |
| | | | |
| − | ====1.3.8. Rondeau — Tempo di Menuetto==== | + | ====1.3.8. Rondeau — Tempo di Menuetto==== |
| | | | |
| | <pre> | | <pre> |
| Line 5,470: |
Line 5,472: |
| | =====1.3.9.3. The Formative Tension===== | | =====1.3.9.3. The Formative Tension===== |
| | | | |
| − | <pre>
| + | The incidental arena or the informal context is presently described in casual, derivative, and negative terms, simply as the "not yet formal", and so this admittedly unruly region is currently depicted in ways that suggest a purely unformed and a wholly formless chaos, which it is not. But increasing experience with the formalization process can help one to develop a better appreciation of the informal context, and in time one can argue for a more positive characterization of this realm as a truly "formative context". The formal domain is where risks are contemplated, but the formative context is where risks are taken. |
| − | The incidental arena or the informal context is presently described in | |
| − | casual, derivative, and negative terms, simply as the "not yet formal", | |
| − | and so this admittedly unruly region is currently depicted in ways that | |
| − | suggest a purely unformed and a wholly formless chaos, which it is not. | |
| − | But increasing experience with the formalization process can help one | |
| − | to develop a better appreciation of the informal context, and in time | |
| − | one can argue for a more positive characterization of this realm as | |
| − | a truly "formative context". The formal domain is where risks are | |
| − | contemplated, but the formative context is where risks are taken. | |
| | | | |
| − | In this view, the informal context is more clearly seen as the off-stage | + | In this view, the informal context is more clearly seen as the off-stage staging ground where everything that appears on the formal scene is first assembled for a formal presentation. In taking this view, one steps back a bit in one's imagination from the scene that presses on one's attention, gets a sense of its frame and its stage, and becomes accustomed to see what appears in ever dimmer lights, in effect, one is learning to reflect on the more obvious actions, to read their pretexts, and to detect the motives that end in them. |
| − | staging ground where everything that appears on the formal scene is first | |
| − | assembled for a formal presentation. In taking this view, one steps back | |
| − | a bit in one's imagination from the scene that presses on one's attention, | |
| − | gets a sense of its frame and its stage, and becomes accustomed to see what | |
| − | appears in ever dimmer lights, in effect, one is learning to reflect on the | |
| − | more obvious actions, to read their pretexts, and to detect the motives that | |
| − | end in them. | |
| | | | |
| − | It is fair to assume that an agent of inquiry possesses a faculty of inquiry | + | It is fair to assume that an agent of inquiry possesses a faculty of inquiry that is available for exercise in the informal context, that is, without the agent being required to formalize its properties prior to their initial use. If this faculty of inquiry is a unity, then it appears as a whole on both sides of the "glass", that is, on both sides of the imaginary line that one pretends to draw between a formal arena and its informal context. |
| − | that is available for exercise in the informal context, that is, without the | |
| − | agent being required to formalize its properties prior to their initial use. | |
| − | If this faculty of inquiry is a unity, then it appears as a whole on both | |
| − | sides of the "glass", that is, on both sides of the imaginary line that | |
| − | one pretends to draw between a formal arena and its informal context. | |
| | | | |
| − | Recognizing the positive value of an informal context as | + | Recognizing the positive value of an informal context as an open forum or a formative space, it is possible to form the alignments of capacities that are indicated in Table 5. |
| − | an open forum or a formative space, it is possible to form | |
| − | the alignments of capacities that are indicated in Table 5. | |
| | | | |
| | + | <pre> |
| | Table 5. Alignments of Capacities | | Table 5. Alignments of Capacities |
| | o-------------------o-----------------------------o | | o-------------------o-----------------------------o |
| Line 5,510: |
Line 5,490: |
| | | Afforded | Possessed | Exercised | | | | Afforded | Possessed | Exercised | |
| | o-------------------o--------------o--------------o | | o-------------------o--------------o--------------o |
| | + | </pre> |
| | | | |
| − | This arrangement of capacities, based on the distinction between | + | This arrangement of capacities, based on the distinction between possession and exercise that arises so naturally in this context, stems from a root that is old indeed. In this connection, it is instructive to compare these alignments with those that we find in Aristotle's treatise ''On the Soul'', a germinal textbook of psychology that ventures to analyze the concept of the mind, psyche, or soul to the point of arriving at a definition. The alignments of capacites, analogous correspondences, and illustrative materials outlined by Aristotle are summarized in Table 6. |
| − | possession and exercise that arises so naturally in this context, | |
| − | stems from a root that is old indeed. In this connection, it is | |
| − | instructive to compare these alignments with those that we find | |
| − | in Aristotle's treatise 'On the Soul', a germinal textbook of | |
| − | psychology that ventures to analyze the concept of the mind, | |
| − | psyche, or soul to the point of arriving at a definition. | |
| − | The alignments of capacites, analogous correspondences, | |
| − | and illustrative materials outlined by Aristotle are | |
| − | summarized in Table 6. | |
| | | | |
| | + | <pre> |
| | Table 6. Alignments of Capacities in Aristotle | | Table 6. Alignments of Capacities in Aristotle |
| | o-------------------o-----------------------------o | | o-------------------o-----------------------------o |
| Line 5,536: |
Line 5,509: |
| | | Ship? | Sailor? | | | | Ship? | Sailor? | |
| | o-------------------o-----------------------------o | | o-------------------o-----------------------------o |
| | + | </pre> |
| | | | |
| − | An attempt to synthesize the materials and the schemes that are given | + | An attempt to synthesize the materials and the schemes that are given in Tables 5 and 6 leads to the alignments of capacities that are shown in Table 7. I do not pretend that the resulting alignments are perfect, since there is clearly some sort of twist taking place between the top and the bottom of this synthetic arrangement. Perhaps this is due to the modifications of case, tense, and grammatical category that occur throughout the paradigm, or perhaps it has to do with the fact that the relations through the middle of the Table are more analogical than categorical. For the moment I am content to leave all of these paradoxes intact, taking the pattern of tensions and torsions as a puzzle for future study. |
| − | in Tables 5 and 6 leads to the alignments of capacities that are shown | |
| − | in Table 7. I do not pretend that the resulting alignments are perfect, | |
| − | since there is clearly some sort of twist taking place between the top | |
| − | and the bottom of this synthetic arrangement. Perhaps this is due to | |
| − | the modifications of case, tense, and grammatical category that occur | |
| − | throughout the paradigm, or perhaps it has to do with the fact that | |
| − | the relations through the middle of the Table are more analogical | |
| − | than categorical. For the moment I am content to leave all of | |
| − | these paradoxes intact, taking the pattern of tensions and | |
| − | torsions as a puzzle for future study. | |
| | | | |
| | + | <pre> |
| | Table 7. Synthesis of Alignments | | Table 7. Synthesis of Alignments |
| | o-------------------o-----------------------------o | | o-------------------o-----------------------------o |
| Line 5,561: |
Line 5,526: |
| | | Matter | Form | | | | Matter | Form | |
| | o-------------------o-----------------------------o | | o-------------------o-----------------------------o |
| | + | </pre> |
| | | | |
| − | Due to the importance of Aristotle's account for every discussion that | + | Due to the importance of Aristotle's account for every discussion that follows it, not to mention for those that follow it without knowing it, and because the issues that it raises arise repeatedly throughout this project, I am going to cite an extended extract from the relevant text (Aristotle, ''Peri Psyche'', 2.1), breaking up the argument into a number of individual premisses, stages, and examples. |
| − | follows it, not to mention for those that follow it without knowing it, | |
| − | and because the issues that it raises arise repeatedly throughout this | |
| − | project, I am going to cite an extended extract from the relevant text | |
| − | (Aristotle, 'Peri Psyche', 2.1), breaking up the argument into a number | |
| − | of individual premisses, stages, and examples. | |
| | | | |
| | Aristotle wrote (W.S. Hett translation): | | Aristotle wrote (W.S. Hett translation): |
| | | | |
| | + | <pre> |
| | | a. The theories of the soul (psyche) | | | a. The theories of the soul (psyche) |
| | | handed down by our predecessors have | | | handed down by our predecessors have |
| Line 7,187: |
Line 7,149: |
| | </pre> | | </pre> |
| | | | |
| − | =====1.3.10.8. The Cactus Patch=====
| + | ====1.3.11. The Cactus Patch==== |
| | | | |
| | <pre> | | <pre> |
| Line 7,335: |
Line 7,297: |
| | </pre> | | </pre> |
| | | | |
| − | =====1.3.10.9. The Cactus Language : Syntax===== | + | =====1.3.11.1. The Cactus Language : Syntax===== |
| | | | |
| | <pre> | | <pre> |
| Line 8,649: |
Line 8,611: |
| | </pre> | | </pre> |
| | | | |
| − | =====1.3.10.10. The Cactus Language : Stylistics===== | + | =====1.3.11.2. Generalities About Formal Grammars===== |
| | + | |
| | + | =====1.3.11.3. The Cactus Language : Stylistics===== |
| | | | |
| | <pre> | | <pre> |
| Line 8,748: |
Line 8,712: |
| | manifest themselves in the process of inquiry and in the communication | | manifest themselves in the process of inquiry and in the communication |
| | of its results. | | of its results. |
| − |
| |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| |
| − |
| |
| − | IDS. Note 159
| |
| − |
| |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| |
| − |
| |
| − | 1.3.10.10. The Cactus Language: Stylistics (cont.)
| |
| | | | |
| | This patch of the ongoing discussion is concerned with describing a | | This patch of the ongoing discussion is concerned with describing a |
| Line 8,808: |
Line 8,764: |
| | and whether it can be compounded to cover the complexity that actually exists | | and whether it can be compounded to cover the complexity that actually exists |
| | in the realm of meaning -- these are questions for an extended future inquiry. | | in the realm of meaning -- these are questions for an extended future inquiry. |
| − |
| |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| |
| − |
| |
| − | IDS. Note 160
| |
| − |
| |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| |
| − |
| |
| − | 1.3.10.10. The Cactus Language: Stylistics (cont.)
| |
| | | | |
| | Perhaps I ought to comment on the differences between the present and | | Perhaps I ought to comment on the differences between the present and |
| Line 8,857: |
Line 8,805: |
| | to permit the initial symbol to characterize, to cover, to regenerate, | | to permit the initial symbol to characterize, to cover, to regenerate, |
| | or to produce itself, if that turns out to be the best way in the end. | | or to produce itself, if that turns out to be the best way in the end. |
| − |
| |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| |
| − |
| |
| − | IDS. Note 161
| |
| − |
| |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| |
| − |
| |
| − | 1.3.10.10. The Cactus Language: Stylistics (cont.)
| |
| | | | |
| | Before I leave this Subsection, I need to say a few things about | | Before I leave this Subsection, I need to say a few things about |
| Line 8,968: |
Line 8,908: |
| | are demanded by the application and intended by the designer, and not so much the | | are demanded by the application and intended by the designer, and not so much the |
| | peculiar characters of the signs that represent these classes of practical meaning. | | peculiar characters of the signs that represent these classes of practical meaning. |
| − |
| |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| |
| − |
| |
| − | IDS. Note 162
| |
| − |
| |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| |
| − |
| |
| − | 1.3.10.10. The Cactus Language: Stylistics (cont.)
| |
| | | | |
| | Any description of a language is bound to have alternative descriptions. | | Any description of a language is bound to have alternative descriptions. |
| Line 9,091: |
Line 9,023: |
| | this piece not only fits the type q but even comes to be generated under | | this piece not only fits the type q but even comes to be generated under |
| | the auspices of the non-terminal symbol "q". | | the auspices of the non-terminal symbol "q". |
| − |
| |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| |
| − |
| |
| − | IDS. Note 163
| |
| − |
| |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| |
| − |
| |
| − | 1.3.10.10. The Cactus Language: Stylistics (cont.)
| |
| | | | |
| | A moment's reflection on the issue of style, giving due consideration to the | | A moment's reflection on the issue of style, giving due consideration to the |
| Line 9,158: |
Line 9,082: |
| | as the simplest and the most primitive in principle, even if they are | | as the simplest and the most primitive in principle, even if they are |
| | scarcely recognized as lying among the more familiar elements of logic. | | scarcely recognized as lying among the more familiar elements of logic. |
| − |
| |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| |
| − |
| |
| − | IDS. Note 164
| |
| − |
| |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| |
| − |
| |
| − | 1.3.10.10. The Cactus Language: Stylistics (cont.)
| |
| | | | |
| | I am throwing together a wide variety of different operations into | | I am throwing together a wide variety of different operations into |
| Line 9,269: |
Line 9,185: |
| | literally embedded, if tacitly expressed, in a yet to be fully specified | | literally embedded, if tacitly expressed, in a yet to be fully specified |
| | relation, one that involves an unspecified number of unspecified domains. | | relation, one that involves an unspecified number of unspecified domains. |
| − |
| |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| |
| − |
| |
| − | IDS. Note 165
| |
| − |
| |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| |
| − |
| |
| − | 1.3.10.10. The Cactus Language: Stylistics (cont.)
| |
| | | | |
| | A quantity of information is a measure of constraint. In this respect, | | A quantity of information is a measure of constraint. In this respect, |
| Line 9,356: |
Line 9,264: |
| | by the indices "<1>" and "<2>" can be recognized as a special case of concatenation, | | by the indices "<1>" and "<2>" can be recognized as a special case of concatenation, |
| | albeit through the posting of editorial remarks from an external "mark-up" language. | | albeit through the posting of editorial remarks from an external "mark-up" language. |
| − |
| |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| |
| − |
| |
| − | IDS. Note 166
| |
| − |
| |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| |
| − |
| |
| − | 1.3.10.10. The Cactus Language: Stylistics (concl.)
| |
| | | | |
| | In order to systematize the relationships that strictures and straits | | In order to systematize the relationships that strictures and straits |
| Line 9,397: |
Line 9,297: |
| | There is a measure of ambiguity that remains in this formulation, | | There is a measure of ambiguity that remains in this formulation, |
| | but it is the best that I can do in the present informal context. | | but it is the best that I can do in the present informal context. |
| | + | </pre> |
| | | | |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| + | =====1.3.11.4. The Cactus Language : Mechanics===== |
| − | | |
| − | IDS. Note 167
| |
| − | | |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| |
| − | | |
| − | 1.3.10.11. The Cactus Language: Mechanics | |
| | | | |
| | + | <pre> |
| | | We are only now beginning to see how this works. Clearly one of the | | | We are only now beginning to see how this works. Clearly one of the |
| | | mechanisms for picking a reality is the sociohistorical sense of what | | | mechanisms for picking a reality is the sociohistorical sense of what |
| Line 9,525: |
Line 9,421: |
| | | | |
| | = a lobe with the accoutrements C_1, ..., C_k. | | = a lobe with the accoutrements C_1, ..., C_k. |
| − |
| |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| |
| − |
| |
| − | IDS. Note 168
| |
| − |
| |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| |
| − |
| |
| − | 1.3.10.11. The Cactus Language: Mechanics (concl.)
| |
| | | | |
| | Working from a structural description of the cactus language, | | Working from a structural description of the cactus language, |
| Line 9,622: |
Line 9,510: |
| | In particular, this generally makes it easier to observe the | | In particular, this generally makes it easier to observe the |
| | various properties of its underlying graphical structure. | | various properties of its underlying graphical structure. |
| | + | </pre> |
| | | | |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| + | =====1.3.11.5. The Cactus Language : Semantics===== |
| − | | |
| − | IDS. Note 169
| |
| − | | |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| |
| − | | |
| − | 1.3.10.12. The Cactus Language: Semantics | |
| | | | |
| | + | <pre> |
| | | Alas, and yet what 'are' you, my written and painted thoughts! | | | Alas, and yet what 'are' you, my written and painted thoughts! |
| | | It is not long ago that you were still so many-coloured, | | | It is not long ago that you were still so many-coloured, |
| Line 9,736: |
Line 9,620: |
| | For the generic case of k > 0, the "bound connective" takes the | | For the generic case of k > 0, the "bound connective" takes the |
| | form "-(S_1, ..., S_k)-". | | form "-(S_1, ..., S_k)-". |
| − |
| |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| |
| − |
| |
| − | IDS. Note 170
| |
| − |
| |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| |
| − |
| |
| − | 1.3.10.12. The Cactus Language: Semantics (cont.)
| |
| | | | |
| | At this point, there are actually two different "dialects", "scripts", | | At this point, there are actually two different "dialects", "scripts", |
| Line 9,816: |
Line 9,692: |
| | accoutrements. As a corollary, the logical denotation of the parse graph | | accoutrements. As a corollary, the logical denotation of the parse graph |
| | of "-()-", otherwise called a "needle", is the boolean value %0% = "false". | | of "-()-", otherwise called a "needle", is the boolean value %0% = "false". |
| − |
| |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| |
| − |
| |
| − | IDS. Note 171
| |
| − |
| |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| |
| − |
| |
| − | 1.3.10.12. The Cactus Language: Semantics (cont.)
| |
| | | | |
| | If one takes the point of view that PARC's and PARCE's amount to a | | If one takes the point of view that PARC's and PARCE's amount to a |
| Line 9,907: |
Line 9,775: |
| | Indeed, the "roughly" can be made "exactly" as soon as the domains of | | Indeed, the "roughly" can be made "exactly" as soon as the domains of |
| | a suitable sign relation are specified precisely. | | a suitable sign relation are specified precisely. |
| − |
| |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| |
| − |
| |
| − | IDS. Note 172
| |
| − |
| |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| |
| − |
| |
| − | 1.3.10.12. The Cactus Language: Semantics (concl.)
| |
| | | | |
| | A good way to illustrate the action of the conjunction and surjunction | | A good way to illustrate the action of the conjunction and surjunction |
| Line 10,088: |
Line 9,948: |
| | or whether its inverse is being invoked to indicate the fibers | | or whether its inverse is being invoked to indicate the fibers |
| | of truth or untruth under the propositional function in question. | | of truth or untruth under the propositional function in question. |
| | + | </pre> |
| | | | |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| + | =====1.3.11.6. Stretching Exercises===== |
| − | | |
| − | IDS. Note 173
| |
| − | | |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| |
| − | | |
| − | 1.3.10.13. Stretching Exercises | |
| | | | |
| | + | <pre> |
| | For ease of reference, I repeat here a couple of the | | For ease of reference, I repeat here a couple of the |
| | definitions that are needed again in this discussion. | | definitions that are needed again in this discussion. |
| Line 10,286: |
Line 10,142: |
| | | | |
| | Which was to be shown. | | Which was to be shown. |
| | + | </pre> |
| | | | |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| + | ====1.3.12. Syntactic Transformations==== |
| | | | |
| − | IDS. Note 174
| + | We have been examining several distinct but closely related notions of ''indication''. To discuss the import of these ideas in greater depth, it serves to establish a number of logical relations and set-theoretic identities that can be found to hold among their roughly parallel arrays of conceptions and constructions. Facilitating this task requires in turn a number of auxiliary concepts and notations. |
| | | | |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| + | The diverse notions of indication presently under discussion are expressed in a variety of different notations, enumerated as follows: |
| | | | |
| − | 1.3.10.14. Syntactic Transformations
| + | # The functional language of propositions |
| | + | # The logical language of sentences |
| | + | # The geometric language of sets |
| | | | |
| − | We have been examining several distinct but closely related
| + | Correspondingly, one way to explain the relationships that exist among the various notions of indication is to describe the translations that they induce among the associated families of notation. |
| − | notions of indication. To discuss the import of these ideas | |
| − | in greater depth, it serves to establish a number of logical
| |
| − | relations and set-theoretic identities that can be found to
| |
| − | hold among their roughly parallel arrays of conceptions and
| |
| − | constructions. Facilitating this task, in turn, requires
| |
| − | a number of auxiliary concepts and notations.
| |
| | | | |
| − | The diverse notions of "indication" presently under discussion
| + | =====1.3.12.1. Syntactic Transformation Rules===== |
| − | are expressed in a variety of different notations, for example,
| |
| − | the functional language of propositions, the geometric language
| |
| − | of sets, and the logical language of sentences. Correspondingly,
| |
| − | one way to explain the relationships that exist among the various
| |
| − | notions of indication is to describe the "translations" that they
| |
| − | induce among the asssociated families of notation. A good way to
| |
| − | summarize the necessary translations between different styles of
| |
| − | indication, and along the way to organize their use in practice,
| |
| − | is by means of the "rules of syntactic transformation" (ROST's)
| |
| − | that partially formalize the translations in question.
| |
| | | | |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| + | A good way to summarize the necessary translations between different styles of indication, and along the way to organize their use in practice, is by means of the ''rules of syntactic transformation'' (ROSTs) that partially formalize the translations in question. |
| | | | |
| − | IDS. Note 175
| + | Rudimentary examples of ROSTs are readily mined from the raw materials that are already available in this area of discussion. To begin as near the beginning as possible, let the definition of an indicator function be recorded in the following form: |
| − | | |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| |
| − | | |
| − | 1.3.10.14. Syntactic Transformations (cont.)
| |
| − | | |
| − | Rudimentary examples of ROST's are readily mined from the | |
| − | raw materials that are already available in this area of | |
| − | discussion. To begin as near the beginning as possible, | |
| − | let the definition of an indicator function be recorded | |
| − | in the following form: | |
| | | | |
| | + | <pre> |
| | o-------------------------------------------------o | | o-------------------------------------------------o |
| | | Definition 1. Indicator Function | | | | Definition 1. Indicator Function | |
| Line 10,344: |
Line 10,178: |
| | | | | | | | |
| | o-------------------------------------------------o | | o-------------------------------------------------o |
| | + | </pre> |
| | | | |
| − | In practice, a definition like this is commonly used to substitute | + | In practice, a definition like this is commonly used to substitute one of two logically equivalent expressions or sentences for the other in a context where the conditions of using the definition in this way are satisfied and where the change is perceived as potentially advancing a proof. The employment of a definition in this way can be expressed in the form of a ROST that allows one to exchange two expressions of logically equivalent forms for one another in every context where their logical values are the only consideration. To be specific, the ''logical value'' of an expression is the value in the boolean domain %B% = {%0%, %1%} that the expression represents to its context or that it stands for in its context. |
| − | one of two logically equivalent expressions or sentences for the | |
| − | other in a context where the conditions of using the definition | |
| − | in this way are satisfied and where the change is perceived as | |
| − | potentially advancing a proof. The employment of a definition | |
| − | in this way can be expressed in the form of a ROST that allows | |
| − | one to exchange two expressions of logically equivalent forms | |
| − | for one another in every context where their logical values are | |
| − | the only consideration. To be specific, the "logical value" of | |
| − | an expression is the value in the boolean domain %B% = {%0%, %1%} | |
| − | that the expression represents to its context or that it stands for | |
| − | in its context. | |
| | | | |
| − | In the case of Definition 1, the corresponding ROST permits one | + | In the case of Definition 1, the corresponding ROST permits one to exchange a sentence of the form "x in Q" with an expression of the form "-{Q}-(x)" in any context that satisfies the conditions of its use, namely, the conditions of the definition that lead up to the stated equivalence. The relevant ROST is recorded in Rule 1. By way of convention, I list the items that fall under a rule in rough order of their ascending conceptual subtlety or their increasing syntactic complexity, without regard for the normal or the typical orders of their exchange, since this can vary from widely from case to case. |
| − | to exchange a sentence of the form "x in Q" with an expression of | |
| − | the form "-{Q}-(x)" in any context that satisfies the conditions of | |
| − | its use, namely, the conditions of the definition that lead up to the | |
| − | stated equivalence. The relevant ROST is recorded in Rule 1. By way | |
| − | of convention, I list the items that fall under a rule in rough order | |
| − | of their ascending conceptual subtlety or their increasing syntactic | |
| − | complexity, without regard for the normal or the typical orders of | |
| − | their exchange, since this can vary from widely from case to case. | |
| | | | |
| | + | <pre> |
| | o-------------------------------------------------o | | o-------------------------------------------------o |
| | | Rule 1 | | | | Rule 1 | |
| Line 10,387: |
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| | | | | | | | |
| | o-------------------------------------------------o | | o-------------------------------------------------o |
| − |
| |
| − | Conversely, any rule of this sort, properly qualified by the
| |
| − | conditions under which it applies, can be turned back into a
| |
| − | summary statement of the logical equivalence that is involved
| |
| − | in its application. This mode of conversion between a static
| |
| − | principle and a transformational rule, in other words, between
| |
| − | a statement of equivalence and an equivalence of statements, is
| |
| − | so automatic that it is usually not necessary to make a separate
| |
| − | note of the "horizontal" versus the "vertical" versions of what
| |
| − | amounts to the same abstract principle.
| |
| | </pre> | | </pre> |
| | | | |
| − | ==Where I Left Off In June 2004==
| + | Conversely, any rule of this sort, properly qualified by the conditions under which it applies, can be turned back into a summary statement of the logical equivalence that is involved in its application. This mode of conversion between a static principle and a transformational rule, in other words, between a statement of equivalence and an equivalence of statements, is so automatic that it is usually not necessary to make a separate note of the "horizontal" versus the "vertical" versions of what amounts to the same abstract principle. |
| − | | |
| − | <pre>
| |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| |
| | | | |
| − | IDS. Note 176
| + | As another example of a ROST, consider the following logical equivalence, that holds for any <math>X \subseteq U\!</math> and for all <math>u \in U.</math> |
| | | | |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| + | : -{X}-(u) <=> -{X}-(u) = 1. |
| | | | |
| − | 1.3.10.14. Syntactic Transformations (cont.)
| + | In practice, this logical equivalence is used to exchange an expression of the form "-{X}-(u)" with a sentence of the form "-{X}-(u) = 1" in any context where one has a relatively fixed X c U in mind and where one is conceiving u in U to vary over its whole domain, namely, the universe U. This leads to the ROST that is given in Rule 2. |
| − | | |
| − | As another example of a ROST, consider the
| |
| − | following logical equivalence, that holds
| |
| − | for any X c U and for all u in U:
| |
| − | | |
| − | -{X}-(u) <=> -{X}-(u) = 1.
| |
| − | | |
| − | In practice, this logical equivalence is used to exchange | |
| − | an expression of the form "-{X}-(u)" with a sentence of the | |
| − | form "-{X}-(u) = 1" in any context where one has a relatively | |
| − | fixed X c U in mind and where one is conceiving u in U to vary | |
| − | over its whole domain, namely, the universe U. This leads to | |
| − | the ROST that is given in Rule 2. | |
| | | | |
| | + | <pre> |
| | o-------------------------------------------------o | | o-------------------------------------------------o |
| | | Rule 2 | | | | Rule 2 | |
| Line 10,440: |
Line 10,232: |
| | | | | | | | |
| | o-------------------------------------------------o | | o-------------------------------------------------o |
| | + | </pre> |
| | | | |
| − | Rules like these can be chained together to establish extended | + | Rules like these can be chained together to establish extended rules, just so long as their antecedent conditions are compatible. For example, Rules 1 and 2 combine to give the equivalents that are listed in Rule 3. This follows from a recognition that the function -{X}- : U -> %B% that is introduced in Rule 1 is an instance of the function f : U -> %B% that is mentioned in Rule 2. By the time one arrives in the "consequence box" of either Rule, then, one has in mind a comparatively fixed X c U, a proposition f or -{X}- about things in U, and a variable argument u in U. |
| − | rules, just so long as their antecedent conditions are compatible. | |
| − | For example, Rules 1 and 2 combine to give the equivalents that are | |
| − | listed in Rule 3. This follows from a recognition that the function | |
| − | -{X}- : U -> %B% that is introduced in Rule 1 is an instance of the | |
| − | function f : U -> %B% that is mentioned in Rule 2. By the time one | |
| − | arrives in the "consequence box" of either Rule, then, one has in | |
| − | mind a comparatively fixed X c U, a proposition f or -{X}- about | |
| − | things in U, and a variable argument u in U. | |
| | | | |
| | + | <pre> |
| | o-------------------------------------------------o---------o | | o-------------------------------------------------o---------o |
| | | Rule 3 | | | | | Rule 3 | | |
| Line 10,471: |
Line 10,257: |
| | | | | | | | | | |
| | o-------------------------------------------------o---------o | | o-------------------------------------------------o---------o |
| | + | </pre> |
| | | | |
| − | A large stock of rules can be derived in this way, by chaining together | + | A large stock of rules can be derived in this way, by chaining together segments that are selected from a stock of previous rules, with perhaps the whole process of derivation leading back to an axial body or a core stock of rules, with all recurring to and relying on an axiomatic basis. In order to keep track of their derivations, as their pedigrees help to remember the reasons for trusting their use in the first place, derived rules can be annotated by citing the rules from which they are derived. |
| − | segments that are selected from a stock of previous rules, with perhaps | |
| − | the whole process of derivation leading back to an axial body or a core | |
| − | stock of rules, with all recurring to and relying on an axiomatic basis. | |
| − | In order to keep track of their derivations, as their pedigrees help to | |
| − | remember the reasons for trusting their use in the first place, derived | |
| − | rules can be annotated by citing the rules from which they are derived. | |
| | | | |
| − | In the present discussion, I am using a particular style of annotation | + | In the present discussion, I am using a particular style of annotation for rule derivations, one that is called "proof by grammatical paradigm" or "proof by syntactic analogy". The annotations in the right margin of the Rule box can be read as the "denominators" of the paradigm that is being employed, in other words, as the alternating terms of comparison in a sequence of analogies. This can be illustrated by considering the derivation Rule 3 in detail. Taking the steps marked in the box one at a time, one can interweave the applications in the central body of the box with the annotations in the right margin of the box, reading "is to" for the ":" sign and "as" for the "::" sign, in the following fashion: |
| − | for rule derivations, one that is called "proof by grammatical paradigm" | |
| − | or "proof by syntactic analogy". The annotations in the right margin of | |
| − | the Rule box can be read as the "denominators" of the paradigm that is | |
| − | being employed, in other words, as the alternating terms of comparison | |
| − | in a sequence of analogies. This can be illustrated by considering the | |
| − | derivation Rule 3 in detail. Taking the steps marked in the box one at | |
| − | a time, one can interweave the applications in the central body of the | |
| − | box with the annotations in the right margin of the box, reading "is to" | |
| − | for the ":" sign and "as" for the "::" sign, in the following fashion: | |
| | | | |
| | + | <pre> |
| | R3a. "u in X" is to R1a, namely, "u in X", | | R3a. "u in X" is to R1a, namely, "u in X", |
| | | | |
| Line 10,504: |
Line 10,277: |
| | | | |
| | R3c. "{X}(u) = 1" is to R2b, namely, "f(u) = 1". | | R3c. "{X}(u) = 1" is to R2b, namely, "f(u) = 1". |
| | + | </pre> |
| | | | |
| − | Notice how the sequence of analogies pivots on the item R3b, | + | Notice how the sequence of analogies pivots on the item R3b, viewing it first under the aegis of R1b, as the second term of the first analogy, and then turning to view it again under the guise of R2a, as the first term of the second analogy. |
| − | viewing it first under the aegis of R1b, as the second term of | |
| − | the first analogy, and then turning to view it again under the | |
| − | guise of R2a, as the first term of the second analogy. | |
| | | | |
| − | By way of convention, rules that are tailored to a particular | + | By way of convention, rules that are tailored to a particular application, case, or subject, and rules that are adapted to a particular goal, object, or purpose, I frequently refer to as "Facts". |
| − | application, case, or subject, and rules that are adapted to | |
| − | a particular goal, object, or purpose, I frequently refer to | |
| − | as "Facts". | |
| − | </pre>
| |
| | | | |
| − | =====1.3.10.14. Syntactic Transformations (cont.)=====
| + | Besides linking rules together into extended sequences of equivalents, there is one other way that is commonly used to get new rules from old. Novel starting points for rules can be obtained by extracting pairs of equivalent expressions from a sequence that falls under an established rule, and then by stating their equality in the proper form of equation. For example, by extracting the equivalent expressions that are annotated as "R3a" and "R3c" in Rule 3 and by explictly stating their equivalence, one obtains the specialized result that is recorded in Corollary 1. |
| − | | |
| − | Besides linking rules together into extended sequences of equivalents, | |
| − | there is one other way that is commonly used to get new rules from old. | |
| − | Novel starting points for rules can be obtained by extracting pairs of | |
| − | equivalent expressions from a sequence that falls under an established | |
| − | rule, and then by stating their equality in the proper form of equation. | |
| − | For example, by extracting the equivalent expressions that are annotated | |
| − | as "R3a" and "R3c" in Rule 3 and by explictly stating their equivalence, | |
| − | one obtains the specialized result that is recorded in Corollary 1. | |
| | | | |
| | + | <pre> |
| | Corollary 1 | | Corollary 1 |
| | | | |
| Line 10,536: |
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| | | | |
| | C1a. u C X <=> {X}(u) = 1. R3a=R3c | | C1a. u C X <=> {X}(u) = 1. R3a=R3c |
| | + | </pre> |
| | | | |
| − | There are a number of issues, that arise especially in establishing the proper use of STR's, that are appropriate to discuss at this juncture. The notation "[S]" is intended to represent "the proposition denoted by the sentence S". There is only one problem with the use of this form. There is, in general, no such thing as "the" proposition denoted by S. Generally speaking, if a sentence is taken out of context and considered across a variety of different contexts, there is no unique proposition that it can be said to denote. But one is seldom ever speaking at the maximum level of generality, or even found to be thinking of it, and so this notation is usually meaningful and readily understandable whenever it is read in the proper frame of mind. Still, once the issue is raised, the question of how these meanings and understandings are possible has to be addressed, especially if one desires to express the regulations of their syntax in a partially computational form. This requires a closer examination of the very notion of "context", and it involves engaging in enough reflection on the "contextual evaluation" of sentences that the relevant principles of its successful operation can be discerned and rationalized in explicit terms. | + | There are a number of issues, that arise especially in establishing the proper use of ROSTs, that are appropriate to discuss at this juncture. The notation "[S]" is intended to represent "the proposition denoted by the sentence S". There is only one problem with the use of this form. There is, in general, no such thing as "the" proposition denoted by S. Generally speaking, if a sentence is taken out of context and considered across a variety of different contexts, there is no unique proposition that it can be said to denote. But one is seldom ever speaking at the maximum level of generality, or even found to be thinking of it, and so this notation is usually meaningful and readily understandable whenever it is read in the proper frame of mind. Still, once the issue is raised, the question of how these meanings and understandings are possible has to be addressed, especially if one desires to express the regulations of their syntax in a partially computational form. This requires a closer examination of the very notion of "context", and it involves engaging in enough reflection on the "contextual evaluation" of sentences that the relevant principles of its successful operation can be discerned and rationalized in explicit terms. |
| | | | |
| | A sentence that is written in a context where it represents a value of 1 or 0 as a function of things in the universe U, where it stands for a value of "true" or "false", depending on how the signs that constitute its proper syntactic arguments are interpreted as denoting objects in U, in other words, where it is bound to lead its interpreter to view its own truth or falsity as determined by a choice of objects in U, is a sentence that might as well be written in the context "[ ... ]", whether or not this frame is explicitly marked around it. | | A sentence that is written in a context where it represents a value of 1 or 0 as a function of things in the universe U, where it stands for a value of "true" or "false", depending on how the signs that constitute its proper syntactic arguments are interpreted as denoting objects in U, in other words, where it is bound to lead its interpreter to view its own truth or falsity as determined by a choice of objects in U, is a sentence that might as well be written in the context "[ ... ]", whether or not this frame is explicitly marked around it. |
| Line 10,543: |
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| | More often than not, the context of interpretation fixes the denotations of most of the signs that make up a sentence, and so it is safe to adopt the convention that only those signs whose objects are not already fixed are free to vary in their denotations. Thus, only the signs that remain in default of prior specification are subject to treatment as variables, with a decree of functional abstraction hanging over all of their heads. | | More often than not, the context of interpretation fixes the denotations of most of the signs that make up a sentence, and so it is safe to adopt the convention that only those signs whose objects are not already fixed are free to vary in their denotations. Thus, only the signs that remain in default of prior specification are subject to treatment as variables, with a decree of functional abstraction hanging over all of their heads. |
| | | | |
| − | [u C X] = Lambda (u, C, X).(u C X). | + | : [u C X] = Lambda (u, C, X).(u C X). |
| | | | |
| | As it is presently stated, Rule 1 lists a couple of manifest sentences, and it authorizes one to make exchanges in either direction between the syntactic items that have these two forms. But a sentence is any sign that denotes a proposition, and thus there are a number of less obvious sentences that can be added to this list, extending the number of items that are licensed to be exchanged. Consider the sense of equivalence among sentences that is recorded in Rule 4. | | As it is presently stated, Rule 1 lists a couple of manifest sentences, and it authorizes one to make exchanges in either direction between the syntactic items that have these two forms. But a sentence is any sign that denotes a proposition, and thus there are a number of less obvious sentences that can be added to this list, extending the number of items that are licensed to be exchanged. Consider the sense of equivalence among sentences that is recorded in Rule 4. |
| | | | |
| | + | <pre> |
| | Rule 4 | | Rule 4 |
| | | | |
| Line 10,564: |
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| | | | |
| | R4e. {X}(u) = 1. | | R4e. {X}(u) = 1. |
| | + | </pre> |
| | | | |
| | The first and last items on this list, namely, the sentences "u C X" and "{X}(u) = 1" that are annotated as "R4a" and "R4e", respectively, are just the pair of sentences from Rule 3 whose equivalence for all u C U is usually taken to define the idea of an indicator function {X} : U -> B. At first sight, the inclusion of the other items appears to involve a category confusion, in other words, to mix the modes of interpretation and to create an array of mismatches between their own ostensible types and the ruling type of a sentence. On reflection, and taken in context, these problems are not as serious as they initially seem. For instance, the expression "[u C X]" ostensibly denotes a proposition, but if it does, then it evidently can be recognized, by virtue of this very fact, to be a genuine sentence. As a general rule, if one can see it on the page, then it cannot be a proposition, but can be, at best, a sign of one. | | The first and last items on this list, namely, the sentences "u C X" and "{X}(u) = 1" that are annotated as "R4a" and "R4e", respectively, are just the pair of sentences from Rule 3 whose equivalence for all u C U is usually taken to define the idea of an indicator function {X} : U -> B. At first sight, the inclusion of the other items appears to involve a category confusion, in other words, to mix the modes of interpretation and to create an array of mismatches between their own ostensible types and the ruling type of a sentence. On reflection, and taken in context, these problems are not as serious as they initially seem. For instance, the expression "[u C X]" ostensibly denotes a proposition, but if it does, then it evidently can be recognized, by virtue of this very fact, to be a genuine sentence. As a general rule, if one can see it on the page, then it cannot be a proposition, but can be, at best, a sign of one. |
| | | | |
| − | The use of the basic connectives can be expressed in the form of a STR as follows: | + | The use of the basic connectives can be expressed in the form of a ROST as follows: |
| | | | |
| | + | <pre> |
| | Logical Translation Rule 0 | | Logical Translation Rule 0 |
| | | | |
| Line 10,588: |
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| | | | |
| | L0c. [SurcJj Sj] = SurjJj [Sj] = SurjJj Pj. | | L0c. [SurcJj Sj] = SurjJj [Sj] = SurjJj Pj. |
| | + | </pre> |
| | | | |
| − | As a general rule, the application of a STR involves the recognition of an antecedent condition and the facilitation of a consequent condition. The antecedent condition is a state whose initial expression presents a match, in a formal sense, to one of the sentences that are listed in the STR, and the consequent condition is achieved by taking its suggestions seriously, in other words, by following its sequence of equivalents and implicants to some other link in its chain. | + | As a general rule, the application of a ROST involves the recognition of an antecedent condition and the facilitation of a consequent condition. The antecedent condition is a state whose initial expression presents a match, in a formal sense, to one of the sentences that are listed in the STR, and the consequent condition is achieved by taking its suggestions seriously, in other words, by following its sequence of equivalents and implicants to some other link in its chain. |
| | | | |
| | Generally speaking, the application of a rule involves the recognition of an antecedent condition as a case that falls under a clause of the rule. This means that the antecedent condition is able to be captured in the form, conceived in the guise, expressed in the manner, grasped in the pattern, or recognized in the shape of one of the sentences in a list of equivalents or a chain of implicants. | | Generally speaking, the application of a rule involves the recognition of an antecedent condition as a case that falls under a clause of the rule. This means that the antecedent condition is able to be captured in the form, conceived in the guise, expressed in the manner, grasped in the pattern, or recognized in the shape of one of the sentences in a list of equivalents or a chain of implicants. |
| Line 10,595: |
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| | A condition is "amenable" to a rule if any of its conceivable expressions formally match any of the expressions that are enumerated by the rule. Further, it requires the relegation of the other expressions to the production of a result. Thus, there is the choice of an initial expression that needs to be checked on input for whether it fits the antecedent condition and there are several types of output that are generated as a consequence, only a few of which are usually needed at any given time. | | A condition is "amenable" to a rule if any of its conceivable expressions formally match any of the expressions that are enumerated by the rule. Further, it requires the relegation of the other expressions to the production of a result. Thus, there is the choice of an initial expression that needs to be checked on input for whether it fits the antecedent condition and there are several types of output that are generated as a consequence, only a few of which are usually needed at any given time. |
| | | | |
| | + | <pre> |
| | Logical Translation Rule 1 | | Logical Translation Rule 1 |
| | | | |
| Line 10,614: |
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| | | | |
| | L1b11. [True] = (()) = 1 : U->B. | | L1b11. [True] = (()) = 1 : U->B. |
| | + | </pre> |
| | | | |
| | + | <pre> |
| | Geometric Translation Rule 1 | | Geometric Translation Rule 1 |
| | | | |
| Line 10,632: |
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| | | | |
| | G1b11. {U} = (()) = 1 : U->B. | | G1b11. {U} = (()) = 1 : U->B. |
| | + | </pre> |
| | | | |
| | + | <pre> |
| | Logical Translation Rule 2 | | Logical Translation Rule 2 |
| | | | |
| Line 10,676: |
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| | | | |
| | L2b15. [True] = (()) = 1 : U->B. | | L2b15. [True] = (()) = 1 : U->B. |
| | + | </pre> |
| | | | |
| − | | + | <pre> |
| | Geometric Translation Rule 2 | | Geometric Translation Rule 2 |
| | | | |
| | If X, Y c U | | If X, Y c U |
| − |
| |
| − |
| |
| | | | |
| | and P, Q U -> B, such that: | | and P, Q U -> B, such that: |
| − |
| |
| − |
| |
| | | | |
| | G2a. {X} = P and {Y} = Q, | | G2a. {X} = P and {Y} = Q, |
| − |
| |
| − |
| |
| | | | |
| | then the following equations hold: | | then the following equations hold: |
| − |
| |
| − |
| |
| | | | |
| | G2b00. {{}} = () = 0 : U->B. | | G2b00. {{}} = () = 0 : U->B. |
| − |
| |
| − |
| |
| | | | |
| | G2b01. {~X n ~Y} = ({X})({Y}) = (P)(Q). | | G2b01. {~X n ~Y} = ({X})({Y}) = (P)(Q). |
| − |
| |
| − |
| |
| | | | |
| | G2b02. {~X n Y} = ({X}){Y} = (P) Q. | | G2b02. {~X n Y} = ({X}){Y} = (P) Q. |
| − |
| |
| − |
| |
| | | | |
| | G2b03. {~X} = ({X}) = (P). | | G2b03. {~X} = ({X}) = (P). |
| − |
| |
| − |
| |
| | | | |
| | G2b04. {X n ~Y} = {X}({Y}) = P (Q). | | G2b04. {X n ~Y} = {X}({Y}) = P (Q). |
| − |
| |
| − |
| |
| | | | |
| | G2b05. {~Y} = ({Y}) = (Q). | | G2b05. {~Y} = ({Y}) = (Q). |
| − |
| |
| − |
| |
| | | | |
| | G2b06. {X + Y} = ({X}, {Y}) = (P, Q). | | G2b06. {X + Y} = ({X}, {Y}) = (P, Q). |
| − |
| |
| − |
| |
| | | | |
| | G2b07. {~(X n Y)} = ({X}.{Y}) = (P Q). | | G2b07. {~(X n Y)} = ({X}.{Y}) = (P Q). |
| − |
| |
| − |
| |
| | | | |
| | G2b08. {X n Y} = {X}.{Y} = P.Q. | | G2b08. {X n Y} = {X}.{Y} = P.Q. |
| − |
| |
| − |
| |
| | | | |
| | G2b09. {~(X + Y)} = (({X}, {Y})) = ((P, Q)). | | G2b09. {~(X + Y)} = (({X}, {Y})) = ((P, Q)). |
| − |
| |
| − |
| |
| | | | |
| | G2b10. {Y} = {Y} = Q. | | G2b10. {Y} = {Y} = Q. |
| − |
| |
| − |
| |
| | | | |
| | G2b11. {~(X n ~Y)} = ({X}({Y})) = (P (Q)). | | G2b11. {~(X n ~Y)} = ({X}({Y})) = (P (Q)). |
| − |
| |
| − |
| |
| | | | |
| | G2b12. {X} = {X} = P. | | G2b12. {X} = {X} = P. |
| − |
| |
| − |
| |
| | | | |
| | G2b13. {~(~X n Y)} = (({X}) {Y}) = ((P) Q). | | G2b13. {~(~X n Y)} = (({X}) {Y}) = ((P) Q). |
| − |
| |
| − |
| |
| | | | |
| | G2b14. {X u Y} = (({X})({Y})) = ((P)(Q)). | | G2b14. {X u Y} = (({X})({Y})) = ((P)(Q)). |
| − |
| |
| − |
| |
| | | | |
| | G2b15. {U} = (()) = 1 : U->B. | | G2b15. {U} = (()) = 1 : U->B. |
| | + | </pre> |
| | | | |
| − | | + | <pre> |
| − | | |
| − | | |
| − | | |
| | Value Rule 1 | | Value Rule 1 |
| | | | |
| | If v, w C B | | If v, w C B |
| − |
| |
| − |
| |
| | | | |
| | then "v = w" is a sentence about <v, w> C B2, | | then "v = w" is a sentence about <v, w> C B2, |
| − |
| |
| − |
| |
| | | | |
| | [v = w] is a proposition : B2 -> B, | | [v = w] is a proposition : B2 -> B, |
| − |
| |
| − |
| |
| | | | |
| | and the following are identical values in B: | | and the following are identical values in B: |
| − |
| |
| − |
| |
| | | | |
| | V1a. [ v = w ](v, w) | | V1a. [ v = w ](v, w) |
| − |
| |
| − |
| |
| | | | |
| | V1b. [ v <=> w ](v, w) | | V1b. [ v <=> w ](v, w) |
| − |
| |
| − |
| |
| | | | |
| | V1c. ((v , w)) | | V1c. ((v , w)) |
| | + | </pre> |
| | | | |
| − | | + | <pre> |
| − | | |
| | Value Rule 1 | | Value Rule 1 |
| | | | |
| | If v, w C B, | | If v, w C B, |
| − |
| |
| − |
| |
| | | | |
| | then the following are equivalent: | | then the following are equivalent: |
| − |
| |
| − |
| |
| | | | |
| | V1a. v = w. | | V1a. v = w. |
| − |
| |
| − |
| |
| | | | |
| | V1b. v <=> w. | | V1b. v <=> w. |
| − |
| |
| − |
| |
| | | | |
| | V1c. (( v , w )). | | V1c. (( v , w )). |
| | + | </pre> |
| | | | |
| | A rule that allows one to turn equivalent sentences into identical propositions: | | A rule that allows one to turn equivalent sentences into identical propositions: |
| | | | |
| − | (S <=> T) <=> ([S] = [T]) | + | : (S <=> T) <=> ([S] = [T]) |
| | | | |
| | Consider [ v = w ](v, w) and [ v(u) = w(u) ](u) | | Consider [ v = w ](v, w) and [ v(u) = w(u) ](u) |
| | | | |
| | + | <pre> |
| | Value Rule 1 | | Value Rule 1 |
| | | | |
| | If v, w C B, | | If v, w C B, |
| − |
| |
| − |
| |
| | | | |
| | then the following are identical values in B: | | then the following are identical values in B: |
| − |
| |
| − |
| |
| | | | |
| | V1a. [ v = w ] | | V1a. [ v = w ] |
| − |
| |
| − |
| |
| | | | |
| | V1b. [ v <=> w ] | | V1b. [ v <=> w ] |
| − |
| |
| − |
| |
| | | | |
| | V1c. (( v , w )) | | V1c. (( v , w )) |
| | + | </pre> |
| | | | |
| − | | + | <pre> |
| − | | |
| | Value Rule 1 | | Value Rule 1 |
| | | | |
| | If f, g : U -> B, | | If f, g : U -> B, |
| − |
| |
| − |
| |
| | | | |
| | and u C U | | and u C U |
| − |
| |
| − |
| |
| | | | |
| | then the following are identical values in B: | | then the following are identical values in B: |
| − |
| |
| − |
| |
| | | | |
| | V1a. [ f(u) = g(u) ] | | V1a. [ f(u) = g(u) ] |
| − |
| |
| − |
| |
| | | | |
| | V1b. [ f(u) <=> g(u) ] | | V1b. [ f(u) <=> g(u) ] |
| − |
| |
| − |
| |
| | | | |
| | V1c. (( f(u) , g(u) )) | | V1c. (( f(u) , g(u) )) |
| | + | </pre> |
| | | | |
| − | | + | <pre> |
| − | | |
| | Value Rule 1 | | Value Rule 1 |
| | | | |
| | If f, g : U -> B, | | If f, g : U -> B, |
| − |
| |
| − |
| |
| | | | |
| | then the following are identical propositions on U: | | then the following are identical propositions on U: |
| − |
| |
| − |
| |
| | | | |
| | V1a. [ f = g ] | | V1a. [ f = g ] |
| − |
| |
| − |
| |
| | | | |
| | V1b. [ f <=> g ] | | V1b. [ f <=> g ] |
| − |
| |
| − |
| |
| | | | |
| | V1c. (( f , g ))$ | | V1c. (( f , g ))$ |
| | + | </pre> |
| | | | |
| − | | + | <pre> |
| − | | |
| | Evaluation Rule 1 | | Evaluation Rule 1 |
| | | | |
| | If f, g : U -> B | | If f, g : U -> B |
| − |
| |
| − |
| |
| | | | |
| | and u C U, | | and u C U, |
| − |
| |
| − |
| |
| | | | |
| | then the following are equivalent: | | then the following are equivalent: |
| − |
| |
| − |
| |
| | | | |
| | E1a. f(u) = g(u). :V1a | | E1a. f(u) = g(u). :V1a |
| Line 10,917: |
Line 10,597: |
| | | | |
| | E1d. (( f , g ))$(u). :$1b | | E1d. (( f , g ))$(u). :$1b |
| | + | </pre> |
| | | | |
| − | | + | <pre> |
| − | | |
| | Evaluation Rule 1 | | Evaluation Rule 1 |
| | | | |
| Line 10,925: |
Line 10,605: |
| | | | |
| | about things in the universe U, | | about things in the universe U, |
| − |
| |
| − |
| |
| | | | |
| | f, g are propositions: U -> B, | | f, g are propositions: U -> B, |
| − |
| |
| − |
| |
| | | | |
| | and u C U, | | and u C U, |
| − |
| |
| − |
| |
| | | | |
| | then the following are equivalent: | | then the following are equivalent: |
| − |
| |
| − |
| |
| | | | |
| | E1a. f(u) = g(u). :V1a | | E1a. f(u) = g(u). :V1a |
| Line 10,955: |
Line 10,627: |
| | | | |
| | E1d. (( f , g ))$(u). :$1b | | E1d. (( f , g ))$(u). :$1b |
| | + | </pre> |
| | | | |
| − | | + | <pre> |
| − | | |
| − | | |
| − | | |
| | Definition 2 | | Definition 2 |
| | | | |
| | If X, Y c U, | | If X, Y c U, |
| − |
| |
| − |
| |
| | | | |
| | then the following are equivalent: | | then the following are equivalent: |
| − |
| |
| − |
| |
| | | | |
| | D2a. X = Y. | | D2a. X = Y. |
| − |
| |
| − |
| |
| | | | |
| | D2b. u C X <=> u C Y, for all u C U. | | D2b. u C X <=> u C Y, for all u C U. |
| | + | </pre> |
| | | | |
| − | | + | <pre> |
| − | | |
| | Definition 3 | | Definition 3 |
| | | | |
| | If f, g : U -> V, | | If f, g : U -> V, |
| − |
| |
| − |
| |
| | | | |
| | then the following are equivalent: | | then the following are equivalent: |
| − |
| |
| − |
| |
| | | | |
| | D3a. f = g. | | D3a. f = g. |
| − |
| |
| − |
| |
| | | | |
| | D3b. f(u) = g(u), for all u C U. | | D3b. f(u) = g(u), for all u C U. |
| | + | </pre> |
| | | | |
| − | | + | <pre> |
| − | | |
| | Definition 4 | | Definition 4 |
| | | | |
| | If X c U, | | If X c U, |
| − |
| |
| − |
| |
| | | | |
| | then the following are identical subsets of UxB: | | then the following are identical subsets of UxB: |
| − |
| |
| − |
| |
| | | | |
| | D4a. {X} | | D4a. {X} |
| − |
| |
| − |
| |
| | | | |
| | D4b. {< u, v> C UxB : v = [u C X]} | | D4b. {< u, v> C UxB : v = [u C X]} |
| | + | </pre> |
| | | | |
| − | | + | <pre> |
| − | | |
| | Definition 5 | | Definition 5 |
| | | | |
| | If X c U, | | If X c U, |
| − |
| |
| − |
| |
| | | | |
| | then the following are identical propositions: | | then the following are identical propositions: |
| − |
| |
| − |
| |
| | | | |
| | D5a. {X}. | | D5a. {X}. |
| − |
| |
| − |
| |
| | | | |
| | D5b. f : U -> B | | D5b. f : U -> B |
| − |
| |
| − |
| |
| | | | |
| | : f(u) = [u C X], for all u C U. | | : f(u) = [u C X], for all u C U. |
| | + | </pre> |
| | | | |
| | Given an indexed set of sentences, Sj for j C J, it is possible to consider the logical conjunction of the corresponding propositions. Various notations for this concept are be useful in various contexts, a sufficient sample of which are recorded in Definition 6. | | Given an indexed set of sentences, Sj for j C J, it is possible to consider the logical conjunction of the corresponding propositions. Various notations for this concept are be useful in various contexts, a sufficient sample of which are recorded in Definition 6. |
| | | | |
| | + | <pre> |
| | Definition 6 | | Definition 6 |
| | | | |
| Line 11,043: |
Line 10,689: |
| | | | |
| | for all j C J, | | for all j C J, |
| − |
| |
| − |
| |
| | | | |
| | then the following are equivalent: | | then the following are equivalent: |
| − |
| |
| − |
| |
| | | | |
| | D6a. Sj, for all j C J. | | D6a. Sj, for all j C J. |
| − |
| |
| − |
| |
| | | | |
| | D6b. For all j C J, Sj. | | D6b. For all j C J, Sj. |
| − |
| |
| − |
| |
| | | | |
| | D6c. Conj(j C J) Sj. | | D6c. Conj(j C J) Sj. |
| − |
| |
| − |
| |
| | | | |
| | D6d. ConjJ,j Sj. | | D6d. ConjJ,j Sj. |
| − |
| |
| − |
| |
| | | | |
| | D6e. ConjJj Sj. | | D6e. ConjJj Sj. |
| | + | </pre> |
| | | | |
| − | | + | <pre> |
| − | | |
| | Definition 7 | | Definition 7 |
| | | | |
| Line 11,075: |
Line 10,709: |
| | | | |
| | about things in the universe U, | | about things in the universe U, |
| − |
| |
| − |
| |
| | | | |
| | then the following are equivalent: | | then the following are equivalent: |
| − |
| |
| − |
| |
| | | | |
| | D7a. S <=> T. | | D7a. S <=> T. |
| − |
| |
| − |
| |
| | | | |
| | D7b. [S] = [T]. | | D7b. [S] = [T]. |
| | + | </pre> |
| | | | |
| − | | + | <pre> |
| − | | |
| | Rule 5 | | Rule 5 |
| | | | |
| | If X, Y c U, | | If X, Y c U, |
| − |
| |
| − |
| |
| | | | |
| | then the following are equivalent: | | then the following are equivalent: |
| − |
| |
| − |
| |
| | | | |
| | R5a. X = Y. :D2a | | R5a. X = Y. :D2a |
| Line 11,127: |
Line 10,751: |
| | | | |
| | R5e. {X} = {Y}. :D5a | | R5e. {X} = {Y}. :D5a |
| | + | </pre> |
| | | | |
| − | | + | <pre> |
| − | | |
| | Rule 6 | | Rule 6 |
| | | | |
| | If f, g : U -> V, | | If f, g : U -> V, |
| − |
| |
| − |
| |
| | | | |
| | then the following are equivalent: | | then the following are equivalent: |
| − |
| |
| − |
| |
| | | | |
| | R6a. f = g. :D3a | | R6a. f = g. :D3a |
| Line 11,151: |
Line 10,771: |
| | | | |
| | R6c. ConjUu (f(u) = g(u)). :D6e | | R6c. ConjUu (f(u) = g(u)). :D6e |
| | + | </pre> |
| | | | |
| − | | + | <pre> |
| − | | |
| | Rule 7 | | Rule 7 |
| | | | |
| | If P, Q : U -> B, | | If P, Q : U -> B, |
| − |
| |
| − |
| |
| | | | |
| | then the following are equivalent: | | then the following are equivalent: |
| − |
| |
| − |
| |
| | | | |
| | R7a. P = Q. :R6a | | R7a. P = Q. :R6a |
| Line 11,189: |
Line 10,805: |
| | | | |
| | R7f. ConjUu (( P , Q ))$(u). :$1b | | R7f. ConjUu (( P , Q ))$(u). :$1b |
| | + | </pre> |
| | | | |
| − | | + | <pre> |
| − | | |
| − | | |
| − | | |
| | Rule 8 | | Rule 8 |
| | | | |
| Line 11,199: |
Line 10,813: |
| | | | |
| | about things in the universe U, | | about things in the universe U, |
| − |
| |
| − |
| |
| | | | |
| | then the following are equivalent: | | then the following are equivalent: |
| − |
| |
| − |
| |
| | | | |
| | R8a. S <=> T. :D7a | | R8a. S <=> T. :D7a |
| Line 11,233: |
Line 10,843: |
| | | | |
| | R8g. ConjUu (( [S] , [T] ))$(u). :R7f | | R8g. ConjUu (( [S] , [T] ))$(u). :R7f |
| | + | </pre> |
| | | | |
| | For instance, the observation that expresses the equality of sets in terms of their indicator functions can be formalized according to the pattern in Rule 9, namely, at lines (a, b, c), and these components of Rule 9 can be cited in future uses as "R9a", "R9b", "R9c", respectively. Using Rule 7, annotated as "R7", to adduce a few properties of indicator functions to the account, it is possible to extend Rule 9 by another few steps, referenced as "R9d", "R9e", "R9f", "R9g". | | For instance, the observation that expresses the equality of sets in terms of their indicator functions can be formalized according to the pattern in Rule 9, namely, at lines (a, b, c), and these components of Rule 9 can be cited in future uses as "R9a", "R9b", "R9c", respectively. Using Rule 7, annotated as "R7", to adduce a few properties of indicator functions to the account, it is possible to extend Rule 9 by another few steps, referenced as "R9d", "R9e", "R9f", "R9g". |
| | | | |
| | + | <pre> |
| | Rule 9 | | Rule 9 |
| | | | |
| | If X, Y c U, | | If X, Y c U, |
| − |
| |
| − |
| |
| | | | |
| | then the following are equivalent: | | then the following are equivalent: |
| − |
| |
| − |
| |
| | | | |
| | R9a. X = Y. :R5a | | R9a. X = Y. :R5a |
| Line 11,273: |
Line 10,881: |
| | | | |
| | R9g. ConjUu (( {X} , {Y} ))$(u). :R7f | | R9g. ConjUu (( {X} , {Y} ))$(u). :R7f |
| | + | </pre> |
| | | | |
| − | | + | <pre> |
| − | | |
| | Rule 10 | | Rule 10 |
| | | | |
| | If X, Y c U, | | If X, Y c U, |
| − |
| |
| − |
| |
| | | | |
| | then the following are equivalent: | | then the following are equivalent: |
| − |
| |
| − |
| |
| | | | |
| | R10a. X = Y. :D2a | | R10a. X = Y. :D2a |
| Line 11,319: |
Line 10,923: |
| | | | |
| | R10h. ConjUu (( [u C X] , [u C Y] ))$(u). :R8g | | R10h. ConjUu (( [u C X] , [u C Y] ))$(u). :R8g |
| | + | </pre> |
| | | | |
| − | | + | <pre> |
| − | | |
| | Rule 11 | | Rule 11 |
| | | | |
| | If X c U | | If X c U |
| − |
| |
| − |
| |
| | | | |
| | then the following are equivalent: | | then the following are equivalent: |
| − |
| |
| − |
| |
| | | | |
| | R11a. X = {u C U : S}. :R5a | | R11a. X = {u C U : S}. :R5a |
| Line 11,341: |
Line 10,941: |
| | | | |
| | R11c. {X} c UxB | | R11c. {X} c UxB |
| − |
| |
| − |
| |
| | | | |
| | : {X} = {< u, v> C UxB : v = [S](u)}. :R | | : {X} = {< u, v> C UxB : v = [S](u)}. :R |
| Line 11,349: |
Line 10,947: |
| | | | |
| | R11d. {X} : U -> B | | R11d. {X} : U -> B |
| − |
| |
| − |
| |
| | | | |
| | : {X}(u) = [S](u), for all u C U. :R | | : {X}(u) = [S](u), for all u C U. :R |
| Line 11,357: |
Line 10,953: |
| | | | |
| | R11e. {X} = [S]. :R | | R11e. {X} = [S]. :R |
| − | | + | </pre> |
| − | | |
| | | | |
| | An application of Rule 11 involves the recognition of an antecedent condition as a case under the Rule, that is, as a condition that matches one of the sentences in the Rule's chain of equivalents, and it requires the relegation of the other expressions to the production of a result. Thus, there is the choice of an initial expression that has to be checked on input for whether it fits the antecedent condition, and there is the choice of three types of output that are generated as a consequence, only one of which is generally needed at any given time. More often than not, though, a rule is applied in only a few of its possible ways. The usual antecedent and the usual consequents for Rule 11 can be distinguished in form and specialized in practice as follows: | | An application of Rule 11 involves the recognition of an antecedent condition as a case under the Rule, that is, as a condition that matches one of the sentences in the Rule's chain of equivalents, and it requires the relegation of the other expressions to the production of a result. Thus, there is the choice of an initial expression that has to be checked on input for whether it fits the antecedent condition, and there is the choice of three types of output that are generated as a consequence, only one of which is generally needed at any given time. More often than not, though, a rule is applied in only a few of its possible ways. The usual antecedent and the usual consequents for Rule 11 can be distinguished in form and specialized in practice as follows: |
| | | | |
| − | a. R11a marks the usual starting place for an application of the Rule, that is, the standard form of antecedent condition that is likely to lead to an invocation of the Rule. | + | a. R11a marks the usual starting place for an application of the Rule, that is, the standard form of antecedent condition that is likely to lead to an invocation of the Rule. |
| | | | |
| − | b. R11b records the trivial consequence of applying the spiny braces to both sides of the initial equation. | + | b. R11b records the trivial consequence of applying the spiny braces to both sides of the initial equation. |
| | | | |
| − | c. R11c gives a version of the indicator function with {X} c UxB, called its "extensional form". | + | c. R11c gives a version of the indicator function with {X} c UxB, called its "extensional form". |
| | | | |
| − | d. R11d gives a version of the indicator function with {X} : U->B, called its "functional form". | + | d. R11d gives a version of the indicator function with {X} : U->B, called its "functional form". |
| | | | |
| | Applying Rule 9, Rule 8, and the Logical Rules to the special case where S <=> (X = Y), one obtains the following general fact. | | Applying Rule 9, Rule 8, and the Logical Rules to the special case where S <=> (X = Y), one obtains the following general fact. |
| | | | |
| | + | <pre> |
| | Fact 1 | | Fact 1 |
| | | | |
| | If X,Y c U, | | If X,Y c U, |
| − |
| |
| − |
| |
| | | | |
| | then the following are equivalent: | | then the following are equivalent: |
| − |
| |
| − |
| |
| | | | |
| | F1a. S <=> X = Y. :R9a | | F1a. S <=> X = Y. :R9a |
| Line 11,415: |
Line 11,007: |
| | | | |
| | F1h. [S] = ConjUu (( {X} , {Y} ))$(u). :$1b | | F1h. [S] = ConjUu (( {X} , {Y} ))$(u). :$1b |
| − |
| |
| − |
| |
| | | | |
| | /// | | /// |
| Line 11,427: |
Line 11,017: |
| | | | |
| | /// | | /// |
| | + | </pre> |
| | | | |
| − | =====1.3.10.15 Derived Equivalence Relations===== | + | =====1.3.12.2. Derived Equivalence Relations===== |
| | | | |
| | One seeks a method of general application for approaching the individual sign relation, a way to select an aspect of its form, to analyze it with regard to its intrinsic structure, and to classify it in comparison with other sign relations. With respect to a particular sign relation, one approach that presents itself is to examine the relation between signs and interpretants that is given directly by its connotative component and to compare it with the various forms of derived, indirect, mediate, or peripheral relationships that can be found to exist among signs and interpretants by way of secondary considerations or subsequent studies. Of especial interest are the relationships among signs and interpretants that can be obtained by working through the collections of objects that they commonly or severally denote. | | One seeks a method of general application for approaching the individual sign relation, a way to select an aspect of its form, to analyze it with regard to its intrinsic structure, and to classify it in comparison with other sign relations. With respect to a particular sign relation, one approach that presents itself is to examine the relation between signs and interpretants that is given directly by its connotative component and to compare it with the various forms of derived, indirect, mediate, or peripheral relationships that can be found to exist among signs and interpretants by way of secondary considerations or subsequent studies. Of especial interest are the relationships among signs and interpretants that can be obtained by working through the collections of objects that they commonly or severally denote. |
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| | A different way of seeing that two sets are equal, or of seeing whether two sets are equal, is based on the following observation: | | A different way of seeing that two sets are equal, or of seeing whether two sets are equal, is based on the following observation: |
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| | + | <pre> |
| | Two sets are equal as sets | | Two sets are equal as sets |
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| | <=> the values of these functions are equal on all domain elements. | | <=> the values of these functions are equal on all domain elements. |
| | + | </pre> |
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| | It is important to notice the hidden quantifier, of a universal kind, that lurks in all three equivalent statements but is only revealed in the last. | | It is important to notice the hidden quantifier, of a universal kind, that lurks in all three equivalent statements but is only revealed in the last. |
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| | Recall the definition of Con(R), the connotative component of R, in the following form: | | Recall the definition of Con(R), the connotative component of R, in the following form: |
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| − | Con(R) = RSI = {< s, i> C SxI : <o, s, i> C R for some o C O}. | + | : Con(R) = RSI = {< s, i> C SxI : <o, s, i> C R for some o C O}. |
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| | Equivalent expressions for this concept are recorded in Definition 8. | | Equivalent expressions for this concept are recorded in Definition 8. |
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| | + | <pre> |
| | Definition 8 | | Definition 8 |
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| | If R c OxSxI, | | If R c OxSxI, |
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| | then the following are identical subsets of SxI: | | then the following are identical subsets of SxI: |
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| | D8a. RSI | | D8a. RSI |
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| | D8b. ConR | | D8b. ConR |
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| | D8c. Con(R) | | D8c. Con(R) |
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| | D8d. PrSI(R) | | D8d. PrSI(R) |
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| | D8e. {< s, i> C SxI : <o, s, i> C R for some o C O} | | D8e. {< s, i> C SxI : <o, s, i> C R for some o C O} |
| | + | </pre> |
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| | The dyadic relation RIS that constitutes the converse of the connotative relation RSI can be defined directly in the following fashion: | | The dyadic relation RIS that constitutes the converse of the connotative relation RSI can be defined directly in the following fashion: |
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| − | Con(R)^ = RIS = {< i, s> C IxS : <o, s, i> C R for some o C O}. | + | : Con(R)^ = RIS = {< i, s> C IxS : <o, s, i> C R for some o C O}. |
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| | A few of the many different expressions for this concept are recorded in Definition 9. | | A few of the many different expressions for this concept are recorded in Definition 9. |
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| | + | <pre> |
| | Definition 9 | | Definition 9 |
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| | If R c OxSxI, | | If R c OxSxI, |
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| | then the following are identical subsets of IxS: | | then the following are identical subsets of IxS: |
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| | D9a. RIS | | D9a. RIS |
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| | D9b. RSI^ | | D9b. RSI^ |
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| | D9c. ConR^ | | D9c. ConR^ |
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| | D9d. Con(R)^ | | D9d. Con(R)^ |
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| | D9e. PrIS(R) | | D9e. PrIS(R) |
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| | D9f. Conv(Con(R)) | | D9f. Conv(Con(R)) |
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| | D9g. {< i, s> C IxS : <o, s, i> C R for some o C O} | | D9g. {< i, s> C IxS : <o, s, i> C R for some o C O} |
| | + | </pre> |
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| | Recall the definition of Den(R), the denotative component of R, in the following form: | | Recall the definition of Den(R), the denotative component of R, in the following form: |
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| − | Den(R) = ROS = {<o, s> C OxS : <o, s, i> C R for some i C I}. | + | : Den(R) = ROS = {<o, s> C OxS : <o, s, i> C R for some i C I}. |
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| | Equivalent expressions for this concept are recorded in Definition 10. | | Equivalent expressions for this concept are recorded in Definition 10. |
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| | + | <pre> |
| | Definition 10 | | Definition 10 |
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| | If R c OxSxI, | | If R c OxSxI, |
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| | then the following are identical subsets of OxS: | | then the following are identical subsets of OxS: |
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| | D10a. ROS | | D10a. ROS |
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| | D10b. DenR | | D10b. DenR |
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| | D10c. Den(R) | | D10c. Den(R) |
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| | D10d. PrOS(R) | | D10d. PrOS(R) |
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| | D10e. {<o, s> C OxS : <o, s, i> C R for some i C I} | | D10e. {<o, s> C OxS : <o, s, i> C R for some i C I} |
| | + | </pre> |
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| | The dyadic relation RSO that constitutes the converse of the denotative relation ROS can be defined directly in the following fashion: | | The dyadic relation RSO that constitutes the converse of the denotative relation ROS can be defined directly in the following fashion: |
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| − | Den(R)^ = RSO = {< s, o> C SxO : <o, s, i> C R for some i C I}. | + | : Den(R)^ = RSO = {< s, o> C SxO : <o, s, i> C R for some i C I}. |
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| | A few of the many different expressions for this concept are recorded in Definition 11. | | A few of the many different expressions for this concept are recorded in Definition 11. |
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| | + | <pre> |
| | Definition 11 | | Definition 11 |
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| | If R c OxSxI, | | If R c OxSxI, |
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| | then the following are identical subsets of SxO: | | then the following are identical subsets of SxO: |
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| | D11a. RSO | | D11a. RSO |
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| | D11b. ROS^ | | D11b. ROS^ |
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| | D11c. DenR^ | | D11c. DenR^ |
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| | D11d. Den(R)^ | | D11d. Den(R)^ |
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| | D11e. PrSO(R) | | D11e. PrSO(R) |
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| | D11f. Conv(Den(R)) | | D11f. Conv(Den(R)) |
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| | D11g. {< s, o> C SxO : <o, s, i> C R for some i C I} | | D11g. {< s, o> C SxO : <o, s, i> C R for some i C I} |
| | + | </pre> |
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| | The "denotation of x in R", written "Den(R, x)", is defined as follows: | | The "denotation of x in R", written "Den(R, x)", is defined as follows: |
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| − | Den(R, x) = {o C O : <o, x> C Den(R)}. | + | : Den(R, x) = {o C O : <o, x> C Den(R)}. |
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| | In other words: | | In other words: |
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| − | Den(R, x) = {o C O : <o, x, i> C R for some i C I}. | + | : Den(R, x) = {o C O : <o, x, i> C R for some i C I}. |
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| | Equivalent expressions for this concept are recorded in Definition 12. | | Equivalent expressions for this concept are recorded in Definition 12. |
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| | + | <pre> |
| | Definition 12 | | Definition 12 |
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| | If R c OxSxI, | | If R c OxSxI, |
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| | and x C S, | | and x C S, |
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| | then the following are identical subsets of O: | | then the following are identical subsets of O: |
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| | D12a. ROS.x | | D12a. ROS.x |
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| | D12b. DenR.x | | D12b. DenR.x |
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| | D12c. DenR|x | | D12c. DenR|x |
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| | D12d. DenR(, x) | | D12d. DenR(, x) |
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| | D12e. Den(R, x) | | D12e. Den(R, x) |
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| | D12f. Den(R).x | | D12f. Den(R).x |
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| | D12g. {o C O : <o, x> C Den(R)} | | D12g. {o C O : <o, x> C Den(R)} |
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| | D12h. {o C O : <o, x, i> C R for some i C I} | | D12h. {o C O : <o, x, i> C R for some i C I} |
| | + | </pre> |
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| − | Signs are "equiferent" if they refer to all and only the same objects, that is, if they have exactly the same denotations. In other language for the same relation, signs are said to be "denotatively equivalent" or "referentially equivalent", but it is probably best to check whether the extension of this concept over the syntactic domain is really a genuine equivalence relation before jumpimg to the conclusions that are implied by these latter terms. | + | Signs are "equiferent" if they refer to all and only the same objects, that is, if they have exactly the same denotations. In other language for the same relation, signs are said to be "denotatively equivalent" or "referentially equivalent", but it is probably best to check whether the extension of this concept over the syntactic domain is really a genuine equivalence relation before jumping to the conclusions that are implied by these latter terms. |
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| | To define the "equiference" of signs in terms of their denotations, one says that "x is equiferent to y under R", and writes "x =R y", to mean that Den(R, x) = Den(R, y). Taken in extension, this notion of a relation between signs induces an "equiference relation" on the syntactic domain. | | To define the "equiference" of signs in terms of their denotations, one says that "x is equiferent to y under R", and writes "x =R y", to mean that Den(R, x) = Den(R, y). Taken in extension, this notion of a relation between signs induces an "equiference relation" on the syntactic domain. |
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| | For each sign relation R, this yields a binary relation Der(R) c SxI that is defined as follows: | | For each sign relation R, this yields a binary relation Der(R) c SxI that is defined as follows: |
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| − | Der(R) = DerR = {<x, y> C SxI : Den(R, x) = Den(R, y)}. | + | : Der(R) = DerR = {<x, y> C SxI : Den(R, x) = Den(R, y)}. |
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| | These definitions and notations are recorded in the following display. | | These definitions and notations are recorded in the following display. |
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| − | | + | <pre> |
| − | | |
| | Definition 13 | | Definition 13 |
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| | If R c OxSxI, | | If R c OxSxI, |
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| | then the following are identical subsets of SxI: | | then the following are identical subsets of SxI: |
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| | D13a. DerR | | D13a. DerR |
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| | D13b. Der(R) | | D13b. Der(R) |
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| | D13c. {<x,y> C SxI : DenR|x = DenR|y} | | D13c. {<x,y> C SxI : DenR|x = DenR|y} |
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| | D13d. {<x,y> C SxI : Den(R, x) = Den(R, y)} | | D13d. {<x,y> C SxI : Den(R, x) = Den(R, y)} |
| | + | </pre> |
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| | The relation Der(R) is defined and the notation "x =R y" is meaningful in every situation where Den(-,-) makes sense, but it remains to check whether this relation enjoys the properties of an equivalence relation. | | The relation Der(R) is defined and the notation "x =R y" is meaningful in every situation where Den(-,-) makes sense, but it remains to check whether this relation enjoys the properties of an equivalence relation. |
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| − | 1. Reflexive property. Is it true that x =R x for every x C S = I? By definition, x =R x if and only if Den(R, x) = Den(R, x). Thus, the reflexive property holds in any setting where the denotations Den(R, x) are defined for all signs x in the syntactic domain of R.
| + | # Reflexive property. Is it true that x =R x for every x C S = I? By definition, x =R x if and only if Den(R, x) = Den(R, x). Thus, the reflexive property holds in any setting where the denotations Den(R, x) are defined for all signs x in the syntactic domain of R. |
| − | | + | # Symmetric property. Does x =R y => y =R x for all x, y C S? In effect, does Den(R, x) = Den(R, y) imply Den(R, y) = Den(R, x) for all signs x and y in the syntactic domain S? Yes, so long as the sets Den(R, x) and Den(R, y) are well-defined, a fact which is already being assumed. |
| − | 2. Symmetric property. Does x =R y => y =R x for all x, y C S? In effect, does Den(R, x) = Den(R, y) imply Den(R, y) = Den(R, x) for all signs x and y in the syntactic domain S? Yes, so long as the sets Den(R, x) and Den(R, y) are well-defined, a fact which is already being assumed.
| + | # Transitive property. Does x =R y & y =R z => x =R z for all x, y, z C S? To belabor the point, does Den(R, x) = Den(R, y) and Den(R, y) = Den(R, z) imply Den(R, x) = Den(R, z) for all x, y, z in S? Yes, again, under the stated conditions. |
| − | | |
| − | 3. Transitive property. Does x =R y & y =R z => x =R z for all x, y, z C S? To belabor the point, does Den(R, x) = Den(R, y) and Den(R, y) = Den(R, z) imply Den(R, x) = Den(R, z) for all x, y, z in S? Yes, again, under the stated conditions.
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| | It should be clear at this point that any question about the equiference of signs reduces to a question about the equality of sets, specifically, the sets that are indexed by these signs. As a result, so long as these sets are well-defined, the issue of whether equiference relations induce equivalence relations on their syntactic domains is almost as trivial as it initially appears. | | It should be clear at this point that any question about the equiference of signs reduces to a question about the equality of sets, specifically, the sets that are indexed by these signs. As a result, so long as these sets are well-defined, the issue of whether equiference relations induce equivalence relations on their syntactic domains is almost as trivial as it initially appears. |
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| | The uses of the equal sign for denoting equations or equivalences are recalled and extended in the following ways: | | The uses of the equal sign for denoting equations or equivalences are recalled and extended in the following ways: |
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| − | 1. If E is an arbitrary equivalence relation, | + | 1. If E is an arbitrary equivalence relation, |
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| | then the equation "x =E y" means that <x, y> C E. | | then the equation "x =E y" means that <x, y> C E. |
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| − | 2. If R is a sign relation such that RSI is a SER on S = I, | + | 2. If R is a sign relation such that RSI is a SER on S = I, |
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| | then the semiotic equation "x =R y" means that <x, y> C RSI. | | then the semiotic equation "x =R y" means that <x, y> C RSI. |
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| − | 3. If R is a sign relation such that F is its DER on S = I, | + | 3. If R is a sign relation such that F is its DER on S = I, |
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| | then the denotative equation "x =R y" means that <x, y> C F, | | then the denotative equation "x =R y" means that <x, y> C F, |
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| | The uses of square brackets for denoting equivalence classes are recalled and extended in the following ways: | | The uses of square brackets for denoting equivalence classes are recalled and extended in the following ways: |
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| − | 1. If E is an arbitrary equivalence relation, | + | 1. If E is an arbitrary equivalence relation, |
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| | then "[x]E" denotes the equivalence class of x under E. | | then "[x]E" denotes the equivalence class of x under E. |
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| − | 2. If R is a sign relation such that Con(R) is a SER on S = I, | + | 2. If R is a sign relation such that Con(R) is a SER on S = I, |
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| | then "[x]R" denotes the SEC of x under Con(R). | | then "[x]R" denotes the SEC of x under Con(R). |
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| − | 3. If R is a sign relation such that Der(R) is a DER on S = I, | + | 3. If R is a sign relation such that Der(R) is a DER on S = I, |
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| | then "[x]R" denotes the DEC of x under Der(R). | | then "[x]R" denotes the DEC of x under Der(R). |
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| | By applying the form of Fact 1 to the special case where X = Den(R, x) and Y = Den(R, y), one obtains the following facts. | | By applying the form of Fact 1 to the special case where X = Den(R, x) and Y = Den(R, y), one obtains the following facts. |
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| − | | + | <pre> |
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| | Fact 2.1 | | Fact 2.1 |
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| | If R c OxSxI, | | If R c OxSxI, |
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| | then the following are identical subsets of SxI: | | then the following are identical subsets of SxI: |
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| | F2.1a. DerR :D13a | | F2.1a. DerR :D13a |
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| | } :D12a | | } :D12a |
| | + | </pre> |
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| − | | + | <pre> |
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| | Fact 2.2 | | Fact 2.2 |
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| | If R c OxSxI, | | If R c OxSxI, |
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| | then the following are equivalent: | | then the following are equivalent: |
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| | F2.2a. DerR = {<x, y> C SxI : | | F2.2a. DerR = {<x, y> C SxI : |
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| | } :R11a | | } :R11a |
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| | F2.2b. {DerR} = { {<x, y> C SxI : | | F2.2b. {DerR} = { {<x, y> C SxI : |
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| | } :Log | | } :Log |
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| | F2.2e. {DerR} = {<x, y, v> C SxIxB : | | F2.2e. {DerR} = {<x, y, v> C SxIxB : |
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| | } :Log | | } :Log |
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| | F2.2f. {DerR} = {<x, y, v> C SxIxB : | | F2.2f. {DerR} = {<x, y, v> C SxIxB : |
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| | } :$ | | } :$ |
| | + | </pre> |
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| | Fact 2.3 | | Fact 2.3 |
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| | If R c OxSxI, | | If R c OxSxI, |
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| | then the following are equivalent: | | then the following are equivalent: |
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| | F2.3a. DerR = {<x, y> C SxI : | | F2.3a. DerR = {<x, y> C SxI : |
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| | )) :D10a | | )) :D10a |
| | + | </pre> |
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| − | | + | =====1.3.12.3. Digression on Derived Relations===== |
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| − | =====1.3.10.16 Digression on Derived Relations===== | |
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| | A better understanding of derived equivalence relations (DER's) can be achieved by placing their constructions within a more general context, and thus comparing the associated type of derivation operation, namely, the one that takes a triadic relation R into a dyadic relation Der(R), with other types of operations on triadic relations. The proper setting would permit a comparative study of all their constructions from a basic set of projections and a full array of compositions on dyadic relations. | | A better understanding of derived equivalence relations (DER's) can be achieved by placing their constructions within a more general context, and thus comparing the associated type of derivation operation, namely, the one that takes a triadic relation R into a dyadic relation Der(R), with other types of operations on triadic relations. The proper setting would permit a comparative study of all their constructions from a basic set of projections and a full array of compositions on dyadic relations. |
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| | To that end, let the derivation Der(R) be expressed in the following way: | | To that end, let the derivation Der(R) be expressed in the following way: |
| | | | |
| − | {DerR}(x, y) = Conj(o C O) (( {RSO}(x, o) , {ROS}(o, y) )). | + | : {DerR}(x, y) = Conj(o C O) (( {RSO}(x, o) , {ROS}(o, y) )). |
| | | | |
| | From this abstract a form of composition, temporarily notated as "P#Q", where P c XxM and Q c MxY are otherwise arbitrary dyadic relations, and where P#Q c XxY is defined as follows: | | From this abstract a form of composition, temporarily notated as "P#Q", where P c XxM and Q c MxY are otherwise arbitrary dyadic relations, and where P#Q c XxY is defined as follows: |
| | | | |
| − | {P#Q}(x, y) = Conj(m C M) (( {P}(x, m) , {Q}(m, y) )). | + | : {P#Q}(x, y) = Conj(m C M) (( {P}(x, m) , {Q}(m, y) )). |
| | | | |
| | Compare this with the usual form of composition, typically notated as "P.Q" and defined as follows: | | Compare this with the usual form of composition, typically notated as "P.Q" and defined as follows: |
| | | | |
| − | {P.Q}(x, y) = Disj(m C M) ( {P}(x, m) . {Q}(m, y) ). | + | : {P.Q}(x, y) = Disj(m C M) ( {P}(x, m) . {Q}(m, y) ). |
| | | | |
| | + | ===1.4. Outlook of the Project : All Ways Lead to Inquiry=== |
| | | | |
| | + | I am using the word ''inquiry'' in a way that is roughly synonymous with the term ''scientific method''. Use of ''inquiry'' is more convenient, aside from being the shorter term, because of the following advantages: |
| | | | |
| − | 1.4 Outlook of the Project: All Ways Lead to Inquiry
| + | # It allows one to broaden the scope of investigation to include any form of proceeding toward knowledge that merely aims at such a method. |
| | + | # It allows one to finesse the issue, for the time being, of how much "method" there is in science. |
| | | | |
| | + | This Subdivision and the next deal with opposite aspects of inquiry. In many ways it might have been better to interlace the opposing points of comparison, taking them up in a parallel fashion, but this plan was judged to be too distracting for a first approach. In other ways, the negative sides of each topic are prior in point of time to the positive sides of the issue, but sensible people like to see the light at the end of the tunnel before they trouble themselves with the obscurities of the intervening journey. Thus, this Subdivision of the text emphasizes the positive features of inquiry and the positive qualities of its objective, while the next Subdivision is reserved to examine the negative aspects of each question. |
| | | | |
| | + | In the order of nature, the absence of a feature naturally precedes the full development of its presence. In the order of discussion, however, positive terms must be proposed if it is desired to say anything at all. |
| | | | |
| − | 1.4 Outlook of the Project: All Ways Lead to Inquiry
| + | The discussion in this Subdivision is placed to serve a primer, declaring at least the names of enough positive concepts to propose addressing the negative conditions of knowledge in which inquiry necessarily starts. |
| | | | |
| | + | In this Subdivision I stand back once again from the problem of inquiry and allow myself take a more distant view of the subject, settling into what I think is a comfortable and a natural account of inquiry, the best that I have at my command, and attending to the task of describing its positive features in a positive light. I present my personal view of inquiry as I currently understand it, without stopping to justify every concept in detail or to examine every objection that might be made to this view. In the next Subdivision I discuss a few of the more obvious problems that stand in the way of this view and I try to remove a few of the more tractable obscurities that appear ready to be cleared up. The fact that I treat them as my "personal insights" does not mean that all of these ideas about inquiry originate with me, but only that I have come to adopt them for my personal use. There will be many occasions, the next time that I go over this ground, to point out the sources of these ideas, so far as I know them. |
| | | | |
| | + | The reader may take my apology for this style of presentation to be implicit in its dogmatic character. It is done this way in a first approach for the sake of avoiding an immense number of distractions, each of which is not being slighted but demands to be addressed in its own good time. I want to convey the general drift of my current model, however conjectural, naive, uncritical, and unreflective it may seem. |
| | | | |
| − | I am using the word "inquiry" in a way that is roughly synonymous with the
| + | ====1.4.1. The Matrix of Inquiry==== |
| | | | |
| − | term "scientific method". Use of "inquiry" is more convenient, aside from
| + | <blockquote> |
| | + | <p>Thus when mothers have children suffering from sleeplessness, and want to lull them to rest, the treatment they apply is to give them, not quiet, but motion, for they rock them constantly in their arms; and instead of silence, they use a kind of crooning noise; and thus they literally cast a spell upon the children (like the victims of a Bacchic frenzy) by employing the combined movements of dance and song as a remedy.</p> |
| | | | |
| − | being the shorter term, because of the following advantages:
| + | <p>(Plato, ''Laws'', VII, 790D).</p> |
| | + | </blockquote> |
| | | | |
| | + | Try as I might, I do not see a way to develop a theory of inquiry from nothing: To take for granted nothing more than is already given, to set out from nothing but absolutely certain beginnings, or to move forward with nothing but absolutely certain means of proceeding. In particular, the present inquiry into inquiry, <math>y_0 = y \cdot y,</math> ought not to be misconstrued as a device for magically generating a theory of inquiry from nothing. Like any other inquiry, it requires an agent to invest in a conjecture, to make a guess about the relevant features of the subject of interest, and to choose the actions, the aspects, and the attitudes with regard to the subject that are critical to achieving the objectives of the study. |
| | | | |
| | + | I can sum all this up by saying that an inquiry requires an inquirer to suggest a hypothesis about the subject of interest and then to put that particular model of the subject to the test. This in turn requires one to devote a modicum of personal effort to the task of testing the chosen hypothesis, to put a quantum of personal interest at stake for the sake of finding out whether the model fits the subject, and, overall, to take the risk of being wrong. Any model that is feasible is also defeasible, at least, where it concerns a contingent subject of inquiry. |
| | | | |
| − | 1. It allows one to broaden the scope of investigation
| + | The first step, then, of an inquiry into inquiry, is to put forth a tentative model of inquiry, to make a hypothesis about the features of inquiry that are essential to explaining its experienced characteristics, and thus, in a sense, to make a guess at the very definition of inquiry. This requirement seems both obvious and outrageous at the same time. One is perfectly justified in objecting that there is much that precedes this so-called "first step", namely, the body of experience that prepares one to see it and the mass of observation that prompts one to take it. I can deal with this objection by making a distinction between mundane experience and olympian theory, and then by saying that the making of a conjecture is really the first "theoretical" step, but this is a hedge that covers the tracks of theory in a deceptive way, hiding how early in the empirical process the "cloven hoof" of theory actually enters. |
| | | | |
| − | to include any form of proceeding toward knowledge
| + | Leaving behind the mythical conditions of pure experience and naive observation, and at least by the time that one comes to give a name to the subject of investigation, one's trek through the data is already half-shod, half-fettered by the connotations of the name, and in turn by all of the concepts that it invokes in its train. The name, the concepts that it suggests, and the tacit but vague definition of the subject that this complex of associations is already beginning to constellate, attract certain experiences to the complex and filter out other observations from having any bearing on the subject matter. By this point, one is already busy translating one's empirical acquaintance with the subject into an arrangement of concepts that is intended to define its essential nature. |
| | | | |
| − | that merely aims at such a method.
| + | An array of concepts that is set up to capture the essence of a subject is a provisional definition of it, an implicit model of the subject that contains the makings of an explicit theory. It amounts to a selection from the phenomenal aspects of the subject, expresses a guess about its relevant features, and constitutes a hypothesis in explanation of its experienced characteristics. This incipient order of model or theory is tantamount to a definition because it sets bounds on the "stretches" and the "holds" of a term — its extension, intension, and intention — but this is not the kind of definition that has to be taken on faith, or that constitutes the first and the last word on the subject. In other words, it is an empirical definition, one that is subject to being falsified in reference to its intended subject, by failing to indicate the necessary, the pertinent, or the relevant features that account for the presence of its phenomena or the persistence of its process. |
| | | | |
| | + | If I reflect on the conduct of inquiry, seeking to fix it in a fitting image and trying to cast it in a positive light, the best I can do is this: |
| | | | |
| | + | : Inquiry is a process that aims at achieving belief or knowledge. |
| | | | |
| − | 2. It allows one to finesse the issue, for the time being,
| + | But even this simple a description already plunges the discussion deep into a number of obscurities. Most prominently, there is the disjunction between belief and knowledge that cries out to be explained or resolved. Stirring beneath the surface, and not quite fading into the background, many of the other terms that are invoked in the description are capable of hiding the entire contents of the original ignorance that the image as a whole is aimed to dispel. And yet, there is nothing that I can do in this avowedly positive context but to mark these points down as topics for future discussion. |
| | | | |
| − | of how much "method" there is in science.
| + | There is already a model of inquiry that is implicit, at least partially, in the text of the above description. Let me see if I can tease out a few of its tacit assumptions. |
| | | | |
| | + | =====1.4.1.1. Inquiry as Conduct===== |
| | | | |
| | + | First of all, inquiry is conceived to be a form of conduct. This invokes the technical term ''conduct'', referring to the species of prototypically human action that is both dynamic and deliberate, or conceived to fall under a form of purposeful control, usually conscious but possibly not. For the sake of clarity, it helps to seek a more formal definition of conduct, one that expresses the concept in terms of abstract features rather than trying to suggest it by means of typical examples. |
| | | | |
| − | This Subdivision and the next deal with opposite aspects of inquiry.
| + | Conduct is action with respect to an object. The distinction between action and conduct, reduced to the level of the most abstract formal relations that are involved, can be described in the following manner. |
| | | | |
| − | In many ways it might have been better to interlace the opposing points | + | Action is a matter of going from A to B, whereas conduct is matter of going from A to B in relation to C. In describing particular cases and types of conduct, the phrase "in relation to" can be filled out in more detail as "on account of", "in the cause of", "in order to bring about", "for the sake of", "in the interests of", or in many other ways. Thus, action by itself has a dyadic character, involving transitions through pairs of states, while conduct has a triadic character, involving the kinds of transactions between states that relate throughout to an object. |
| | | | |
| − | of comparison, taking them up in a parallel fashion, but this plan was | + | With regard to this distinction, notice that "action" is used inclusively, to name the genus of which "conduct" names a species, and thus depicts whatever has the aspect of action, even if it is actually more complex. |
| | | | |
| − | judged to be too distracting for a first approach. In other ways, the
| + | This creates the difficulty that the reputed "genus" is less than fully "generative", "generic", "genetic", or even "genuine" -- and so it is necessary to remain on guard against this source of misunderstanding. |
| | | | |
| − | negative sides of each topic are prior in point of time to the positive
| + | What does this definition of conduct say about the temporal ordering of the object with respect to the states? The states are conceived to be ordered in time, but so far nothing has been said to pin down where in relation to these states the object must be conceived to fall in time. Nor does the definition make any particular specification necessary. This makes the question of relative time a secular parameter of the definition, allowing the consideration of the following options: |
| | | | |
| − | sides of the issue, but sensible people like to see the light at the end
| + | # If the object is thought to precede the action of the conduct, then it tends to be regarded as a creative act, an initial intention, an original stimulus, a principal cause, or a prime mover. |
| | + | # If the object is thought to succeed the action of the conduct, then it tends to be regarded as an end, a goal, or a purpose, in other words, a state envisioned to be fulfilled. |
| | + | # If the object is thought to be concurrent, immanent, or transcendent throughout the action of the conduct, then it tends to be regarded as falling under one of the following possibilities: a prevailing value, a controlling parameter, a universal system of effective forces, a pervasive field of potentials, a ruling law, or a governing principle. |
| | | | |
| − | of the tunnel before they trouble themselves with the obscurities of the | + | A prevailing value or a controlling parameter, which guides the temporal development of a system, is a term that fits into a law or a principle, which governs the system at a higher level. The existence of a value or a law that rules a system, and the information that an agent of the system has about its parameters and its principles, are two different matters. Indeed, a major task of development for an inquiring agent is to inform itself about the values and the laws that form its own system. Thus, one of the objects of the conduct of inquiry is a description in terms of laws and values of the rules that govern and guide inquiry. |
| | | | |
| − | intervening journey. Thus, this subdivison of the text emphasizes the
| + | The elaboration of an object in terms of this rich vocabulary — as a cause, end, field, force, goal, intention, law, parameter, principle, purpose, system, or value — adds colorful detail and concrete sensation to the account, and it helps to establish connections with the arrays of terminology that are widely used to discuss these issues. From a formal and relational point of view, however, all of these concepts are simply different ways of describing, at possibly different levels of generality, the object of a form of conduct. With that in mind, I find it useful to return to the simpler form of description as often as possible. |
| | | | |
| − | positive features of inquiry and the positive qualities of its objective,
| + | This account of conduct brings to the fore a number of issues, some of them new and some of them familiar, but each of them allowing itself to be approached from a fresh direction by treating it as an implication of a critical thesis just laid down. I next examine these issues in accord with the tenets from which they stem. |
| | | | |
| − | while the next Subdivision is reserved to examine the negative aspects
| + | 1. Inquiry is a form of conduct. |
| | | | |
| − | of each question. | + | This makes inquiry into inquiry a special case of inquiry into conduct. |
| | | | |
| | + | Certainly, it must be possible to reason about conduct in general, especially if forms of conduct need to be learned, examined, modified, and improved. |
| | | | |
| | + | Placing the subject of inquiry within the subject of conduct and making the inquiry into inquiry a subordinate part of the inquiry into conduct does not automatically further the investigation, especially if it turns out that the general subject of conduct is more difficult to understand than the specialized subject of inquiry. But in those realms of inquiry where it is feasible to proceed hypothetically and recursively, stretching the appropriate sort of hypothesis over a wider subject area can act to prime the pump of mathematical induction all the more generously, and actually increase the power of the recursion. Of course, the use of a recursive strategy comes at the expense of having to establish a more extended result at the base. |
| | | | |
| − | In the order of nature, the absence of a feature naturally precedes the
| + | 2. The existence of an object that rules a form of conduct and the information that an agent of the conduct has about the object are two different matters. |
| | | | |
| − | full development of its presence. In the order of discussion, however,
| + | This means that the exact specification of the object can demand an order of information that the agent does not have available, at least, not for use in reflective action, or even require an amount of information that the agent lacks the capacity to store. No matter how true it is that the actual course of the agent's conduct exactly reflects the influence of the object, and thus, in a sense, represents the object exactly, the question is whether the agent possesses the equivalent of this information in any kind of accessible, exploitable, reflective, surveyable, or usable form of representation, in effect, in any mode of information that the agent can use to forsee, to modify, or to temper its own temporal course. |
| | | | |
| − | positive terms must be proposed if it is desired to say anything at all.
| + | This issue may seem familiar as a repetition of the "meta" question. |
| | | | |
| − | The discussion in this Subdivision is placed to serve a primer, declaring
| + | Once again, there is a distinction between (a) the properties of an action, agent, conduct, or system, as expressible by the agent that is engaged in the conduct, or as representable within the system that is undergoing the action, and (b) the properties of the same entities, as evident from an "external viewpoint", or as statable by the equivalent of an "outside observer". |
| | | | |
| − | at least the names of enough positive concepts to propose addressing the
| + | 3. Reflection is a part of inquiry. Reflection is a form of conduct. |
| | | | |
| − | negative conditions of knowledge in which inquiry necessarily starts.
| + | The task of reflection on conduct is to pass from a purely interior view of one's own conduct to an outlook that is, effectively, an exterior view. |
| | | | |
| | + | What is sought is a wider perspective, one that is able to incorporate the sort of information that might be available to an outside observer, that ought to be evident from an external vantage point, or that one reasonably imagines might be obvious from an independent viewpoint. I am tempted to refer to such a view as a "quasi-objective perspective", but only so long as it possible to keep in mind that there is no such thing as a "completely outside perspective", at least, not one that a finite and mortal agent can hope to achieve, nor one that a reasonably socialized member of a community can wish to take up as a permanent station in life. |
| | | | |
| | + | With these qualifications, reflection is a form of conduct that can serve inquiry into conduct. Inquiry and its component reflection, applied to a form of conduct, are intended to provide information that can be used to develop the conduct in question. The "reflective development" that occurs depends on the nature of the case. It can be the continuation, the correction, or the complete cessation of the conduct in question. |
| | | | |
| − | In this Subdivision I stand back once again from the problem of inquiry
| + | If it is to have the properties that it is commonly thought to have, then reflection must be capable of running in parallel, and not interfering too severely, with the conduct on which it reflects. If this turns out to be an illusion of reflection that is not really possible in actuality, then reflection must be capable, at the very least, of reviewing the memory record of the conduct in question, in ways that appear concurrent with a replay of its action. But these are the abilities that reflection is "pre-reflectively" thought to have, that is, before the reflection on reflection can get under way. If reflection is truly a form of conduct, then it becomes conceivable as a project to reflect on reflection itself, and this reflection can even lead to the conclusion that reflection does not have all of the powers that it is commonly portrayed to have. |
| | | | |
| − | and allow myself take a more distant view of the subject, settling into | + | First of all, inquiry is conceived to be a form of conduct. This invokes the technical term "conduct", referring to the species of prototypically human action that is both dynamic and deliberate, or conceived to fall under a form of purposeful control, usually conscious but possibly not. For the sake of clarity, it helps to seek a more formal definition of conduct, one that expresses the concept in terms of abstract features rather than trying to suggest it by means of typical examples. |
| | | | |
| − | what I think is a comfortable and a natural account of inquiry, the best
| + | Conduct is action with respect to an object. The distinction between action and conduct, reduced to the level of the most abstract formal relations that are involved, can be described in the following manner. Action is a matter of going from A to B, whereas conduct is matter of going from A to B in relation to C. In describing particular cases and types of conduct, the phrase "in relation to" can be filled out in more detail as "on account of", "in the cause of", "in order to bring about", "for the sake of", "in the interests of", or in many other ways. Thus, action by itself has a dyadic character, involving transitions through pairs of states, while conduct has a triadic character, involving the kinds of transactions between states that relate throughout to an object. |
| | | | |
| − | that I have at my command, and attending to the task of describing its | + | With regard to this distinction, notice that "action" is used inclusively, to name the genus of which "conduct" names a species, and thus depicts whatever has the aspect of action, even if it is actually more complex. This creates the difficulty that the reputed "genus" is less than fully "generative", "generic", "genetic", or even "genuine" - and so it is necessary to remain on guard against this source of misunderstanding. |
| | | | |
| − | positive features in a positive light. I present my personal view of
| + | What does this definition of conduct say about the temporal ordering of the object with respect to the states? The states are conceived to be ordered in time, but so far nothing has been said to pin down where in relation to these states the object must be conceived to fall in time. Nor does the definition make any particular specification necessary. This makes the question of relative time a secular parameter of the definition, allowing the consideration of the following options: |
| | | | |
| − | inquiry as I currently understand it, without stopping to justify every
| + | # If the object is thought to precede the action of the conduct, then it tends to be regarded as a creative act, an initial intention, an original stimulus, a principal cause, or a prime mover. |
| | + | # If the object is thought to succeed the action of the conduct, then it tends to be regarded as an end, a goal, or a purpose, in other words, a state envisioned to be fulfilled. |
| | + | # If the object is thought to be concurrent, immanent, or transcendent throughout the action of the conduct, then it tends to be regarded as falling under one of the following possibilities: a prevailing value, a controlling parameter, a universal system of effective forces, a pervasive field of potentials, a ruling law, or a governing principle. |
| | | | |
| − | concept in detail or to examine every objection that might be made to
| + | A prevailing value or a controlling parameter, which guides the temporal development of a system, is a term that fits into a law or a principle, which governs the system at a higher level. The existence of a value or a law that rules a system, and the information that an agent of the system has about its parameters and its principles, are two different matters. Indeed, a major task of development for an inquiring agent is to inform itself about the values and the laws that form its own system. Thus, one of the objects of the conduct of inquiry is a description in terms of laws and values of the rules that govern and guide inquiry. |
| | | | |
| − | this view. In the next Subdivision I discuss a few of the more obvious | + | The elaboration of an object in terms of this rich vocabulary — as a cause, end, field, force, goal, intention, law, parameter, principle, purpose, system, or value — adds colorful detail and concrete sensation to the account, and it helps to establish connections with the arrays of terminology that are widely used to discuss these issues. From a formal and relational point of view, however, all of these concepts are simply different ways of describing, at possibly different levels of generality, the object of a form of conduct. With that in mind, I find it useful to return to the simpler form of description as often as possible. |
| | | | |
| − | problems that stand in the way of this view and I try to remove a few
| + | This account of conduct brings to the fore a number of issues, some of them new and some of them familiar, but each of them allowing itself to be approached from a fresh direction by treating it as an implication of a critical thesis just laid down. I next examine these issues in accord with the tenets from which they stem. |
| | | | |
| − | of the more tractable obscurities that appear ready to be cleared up. | + | 1. Inquiry is a form of conduct. |
| | | | |
| − | The fact that I treat them as my "personal insights" does not mean that
| + | This makes inquiry into inquiry a special case of inquiry into conduct. Certainly, it must be possible to reason about conduct in general, especially if forms of conduct need to be learned, examined, modified, and improved. |
| | | | |
| − | all of these ideas about inquiry originate with me, but only that I have
| + | Placing the subject of inquiry within the subject of conduct and making the inquiry into inquiry a subordinate part of the inquiry into conduct does not automatically further the investigation, especially if it turns out that the general subject of conduct is more difficult to understand than the specialized subject of inquiry. But in those realms of inquiry where it is feasible to proceed hypothetically and recursively, stretching the appropriate sort of hypothesis over a wider subject area can act to prime the pump of mathematical induction all the more generously, and actually increase the power of the recursion. Of course, the use of a recursive strategy comes at the expense of having to establish a more extended result at the base. |
| | | | |
| − | come to adopt them for my personal use. There will be many occasions,
| + | 2. The existence of an object that rules a form of conduct and the information that an agent of the conduct has about the object are two different matters. |
| | | | |
| − | the next time that I go over this ground, to point out the sources of | + | This means that the exact specification of the object can require an order of information that the agent does not have available, at least, not for use in reflective action, or even an amount of information that the agent lacks the capacity to store. No matter how true it is that the actual course of the agent's conduct exactly reflects the influence of the object, and thus, in a sense, represents the object exactly, the question is whether the agent possesses the equivalent of this information in any kind of accessible, exploitable, reflective, surveyable, or usable form of representation, in effect, any mode of information that the agent can use to forsee, to modify, or to temper its own temporal course. |
| | | | |
| − | these ideas, so far as I know them.
| + | This issue may seem familiar as a repetition of the "meta" question. Once again, there is a distinction between (a) the properties of an action, agent, conduct, or system, as expressible by the agent that is engaged in the conduct, or as representable within the system that is undergoing the action, and (b) the properties of the same entities, as evident from an "external viewpoint", or as statable by the equivalent of an "outside observer". |
| | | | |
| | + | 3. Reflection is a part of inquiry. Reflection is a form of conduct. |
| | | | |
| | + | The task of reflection on conduct is to pass from a purely interior view of one's own conduct to an outlook that is, effectively, an exterior view. What is sought is a wider perspective, one that is able to incorporate the sort of information that might be available to an outside observer, that ought to be evident from an external vantage point, or that one reasonably imagines might be obvious from an independent viewpoint. I am tempted to refer to such a view as a "quasi-objective perspective", but only so long as it possible to keep in mind that there is no such thing as a "completely outside perspective", at least, not one that a finite and mortal agent can hope to achieve, nor one that a reasonably socialized member of a community can wish to take up as a permanent station in life. |
| | | | |
| − | The reader may take my apology for this style of presentation to be | + | With these qualifications, reflection is a form of conduct that can serve inquiry into conduct. Inquiry and its component reflection, applied to a form of conduct, are intended to provide information that can be used to develop the conduct in question. The "reflective development" that occurs depends on the nature of the case. It can be the continuation, the correction, or the complete cessation of the conduct in question. |
| | | | |
| − | implicit in its dogmatic character. It is done this way in a first
| + | If it is to have the properties that it is commonly thought to have, then reflection must be capable of running in parallel, and not interfering too severely, with the conduct on which it reflects. If this turns out to be an illusion of reflection that is not really possible in actuality, then reflection must be capable, at the very least, of reviewing the memory record of the conduct in question, in ways that appear concurrent with a replay of its action. But these are the abilities that reflection is "pre-reflectively" thought to have, that is, before the reflection on reflection can get under way. If reflection is truly a form of conduct, then it becomes conceivable as a project to reflect on reflection itself, and this reflection can even lead to the conclusion that reflection does not have all of the powers that it is commonly portrayed to have. |
| | | | |
| − | approach for the sake of avoiding an immense number of distractions,
| + | =====1.4.1.2. Types of Conduct===== |
| | | | |
| − | each of which is not being slighted but demands to be addressed in
| + | The chief distinction that applies to different forms of conduct is whether the object is the same sort of thing as the states or whether it is something entirely different, a thing apart, of a wholly other order. Although I am using different words for objects and states, it is always possible that these words are indicative of different roles in a formal relation and not indicative of substantially different types of things. If objects and states are but formal points and naturally belong to the same domain, then it is conceivable that a temporal sequence of states can include the object in its succession, in other words, that a path through a state space can reach or pass through an object of conduct. But if a form of conduct has an object that is completely different from any one of its temporal states, then the role of the object in regard to the action cannot be like the end or goal of a temporal development. |
| | | | |
| − | its own good time. I want to convey the general drift of my current
| + | What names can be given to these two orders of conduct? |
| | | | |
| − | model, however conjectural, naive, uncritical, and unreflective it
| + | =====1.4.1.3. Perils of Inquiry===== |
| | | | |
| − | may seem.
| + | Now suppose that making a hypothesis is a kind of action, no matter how covert, or that testing a hypothesis takes an action that is more overt. If entertaining a hypothesis in any serious way requires action, and if action is capable of altering the situation in which it acts, then what prevents this action from interfering with the subject of inquiry in a way that undermines, with positive or negative intentions, the very aim of inquiry, namely, to understand the situation as it is in itself? |
| | | | |
| − | ====1.4.1 The Matrix of Inquiry====
| + | That making a hypothesis is a type of action may seem like a hypothesis that is too far-fetched, but it appears to follow without exception from thinking that thinking is a form of conduct, in other words, an activity with a purpose or an action that wants an end. The justification of a hypothesis is not to be found in a rational pedigree, by searching back through a deductive genealogy, or determined by that which precedes it in the logical order, since a perfectly trivial tautology caps them all. Since a logical tautology, that conveys no empirical information, finds every proposition appearing to implicate it, in other words, since it is an ultimate implication of every proposition and a conceivable conclusion that is implicit in every piece of reasoning, it is obvious that seeking logical precedents is the wrong way to go for empirical content. |
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| − | <pre>
| + | In making a hypothesis or choosing a model, one appears to select from a vaster number of conceivable possibilities than a finite agent could ever enumerate in complete detail or consider as an articulate totality. As the very nature of a contingent description and the very character of a discriminate action is to apply in some cases but not in others, there is no escaping the making of a risky hypothesis or a speculative interpretation, even in the realm of a purely mental action. Thus, all significant thought, even thinking to any purpose about thought itself, demands a guess at the subject or a grasp of the situation that is contingent, dubious, fallible, and uncertain. |
| − | | Thus when mothers have chidren suffering from sleeplessness,
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| − | | and want to lull them to rest, the treatment they apply is
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| − | | to give them, not quiet, but motion, for they rock them
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| − | | constantly in their arms; and instead of silence, they
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| − | | use a kind of crooning noise; and thus they literally
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| − | | cast a spell upon the children (like the victims of
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| − | | a Bacchic frenzy) by employing the combined movements
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| − | | of dance and song as a remedy.
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| − | |
| |
| − | | Plato, 'Laws', VII, 790D
| |
| − | </pre>
| |
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| − | Try as I may, I've never seen a way to develop a theory of inquiry from nothing:
| + | If all this is true — if inquiry begins with doubt, if every significant hypothesis is itself a dubious proposition, if the making and the testing of a hypothesis are instances of equally doubtful actions, and if every action has the potential to alter the very situation and the very subject matter that are being addressed — then it leads to the critical question: How is the conduct of inquiry, that begins by making a hypothesis and that continues by testing this description in action, supposed to help with the situation of uncertainty that incites it in the first place and that is supposed to maintain its motivation until the end is reached? The danger is that the posing of a hypothesis may literally introduce an irreversible change in the situation or the subject matter in question. The fear is that this change might be one that too conveniently fulfills or too perversely subverts the very hypothesis that engenders it, that it may obstruct the hypothesis from ever being viewed with equanimity again, and thus prevent the order of reflection that is needed to amend or discard the hypothesis when the occasion to do so arises. |
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| − | To take for granted nothing more than is already given, to set out from nothing
| + | If one fears that merely contemplating a special hypothesis is enough to admit a spurious demonstration into the foundations of one's reasoning, even to allow a specious demon to subvert all one's hopes of a future rationality and to destroy all one's chances of a reasonable share of knowledge, then one is hardly in a state of mind that can tolerate the tensions of a full-fledged, genuine inquiry. If one is beset with such radical doubts, then all inquiry is no more comfort than pure enchoiry. Sometimes it seems like the best you can do is sing yourself a song that soothes your doubts. Perhaps it is even quite literally true that all inquiry comes back at last to a form of "enchoiry", the invocation of a nomos, a way of life, or a song and a dance. But even if this is the ultimate case, it does no harm and it does not seem like a bad idea to store up in this song one or two bits of useful lore, and to weave into its lyric a few suggestions of a practical character. |
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| − | but absolutely certain beginnings, to move forward with nothing but absolutely
| + | Let us now put aside these more radical doubts. This putting aside of doubts is itself a form of inquiry, that is, a way of allaying doubts. The fact that I appear to do this by fiat, and to beg for tacit assent, tends to make me suspect the validity of this particular tactic. Still, it is not too inanely dismissive, as its appeal is based on an argument, the argument that continuing to entertain this type of doubt leads to a paralysis of the reason, and that paralyzing the ability to think is not in the interests of the agent concerned. Thus, I adopt the hypothesis that the relationship between the world and the mind is not so perverse that merely making a hypothesis is enough to alter the nature of either. If, in future, I or anyone sees the need to reconsider this hypothesis, then I see nothing about making it that prevents anyone from doing so. Indeed, making it explicit only renders it more subject to reflection. |
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| − | certain means of proceeding. In particular, the present inquiry into inquiry,
| + | Of course, a finite person can only take up so many causes in a single lifetime, and so there is always the excuse of time for not chasing down every conceivable hypothesis that comes to mind. |
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| − | foreshadowed in the form y_0 = y·y, ought not to be misconstrued as a device
| + | =====1.4.1.4. Forms of Relations===== |
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| − | for magically generating a theory of inquiry from nothing. Like any other
| + | The next distinguishing trait that I can draw out of this incipient treatise is its emphasis on the forms of relations. From a sufficiently formal and relational point of view, many of the complexities that arise from throwing intentions, objectives, and purposes into the mix of discussion are conceivably due to the greater arity of triadic relations over dyadic relations, and do not necessarily implicate any differences of essence inhering in the entities and the states invoked. As far as this question goes, whether a dynamic object is essentially different from a deliberate object, I intend to remain as neutral as possible, at least, until forced by some good reason to do otherwise. In the meantime, the factors that are traceable to formal differences among relations are ready to be investigated and useful to examine. With this in mind, it it useful to make the following definition: |
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| − | inquiry, it requires an agent to invest in a conjecture, to make a guess
| + | A ''conduct relation'' is a triadic relation involving a domain of objects and two domains of states. When a shorter term is desired, I refer to a conduct relation as a ''conduit''. A conduit is given in terms of its extension as a subset C c XxYxZ, where X is the ''object domain'' and where Y and Z are the ''state domains''. Typically, Y = Z. |
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| − | about the pertinent features of the subject of interest, and to choose
| + | In general, a conduct relation serves as a ''model of conduct'' (MOC), not always the kind of model that is meant to be emulated, but the type of model that captures an aspect of structure in a form of conduct. |
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| − | the actions, the aspects, and the attitudes with regard to the subject | + | The question arises: What is the relationship between signs and states? On the assumption that signs and states are comparable in their levels of generality, consider the following possibilities: |
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| − | that are critical to achieving the intended objectives of the study.
| + | # Signs are special cases of states. |
| | + | # Signs and states are the same sorts of things. |
| | + | # States are special cases of signs. |
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| | + | Depending on how one answers this question, one is also choosing among the following options: |
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| | + | # Sign relations are special cases of conduct relations. |
| | + | # Sign relations and conduct relations are the same sorts of things. |
| | + | # Conduct relations are special cases of sign relations. |
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| − | I can sum all this up by saying that an inquiry requires an inquirer to | + | I doubt if there is any hard and fast answer to this question, but think that it depends on particular interpreters and particular observers, to what extent each one interprets a state as a sign, and to what degree each one recognizes a sign as a component of a state. |
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| − | suggest a hypothesis about the subject of interest and then to put that
| + | =====1.4.1.5. Models of Inquiry===== |
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| − | particular model of the subject to the test. This in turn requires one
| + | The value of a hypothesis, or the worth of a model, is not to be given a prior justification, as by a deductive proof, but has to be examined in practice, as by an empirical probation. It is not intended to be taken for granted or to go untested, but its meaning in practice has to be articulated before its usefulness can be judged. This means that the conceivable practical import of the hypothesis or the model has to be developed in terms of its predicted and its promised consequences, after which it is judged by the comparison of these speculative consequences with the actual results. But this is not the end of the matter, for it can be a useful piece of information to discover that a particular kind of conception fails a particular kind of comparison. Thus, the final justification for a hypothesis or a model is contained in the order of work that it leads one to do, and the value of this work is often the same whether or not its premiss is true. Indeed, the fruitfulness of a suggestion can lie in the work that proves it untrue. |
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| − | to devote a modicum of personal effort to the task of testing the chosen | + | My plan then has to be, rather than trying to derive a model of inquiry in a deductive fashion from a number of conditions like <math>y_0 = y \cdot y,</math> only to propose a plausible model, and then to test it under such conditions. Each of these tests is a two-edged sword, and the result of applying a particular test to a proposed model can have either one of two effects. If one believes that a particular test is a hard and fast rule of inquiry, or a condition that any inquiry is required to satisfy, then the failure of a model to live up to its standard tends only to rule out that model. If one has reason to believe that a particular model of inquiry covers a significant number of genuine examples, then the failure of these models to follow the prescribed rule can reflect badly on the test itself. |
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| − | hypothesis, to put a quantum of personal interest at stake for the sake
| + | In order to prime the pump, therefore, let me offer the following account of inquiry in general, the whole of which can be taken as a plausible hypothesis about the nature of inquiry in general. |
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| − | of finding out whether the model fits the subject, and, overall, to take | + | My observations of inquiry in general, together with a few suggestions that seem apt to me, have led me to believe that inquiry begins with a "surprise" or a "problem". The way I understand these words, they refer to departures, differences, or discrepancies among various modalities of experience, in particular, among "observations", "expectations", and "intentions". |
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| − | the risk of being wrong. Any model that is feasible is also defeasible, | + | # A ''surprise'' is a departure of an observation from an expectation, and thus it invokes a comparison between present experience and past experience, since expectations are based on the remembered disposition of past experience. |
| | + | # A ''problem'' is a departure of an observation from an intention, and thus it invokes a comparison between present experience and future experience, since intentions choose from the envisioned disposition of future experience. |
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| − | at least, where it concerns a contingent subject of contingent inquiry.
| + | With respect to these |
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| | + | With respect to this hypothetical |
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| | + | I now test this model of inquiry under the conditions of an inquiry into inquiry, asking whether it is consistent in its application to itself. This leaves others to test the models they like best under the same conditions, should they ever see the need to do so. |
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| − | The first step, then, of an inquiry into inquiry, is to put forth a tentative
| + | Does the inquiry into inquiry begin with a surprise or a problem concerning the process or the conduct of inquiry? In other words, does the inquiry into inquiry start with one of the following forms of departure: (1) a surprising difference between what is expected of inquiry and what is observed about it, or (2) a problematic difference between what is observed about inquiry and what is intended for it? |
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| − | model of inquiry, to make a hypothesis about the features of inquiry that are
| + | ====1.4.2. The Moment of Inquiry==== |
| | | | |
| − | essential to explaining its experienced characteristics, and thus, in a sense,
| + | <blockquote> |
| | + | <p>Every young man — not to speak of old men — on hearing or seeing anything unusual and strange, is likely to avoid jumping to a hasty and impulsive solution of his doubts about it, and to stand still; just as a man who has come to a crossroads and is not quite sure of his way, if he be travelling alone, will question himself, or if travelling with others, will question them too about the matter in doubt, and refuse to proceed until he has made sure by investigation of the direction of his path.</p> |
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| − | to make a guess at the very definition of inquiry. This requirement seems both
| + | <p>(Plato, ''Laws'', VII, 799C).</p> |
| | + | </blockquote> |
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| − | obvious and outrageous at the same time. One is perfectly justified in objecting
| + | Observe the paradox of this precise ambiguity: That both the occasion and the impulse of inquiry are instances of a negative moment. But the immediate discussion is aimed at the positive aspects of inquiry, and so I convert this issue into its corresponding positive form. |
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| − | that there is much that precedes this so-called "first step", namely, the body of | + | The positive aim of inquiry is a state of belief, certainty, or knowledge. There are distinctions that can be made in the use of these words, but the question remains as to what kind of distinctions these are. In my opinion, the differences that arise in practice have more to do with the purely grammatical distinctions of "case", "mood", "number", "person", and "voice", and thus raise the issues of plurality and point of view, as opposed to indicating substantial differences in the relevant features of state, as actually experienced by the agent concerned. |
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| − | experience that prepares one to see it and the mass of observation that prompts one
| + | It is often claimed that there are signficant differences between the conditions of belief and knowledge, but the way that I understand the distinction is as follows. One says that a person "knows" something when that person believes exactly the same thing that one believes. When one is none other than the person in question, then one says that one "knows" exactly what one believes. Differences arise between the invocations of "belief" and "knowledge" only when more than one person is involved in the issue. Thus, there is no occasion for a difference between belief and knowledge unless there is more than one person that is being consulted about the matter in question, or else a single person in a divided state of opinion, in any case, when there is more than one impulse, moment, or occasion that currently falls under consideration. |
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| − | to take it. I can deal with this objection by making a distinction between mundane | + | In any case, belief or knowledge is the feature of state that an agent of inquiry lacks at the moment of setting out. Inquiry begins in a state of impoverishment, need, or privation, a state that is absent the quality of certainty. It is due to this feature that the agent is motivated, and it is on account of its continuing absence that the agent keeps on striving to achieve it, at least, with respect to the subject in question, and, at any rate, in sufficient measure to make action possible. |
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| − | experience and olympian theory, and then by saying that the making of a conjecture
| + | ====1.4.3. The Modes of Inquiry==== |
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| − | is really the first "theoretical" step, but this is a hedge that covers the tracks
| + | <blockquote> |
| | + | <p>Let the strange fact be granted, we say, that our hymns are now made into "nomes" (laws), just as the men of old, it would seem, gave this name to harp-tunes, — so that they, too, perhaps, would not wholly disagree with our present suggestion, but one of them may have divined it vaguely, as in a dream by night or a waking vision: anyhow, let this be the decree on the matter: — In violation of public tunes and sacred songs and the whole choristry of the young, just as in violation of any other "nome" (law), no person shall utter a note or move a limb in the dance.</p> |
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| − | of theory in a very deceptive way, hiding how early in the empirical process the
| + | <p>(Plato, ''Laws'', VII, 799E–800A).</p> |
| | + | </blockquote> |
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| − | "cloven hoof" of theory actually enters.
| + | In the present section, I am concerned with the kinds of reasoning that might be involved in the choice of a method, that is, in discovering a way to go about inquiry, in constructing a way to carry it through, and in justifying the way that one chooses. If the choice of a method can be established on the basis of reasoning, if it can be rationalized or reconstructed on grounds that are commonly thought to be sensible, or if it is likely to be affected or influenced in any way by a rational argument, then there is reason to examine the kinds of reasoning that go into this choice. All of this requires a minimal discussion of different modes of reasoning. |
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| | + | In this work as a whole, each instance of inquiry is analyzed in accord with various modes of reasoning, the prospective "elements of inquiry", and its structure as an object of inquiry is articulated, rationalized, and reconstructed with respect to the corresponding "form of analysis", "form of synthesis", or "objective genre" (OG). |
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| | + | According to my current understanding, the elements of inquiry can be found to rest on three types of steps, called "abductive", "deductive", and "inductive" modes of inference. As a result of this opinion, I do not believe that I can do any better at present than to articulate the structure of each instance of learning or reasoning according to these three types of motions of the mind. But since this work as a whole is nowhere near complete, I cannot dictate these steps in a dogmatic style, nor will it do for me to to call the tune of this form of analysis in a purely ritual or a wholly routine fashion. |
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| − | Leaving behind the mythical states of "pure" experience and "naive" observation,
| + | Since the complexity of reasoning about different modes of reasoning is enough of a complication to occupy my attention at the present stage of development in this work, it is proably best to restrain this discussion along the majority of its other dimensions. A convenient way to do this is to limit its scope to simple examples and concrete situations, just enough to illustrate the selected modes of reasoning. |
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| − | and at least by the time that one has come to give a name to the subject of the | + | With all of these considerations in mind, the best plan that I can find for addressing the tasks of the present section is to proceed as follows: I make it my primary aim to examine only a few of the simplest settings in which these different modes of reasoning are able to appear, and I try to plot my path through this domain by way of concrete examples. Along the way, I discuss a few of the problems that are associated with reasoning about different modes of reasoning. Given the present stage of development, the majority of these issues have to be put aside almost as quickly as they are taken up. If they are ever going to be subject to resolution, it is not within reach of the present moment of discussion. In the body of this section, I therefore return to the initial strategy: to examine a few of the simplest cases and situations that can serve to illustrate the distinctions among the chosen modes of reasoning. |
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| − | investigation, one's trek through the data is already half-shod, half-fettered
| + | In trying to initiate a general discussion of the different modes of reasoning that might be available, and thus to motivate a model of this subject matter that makes an initial kind of sense to me, I meet once again with all the old "difficulties at the beginning", the kinds of obstructions that always seem to arise on trying to open up any new subject for discussion or in trying to introduce any new model of an old subject area. Much of this gratuitous bedevilment is probably due to the inherent conservatism of the human mind. Everything familiar is taken for granted, but each new picture of the situation is immediately subjected to the severest suspicions. |
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| − | by the connotations of the name, and in their turn by all of the concepts that
| + | Now, I cannot reason with necessary force that the mind must use these particular modes of reasoning, any more than I can say that it must use a given language in order to express itself. But I can argue, relative to a particular model of thinking that must be proposed hypothetically, that certain modes of reasoning are available to the mind and are likely to be evident in its operation, if one only takes the trouble to look. |
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| − | it invokes in its train. That name, the concepts that it suggests, and the
| + | Ultimately, the model of thinking that I plan to propose makes use of the proposition that all thinking takes place in signs, and thus that inquiry is the transformation of a sign relation. Relative to this hypothesis, it would be possible to discharge the current assumptions about the basic modes of reasoning, that is, to derive the elementary modes of inquiry from a sign relational model of inquiry, and then to compare them with the current suggestions. Until this work is done, however, the assumption that these really are the most basic modes of reasoning has to be treated as a still more tentative hypothesis. |
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| − | tacit but vague definition of the subject that this complex of associations
| + | When a subject matter is so familiar that the logical connections between its parts are known both forwards and backwards, then it is reasonable and convenient to organize its presentation in an axiomatic fashion. This would not be such a bad idea, if it did not make it so easy to forget the nature of the reorganization that goes into a representation, and it would not constitute such a deceptive conception of the subject, if it did not mean that the exposition of the subject matter is just as often the falsification of its actual development and the covering up of its real excavation. Indeed, the logical order of axioms and theorems may have little to do with the original order of discovery and invention. In practice, the deepest axioms are often the last to come to light. |
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| − | is already beginning to constellate, to attract certain experiences to the | + | Once again, the structure of a reflective context means that each mode of reasoning is able to appear in a double role, once as an object and once as an instrument of the same extended discussion. And once again, the discussion runs into an array of obstructions, whose structures are becoming, if not more clear, at least, more familiar with each encounter. In particular, a description of different modes of reasoning involves a classification, and a classification presupposes a basis of distinctive features that cannot be treated as categorical, or objectively neutral, but has to be regarded as hypothetical, or potentially biased. In other words, the language that I use to describe different modes of reasoning may already have a particular model of reasoning built into it, and this disposition to a particular conception of logic may be lodged in such a way that it makes it nearly impossible to reflect on the operations and the limitations of this model. |
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| − | complex, and to filter out other observations from having any bearing on
| + | Inquiry begins when a law is violated. It marks a time when a certain peace of mind is breached, it reigns all the while that a common accord is broken, disturbed, forgotten, or lost, and it rules right up until the time when a former condition of harmony is restored or until the moment when a new state of accord is established. Of course, the word "law" is a highly equivocal choice, especially to convey the sense of a founding principle. It renders not just its own meaning irrevocably subject to interpretation, but delivers into a similar subjection all the forms of understanding that depend on it. But the letter must release its hold on the spirit, if the word "law" is meant to evoke the requisite variety of connotations, and yet to maintain a sensible degree of order among their concrete meanings. Only in this way can it rise above the many different kinds of law that come into play. |
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| − | the subject matter. By this time, one is already busy translating one's
| + | There are descriptive laws, that organize experiences into expectations. There are prescriptive laws, that organize performances into intentions. |
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| − | empirical acquaintance with the subject into an arrangement of concepts | + | Other names for descriptive laws are "declarative" or "empirical" laws. Other names for prescriptive laws are "procedural" or "normative" laws. |
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| − | that is intended to define its essential nature.
| + | Implicit in a descriptive law is the connection to be found or made, discovered or created, between past experience and present expectation. What one knows about these connections is kept in a descriptive model. |
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| | + | Implicit in a prescriptive law is the connection to be found or made, discovered or created, between current conduct and future experience. What one knows about these connections is kept in a prescriptive model. |
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| | + | A violation of an expectation, the contravention of a descriptive law, occurs when a present experience departs from a predicted experience, which is what a past expectation or description projected to be present. This is a "surprise", a state of affairs that calls for an explanation. An explanation points to other descriptions that better predict the actual experience, and suggests an alteration to the descriptive model that generated the expectation from a past experience. |
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| − | An array of concepts that is set up in order to capture the essence
| + | A violation of an intention, the contravention of a prescriptive law, occurs when a present experience departs from a desired experience, which is what a past intention or prescription projected to be present. This is a "problem", a state of affairs that calls for a plan of action. , A plan of action points to other actions that better achieve the desired experience, and suggests an alteration to the prescriptive model that generated the conduct toward a prospective experience. |
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| − | of a subject is a provisional definition of it, an implicit model | + | In the rest of this section, I treat the different modes of reasoning according to the forms that Aristotle gave them, collectively referred to as the "syllogistic" model. The discussion is kept within the bounds of propositional reasoning by considering only those "figures of syllogism" that are "purely universal", that is, the forms of argument all of whose premisses, and therefore all of whose conclusions, involve nothing but universal quantifications. |
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| − | of the subject that contains the makings of an explicit theory. | + | If it were only a matter of doing propositional reasoning as efficiently as possible, I would simply use the cactus language and be done with it, but there are several other reasons for revisiting the syllogistic model. Treating the discipline that is commonly called "logic" as a cultural subject with a rich and varied history of development, and attending to the thread of tradition in which I currently find myself, I observe what looks like a critical transition that occurs between the classical and the modern ages. Aside from supplying the barest essentials of a historical approach to the subject, a consideration of this elder standard makes it easier to appreciate the nature and the character of this transformation. In addition, and surprisingly enough to warrant further attention, there appear to be a number of cryptic relationships that exist between the syllogistic patterns of reasoning and the ostensibly more advanced forms of analysis and synthesis that are involved in the logic of relations. |
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| − | It amounts to a selection from the phenomenal aspects of the
| + | =====1.4.3.1. Deductive Reasoning===== |
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| − | subject, expresses a guess about its relevant features, and
| + | In this subsection, I present a trimmed-down version of deductive reasoning in Aristotle, limiting the account to universal syllogisms, in effect, keeping to the level of propositional reasoning. Within these constraints, there are three basic "figures" of the syllogism. |
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| − | constitutes a hypothesis in explanation of its experienced
| + | In order to understand Aristotle's description of these figures, it is necessary to explain a few items of his technical terminology. In each figure of the syllogism, there are three "terms". Each term can be read as denoting either (1) a class of entities or (2) all of the members of a class of entities, depending on which interpretation the reader prefers. These terms are ranked in two ways: With respect to the "magnitudes" that they have in relation to each other, there are "major", "middle", and "minor" terms. With respect to the "positions" that they take up within the figure, there are "first", "intermediate", and "last" terms. The figures are distinguished by how the magnitudes correlate with the positions. However, the names for these rankings are not always used or translated in a rigorously systematic manner, so the reader has to be on guard to guess which type of ranking is meant. |
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| − | characteristics. This incipient order of model or theory
| + | In addition to this terminology, it is convenient to make use of the following nomenclature: |
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| − | is tantamount to a definition because it sets bounds on | + | # The ''Fact'' is the proposition that applies the term in the first position to the term in the third or last position. |
| | + | # The ''Case'' is the proposition that applies the term in the second or intermediate position to the term in the third or last position. |
| | + | # The ''Rule'' is the proposition that applies the term in the first position to the term in the second or intermediate position. |
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| − | the "stretches" and the "holds" of a term -- that is, | + | Because the roles of Fact, Case, and Rule are defined with regard to positions rather than magnitudes they are insensitive to whether the proposition in question is being used as a premiss or is being drawn as a conclusion. |
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| − | the extension, intension, and intention of the term --
| + | The ''first figure'' of the syllogism is explained as follows: |
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| − | but this is not the kind of definition that has to
| + | <blockquote> |
| | + | <p>When three terms are so related to one another that the last is wholly contained in the middle and the middle is wholly contained in or excluded from the first, the extremes must admit of perfect syllogism. By "middle term" I mean that which both is contained in another and contains another in itself, and which is the middle by its position also; and by "extremes" (a) that which is contained in another, and (b) that in which another is contained. For if A is predicated of all B, and B of all C, A must necessarily be predicated of all C. ... I call this kind of figure the First.</p> |
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| − | be taken on faith, that constitutes the first and
| + | <p>(Aristotle, ''Prior Analytics'', 1.4).</p> |
| | + | </blockquote> |
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| − | the last word on the subject. In other words, | + | For example, suppose A is "animal", B is "bird", and C is "canary". Then there is a deductive conclusion to be drawn in the first figure. |
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| − | it is an empirical definition, one that is
| + | There is the Case: |
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| − | subject to being falsified in reference
| + | : "All canaries are birds." (C => B) |
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| − | to its intended subject, by failing to
| + | There is the Rule: |
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| − | indicate the necessary, the pertinent,
| + | : "All birds are animals." (B => A) |
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| − | or the relevant features that account
| + | One deduces the Fact: |
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| − | for the presence of its phenomena or
| + | : "All canaries are animals." (C => A) |
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| − | the persistence of its process. | + | The propositional content of this deduction is summarized on the right. Taken at this level of detail, deductive reasoning is nothing more than an application of the transitive rule for logical implications. |
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| | + | The ''second figure'' of the syllogism is explained as follows: |
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| | + | <blockquote> |
| | + | <p>When the same term applies to all of one subject and to none of the other, or to all or none of both, I call this kind of figure the Second; and in it by the middle term I mean that which is predicated of both subjects; by the extreme terms, the subjects of which the middle is predicated; by the major term, that which comes next to the middle; and by the minor that which is more distant from it. The middle is placed outside the extreme terms, and is first by position.</p> |
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| − | If I reflect on the conduct of inquiry,
| + | <p>(Aristotle, ''Prior Analytics'', 1.5).</p> |
| | + | </blockquote> |
| | | | |
| − | seeking to fix it in a fitting image
| + | For example, suppose M is "mammal", N is "newt", and O is "opossum". Then there is a deductive conclusion to be drawn in the second figure. |
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| − | and trying to cast it in a positive
| + | There is the Fact: |
| | | | |
| − | light, the best I can do is this:
| + | : "All opossums are mammals." (O => M) |
| | | | |
| | + | There is the Rule: |
| | | | |
| | + | : "No newts are mammals." (N.M = 0) |
| | | | |
| − | Inquiry is a process that aims at achieving belief or knowledge.
| + | One deduces the Case: |
| | | | |
| | + | : "No newts are opossums." (N.O = 0) |
| | | | |
| | + | The propositional content of this deduction is summarized on the right. Expressed in terms of the corresponding classes, it says that if O c M and if N intersects M trivially, then N must also intersect O trivially. Here, I use a raised dot "." to indicate either the conjunction of two propositions or the intersection of two classes, and I use a zero "0" to indicate either the identically false proposition or the empty class, leaving the choice of interpretation to the option of the reader. |
| | | | |
| − | But even this simple a description already plunges the discussion deep into
| + | The ''third figure'' of the syllogism is explained as follows: |
| | | | |
| − | a number of obscurities. Most prominently, there is the disjunction between
| + | <blockquote> |
| | + | <p>If one of the terms applies to all and the other to none of the same subject, or if both terms apply to all or none of it, I call this kind of figure the Third; and in it by the middle I mean that of which both the predications are made; by extremes the predicates; by the major term that which is [further from] the middle; and by the minor that which is nearer to it. The middle is placed outside the extremes, and is last by position.</p> |
| | | | |
| − | belief and knowledge that cries out to be explained or resolved. Stirring a
| + | <p>(Aristotle, ''Prior Analytics'', 1.6).</p> |
| | + | </blockquote> |
| | | | |
| − | little beneath the surface, and not quite fading into the background, many of
| + | It appears that this passage is only meant to mark out the limiting cases of the type. From the examples that Aristotle gives it is clear that he includes many other kinds of logical situation under this figure. Perhaps the phrase "applies to all or none" is intended to specify that a term applies "affirmatively or negatively" to another term, but is not meant to require that it applies universally so. |
| | | | |
| − | the other terms that are invoked in the description are capable of hiding the
| + | For example, suppose P is "poem", R is "rhapsody", and S is "sonnet". Then there is deductive conclusion to be drawn in the third figure: |
| | | | |
| − | entire contents of the original ignorance that the image as a whole is aimed
| + | There is the Fact: |
| | | | |
| − | to dispell. And yet there is nothing that I can do in this avowedly positive
| + | : "All sonnets are poems." (S => P) |
| | | | |
| − | context but to mark these points down as topics for future discussion.
| + | There is the Case: |
| | | | |
| | + | : "Some sonnets are rhapsodies." (S.R > 0) |
| | | | |
| | + | One deduces the Rule: |
| | | | |
| − | There is already a model of inquiry that is implicit,
| + | : "Some rhapsodies are poems." (R.P > 0) |
| | | | |
| − | at least partially, in the text of the above description.
| + | The propositional content of this deduction is summarized on the right. Expressed in terms of the corresponding classes, it says that if S c P and if R intersects S non-trivially then R must intersect P non-trivially. |
| | | | |
| − | Let me see if I can tease out a few of its tacit assumptions.
| + | =====1.4.3.2. Inductive Reasoning===== |
| | | | |
| | + | (Aristotle, ''Prior Analytics'', 2.23). |
| | | | |
| | + | =====1.4.3.3. Abductive Reasoning===== |
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| − | o20:56, 26 May 2007 (PDT)[[User:Jon Awbrey|Jon Awbrey]] 20:56, 26 May 2007 (PDT)o20:56, 26 May 2007 (PDT)[[User:Jon Awbrey|Jon Awbrey]] 20:56, 26 May 2007 (PDT)o20:56, 26 May 2007 (PDT)[[User:Jon Awbrey|Jon Awbrey]] 20:56, 26 May 2007 (PDT)o20:56, 26 May 2007 (PDT)[[User:Jon Awbrey|Jon Awbrey]] 20:56, 26 May 2007 (PDT)o20:56, 26 May 2007 (PDT)[[User:Jon Awbrey|Jon Awbrey]] 20:56, 26 May 2007 (PDT)o
| + | A choice of method cannot be justified by deduction or by induction, at least, not wholly, but involves an element of hypothesis. In ancient times, this mode of inference to an explanatory hypothesis was described by the Greek word "apagoge", articulating an action or a process that "carries", "drives", or "leads" in a direction "away", "from", or "off". This was later translated into the Latin "abductio", and that is the source of what is today called "abduction" or "abductive reasoning". Another residue of this sense survives today in the terminology for "abductor muscles", those that "draw away (say, a limb or an eye) from a position near or parallel to the median axis of the body" (Webster's). |
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| | + | If an image is needed, one may think of Prometheus, arrogating for the sake of an earthly purpose the divine prerogative of the gods, and then drawing the fire of their heavenly ire for the presumption of this act. This seems to sum up pretty well, not only the necessity and the utility of hypotheses, but also the risks that one incurs in making conjectures. In other guises, abductive reasoning is the mode of inference that is used to diagnose a complex situation, one that originally presents itself under a bewildering array of signs and symptoms, and fixes it subject to the terms of a succinct "nomen" or a summary predicate. Finally, by way of offering a personal speculation, I think it is likely that this entire trio of terms, "abduction", "deduction", and "induction", have reference to a style of geometric diagrams that the Ancients originally used to illustrate their reasonings. |
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| | + | Abductive reasoning has also been called by other names. C.S. Peirce at times called it "presumption", perhaps because it puts a plausible assumption logically prior to the observed facts, and at other times referred to it as "retroduction", because it reasons backwards from the consequent to the antecedent of a logical implication. |
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| − | I am using the word "inquiry" in a way that is roughly synonymous with the term "scientific method". Use of "inquiry" is more convenient, aside from being the shorter term, because of the following advantages: (1) It allows one to broaden the scope of investigation to include any form of proceeding toward knowledge that merely aims at such a method. (2) It allows one to finesse the issue, for the time being, of how much "method" there is in science.
| + | In its simplest form, abductive reasoning proceeds from a "fact" that A is true, using a "rule" that B => A, to presume a "case" that B is true. Thus, if A is a surprising fact that one happens to observe, and B => A is a rule to the effect that if B is true then A necessarily follows, then guessing the case that B is true is an instance of abductive reasoning. This is a backward form of reasoning, and therefore extremely fallible, but when it works it has the effect of reducing the amount of surprise in the initial observation, and thus of partially explaining the fact. |
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| − | This subdivision and the next deal with opposite aspects of inquiry. In many ways it might have been better to interlace the opposing points of comparison, taking them up in a parallel fashion, but this plan was judged to be too distracting for a first approach. In other ways, the negative sides of each topic are prior in point of time to the positive sides of the issue, but sensible people like to see the light at the end of the tunnel before they trouble themselves with the obscurities of the intervening journey. Thus, this subdivison of the text emphasizes the positive features of inquiry and the positive qualities of its objective, while the next subdivision is reserved to examine the negative aspects of each question.
| + | In a slightly more complicated version, abduction proceeds from a fact that C => A, using a rule that B => A, to presume a case that C => B. This is an inessential complication, since the rule of modus ponens and the rule of transitivity are essentially equivalent in their logical force, but it is often convenient to imagine that C is the "common subject" or the "current situation" that is implicit throughout the argument, namely, the existing entity that substantiates or instantiates all of the other predicates that are invoked in its course. |
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| − | In the order of nature, the absence of a feature naturally precedes the full development of its presence. In the order of discussion, however, positive terms must be proposed if it is desired to say anything at all. The discussion in this subdivision is placed to serve a primer, declaring at least the names of enough positive concepts to propose addressing the negative conditions of knowledge in which inquiry necessarily starts.
| + | Suppose I have occasion to reason as follows: |
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| − | In this subdivision I stand back once again from the problem of inquiry and allow myself take a more distant view of the subject, settling into what I think is a comfortable and a natural account of inquiry, the best that I have at my command, and attending to the task of describing its positive features in a positive light. I present my personal view of inquiry as I currently understand it, without stopping to justify every concept in detail or to examine every objection that might be made to this view. In the next subdivision I discuss a few of the more obvious problems that stand in the way of this view and I try to remove a few of the more tractable obscurities that appear ready to be cleared up. The fact that I treat them as my "personal insights" does not mean that all of these ideas about inquiry originate with me, but only that I have come to adopt them for my personal use. There will be many occasions, the next time that I go over this ground, to point out the sources of these ideas, so far as I know them.
| + | : "It looks like a duck, so I guess it is a duck." |
| | | | |
| − | The reader may take my apology for this style of presentation to be implicit in its dogmatic character. It is done this way in a first approach for the sake of avoiding an immense number of distractions, each of which is not being slighted but demands to be addressed in its own good time. I want to convey the general drift of my current model, however conjectural, naive, uncritical, and unreflective it may seem.
| + | Or even more simply: |
| | | | |
| − | ====1.4.1 The Matrix of Inquiry (2)====
| + | : "It looks blue, therefore it is blue." |
| | | | |
| − | <blockquote>
| + | These are instances in which I am using abductive reasoning, according to the pattern of the following schema: |
| − | <p>Thus when mothers have chidren suffering from sleeplessness, and want to lull them to rest, the treatment they apply is to give them, not quiet, but motion, for they rock them constantly in their arms; and instead of silence, they use a kind of crooning noise; and thus they literally cast a spell upon the children (like the victims of a Bacchic frenzy) by employing the combined movements of dance and song as a remedy.</p>
| |
| | | | |
| − | <p>(Plato, Laws, VII, 790D).</p>
| + | I observe a Fact: |
| − | </blockquote>
| |
| | | | |
| − | Try as I might, I do not see a way to develop a theory of inquiry from nothing: To take for granted nothing more than is already given, to set out from nothing but absolutely certain beginnings, or to move forward with nothing but absolutely certain means of proceeding. In particular, the present inquiry into inquiry, y0 = y.y, ought not to be misconstrued as a device for magically generating a theory of inquiry from nothing. Like any other inquiry, it requires an agent to invest in a conjecture, to make a guess about the relevant features of the subject of interest, and to choose the actions, the aspects, and the attitudes with regard to the subject that are critical to achieving the objectives of the study.
| + | : "It looks like X." (X') |
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| − | I can sum all this up by saying that an inquiry requires an inquirer to suggest a hypothesis about the subject of interest and then to put that particular model of the subject to the test. This in turn requires one to devote a modicum of personal effort to the task of testing the chosen hypothesis, to put a quantum of personal interest at stake for the sake of finding out whether the model fits the subject, and, overall, to take the risk of being wrong. Any model that is feasible is also defeasible, at least, where it concerns a contingent subject of inquiry. | + | I have in the back of my mind a general Rule: |
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| − | The first step, then, of an inquiry into inquiry, is to put forth a tentative model of inquiry, to make a hypothesis about the features of inquiry that are essential to explaining its experienced characteristics, and thus, in a sense, to make a guess at the very definition of inquiry. This requirement seems both obvious and outrageous at the same time. One is perfectly justified in objecting that there is much that precedes this so-called "first step", namely, the body of experience that prepares one to see it and the mass of observation that prompts one to take it. I can deal with this objection by making a distinction between mundane experience and olympian theory, and then by saying that the making of a conjecture is really the first "theoretical" step, but this is a hedge that covers the tracks of theory in a deceptive way, hiding how early in the empirical process the "cloven hoof" of theory actually enters.
| + | : "If it is X, then it looks like X." (X => X') |
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| − | Leaving behind the mythical conditions of pure experience and naive observation, and at least by the time that one comes to give a name to the subject of investigation, one's trek through the data is already half-shod, half-fettered by the connotations of the name, and in turn by all of the concepts that it invokes in its train. The name, the concepts that it suggests, and the tacit but vague definition of the subject that this complex of associations is already beginning to constellate, attract certain experiences to the complex and filter out other observations from having any bearing on the subject matter. By this point, one is already busy translating one's empirical acquaintance with the subject into an arrangement of concepts that is intended to define its essential nature.
| + | I reason my way back from the observed Fact and the assumed Rule to assert what I guess to be the Case: |
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| − | An array of concepts that is set up to capture the essence of a subject is a provisional definition of it, an implicit model of the subject that contains the makings of an explicit theory. It amounts to a selection from the phenomenal aspects of the subject, expresses a guess about its relevant features, and constitutes a hypothesis in explanation of its experienced characteristics. This incipient order of model or theory is tantamount to a definition because it sets bounds on the "stretches" and the "holds" of a term - its extension, intension, and intention - but this is not the kind of definition that has to be taken on faith, or that constitutes the first and the last word on the subject. In other words, it is an empirical definition, one that is subject to being falsified in reference to its intended subject, by failing to indicate the necessary, the pertinent, or the relevant features that account for the presence of its phenomena or the persistence of its process.
| + | : "It is X." (X) |
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| − | If I reflect on the conduct of inquiry, seeking to fix it in a fitting image and trying to cast it in a positive light, the best I can do is this:
| + | The abduction is a hypothetical inference that results in a diagnostic conclusion, that is, a statement of opinion as to what is conjectured to be the case. In each case the operation of abductive reasoning starts from a complex configuration, involving a number of explicit observations in the foreground and a class of implicit assumptions in the background, and it offers a provisional statement about certain possibility, one that is typically less conspicuous, obvious, or prominent, but still potentially present in the situation, and hopefully serving to explain the surprising or the problematic aspects of the whole state of affairs. |
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| − | Inquiry is a process that aims at achieving belief or knowledge.
| + | What results from the abductive inference is a concept and possibly a term, for instance, "duck" or "blue". The concept attempts to grasp a vast complex of appearances within a unitary form, and the term that connotes the concept is used to put explicit bounds on what it conveys. Working in tandem, they express an approximation or a simplification, "a reduction of the manifold of phenomena to a unified conception". Finite minds cannot operate for very long with anything more than this. |
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| − | But even this simple a description already plunges the discussion deep into a number of obscurities. Most prominently, there is the disjunction between belief and knowledge that cries out to be explained or resolved. Stirring beneath the surface, and not quite fading into the background, many of the other terms that are invoked in the description are capable of hiding the entire contents of the original ignorance that the image as a whole is aimed to dispell. And yet, there is nothing that I can do in this avowedly positive context but to mark these points down as topics for future discussion.
| + | The reader may have noticed some obvious distinctions between the two examples of abductive reasoning that I gave above, between the case of "looking like a duck" and the case of "looking blue". Just to mention the most glaring difference: Although a person is occasionally heard to reason out loud after the fashion of the former example, it is rare to hear anyone naturally reasoning along the lines of the latter example. Indeed, it is more likely that any appearance of doing so is always an artificial performance and a self-conscious reconstruction, if not a complete fabrication, and it is doubtful that the process of arriving at a perceptual judgment can follow this rule in just so literal a fashion. |
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| − | There is already a model of inquiry that is implicit, at least partially, in the text of the above description. Let me see if I can tease out a few of its tacit assumptions.
| + | This is true and important, but it is beside the point of the immediate discussion, which is only to identify the logical form of the inference, that is, to specify up to informational equivalence the class of conduct that is involved in each example. Thus, considering the inference as an information process, I do not care at this point whether the process is implemented by a literal-minded variety of rule-following procedure, so long as it "follows", "obeys", or "respects" these rules in the form of what it does. One can say that an information process "obeys" a set of rules in a "figurative" and a "formal" sense if the transformation that occurs in the state of information between the beginning and the end of the process has the form of a relation that can be achieved by literally following these rules with respect to the prospective class of materials. |
| | | | |
| − | =====1.4.1.1 Inquiry as Conduct=====
| + | The general drift of the strategy that is being mapped out here, the "abstract", the "formal", or the "functional" approach, is now evident. Conceptually, one partitions the space of processes into "effective", "informational", or "pragmatic" equivalence classes and then adopts the inditement of a sequence of rules as a symbolic "nomen" for the class of processes that all achieve the same class of effects. At this level of functional abstraction, the conception of a process is indifferent to the particulars of its implemenation, so long as it lives within the means of the indicated constraints. Moreover, unless there is a way to detect the nature of the "actual" process without interfering too severely with it, that is, a path-sensitive but still unobtrusive measure that can sort out a finer structure from these equivalence classes, then it is not possible to inquire any further into the supposedly "actual" details. |
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| − | First of all, inquiry is conceived to be a form of conduct.
| + | Similar remarks apply to every case where one attributes "law-abiding" or "rule-governed" behavior to oneself, to another person, or even to a physical process. Across this diverse spectrum of cases, it ranges from likely but not certain to unlikely but still conceivable that the action in question depends on the agent "knowing" the laws that abide or the rules that are effectively being obeyed. With this in mind, I can draw this digression on appearances to a conclusion: When I say that agents are acting according to a particular pattern of rules, it only means that it "looks like" they are. In other words, they are acting "as if" they are consciously following these rules, or they are acting just like I act when I conscientiously follow such rules. A concise way to sum all of this up is to say that a pattern of rules constitutes a model of conduct, one that I can deliberately emulate, or one that I can attribute to others by way of explaining their conduct. In attributing this model to others, or even in using it to account for my own less deliberate behavior, I am making an abductive inference. |
| − | This invokes the technical term "conduct", referring to the
| |
| − | species of prototypically human action that is both dynamic
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| − | and deliberate, or conceived to fall under a form of purposeful
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| − | control, usually conscious but possibly not. For the sake of
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| − | clarity, it helps to seek a more formal definition of conduct,
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| − | one that expresses the concept in terms of abstract features | |
| − | rather than trying to suggest it by means of typical examples.
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| − | Conduct is action with respect to an object. The distinction between action and conduct, reduced to the level of the most abstract formal relations that are involved, can be described in the following manner.
| + | One way to appreciate the pertinence of this point is to notice that this entire digression, concerned with explaining the similarities between "looking like a duck" and "looking blue", is itself a form of argument, making a case of abductive inference to a case of abductive inference. In short, I am reasoning according to the following pattern: |
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| − | Action is a matter of going from A to B, whereas conduct is matter of going from A to B in relation to C. In describing particular cases and types of conduct, the phrase "in relation to" can be filled out in more detail as "on account of", "in the cause of", "in order to bring about", "for the sake of", "in the interests of", or in many other ways. Thus, action by itself has a dyadic character, involving transitions through pairs of states, while conduct has a triadic character, involving the kinds of transactions between states that relate throughout to an object.
| + | It appears to be the making of an abductive inference, |
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| − | With regard to this distinction, notice that "action" is used inclusively, to name the genus of which "conduct" names a species, and thus depicts whatever has the aspect of action, even if it is actually more complex.
| + | so I guess it is the making of an abductive inference. |
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| − | This creates the difficulty that the reputed "genus" is less than fully "generative", "generic", "genetic", or even "genuine" -- and so it is necessary to remain on guard against this source of misunderstanding.
| + | Anyone who thinks that this style of reasoning is too chancy to be tolerated ought to observe that it is only the pattern of inference that one follows in attributing minds to others, solely on the evidence that they exhibit roughly the same array of external behaviors in reaction to various external conditions as one employs to express one's experience of roughly the same conditions. |
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| − | What does this definition of conduct say about the temporal ordering of the object with respect to the states? The states are conceived to be ordered in time, but so far nothing has been said to pin down where in relation to these states the object must be conceived to fall in time. Nor does the definition make any particular specification necessary. This makes the question of relative time a secular parameter of the definition, allowing the consideration of the following options:
| + | It goes without saying that abductive reasoning is extremely fallible. The fact that it looks like a duck does not necessarily mean that it is a duck - it might be a decoy. Moreover, in most cases of actual practice the implicit rule that serves to catalyze the abductive inference is not an absolute rule or a necessary truth in its own right but may be only a contingent rule or a probable premiss. For instance, not every case of being blue presents the fact of looking blue - the conditions of observation may be trickier than that. This brings to the fore another mark that distinguishes the two examples, highlighting a potentially important difference between "looking like a duck" and "looking blue". This is the amount of oversight, or awareness and control, that an agent has with regard to an inference, in other words, the extent to which an inference really does "go without saying". |
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| − | 1. If the object is thought to precede the action of the conduct, then it tends to be regarded as a creative act, an initial intention, an original stimulus, a principal cause, or a prime mover.
| + | The abductive inference from "it looks blue" to "it is blue" and the abductive inference from "it looks like a duck" to "it is a duck" differ in the degrees to which they exhibit a complex of correlated properties. These variations are summed up in one sense by saying that the first, more perceptual inference is more automatic, compulsive, habitual, incorrigible, and inveterate. The correlations are summed up in the opposite sense by saying that the second, more conceptual inference is more aware, controllable, correctable, critical, deliberate, guarded, and reflective. From a fully pragmatic standpoint, these differences are naturally of critical importance. But from a purely logical standpoint, they have to be regarded as incidental aspects or secondary features of the underlying forms of inference. |
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| − | 2. If the object is thought to succeed the action of the conduct, then it tends to be regarded as an end, a goal, or a purpose, in other words, a state envisioned to be fulfilled.
| + | There is one thing yet missing from this description of abductive reasoning, and that is its creative aspect. The description so far is likely to leave the impression that the posing of a hypothesis always takes place against a narrowly circumscribed background of established terms that are available for describing cases, and thus that it amounts to nothing more original than picking out the right label for the case. Of course, the forming of a hypothesis may be bound by the generative potential of the language that is ultimately in force, but that is a far cry from a prescriptively finite list of more or less obvious choices. |
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| − | 3. If the object is thought to be concurrent, immanent, or transcendent throughout the action of the conduct, then it tends to be regarded as falling under one of the following possibilities: a prevailing value, a controlling parameter, a universal system of effective forces, a pervasive field of potentials, a ruling law, or a governing principle.
| + | How does all of this bear on the choice of a method? In order to make a start toward answering that question, I need to consider the part that abductive reasoning plays in the inquiry into method, which is, after all, just another name for the inquiry into inquiry. |
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| − | A prevailing value or a controlling parameter, which guides the temporal development of a system, is a term that fits into a law or a principle, which governs the system at a higher level. The existence of a value or a law that rules a system, and the information that an agent of the system has about its parameters and its principles, are two different matters. Indeed, a major task of development for an inquiring agent is to inform itself about the values and the laws that form its own system. Thus, one of the objects of the conduct of inquiry is a description in terms of laws and values of the rules that govern and guide inquiry.
| + | There are times when choosing a method looks more like discovering or inventing a method, a purely spontaneous creation of a novel way to proceed, but normally the choice of a path picks its way through a landscape of familiar options and mapped out opportunities, and this presupposes a description of previously observed forms of conduct and a classification of different paths from which to choose. Hence the etymology of the word "method", indicating a review of means or a study of ways. |
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| − | The elaboration of an object in terms of this rich vocabulary -- as a cause, end, field, force, goal, intention, law, parameter, principle, purpose, system, or value -- adds colorful detail and concrete sensation to the account, and it helps to establish connections with the arrays of terminology that are widely used to discuss these issues. From a formal and relational point of view, however, all of these concepts are simply different ways of describing, at possibly different levels of generality, the object of a form of conduct. With that in mind, I find it useful to return to the simpler form of description as often as possible.
| + | I would now like to examine several types situations where a choice of method is involved, paying special attention to the way that abductive reasoning enters into the consideration. |
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| − | This account of conduct brings to the fore a number of issues, some of them new and some of them familiar, but each of them allowing itself to be approached from a fresh direction by treating it as an implication of a critical thesis just laid down. I next examine these issues in accord with the tenets from which they stem.
| + | Example 1. |
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| − | 1. Inquiry is a form of conduct.
| + | Suppose I have occasion to reason along the following lines: |
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| − | This makes inquiry into inquiry a special case of inquiry into conduct. | + | This situation looks like one in which this method will work, therefore I will proceed on the hypothesis that it will work. |
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| − | Certainly, it must be possible to reason about conduct in general, especially if forms of conduct need to be learned, examined, modified, and improved.
| + | The current situation (C) looks amenable (A') to this method, so I guess it really is amenable (A) to this method. |
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| − | Placing the subject of inquiry within the subject of conduct and making the inquiry into inquiry a subordinate part of the inquiry into conduct does not automatically further the investigation, especially if it turns out that the general subject of conduct is more difficult to understand than the specialized subject of inquiry. But in those realms of inquiry where it is feasible to proceed hypothetically and recursively, stretching the appropriate sort of hypothesis over a wider subject area can act to prime the pump of mathematical induction all the more generously, and actually increase the power of the recursion. Of course, the use of a recursive strategy comes at the expense of having to establish a more extended result at the base.
| + | In this type of situation, my observations of the situation are reduced to a form of description that portrays it in the light of a given method, amounting to an estimate of whether the situation is a case to which the method applies. The form of the entire argument hinges on the question of whether the assurance of this application is apparent or actual. |
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| − | 2. The existence of an object that rules a form of conduct and the information that an agent of the conduct has about the object are two different matters.
| + | I express my observations of the situation as a Fact: |
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| − | This means that the exact specification of the object can demand an order of information that the agent does not have available, at least, not for use in reflective action, or even require an amount of information that the agent lacks the capacity to store. No matter how true it is that the actual course of the agent's conduct exactly reflects the influence of the object, and thus, in a sense, represents the object exactly, the question is whether the agent possesses the equivalent of this information in any kind of accessible, exploitable, reflective, surveyable, or usable form of representation, in effect, in any mode of information that the agent can use to forsee, to modify, or to temper its own temporal course.
| + | "The current situation looks amenable." (C => A') |
| | | | |
| − | This issue may seem familiar as a repetition of the "meta" question.
| + | I have in the back of my mind a general Rule: |
| | | | |
| − | Once again, there is a distinction between (a) the properties of an action, agent, conduct, or system, as expressible by the agent that is engaged in the conduct, or as representable within the system that is undergoing the action, and (b) the properties of the same entities, as evident from an "external viewpoint", or as statable by the equivalent of an "outside observer".
| + | "If it is amenable, then it looks amenable." (A => A') |
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| − | 3. Reflection is a part of inquiry.
| + | I reason my way back from the observed Fact and the assumed Rule to assert what I guess to be the Case: |
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| − | Reflection is a form of conduct.
| + | "The current situation is amenable." (C => A) |
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| − | The task of reflection on conduct is to pass from a purely interior view of one's own conduct to an outlook that is, effectively, an exterior view.
| + | As far as it goes, this style of reasoning follows the basic pattern of abductive inference. Its obvious facticity is due to the fact that the situation is being described solely in the light of a pre-selected method. That is a relatively specious way to go about describing a situation, in spite of the fact that it may be inevitable in many of the most ultimate and limiting cases. The overall effect is noticeably strained, perhaps because it results from dictating an artificial setting, attempting to reduce a situation to the patterns that one is prepared to observe, and trying to fit what is there to see into a precut frame. A more natural way to describe a situation is in terms of the freely chosen perceptual features that inform a language of affects, impressions, and sensations. But here a situation is forced to be described in terms of the prevailing operational features that constitute a language of actions, forcing the description to be limited by the actions that are available within a prescribed framework of methods. |
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| − | What is sought is a wider perspective, one that is able to incorporate the sort of information that might be available to an outside observer, that ought to be evident from an external vantage point, or that one reasonably imagines might be obvious from an independent viewpoint. I am tempted to refer to such a view as a "quasi-objective perspective", but only so long as it possible to keep in mind that there is no such thing as a "completely outside perspective", at least, not one that a finite and mortal agent can hope to achieve, nor one that a reasonably socialized member of a community can wish to take up as a permanent station in life.
| + | Instead of describing a situation solely in terms of its reactive bearing, that is, wholly in terms of how it reacts to the application of a method, one can try to describe it in terms that appear to be more its own, its independent, natural, observational, perceptual, or "proper" features. What the "proper" or "object-oriented" features are and whether they can be distinguished in the end from "reactive" or "method-oriented" features are questions that cannot be answered in the early phases of an investigation. |
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| − | With these qualifications, reflection is a form of conduct that can serve inquiry into conduct. Inquiry and its component reflection, applied to a form of conduct, are intended to provide information that can be used to develop the conduct in question. The "reflective development" that occurs depends on the nature of the case. It can be the continuation, the correction, or the complete cessation of the conduct in question.
| + | Example 2. |
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| − | If it is to have the properties that it is commonly thought to have, then reflection must be capable of running in parallel, and not interfering too severely, with the conduct on which it reflects. If this turns out to be an illusion of reflection that is not really possible in actuality, then reflection must be capable, at the very least, of reviewing the memory record of the conduct in question, in ways that appear concurrent with a replay of its action. But these are the abilities that reflection is "pre-reflectively" thought to have, that is, before the reflection on reflection can get under way. If reflection is truly a form of conduct, then it becomes conceivable as a project to reflect on reflection itself, and this reflection can even lead to the conclusion that reflection does not have all of the powers that it is commonly portrayed to have.
| + | Suppose I find myself reasoning as follows: |
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| − | First of all, inquiry is conceived to be a form of conduct. This invokes the technical term "conduct", referring to the species of prototypically human action that is both dynamic and deliberate, or conceived to fall under a form of purposeful control, usually conscious but possibly not. For the sake of clarity, it helps to seek a more formal definition of conduct, one that expresses the concept in terms of abstract features rather than trying to suggest it by means of typical examples.
| + | If the current world (C) is a blessed world (B), |
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| − | Conduct is action with respect to an object. The distinction between action and conduct, reduced to the level of the most abstract formal relations that are involved, can be described in the following manner. Action is a matter of going from A to B, whereas conduct is matter of going from A to B in relation to C. In describing particular cases and types of conduct, the phrase "in relation to" can be filled out in more detail as "on account of", "in the cause of", "in order to bring about", "for the sake of", "in the interests of", or in many other ways. Thus, action by itself has a dyadic character, involving transitions through pairs of states, while conduct has a triadic character, involving the kinds of transactions between states that relate throughout to an object.
| + | then it is a world in which my method works (A). |
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| − | With regard to this distinction, notice that "action" is used inclusively, to name the genus of which "conduct" names a species, and thus depicts whatever has the aspect of action, even if it is actually more complex. This creates the difficulty that the reputed "genus" is less than fully "generative", "generic", "genetic", or even "genuine" - and so it is necessary to remain on guard against this source of misunderstanding.
| + | Here, I call to mind an independent property of being, B, that a world or a situation can have, and I use it as a middle term to reason along the lines of the following scheme: |
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| − | What does this definition of conduct say about the temporal ordering of the object with respect to the states? The states are conceived to be ordered in time, but so far nothing has been said to pin down where in relation to these states the object must be conceived to fall in time. Nor does the definition make any particular specification necessary. This makes the question of relative time a secular parameter of the definition, allowing the consideration of the following options:
| + | I express my inquiry by questioning the possibility of a certain Fact, that is, by interrogating the following statement: |
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| − | 1. If the object is thought to precede the action of the conduct, then it tends to be regarded as a creative act, an initial intention, an original stimulus, a principal cause, or a prime mover.
| + | "The current world is amenable." (C =?> A) |
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| − | 2. If the object is thought to succeed the action of the conduct, then it tends to be regarded as an end, a goal, or a purpose, in other words, a state envisioned to be fulfilled.
| + | I have in the back of my mind a general Rule: |
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| − | 3. If the object is thought to be concurrent, immanent, or transcendent throughout the action of the conduct, then it tends to be regarded as falling under one of the following possibilities: a prevailing value, a controlling parameter, a universal system of effective forces, a pervasive field of potentials, a ruling law, or a governing principle.
| + | "What is blessed, is amenable." (B => A) |
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| | + | I reason my way back from the interrogated Fact and the assumed Rule to guess that I ought to contemplate the chances of the following Case: |
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| − | A prevailing value or a controlling parameter, which guides the temporal development of a system, is a term that fits into a law or a principle, which governs the system at a higher level. The existence of a value or a law that rules a system, and the information that an agent of the system has about its parameters and its principles, are two different matters. Indeed, a major task of development for an inquiring agent is to inform itself about the values and the laws that form its own system. Thus, one of the objects of the conduct of inquiry is a description in terms of laws and values of the rules that govern and guide inquiry.
| + | "The current world is blessed." (C =?> B) |
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| − | The elaboration of an object in terms of this rich vocabulary - as a cause, end, field, force, goal, intention, law, parameter, principle, purpose, system, or value - adds colorful detail and concrete sensation to the account, and it helps to establish connections with the arrays of terminology that are widely used to discuss these issues. From a formal and relational point of view, however, all of these concepts are simply different ways of describing, at possibly different levels of generality, the object of a form of conduct. With that in mind, I find it useful to return to the simpler form of description as often as possible.
| + | Altogether, the argument that underlies the current question of method falls into line with the following example of abductive reasoning: |
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| − | This account of conduct brings to the fore a number of issues, some of them new and some of them familiar, but each of them allowing itself to be approached from a fresh direction by treating it as an implication of a critical thesis just laid down. I next examine these issues in accord with the tenets from which they stem.
| + | I hope that C is A, so I guess I hope that C is B. |
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| − | 1. Inquiry is a form of conduct.
| + | To proceed with the application of a given method on the basis of such a piece of reasoning is tantamount to the faith, the hope, or the wish that there is already the right kind of justice in the world that would make the prejudices of one's favorite method turn out to be right, that one is just lucky enough to be playing in accord with a pre-established harmony. If such a confidence is all that allows one to go on inquiring, then there is no harm in assuming it, so long as one reserves the right to question every particular of its grant, should the occasion arise. |
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| − | This makes inquiry into inquiry a special case of inquiry into conduct. Certainly, it must be possible to reason about conduct in general, especially if forms of conduct need to be learned, examined, modified, and improved.
| + | If one abstracts from the specific content of this example and examines its underlying structure, it reveals itself as the pattern of abductive reasoning that occurs in relating complex questions to simpler questions or in reducing difficult problems to easier problems. Furthermore, the iteration of this basic kind of step motivates a downward recursion from questions of fact to questions of cases, in a hopeful search for a level of cases where most of the answers are already known. |
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| − | Placing the subject of inquiry within the subject of conduct and making the inquiry into inquiry a subordinate part of the inquiry into conduct does not automatically further the investigation, especially if it turns out that the general subject of conduct is more difficult to understand than the specialized subject of inquiry. But in those realms of inquiry where it is feasible to proceed hypothetically and recursively, stretching the appropriate sort of hypothesis over a wider subject area can act to prime the pump of mathematical induction all the more generously, and actually increase the power of the recursion. Of course, the use of a recursive strategy comes at the expense of having to establish a more extended result at the base.
| + | The previous examples of inquiry into method are not very satisfactory. Indeed, their schematic forms have an absurdly sketchy character about them, and they fail to convey the realistic sorts of problems that are usually involved in reasoning about the choice of a method. The first example characterizes a situation wholly in terms of a selected method. The second example characterizes a situation in terms of a property that is nominally independent of the method chosen, but the ad hoc character of this property remains obvious. In order to reason "properly" about the choice of method, it is necessary to contemplate properties of the methods themselves, and not just the situations in which they are used. |
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| − | 2. The existence of an object that rules a form of conduct and the information that an agent of the conduct has about the object are two different matters.
| + | Example 3. |
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| − | This means that the exact specification of the object can require an order of information that the agent does not have available, at least, not for use in reflective action, or even an amount of information that the agent lacks the capacity to store. No matter how true it is that the actual course of the agent's conduct exactly reflects the influence of the object, and thus, in a sense, represents the object exactly, the question is whether the agent possesses the equivalent of this information in any kind of accessible, exploitable, reflective, surveyable, or usable form of representation, in effect, any mode of information that the agent can use to forsee, to modify, or to temper its own temporal course.
| + | If I reason that scientific method is wise because wise people use it, then I am making the hypothesis that they use it because they are wise. Here, my reasoning can be explained according to the following pattern: |
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| − | This issue may seem familiar as a repetition of the "meta" question. Once again, there is a distinction between (a) the properties of an action, agent, conduct, or system, as expressible by the agent that is engaged in the conduct, or as representable within the system that is undergoing the action, and (b) the properties of the same entities, as evident from an "external viewpoint", or as statable by the equivalent of an "outside observer".
| + | I observe a fact: |
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| − | 3. Reflection is a part of inquiry. Reflection is a form of conduct.
| + | "A certain conduct is done by wise people." (C => X) |
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| − | The task of reflection on conduct is to pass from a purely interior view of one's own conduct to an outlook that is, effectively, an exterior view. What is sought is a wider perspective, one that is able to incorporate the sort of information that might be available to an outside observer, that ought to be evident from an external vantage point, or that one reasonably imagines might be obvious from an independent viewpoint. I am tempted to refer to such a view as a "quasi-objective perspective", but only so long as it possible to keep in mind that there is no such thing as a "completely outside perspective", at least, not one that a finite and mortal agent can hope to achieve, nor one that a reasonably socialized member of a community can wish to take up as a permanent station in life.
| + | I have in mind a rule: |
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| − | With these qualifications, reflection is a form of conduct that can serve inquiry into conduct. Inquiry and its component reflection, applied to a form of conduct, are intended to provide information that can be used to develop the conduct in question. The "reflective development" that occurs depends on the nature of the case. It can be the continuation, the correction, or the complete cessation of the conduct in question.
| + | "If a wise act, then done by wise people." (A => X) |
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| − | If it is to have the properties that it is commonly thought to have, then reflection must be capable of running in parallel, and not interfering too severely, with the conduct on which it reflects. If this turns out to be an illusion of reflection that is not really possible in actuality, then reflection must be capable, at the very least, of reviewing the memory record of the conduct in question, in ways that appear concurrent with a replay of its action. But these are the abilities that reflection is "pre-reflectively" thought to have, that is, before the reflection on reflection can get under way. If reflection is truly a form of conduct, then it becomes conceivable as a project to reflect on reflection itself, and this reflection can even lead to the conclusion that reflection does not have all of the powers that it is commonly portrayed to have.
| + | I abduce the case: |
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| − | =====1.4.1.2 Types of Conduct=====
| + | "A certain conduct is a wise act." (C => A) |
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| − | The chief distinction that applies to different forms of conduct is whether the object is the same sort of thing as the states or whether it is something entirely different, a thing apart, of a wholly other order. Although I am using different words for objects and states, it is always possible that these words are indicative of different roles in a formal relation and not indicative of substantially different types of things. If objects and states are but formal points and naturally belong to the same domain, then it is conceivable that a temporal sequence of states can include the object in its succession, in other words, that a path through a state space can reach or pass through an object of conduct. But if a form of conduct has an object that is completely different from any one of its temporal states, then the role of the object in regard to the action cannot be like the end or goal of a temporal development.
| + | Example 4. |
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| − | What names can be given to these two orders of conduct?
| + | If I reason that scientific method is a good method on account of the fact that it works for now, then I am guessing that it works for now precisely because it is good. |
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| − | =====1.4.1.3 Perils of Inquiry=====
| + | I observe a fact: |
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| − | Now suppose that making a hypothesis is a kind of action, no matter how covert, or that testing a hypothesis takes an action that is more overt. If entertaining a hypothesis in any serious way requires action, and if action is capable of altering the situation in which it acts, then what prevents this action from interfering with the subject of inquiry in a way that undermines, with positive or negative intentions, the very aim of inquiry, namely, to understand the situation as it is in itself?
| + | "Scientific method works for now." (C => X) |
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| − | That making a hypothesis is a type of action may seem like a hypothesis that is too far-fetched, but it appears to follow without exception from thinking that thinking is a form of conduct, in other words, an activity with a purpose or an action that wants an end. The justification of a hypothesis is not to be found in a rational pedigree, by searching back through a deductive genealogy, or determined by that which precedes it in the logical order, since a perfectly trivial tautology caps them all. Since a logical tautology, that conveys no empirical information, finds every proposition appearing to implicate it, in other words, since it is an ultimate implication of every proposition and a conceivable conclusion that is implicit in every piece of reasoning, it is obvious that seeking logical precedents is the wrong way to go for empirical content.
| + | I have in mind a rule: |
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| − | In making a hypothesis or choosing a model, one appears to select from a vaster number of conceivable possibilities than a finite agent could ever enumerate in complete detail or consider as an articulate totality. As the very nature of a contingent description and the very character of a discriminate action is to apply in some cases but not in others, there is no escaping the making of a risky hypothesis or a speculative interpretation, even in the realm of a purely mental action. Thus, all significant thought, even thinking to any purpose about thought itself, demands a guess at the subject or a grasp of the situation that is contingent, dubious, fallible, and uncertain.
| + | "What is good, works for now." (A => X) |
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| − | If all this is true - if inquiry begins with doubt, if every significant hypothesis is itself a dubious proposition, if the making and the testing of a hypothesis are instances of equally doubtful actions, and if every action has the potential to alter the very situation and the very subject matter that are being addressed - then it leads to the critical question: How is the conduct of inquiry, that begins by making a hypothesis and that continues by testing this description in action, supposed to help with the situation of uncertainty that incites it in the first place and that is supposed to maintain its motivation until the end is reached? The danger is that the posing of a hypothesis may literally introduce an irreversible change in the situation or the subject matter in question. The fear is that this change might be one that too conveniently fulfills or too perversely subverts the very hypothesis that engenders it, that it may obstruct the hypothesis from ever being viewed with equanimity again, and thus prevent the order of reflection that is needed to amend or discard the hypothesis when the occasion to do so arises.
| + | I abduce the case: |
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| − | If one fears that merely contemplating a special hypothesis is enough to admit a spurious demonstration into the foundations of one's reasoning, even to allow a specious demon to subvert all one's hopes of a future rationality and to destroy all one's chances of a reasonable share of knowledge, then one is hardly in a state of mind that can tolerate the tensions of a full-fledged, genuine inquiry. If one is beset with such radical doubts, then all inquiry is no more comfort than pure enchoiry. Sometimes it seems like the best you can do is sing yourself a song that soothes your doubts. Perhaps it is even quite literally true that all inquiry comes back at last to a form of "enchoiry", the invocation of a nomos, a way of life, or a song and a dance. But even if this is the ultimate case, it does no harm and it does not seem like a bad idea to store up in this song one or two bits of useful lore, and to weave into its lyric a few suggestions of a practical character.
| + | "Scientific method is good." (C => A) |
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| − | Let us now put aside these more radical doubts. This putting aside of doubts is itself a form of inquiry, that is, a way of allaying doubts. The fact that I appear to do this by fiat, and to beg for tacit assent, tends to make me suspect the validity of this particular tactic. Still, it is not too inanely dismissive, as its appeal is based on an argument, the argument that continuing to entertain this type of doubt leads to a paralysis of the reason, and that paralyzing the ability to think is not in the interests of the agent concerned. Thus, I adopt the hypothesis that the relationship between the world and the mind is not so perverse that merely making a hypothesis is enough to alter the nature of either. If, in future, I or anyone sees the need to reconsider this hypothesis, then I see nothing about making it that prevents anyone from doing so. Indeed, making it explicit only renders it more subject to reflection.
| + | As always, the abductive argument is extremely fallible. The fact that scientific method works for now can be one of its accidental features, and not due to any essential goodness that it might be thought to have. |
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| − | Of course, a finite person can only take up so many causes in a single lifetime, and so there is always the excuse of time for not chasing down every conceivable hypothesis that comes to mind.
| + | Finally, it is useful to consider an important variation on this style of argument, one that exhibits its close relation to reasoning by analogy or inference from example. Suppose that the above argument is presented in the following manner: |
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| − | =====1.4.1.4 Forms of Relations=====
| + | Scientific method (C) has many of the features that a good method needs to have, for instance, it works for now (X), so I reason that it has all of the features of a good method, in short, that it is a good method (A). |
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| − | The next distingishing trait that I can draw out of this incipient treatise is its emphasis on the forms of relations. From a sufficiently "formal and relational" (FAR) point of view, many of the complexities that arise from throwing intentions, objectives, and purposes into the mix of discussion are conceivably due to the greater arity of triadic relations over dyadic relations, and do not necessarily implicate any differences of essence inhering in the entities and the states invoked. As far as this question goes, whether a dynamic object is essentially different from a deliberate object, I intend to remain as neutral as possible, at least, until forced by some good reason to do otherwise. In the meantime, the factors that are traceable to formal differences among relations are ready to be investigated and useful to examine. With this in mind, it it useful to make the following definition:
| + | So far, the underlying argument is exactly the same. In particular, it is important to notice that the abductive argument does not depend on the prior establishment of any known cases of good methods. As of yet, the phrase "good method" is a purely hypothetical description, a term that could easily turn out to be vacuous. One has in mind a number of properties that one thinks a good method ought to have, but who knows if there is any thing that would satisfy all of these requirements? There may be some sort of subtle contradiction that is involved in the very juxtaposition of the terms "good" and "method". In sum, it can happen that scientific method is the very first method that is being considered for membership in the class of good methods, and so it is still unknown whether the class labeled "good methods" is empty or not. |
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| − | A "conduct relation" is a triadic relation involving a domain of objects and two domains of states. When a shorter term is desired, I refer to a conduct relation as a "conduit". A conduit is given in terms of its extension as a subset C c XxYxZ, where X is the "object domain" and where Y and Z are the "state domains". Typically, Y = Z.
| + | But what if an example of a good method is already known to exist, one that has all of the commonly accepted properties that appear to define what a good method ought to be? In this case, the abductive argument acquires the additional strength of an argument from analogy. |
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| − | In general, a conduct relation serves as a "model of conduct" (MOC), not always the kind of model that is meant to be emulated, but the type of model that captures an aspect of structure in a form of conduct.
| + | =====1.4.3.4. Analogical Reasoning===== |
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| − | The question arises: What is the relationship between signs and states? On the assumption that signs and states are comparable in their levels of generality, consider the following possibilities: | + | The classical treatment of analogical reasoning by Aristotle explains it as a combination of induction and deduction. More recently, C.S. Peirce gave two different ways of viewing the use of analogy, analyzing it into complex patterns of reasoning that involve all three types of inference. In the appropriate place, it will be useful to consider these alternative accounts of analogy in detail. At the present point, it is more useful to illustrate the different versions of analogical reasoning as they bear on the topic of choosing a method. |
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| − | 1. Signs are special cases of states.
| + | The next example, ostensibly concerned with reasoning about a choice of method, is still too artificial to be taken seriously for this purpose, but it does serve to illustrate Aristotle's analysis of analogical reasoning as a mixed mode of inference, involving inductive and deductive phases. |
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| − | 2. Signs and states are the same sorts of things.
| + | Example 5. |
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| − | 3. States are special cases of signs.
| + | Suppose I reason as follows. I think I can establish it as a fact that scientific method is a good method by taking it as a case of a method that always works and by using a rule that what always works is good. I think I can establish this rule, in turn, by pointing to one or more examples of methods that share the criterial property of always working and that are already acknowledged to be good. In form, this pattern of reasoning works by noticing examples of good methods, by identifying a reason why they are good, in other words, by finding a property of the examples that seems sufficient to prove them good, and by noticing that the method in question is similar to these examples precisely in the sense that it has in common this cause, criterion, property, or reason. |
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| − | Depending on how one answers this question, one is also choosing among the following options:
| + | In this situation, I am said to be reasoning by way of analogy, example, or paradigm. That is, I am drawing a conclusion about the main subject of discussion by way of its likeness to similar examples. These cases are like the main subject in the possession of a certain property, and the relation of this critical feature to the consequential feature of interest is assumed to be conclusive. The examples that exhibit the criterial property are sometimes known as "analogues" or "paradigms". For many purposes, one can imagine that the whole weight of evidence present in a body of examples is represented by a single example of the type, an exemplary or typical case, in short, an archetype or epitome. With this in mind, the overall argument can be presented as follows: |
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| − | 1. Sign relations are special cases of conduct relations.
| + | Suppose that there is an exemplary method (E) that I already know to be a good method (A). Then it pays to examine the other properties of the exemplary method, in hopes of finding a property (B) that explains why it is good. If scientific method (C) shares this property, then it can serve to establish that scientific method is good. |
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| − | 2. Sign relations and conduct relations are the same sorts of things.
| + | The first part of the argument is the induction of a rule: |
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| − | 3. Conduct relations are special cases of sign relations.
| + | I notice the case: |
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| − | I doubt if there is any hard and fast answer to this question, but think that it depends on particular interpreters and particular observers, to what extent each one interprets a state as a sign, and to what degree each one recognizes a sign as a component of a state.
| + | "The exemplary method always works." (E => B) |
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| − | =====1.4.1.5 Models of Inquiry=====
| + | I observe the fact: |
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| − | The value of a hypothesis, or the worth of a model, is not to be given a prior justification, as by a deductive proof, but has to be examined in practice, as by an empirical probation. It is not intended to be taken for granted or to go untested, but its meaning in practice has to be articulated before its usefulness can be judged. This means that the conceivable practical import of the hypothesis or the model has to be developed in terms of its predicted and its promised consequences, after which it is judged by the comparison of these speculative consequences with the actual results. But this is not the end of the matter, for it can be a useful piece of information to discover that a particular kind of conception fails a particular kind of comparison. Thus, the final justification for a hypothesis or a model is contained in the order of work that it leads one to do, and the value of this work is often the same whether or not its premiss is true. Indeed, the fruitfulness of a suggestion can lie in the work that proves it untrue. | + | "The exemplary method is a good method." (E => A) |
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| − | My plan then has to be, rather than trying to derive a model of inquiry in a deductive fashion from a number of conditions like y0 = y.y, only to propose a plausible model, and then to test it under such conditions. Each of these tests is a "two-edged sword", and the result of applying a particular test to a proposed model can have either one of two effects. If one believes that a particular test is a hard and fast rule of inquiry, or a condition that any inquiry is required to satisfy, then the failure of a model to live up to its standard tends only to rule out that model. If one has reason to believe that a particular model of inquiry covers a significant number of genuine examples, then the failure of these models to follow the prescribed rule can reflect badly on the test itself.
| + | I induce the rule: |
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| − | In order to prime the pump, therefore, let me offer the following account of inquiry in general, the whole of which can be taken as a plausible hypothesis about the nature of inquiry in general.
| + | "What always works, is good." (B => A) |
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| − | My observations of inquiry in general, together with a few suggestions that seem apt to me, have led me to believe that inquiry begins with a "surprise" or a "problem". The way I understand these words, they refer to departures, differences, or discrepancies among various modalities of experience, in particular, among "observations", "expectations", and "intentions".
| + | The second part of the argument is the deduction of a fact: |
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| − | 1. A "surprise" is a departure of an observation from an expectation, and thus it invokes a comparison between present experience and past experience, since expectations are based on the remembered disposition of past experience.
| + | I notice the case: |
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| − | 2. A "problem" is a departure of an observation from an intention, and thus it invokes a comparison between present experience and future experience, since intentions choose from the envisioned disposition of future experience.
| + | "Scientific method always works." (C => B) |
| | | | |
| − | With respect to these
| + | I recall the rule: |
| | | | |
| − | With respect to this hypothetical
| + | "What always works, is good." (B => A) |
| | | | |
| − | I now test this model of inquiry under the conditions of an inquiry into inquiry, asking whether it is consistent in its application to itself. This leaves others to test the models they like best under the same conditions, should they ever see the need to do so. | + | I deduce the fact: |
| | | | |
| − | Does the inquiry into inquiry begin with a surprise or a problem concerning the process or the conduct of inquiry? In other words, does the inquiry into inquiry start with one of the following forms of departure: (1) a surprising difference between what is expected of inquiry and what is observed about it, or (2) a problematic difference between what is observed about inquiry and what is intended for it?
| + | "Scientific method is good." (C => A) |
| | | | |
| − | ====1.4.2 The Moment of Inquiry====
| + | Example 6. |
| | | | |
| − | <blockquote>
| + | Example 7. |
| − | <p>Every young man - not to speak of old men - on hearing or seeing anything unusual and strange, is likely to avoid jumping to a hasty and impulsive solution of his doubts about it, and to stand still; just as a man who has come to a crossroads and is not quite sure of his way, if he be travelling alone, will question himself, or if travelling with others, will question them too about the matter in doubt, and refuse to proceed until he has made sure by investigation of the direction of his path.</p>
| |
| | | | |
| − | <p>(Plato, Laws, VII, 799C).</p>
| + | Suppose that several examples (S1, S2, S3) of a good method are already known to exist, ones that have a number of the commonly accepted properties (P1, P2, P3) that appear to define what a good method is. Then the abductive argument acquires the additional strength of an argument from analogy. |
| − | </blockquote>
| |
| | | | |
| − | Observe the paradox of this precise ambiguity: That both the occasion and the impulse of inquiry are instances of a negative moment. But the immediate discussion is aimed at the positive aspects of inquiry, and so I convert this issue into its corresponding positive form.
| + | The first part of the argument is the abduction of a case: |
| | | | |
| − | The positive aim of inquiry is a state of belief, certainty, or knowledge. There are distinctions that can be made in the use of these words, but the question remains as to what kind of distinctions these are. In my opinion, the differences that arise in practice have more to do with the purely grammatical distinctions of "case", "mood", "number", "person", and "voice", and thus raise the issues of plurality and point of view, as opposed to indicating substantial differences in the relevant features of state, as actually experienced by the agent concerned.
| + | I observe a set of facts: |
| | | | |
| − | It is often claimed that there are signficant differences between the conditions of belief and knowledge, but the way that I understand the distinction is as follows. One says that a person "knows" something when that person believes exactly the same thing that one believes. When one is none other than the person in question, then one says that one "knows" exactly what one believes. Differences arise between the invocations of "belief" and "knowledge" only when more than one person is involved in the issue. Thus, there is no occasion for a difference between belief and knowledge unless there is more than one person that is being consulted about the matter in question, or else a single person in a divided state of opinion, in any case, when there is more than one impulse, moment, or occasion that currently falls under consideration.
| + | "Scientific method is P1, P2, P3." (C => P) |
| | | | |
| − | In any case, belief or knowledge is the feature of state that an agent of inquiry lacks at the moment of setting out. Inquiry begins in a state of impoverishment, need, or privation, a state that is absent the quality of certainty. It is due to this feature that the agent is motivated, and it is on account of its continuing absence that the agent keeps on striving to achieve it, at least, with respect to the subject in question, and, at any rate, in sufficient measure to make action possible.
| + | I recall a set of rules: |
| | | | |
| − | ====1.4.3 The Modes of Inquiry====
| + | "Bona fide inquiry is P1, P2, P3." (B => P) |
| | | | |
| − | <blockquote>
| + | I abduce the case: |
| − | <p>Let the strange fact be granted, we say, that our hymns are now made into "nomes" (laws), just as the men of old, it would seem, gave this name to harp-tunes, - so that they, too, perhaps, would not wholly disagree with our present suggestion, but one of them may have divined it vaguely, as in a dream by night or a waking vision: anyhow, let this be the decree on the matter:- In violation of public tunes and sacred songs and the whole choristry of the young, just as in violation of any other "nome" (law), no person shall utter a note or move a limb in the dance.</p>
| |
| | | | |
| − | <p>(Plato, Laws, VII, 799E-800A).</p>
| + | "Scientific method is bona fide inquiry." (C => B) |
| − | </blockquote>
| |
| | | | |
| − | In the present section, I am concerned with the kinds of reasoning that might be involved in the choice of a method, that is, in discovering a way to go about inquiry, in constructing a way to carry it through, and in justifying the way that one chooses. If the choice of a method can be established on the basis of reasoning, if it can be rationalized or reconstructed on grounds that are commonly thought to be sensible, or if it is likely to be affected or influenced in any way by a rational argument, then there is reason to examine the kinds of reasoning that go into this choice. All of this requires a minimal discussion of different modes of reasoning.
| + | The second part of the argument is the induction of a rule: |
| | | | |
| − | In this work as a whole, each instance of inquiry is analyzed in accord with various modes of reasoning, the prospective "elements of inquiry", and its structure as an object of inquiry is articulated, rationalized, and reconstructed with respect to the corresponding "form of analysis", "form of synthesis", or "objective genre" (OG).
| + | I notice a set of cases: |
| | | | |
| − | According to my current understanding, the elements of inquiry can be found to rest on three types of steps, called "abductive", "deductive", and "inductive" modes of inference. As a result of this opinion, I do not believe that I can do any better at present than to articulate the structure of each instance of learning or reasoning according to these three types of motions of the mind. But since this work as a whole is nowhere near complete, I cannot dictate these steps in a dogmatic style, nor will it do for me to to call the tune of this form of analysis in a purely ritual or a wholly routine fashion.
| + | "S1, S2, S3 exemplify bona fide inquiry." (S => B) |
| | | | |
| − | Since the complexity of reasoning about different modes of reasoning is enough of a complication to occupy my attention at the present stage of development in this work, it is proably best to restrain this discussion along the majority of its other dimensions. A convenient way to do this is to limit its scope to simple examples and concrete situations, just enough to illustrate the selected modes of reasoning.
| + | I observe a set of facts: |
| | | | |
| − | With all of these considerations in mind, the best plan that I can find for addressing the tasks of the present section is to proceed as follows: I make it my primary aim to examine only a few of the simplest settings in which these different modes of reasoning are able to appear, and I try to plot my path through this domain by way of concrete examples. Along the way, I discuss a few of the problems that are associated with reasoning about different modes of reasoning. Given the present stage of development, the majority of these issues have to be put aside almost as quickly as they are taken up. If they are ever going to be subject to resolution, it is not within reach of the present moment of discussion. In the body of this section, I therefore return to the initial strategy: to examine a few of the simplest cases and situations that can serve to illustrate the distinctions among the chosen modes of reasoning.
| + | "S1, S2, S3 exemplify good method." (S => A) |
| | | | |
| − | In trying to initiate a general discussion of the different modes of reasoning that might be available, and thus to motivate a model of this subject matter that makes an initial kind of sense to me, I meet once again with all the old "difficulties at the beginning", the kinds of obstructions that always seem to arise on trying to open up any new subject for discussion or in trying to introduce any new model of an old subject area. Much of this gratuitous bedevilment is probably due to the inherent conservatism of the human mind. Everything familiar is taken for granted, but each new picture of the situation is immediately subjected to the severest suspicions.
| + | I induce the rule: |
| | | | |
| − | Now, I cannot reason with necessary force that the mind must use these particular modes of reasoning, any more than I can say that it must use a given language in order to express itself. But I can argue, relative to a particular model of thinking that must be proposed hypothetically, that certain modes of reasoning are available to the mind and are likely to be evident in its operation, if one only takes the trouble to look.
| + | "Bona fide inquiry is good method." (B => A) |
| | | | |
| − | Ultimately, the model of thinking that I plan to propose makes use of the proposition that all thinking takes place in signs, and thus that inquiry is the transformation of a sign relation. Relative to this hypothesis, it would be possible to discharge the current assumptions about the basic modes of reasoning, that is, to derive the elementary modes of inquiry from a sign relational model of inquiry, and then to compare them with the current suggestions. Until this work is done, however, the assumption that these really are the most basic modes of reasoning has to be treated as a still more tentative hypothesis.
| + | The third part of the argument is the deduction of a fact: |
| | | | |
| − | When a subject matter is so familiar that the logical connections between its parts are known both forwards and backwards, then it is reasonable and convenient to organize its presentation in an axiomatic fashion. This would not be such a bad idea, if it did not make it so easy to forget the nature of the reorganization that goes into a representation, and it would not constitute such a deceptive conception of the subject, if it did not mean that the exposition of the subject matter is just as often the falsification of its actual development and the covering up of its real excavation. Indeed, the logical order of axioms and theorems may have little to do with the original order of discovery and invention. In practice, the deepest axioms are often the last to come to light.
| + | I recall the case: |
| | | | |
| − | Once again, the structure of a reflective context means that each mode of reasoning is able to appear in a double role, once as an object and once as an instrument of the same extended discussion. And once again, the discussion runs into an array of obstructions, whose structures are becoming, if not more clear, at least, more familiar with each encounter. In particular, a description of different modes of reasoning involves a classification, and a classification presupposes a basis of distinctive features that cannot be treated as categorical, or objectively neutral, but has to be regarded as hypothetical, or potentially biased. In other words, the language that I use to describe different modes of reasoning may already have a particular model of reasoning built into it, and this disposition to a particular conception of logic may be lodged in such a way that it makes it nearly impossible to reflect on the operations and the limitations of this model.
| + | "Scientific method is bona fide inquiry." (C => B) |
| | | | |
| − | Inquiry begins when a law is violated. It marks a time when a certain peace of mind is breached, it reigns all the while that a common accord is broken, disturbed, forgotten, or lost, and it rules right up until the time when a former condition of harmony is restored or until the moment when a new state of accord is established. Of course, the word "law" is a highly equivocal choice, especially to convey the sense of a founding principle. It renders not just its own meaning irrevocably subject to interpretation, but delivers into a similar subjection all the forms of understanding that depend on it. But the letter must release its hold on the spirit, if the word "law" is meant to evoke the requisite variety of connotations, and yet to maintain a sensible degree of order among their concrete meanings. Only in this way can it rise above the many different kinds of law that come into play.
| + | I recall the rule: |
| | | | |
| − | There are descriptive laws, that organize experiences into expectations. There are prescriptive laws, that organize performances into intentions.
| + | "Bona fide inquiry is good method." (B => A) |
| | | | |
| − | Other names for descriptive laws are "declarative" or "empirical" laws. Other names for prescriptive laws are "procedural" or "normative" laws.
| + | I deduce the fact: |
| | | | |
| − | Implicit in a descriptive law is the connection to be found or made, discovered or created, between past experience and present expectation. What one knows about these connections is kept in a descrptive model.
| + | "Scientfic method is good method." (C => A) |
| | | | |
| − | Implicit in a prescriptive law is the connection to be found or made, discovered or created, between current conduct and future experience. What one knows about these connections is kept in a prescriptive model.
| + | Now, logically and rationally in the purest sense, the argument by analogy to an example has no more force than the abductive argument, but, empirically and existentially, the example serves, not only as a model of the method to be emulated, but as an object of experimental variation and a source of further experience. |
| | | | |
| − | A violation of an expectation, the contravention of a descriptive law, occurs when a present experience departs from a predicted experience, which is what a past expectation or description projected to be present. This is a "surprise", a state of affairs that calls for an explanation. An explanation points to other descriptions that better predict the actual experience, and suggests an alteration to the descriptive model that generated the expectation from a past experience. | + | It is time to ask the question: Why do these examples continue to maintain their unrealistic character, their comical and even ridiculous appearance, in spite of all my continuing attempts to reform them in a sensible way? It is not merely their simplicity. A simple example can be telling, if it grasps the essence of the problem, that is, so long as it captures even a single essential feature or highlights even a single critical property of the thing that one seeks to understand. It is more likely due to the circumstance that I am describing agents, methods, and situations all in one piece, that is, without any analysis, articulation, or definition of what exactly constitutes the self, the scientific method, or the world in question. It is not completely useless to consider cases of this type, since many forms of automatic, customary, and unreflective practice are underlain by arguments that are not much better that this. Of course, on reflection, their "commedius" character becomes apparent, and all deny or laugh off the suggestion that they ever think this way, but that is just the way of reflection. |
| | | | |
| − | A violation of an intention, the contravention of a prescriptive law, occurs when a present experience departs from a desired experience, which is what a past intention or prescription projected to be present. This is a "problem", a state of affairs that calls for a plan of action. , A plan of action points to other actions that better achieve the desired experience, and suggests an alteration to the prescriptive model that generated the conduct toward a prospective experience.
| + | In order to improve the character of the discussion on this score ... |
| | | | |
| − | In the rest of this section, I treat the different modes of reasoning according to the forms that Aristotle gave them, collectively referred to as the "syllogistic" model. The discussion is kept within the bounds of propositional reasoning by considering only those "figures of syllogism" that are "purely universal", that is, the forms of argument all of whose premisses, and therefore all of whose conclusions, involve nothing but universal quantifications.
| + | ==References== |
| | | | |
| − | If it were only a matter of doing propositional reasoning as efficiently as possible, I would simply use the cactus language and be done with it, but there are several other reasons for revisiting the syllogistic model. Treating the discipline that is commonly called "logic" as a cultural subject with a rich and varied history of development, and attending to the thread of tradition in which I currently find myself, I observe what looks like a critical transition that occurs between the classical and the modern ages. Aside from supplying the barest essentials of a historical approach to the subject, a consideration of this elder standard makes it easier to appreciate the nature and the character of this transformation. In addition, and surprisingly enough to warrant further attention, there appear to be a number of cryptic relationships that exist between the syllogistic patterns of reasoning and the ostensibly more advanced forms of analysis and synthesis that are involved in the logic of relations.
| + | <pre> |
| | + | Aristotle, "On The Soul", in 'Aristotle, Volume 8', |
| | + | W.S. Hett (trans.), Heinemann, London, UK, 1936, 1986. |
| | | | |
| − | =====1.4.3.1 Deductive Reasoning=====
| + | Charniak, E. & McDermott, D.V., |
| | + | 'Introduction to Artificial Intelligence', |
| | + | Addison-Wesley, Reading, MA, 1985. |
| | | | |
| − | In this subsection, I present a trimmed-down version of deductive reasoning in Aristotle, limiting the account to universal syllogisms, in effect, keeping to the level of propositional reasoning. Within these constraints, there are three basic "figures" of the syllogism.
| + | 2. Charniak, E., Riesbeck, C.K., & McDermott, D.V. Artificial Intelligence Programming. Lawrence Erlbaum Associates, Hillsdale, NJ, 1980. |
| | | | |
| − | In order to understand Aristotle's description of these figures, it is necessary to explain a few items of his technical terminology. In each figure of the syllogism, there are three "terms". Each term can be read as denoting either (1) a class of entities or (2) all of the members of a class of entities, depending on which interpretation the reader prefers. These terms are ranked in two ways: With respect to the "magnitudes" that they have in relation to each other, there are "major", "middle", and "minor" terms. With respect to the "positions" that they take up within the figure, there are "first", "intermediate", and "last" terms. The figures are distinguished by how the magnitudes correlate with the positions. However, the names for these rankings are not always used or translated in a rigorously systematic manner, so the reader has to be on guard to guess which type of ranking is meant.
| + | 3. Holland, J.H., Holyoak, K.J., Nisbett, R.E., & Thagard, P.R. Induction: Processes of Inference, Learning, and Discovery. MIT Press, Cambridge, MA, 1986. |
| | | | |
| − | In addition to this terminology, it is convenient to make use of the following nomenclature:
| + | 4. O'Rorke, P. Review of AAAI 1990 Spring Symposium on Automated Abduction. SIGART Bulletin, Vol. 1, No. 3. ACM Press, October 1990, p. 12-17. |
| | | | |
| − | 1. The "Fact" is the proposition that applies the term in the first position to the term in the third or last position.
| + | 5. Pearl, J. Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Revised 2nd printing. Morgan Kaufmann, San Mateo, CA, 1991. |
| | | | |
| − | 2. The "Case" is the proposition that applies the term in the second or intermediate position to the term in the third or last position.
| + | 6. Peng, Y. & Reggia, J.A. Abductive Inference Models for Diagnostic Problem-Solving. Springer-Verlag, New York, NY, 1990. |
| | | | |
| − | 3. The "Rule" is the proposition that applies the term in the first position to the term in the second or intermediate position.
| + | 7. Sowa, J.F. Conceptual Structures: Information Processing in Mind and Machine. Addison-Wesley, Reading, MA, 1984. |
| | | | |
| − | Because the roles of Fact, Case, and Rule are defined with regard to positions rather than magnitudes they are insensitive to whether the proposition in question is being used as a premiss or is being drawn as a conclusion.
| + | 8. Sowa, J.F. (ed.) Principles of Semantic Networks: Explorations in the Representation of Knowledge. Morgan Kaufmann, San Mateo, CA, 1991. |
| | | | |
| − | The "first figure" of the syllogism is explained as follows:
| + | Dewey, J. (1991). How We Think. Buffalo, NY: Prometheus Books. Originally published 1910. |
| | | | |
| − | <blockquote>
| + | Shakespeare, Wm. (1988). William Shakespeare: The Complete Works. Compact Edition. S. Wells & G. Taylor (eds.). Oxford University Press, Oxford, UK. |
| − | <p>When three terms are so related to one another that the last is wholly contained in the middle and the middle is wholly contained in or excluded from the first, the extremes must admit of perfect syllogism. By "middle term" I mean that which both is contained in another and contains another in itself, and which is the middle by its position also; and by "extremes" (a) that which is contained in another, and (b) that in which another is contained. For if A is predicated of all B, and B of all C, A must necessarily be predicated of all C. ... I call this kind of figure the First.</p>
| + | </pre> |
| | | | |
| − | <p>(Aristotle, Prior Analytics, 1.4).</p>
| + | ==Notes== |
| − | </blockquote>
| |
| | | | |
| − | For example, suppose A is "animal", B is "bird", and C is "canary". Then there is a deductive conclusion to be drawn in the first figure.
| + | ===Critique Of Functional Reason : Note 78=== |
| | | | |
| − | There is the Case:
| + | <pre> |
| | + | MW = Matthew West: |
| | | | |
| − | "All canaries are birds." (C => B)
| + | MW: Do you have a Cactus Manual all in one place please? |
| | | | |
| − | There is the Rule:
| + | the documentation for my 'theme one' program |
| | + | that I wrote up for my quant psy master's |
| | + | contains the last thing like an official |
| | + | manual that I wrote, also an expository |
| | + | introduction to the cactus language and |
| | + | its application to prop calc examples. |
| | + | may still have an ancient ascii version, |
| | + | or else the medieval 'word' doc, or i can |
| | + | send the mac belle version by snail express |
| | + | if you can vouchsafe me your postal address. |
| | | | |
| − | "All birds are animals." (B => A)
| + | in the mean time, i append a few of the expositions that |
| | + | i have outlined here/elsewhere over the last year on-line. |
| | | | |
| − | One deduces the Fact:
| + | pre-scanning this whole mess'o'messages for you, |
| | + | I find one that looks to me shortest & sweetest: |
| | | | |
| − | "All canaries are animals." (C => A)
| + | http://suo.ieee.org/email/msg05694.html |
| | | | |
| − | The propositional content of this deduction is summarized on the right. Taken at this level of detail, deductive reasoning is nothing more than an application of the transitive rule for logical implications.
| + | since this particular synopsis is mercifully short, i will copy it out here |
| | + | and use it to explain surcatenation, along with a few other thing that i am |
| | + | guessing might be puzzling at first sight about what in hey's going on here. |
| | | | |
| − | The "second figure" of the syllogism is explained as follows:
| + | o~~~~~~~~~o~~~~~~~~~o~ARCHIVE~o~~~~~~~~~o~~~~~~~~~o |
| | | | |
| − | <blockquote>
| + | Reflective Extension of Logical Graphs (Ref Log) |
| − | When the same term applies to all of one subject and to none of the other, or to all or none of both, I call this kind of figure the Second; and in it by the middle term I mean that which is predicated of both subjects; by the extreme terms, the subjects of which the middle is predicated; by the major term, that which comes next to the middle; and by the minor that which is more distant from it. The middle is placed outside the extreme terms, and is first by position. (Aristotle, Prior Analytics, 1.5).
| |
| − | </blockquote>
| |
| | | | |
| − | For example, suppose M is "mammal", N is "newt", and O is "opossum". Then there is a deductive conclusion to be drawn in the second figure.
| + | Here is a formal introduction to the RefLog Syntax. |
| | | | |
| − | There is the Fact:
| + | Formally speaking, we have the following set-up: |
| | | | |
| − | "All opossums are mammals." (O => M) | + | Set out the "alphabet of punctuation marks" $M$ = {" ", ",", "(", ")"}. |
| | + | The elements of $M$ are vocalized as "blank, "comma", "links", "right". |
| | | | |
| − | There is the Rule: | + | 1. There is a parametric family of formal languages of character strings |
| | + | such that, for each set $X$ of variable names $X$ = {"x_1", ..., "x_k"}, |
| | + | there is a formal language L($X$) over the alphabet A($X$) = $M$ |_| $X$. |
| | + | The grammar can be given in gory detail, but most folks know it already. |
| | | | |
| − | "No newts are mammals." (N.M = 0) | + | | Examples. If $X$ = {"x", "y"}, then these are typical strings in L($X$): |
| | + | | |
| | + | | " ", "( )", "x", "y", "(x)", "(y)", "x y", "(x y)", "(x, y)", "((x)(y))", "((x, y))", ... |
| | | | |
| − | One deduces the Case:
| + | 2. There is a parallel family of formal languages of graphical structures, |
| | + | generically known as "painted and rooted cacti" (PARC's), that exist in |
| | + | a one-to-one correspondence with these string expressions, being more or |
| | + | less roughly, at a suitable level of abstraction, their parse graphs as |
| | + | data structures in the computer. The PARC's for the above formulas are: |
| | | | |
| − | "No newts are opossums." (N.O = 0) | + | | Examples. |
| | + | | x y x y |
| | + | | o o o---o |
| | + | | x y x y x y \ / \ / |
| | + | | o o o o o---o o o |
| | + | | | x y | | x y | \ / | | |
| | + | | @ @ @ @ @ @ @ @ @ @ @ ... |
| | + | | |
| | + | | " ", "( )", "x", "y", "(x)", "(y)", "x y", "(x y)", "(x, y)", "((x)(y))", "((x, y))", ... |
| | | | |
| − | The propositional content of this deduction is summarized on the right. Expressed in terms of the corresponding classes, it says that if O c M and if N intersects M trivially, then N must also intersect O trivially. Here, I use a raised dot "." to indicate either the conjunction of two propositions or the intersection of two classes, and I use a zero "0" to indicate either the identically false proposition or the empty class, leaving the choice of interpretation to the option of the reader.
| + | Together, these two families of formal languages constitute a system |
| | + | that is called the "reflective extension of logical graphs" (Ref Log). |
| | | | |
| − | The "third figure" of the syllogism is explained as follows:
| + | Strictly speaking, Ref Log is an abstract or "uninterpreted" formal system, |
| | + | but its expressions enjoy, as a rule, two dual interpretations that assign |
| | + | them the meanings of propositions or sentences in "zeroth order logic" (ZOL), |
| | + | to wit, what Peirce called the "alpha level" of his systems of logical graphs. |
| | | | |
| − | <blockquote>
| + | For example, the string expression "(x (y))" parses into the following graph: |
| − | If one of the terms applies to all and the other to none of the same subject, or if both terms apply to all or none of it, I call this kind of figure the Third; and in it by the middle I mean that of which both the predications are made; by extremes the predicates; by the major term that which is [further from] the middle; and by the minor that which is nearer to it. The middle is placed outside the extremes, and is last by position. Aristotle, Prior Analytics, 1.6).
| |
| − | </blockquote>
| |
| | | | |
| − | It appears that this passage is only meant to mark out the limiting cases of the type. From the examples that Aristotle gives it is clear that he includes many other kinds of logical situation under this figure. Perhaps the phrase "applies to all or none" is intended to specify that a term applies "affirmatively or negatively" to another term, but is not meant to require that it applies universally so.
| + | | x y |
| | + | | o---o |
| | + | | | |
| | + | | @ |
| | | | |
| − | For example, suppose P is "poem", R is "rhapsody", and S is "sonnet". Then there is deductive conclusion to be drawn in the third figure:
| + | You can "deparse" the string off the graph by traversing |
| | + | it like so, reading off the marks and varnames as you go. |
| | | | |
| − | There is the Fact:
| + | | o---x->(--y---o |
| | + | | ^ | |
| | + | | | x ( y | |
| | + | | | o-----o v |
| | + | | | | ) ) |
| | + | | ( (|) ) |
| | + | | ^ | | |
| | + | | | @ v |
| | | | |
| − | "All sonnets are poems." (S => P) | + | In the "existential" interpretation of RefLog, |
| | + | in which I do my own thinking most of the time, |
| | + | concatenation of expressions has the meaning of |
| | + | logical conjunction, while "(x)" has the meaning |
| | + | of "not x", and so the above string and graph have |
| | + | a meaning of "x => y", "x implies y", "if x then y", |
| | + | "not x without y", or anything else that's equivalent. |
| | + | The blank expression is assigned the value of "true". |
| | + | Hence, the expression "()" takes the value of "false". |
| | + | The bracket expression "(x_1, x_2, ..., x_k)" is given |
| | + | the meaning "Exactly one of the x_j is false, j=1..k". |
| | + | Therefore, "((x_1),(x_2), ...,(x_k))" partitions the |
| | + | universe of discourse, saying "Just one x_j is true". |
| | + | </pre> |
| | | | |
| − | There is the Case:
| + | ===Critique Of Functional Reason : Note 83=== |
| | | | |
| − | "Some sonnets are rhapsodies." (S.R > 0)
| + | <pre> |
| | + | | Tantum ergo sacramentum |
| | + | | veneremur cernui, |
| | + | | et antiquum documentum |
| | + | | novo cedat ritui, |
| | + | | praestet fides supplementum |
| | + | | sensuum defectui. |
| | + | | |
| | + | | So great therefore a sacrifice |
| | + | | let us humbly adore |
| | + | | and let the old law yield |
| | + | | to the new rite; |
| | + | | let faith supplement |
| | + | | the shortcoming of the senses. |
| | + | | |
| | + | | Lyric by Thomas Aquinas, |
| | + | | Music by Amadeus Mozart, KV 142 & 197. |
| | | | |
| − | One deduces the Rule:
| + | The increasing ossification of asciification |
| | + | is heaping up way too many old bones to bear. |
| | + | So I am going to shift my anklage a bit, and |
| | + | try out a new set of conventions for a while, |
| | + | to see if I can lighten the overloading obit. |
| | | | |
| − | "Some rhapsodies are poems." (R.P > 0)
| + | Let us try to reserve script and singly-underscored fake-fonts or formats |
| | + | for the names of sets, as in the notations !O!, !S!, !I! that I will now |
| | + | set aside and use from now on for the Object, Sign, Interpretant domains, |
| | + | respectively, of an arbitrary sign relation !L! c !O! x !S! x !I!. |
| | | | |
| − | The propositional content of this deduction is summarized on the right. Expressed in terms of the corresponding classes, it says that if S c P and if R intersects S non-trivially then R must intersect P non-trivially.
| + | Among other benefits, this will serve to liberate the plain faced characters |
| | + | for employment as the non-terminal symbols of our formal grammars, rendering |
| | + | our formal grammatical productions far less $Capitalistic$, !Exclamatory!, |
| | + | and overbearingly prescriptive than they be otherwise hell-bent to become. |
| | | | |
| − | =====1.4.3.2 Inductive Reasoning=====
| + | So let me try out this new rite to see how it works out, |
| | + | And I will not pause to rewrite the old law in its font, |
| | + | But advise you solely of its transformed instantiations, |
| | + | And fix my faith on imagination to sense the supplement. |
| | + | </pre> |
| | | | |
| − | (Aristotle, Prior Analytics, 2.23).
| + | ===Critique Of Functional Reason : Note 92=== |
| | | | |
| − | =====1.4.3.3 Abductive Reasoning=====
| + | <pre> |
| | + | I need to try and say some things at his point about |
| | + | why formal language theory is interesting and useful, |
| | + | but all I have at the moment are random remembrances |
| | + | and reflections that enter my mind from time to time. |
| | | | |
| − | A choice of method cannot be justified by deduction or by induction, at least, not wholly, but involves an element of hypothesis. In ancient times, this mode of inference to an explanatory hypothesis was described by the Greek word "apagoge", articulating an action or a process that "carries", "drives", or "leads" in a direction "away", "from", or "off". This was later translated into the Latin "abductio", and that is the source of what is today called "abduction" or "abductive reasoning". Another residue of this sense survives today in the terminology for "abductor muscles", those that "draw away (say, a limb or an eye) from a position near or parallel to the median axis of the body" (Webster's).
| + | In many ways, the study of formal languages and grammars |
| | + | is a paradigm, more, a paragon, of the situation that we |
| | + | face whenever we inquire into a complex reality, that is, |
| | + | all of the ever-renewed sources of puzzling phenomena or |
| | + | pressing problems that we call a world. |
| | | | |
| − | If an image is needed, one may think of Prometheus, arrogating for the sake of an earthly purpose the divine prerogative of the gods, and then drawing the fire of their heavenly ire for the presumption of this act. This seems to sum up pretty well, not only the necessity and the utility of hypotheses, but also the risks that one incurs in making conjectures. In other guises, abductive reasoning is the mode of inference that is used to diagnose a complex situation, one that originally presents itself under a bewildering array of signs and symptoms, and fixes it subject to the terms of a succinct "nomen" or a summary predicate. Finally, by way of offering a personal speculation, I think it is likely that this entire trio of terms, "abduction", "deduction", and "induction", have reference to a style of geometric diagrams that the Ancients originally used to illustrate their reasonings.
| + | The archtypical place of formal language theory is well |
| | + | understood in many quarters, and has been from the very |
| | + | outset of its constellation as an independent viewpoint. |
| | | | |
| − | Abductive reasoning has also been called by other names. C.S. Peirce at times called it "presumption", perhaps because it puts a plausible assumption logically prior to the observed facts, and at other times referred to it as "retroduction", because it reasons backwards from the consequent to the antecedent of a logical implication.
| + | In this paradigmatic (analogical or exemplary) way of |
| | + | understanding it, a formal language is the "data" and |
| | + | a formal grammar is the "theory", and the question is, |
| | + | as always, whether a theory accounts for and explains |
| | + | the data, a "fitting" relationship that may be viewed |
| | + | in many ways, for one, the way that a theory might be |
| | + | said to "generate" the data, or perhaps better stated, |
| | + | not just to "cook" in a precociously specious fashion |
| | + | but more like to "regenerate" the form after the fact. |
| | | | |
| − | In its simplest form, abductive reasoning proceeds from a "fact" that A is true, using a "rule" that B => A, to presume a "case" that B is true. Thus, if A is a surprising fact that one happens to observe, and B => A is a rule to the effect that if B is true then A necessarily follows, then guessing the case that B is true is an instance of abductive reasoning. This is a backward form of reasoning, and therefore extremely fallible, but when it works it has the effect of reducing the amount of surprise in the initial observation, and thus of partially explaining the fact.
| + | That's all that I can manage to express at the moment, |
| | + | but maybe it will supply a grub-stake of motivational |
| | + | victuals for the grueling labors of exploration ahead. |
| | + | </pre> |
| | | | |
| − | In a slightly more complicated version, abduction proceeds from a fact that C => A, using a rule that B => A, to presume a case that C => B. This is an inessential complication, since the rule of modus ponens and the rule of transitivity are essentially equivalent in their logical force, but it is often convenient to imagine that C is the "common subject" or the "current situation" that is implicit throughout the argument, namely, the existing entity that substantiates or instantiates all of the other predicates that are invoked in its course.
| + | ===IDS. Incitatory Note 1=== |
| | | | |
| − | Suppose I have occasion to reason as follows:
| + | <pre> |
| | + | | Each ground-principle must be proved entirely |
| | + | | by that same kind of inference which it supports. |
| | + | | |
| | + | | But we cannot arrive at any conclusion |
| | + | | by mere deduction except about symbols. |
| | + | | |
| | + | | We cannot arrive at any conclusion |
| | + | | by mere induction except about things. |
| | + | | |
| | + | | And we cannot arrive at any conclusion |
| | + | | by mere hypothesis except about forms. |
| | + | | |
| | + | | C.S. Peirce, CE 1, page 290. |
| | + | | |
| | + | | Charles Sanders Peirce, "On the Logic of Science", |
| | + | | Harvard University Lectures (1865), pages 161-302 in: |
| | + | |'Writings of Charles S. Peirce: A Chronological Edition', |
| | + | |'Volume 1, 1857-1866', Peirce Edition Project, |
| | + | | Indiana University Press, Bloomington, IN, 1982. |
| | + | </pre> |
| | | | |
| − | "It looks like a duck, so I guess it is a duck."
| + | ===IDS. Meditative Note 1=== |
| | | | |
| − | Or even more simply:
| + | <pre> |
| | + | I would like to start from a "common sense practical" (CSP) point of view, |
| | + | and, indeed, never to lose sight of what appears evident from that station, |
| | + | no matter how many levels of abstract remove and abstruse mention it might |
| | + | become necessary to interpose along the way. |
| | | | |
| − | "It looks blue, therefore it is blue." | + | So let's examine this initial caltrop |
| | + | "descriptive/normative/prescriptive" |
| | + | from the CSP POV, if you will. |
| | | | |
| − | These are instances in which I am using abductive reasoning, according to the pattern of the following schema:
| + | Reading "Descriptive" to mean "What it is", |
| | + | while "Normative" means "What it oughta be", |
| | + | and "Prescriptive" says "Make it so, or else", |
| | + | I will have very little to say about the last, |
| | + | and only be able to focus on the distinctions |
| | + | that may exist among the first two dimensions. |
| | | | |
| − | I observe a Fact:
| + | From the beginning, from this point of view, difficult words, |
| | + | like "inquiry", "logic", "truth", and so on, must be taken |
| | + | as initially indexical, inchoately succeeding at little |
| | + | more than pointing to a realm of experience that may |
| | + | or may not be common to the e-mitter and re-mitter. |
| | | | |
| − | "It looks like X." (X')
| + | I suspect that this stanza is likely to be controversial, |
| | + | so I'll pause at this point for the countrapunctal verse. |
| | | | |
| − | I have in the back of my mind a general Rule:
| + | Or for a rest ... |
| | + | </pre> |
| | | | |
| − | "If it is X, then it looks like X." (X => X')
| + | ===IDS. Meditative Note 2=== |
| | | | |
| − | I reason my way back from the observed Fact and the assumed Rule to assert what I guess to be the Case: | + | <pre> |
| | + | So I may begin with an object and a sign in a tenuous relation, |
| | + | with the subject matter indexed under the topic name "inquiry", |
| | + | where the sign originates from a "just noticeable differential" |
| | + | of information about the object, and not a single "figit" more. |
| | + | Few would call this a foundation -- I only call it a beginning. |
| | | | |
| − | "It is X." (X)
| + | Yet another of many ... |
| | | | |
| − | The abduction is a hypothetical inference that results in a diagnostic conclusion, that is, a statement of opinion as to what is conjectured to be the case. In each case the operation of abductive reasoning starts from a complex configuration, involving a number of explicit observations in the foreground and a class of implicit assumptions in the background, and it offers a provisional statement about certain possibility, one that is typically less conspicuous, obvious, or prominent, but still potentially present in the situation, and hopefully serving to explain the surprising or the problematic aspects of the whole state of affairs.
| + | But it does provide us with a clue to a signficant difference, |
| | + | however much this difference is bound by this origin to raise |
| | + | itself from egg, germ, seed, spore, or whatever it is that is |
| | + | infinitesimal in its initial condition. In this disjointness |
| | + | of an archetype where what begins, what leads, and what rules |
| | + | are not so trivially identical to one another, one encounters |
| | + | the brand of beginning that begins in the middle of the story, |
| | + | and has no need of any other foundation but the medium itself. |
| | | | |
| − | What results from the abductive inference is a concept and possibly a term, for instance, "duck" or "blue". The concept attempts to grasp a vast complex of appearances within a unitary form, and the term that connotes the concept is used to put explicit bounds on what it conveys. Working in tandem, they express an approximation or a simplification, "a reduction of the manifold of phenomena to a unified conception". Finite minds cannot operate for very long with anything more than this.
| + | ["sign-ficant" [stet]] |
| | + | </pre> |
| | | | |
| − | The reader may have noticed some obvious distinctions between the two examples of abductive reasoning that I gave above, between the case of "looking like a duck" and the case of "looking blue". Just to mention the most glaring difference: Although a person is occasionally heard to reason out loud after the fashion of the former example, it is rare to hear anyone naturally reasoning along the lines of the latter example. Indeed, it is more likely that any appearance of doing so is always an artificial performance and a self-conscious reconstruction, if not a complete fabrication, and it is doubtful that the process of arriving at a perceptual judgment can follow this rule in just so literal a fashion.
| + | ===IDS. Obligatory Note 1=== |
| | | | |
| − | This is true and important, but it is beside the point of the immediate discussion, which is only to identify the logical form of the inference, that is, to specify up to informational equivalence the class of conduct that is involved in each example. Thus, considering the inference as an information process, I do not care at this point whether the process is implemented by a literal-minded variety of rule-following procedure, so long as it "follows", "obeys", or "respects" these rules in the form of what it does. One can say that an information process "obeys" a set of rules in a "figurative" and a "formal" sense if the transformation that occurs in the state of information between the beginning and the end of the process has the form of a relation that can be achieved by literally following these rules with respect to the prospective class of materials.
| + | While I remain compelled to remain silent on the status of the absolute fiat, the irrelative notion of the unmotivated motion and the disinterested stance, let me then turn to the other axes of description, descriptive vs. normative. Axes of description, indeed, you can almost hear one branch of the recursion already beginning to wind up its whine to the verge of a howl, but toss it a sop and try to persevere in the quest. |
| | | | |
| − | The general drift of the strategy that is being mapped out here, the "abstract", the "formal", or the "functional" approach, is now evident. Conceptually, one partitions the space of processes into "effective", "informational", or "pragmatic" equivalence classes and then adopts the inditement of a sequence of rules as a symbolic "nomen" for the class of processes that all achieve the same class of effects. At this level of functional abstraction, the conception of a process is indifferent to the particulars of its implemenation, so long as it lives within the means of the indicated constraints. Moreover, unless there is a way to detect the nature of the "actual" process without interfering too severely with it, that is, a path-sensitive but still unobtrusive measure that can sort out a finer structure from these equivalence classes, then it is not possible to inquire any further into the supposedly "actual" details.
| + | In this view, I regard the very idea of a norm as invoking its due pragma — aim, business, concern, desire, end, function, goal, intention, interest, objective, purpose, its names are legion — and the good sense of the norm is simply to suggest what one ought to do, contingent, of course, on one's motive to achieve that pragma. |
| | | | |
| − | Similar remarks apply to every case where one attributes "law-abiding" or "rule-governed" behavior to oneself, to another person, or even to a physical process. Across this diverse spectrum of cases, it ranges from likely but not certain to unlikely but still conceivable that the action in question depends on the agent "knowing" the laws that abide or the rules that are effectively being obeyed. With this in mind, I can draw this digression on appearances to a conclusion: When I say that agents are acting according to a particular pattern of rules, it only means that it "looks like" they are. In other words, they are acting "as if" they are consciously following these rules, or they are acting just like I act when I conscientiously follow such rules. A concise way to sum all of this up is to say that a pattern of rules constitutes a model of conduct, one that I can deliberately emulate, or one that I can attribute to others by way of explaining their conduct. In attributing this model to others, or even in using it to account for my own less deliberate behavior, I am making an abductive inference.
| + | If we keep in mind the kinds of ''applied research task'' (ART) that your everyday artist, designer, engineer, mathematician, scientist, or other type of technical worker has to carry out on an everyday basis, we note how these axes of description can be used to frame their activities and to depict their forms of conduct, without mistaking either the frame or the picture for the object of the picture so framed. Nor does any body imagine that the observer must flatten out into a single plane or align with a single axis, in order to make a vantage of the frame so pictured. |
| | | | |
| − | One way to appreciate the pertinence of this point is to notice that this entire digression, concerned with explaining the similarities between "looking like a duck" and "looking blue", is itself a form of argument, making a case of abductive inference to a case of abductive inference. In short, I am reasoning according to the following pattern:
| + | Common sense practical wit tells us that effective action toward the achievement of a desirable result will naturally depend on acquiring good descriptions of the lay of the land in which we hope to advance. |
| | | | |
| − | It appears to be the making of an abductive inference,
| + | ===IDS. Projective Note 1=== |
| | | | |
| − | so I guess it is the making of an abductive inference.
| + | <pre> |
| | + | Good morning. Thanks. I had a bad night. |
| | + | I blame Bernard Morand, who wrote me this: |
| | | | |
| − | Anyone who thinks that this style of reasoning is too chancy to be tolerated ought to observe that it is only the pattern of inference that one follows in attributing minds to others, solely on the evidence that they exhibit roughly the same array of external behaviors in reaction to various external conditions as one employs to express one's experience of roughly the same conditions.
| + | BM: But this looks as some God's view. |
| | + | What about us, finite humans, occupied |
| | + | in counting the instants of our lives? |
| | + | And thus condemned to try to improve |
| | + | the fate of our successors? |
| | | | |
| − | It goes without saying that abductive reasoning is extremely fallible. The fact that it looks like a duck does not necessarily mean that it is a duck - it might be a decoy. Moreover, in most cases of actual practice the implicit rule that serves to catalyze the abductive inference is not an absolute rule or a necessary truth in its own right but may be only a contingent rule or a probable premiss. For instance, not every case of being blue presents the fact of looking blue - the conditions of observation may be trickier than that. This brings to the fore another mark that distinguishes the two examples, highlighting a potentially important difference between "looking like a duck" and "looking blue". This is the amount of oversight, or awareness and control, that an agent has with regard to an inference, in other words, the extent to which an inference really does "go without saying".
| + | When you think of this in the future, and of course you may never, |
| | + | you may blame him too, for in writing this he has "erged" me on |
| | + | to return to my deserted dissertation work, into which I have |
| | + | poured my life for lo! these too many years to count, truly, |
| | + | if you stop to contemplate the fact that time is relative. |
| | | | |
| − | The abductive inference from "it looks blue" to "it is blue" and the abductive inference from "it looks like a duck" to "it is a duck" differ in the degrees to which they exhibit a complex of correlated properties. These variations are summed up in one sense by saying that the first, more perceptual inference is more automatic, compulsive, habitual, incorrigible, and inveterate. The correlations are summed up in the opposite sense by saying that the second, more conceptual inference is more aware, controllable, correctable, critical, deliberate, guarded, and reflective. From a fully pragmatic standpoint, these differences are naturally of critical importance. But from a purely logical standpoint, they have to be regarded as incidental aspects or secondary features of the underlying forms of inference.
| + | In that time I have come to the view that we really need |
| | + | a good "theory of inquiry" (TOI), for all sorts of very |
| | + | practical and crucial reasons, also, that we cannot get |
| | + | a good TOI without its being, at one and the same time, |
| | + | a good "theory of information" (TOI too), and also that |
| | + | an integral constituent of TOI 1 and TOI 2 would have to |
| | + | be a good "theory of representation and semiosis" (TORAS) -- |
| | + | "Bull!?", you say, well, so be it. |
| | | | |
| − | There is one thing yet missing from this description of abductive reasoning, and that is its creative aspect. The description so far is likely to leave the impression that the posing of a hypothesis always takes place against a narrowly circumscribed background of established terms that are available for describing cases, and thus that it amounts to nothing more original than picking out the right label for the case. Of course, the forming of a hypothesis may be bound by the generative potential of the language that is ultimately in force, but that is a far cry from a prescriptively finite list of more or less obvious choices.
| + | Further, I think that it is abundantly evident by now that |
| | + | we will get no such good theories of signs or science from |
| | + | the "establishment philosophy of science" (EPOS?) -- which |
| | + | has managed to mince and to trash the best available tries |
| | + | at such theories for over a hundred years now. But Hey! -- |
| | + | don't take my word for it -- waste a century of your own. |
| | | | |
| − | How does all of this bear on the choice of a method? In order to make a start toward answering that question, I need to consider the part that abductive reasoning plays in the inquiry into method, which is, after all, just another name for the inquiry into inquiry.
| + | We just got our regular email back, |
| | + | so I think that I can now get going -- |
| | + | Yes, I have lost the ability to think |
| | + | if not literally writing 'to' somebody. |
| | | | |
| − | There are times when choosing a method looks more like discovering or inventing a method, a purely spontaneous creation of a novel way to proceed, but normally the choice of a path picks its way through a landscape of familiar options and mapped out opportunities, and this presupposes a description of previously observed forms of conduct and a classification of different paths from which to choose. Hence the etymology of the word "method", indicating a review of means or a study of ways.
| + | When it begins, it begins like this: |
| | | | |
| − | I would now like to examine several types situations where a choice of method is involved, paying special attention to the way that abductive reasoning enters into the consideration. | + | Why am I asking this question? |
| | + | </pre> |
| | | | |
| − | Example 1.
| + | ===IDS. Projective Note 2=== |
| | | | |
| − | Suppose I have occasion to reason along the following lines:
| + | <pre> |
| | + | So we may rest assured that we do have a "subject matter", an empirical domain, |
| | + | or a realm of experience that is indexed, however dimly, generally, or vaguely, |
| | + | by the word "inquiry", and only the question how best to describe it remains |
| | + | in doubt at this stage of the play. If we wanted to cast our net as widely |
| | + | as possible, at the risk of anticipating a bounding hypothesis, we could |
| | + | think of all the world's creatures bright and beautiful and of how they |
| | + | conduct themselves when faced with some moment of uncertainty, where |
| | + | their aim is to cope with a surprising phenomenon or to deal with |
| | + | a problematic situation that meets them in the course of their |
| | + | ever-ongoing struggles to live, to revive, and to thrive. |
| | | | |
| − | This situation looks like one in which this method will work, therefore I will proceed on the hypothesis that it will work.
| + | Now, neither the fact that we begin with a descriptive task, |
| | + | nor the fact that it remains of interest for its own sake, |
| | + | necessarily means that we must end there, for it is also |
| | + | the means to a further end, of learning how to better |
| | + | our own skill at inquiry, which means in our time |
| | + | the building of tools that help with the task. |
| | | | |
| − | The current situation (C) looks amenable (A') to this method, so I guess it really is amenable (A) to this method.
| + | I hope I have made this sound as truly and |
| | + | as trivially obvious as it ought to be. |
| | + | </pre> |
| | | | |
| − | In this type of situation, my observations of the situation are reduced to a form of description that portrays it in the light of a given method, amounting to an estimate of whether the situation is a case to which the method applies. The form of the entire argument hinges on the question of whether the assurance of this application is apparent or actual.
| + | ===IDS. Reflective Note 1=== |
| | | | |
| − | I express my observations of the situation as a Fact:
| + | <pre> |
| | + | In reflecting on what in the world a "Theory of Inquiry" (TOI) might be, |
| | + | it occurs to me that there are many different things that one might mean |
| | + | by such a theory. It could just be any number of things that one asserts |
| | + | or has a mind to assert about the ostensible subject matter. But it has |
| | + | been my experience that one can assert pretty much whatever one chooses, |
| | + | and others will choose to heed it or ignore it on many different grounds, |
| | + | the grounds themselves being a matter of choice, conditioning, or custom. |
| | | | |
| − | "The current situation looks amenable." (C => A')
| + | But I am looking for theories that work, that is to say, theories that |
| | + | are subject to probation through proof, probability, and programming. |
| | | | |
| − | I have in the back of my mind a general Rule: | + | Astute readers will have noticed that I've already attempted to finesse |
| | + | a very important, and most likely "infinessible" issue, to wit, that of |
| | + | the scruples dividing descriptive, normative, and prescriptive theories. |
| | | | |
| − | "If it is amenable, then it looks amenable." (A => A')
| + | I will think about that, and get back to you. |
| | + | </pre> |
| | | | |
| − | I reason my way back from the observed Fact and the assumed Rule to assert what I guess to be the Case:
| + | ===IDS. Reflective Note 2=== |
| | | | |
| − | "The current situation is amenable." (C => A)
| + | <pre> |
| | + | | How will I approach this problem about the nature of inquiry? |
| | + | | |
| | + | | The simplest answer is this: |
| | + | | |
| | + | | I will apply the method of inquiry to the problem of inquiry's nature. |
| | + | | |
| | + | | This is the most concise and comprehensive answer that I know, but |
| | + | | it is likely to sound facetious at this point. On the other hand, |
| | + | | if I did not actually use the method of inquiry that I describe |
| | + | | as inquiry, how could the results possibly be taken seriously? |
| | + | | Accordingly, the questions of methodological self-application |
| | + | | and self-referential consistency will be found at the center |
| | + | | of this research. |
| | | | |
| − | As far as it goes, this style of reasoning follows the basic pattern of abductive inference. Its obvious facticity is due to the fact that the situation is being described solely in the light of a pre-selected method. That is a relatively specious way to go about describing a situation, in spite of the fact that it may be inevitable in many of the most ultimate and limiting cases. The overall effect is noticeably strained, perhaps because it results from dictating an artificial setting, attempting to reduce a situation to the patterns that one is prepared to observe, and trying to fit what is there to see into a precut frame. A more natural way to describe a situation is in terms of the freely chosen perceptual features that inform a language of affects, impressions, and sensations. But here a situation is forced to be described in terms of the prevailing operational features that constitute a language of actions, forcing the description to be limited by the actions that are available within a prescribed framework of methods.
| + | These lines image in compact form the crux of the problem, |
| | + | the crucible of the method, and the character that marks |
| | + | relation between the two, if indeed they really are two, |
| | + | in a form whose extended development will wind its way |
| | + | through many a later page of the present exposition. |
| | | | |
| − | Instead of describing a situation solely in terms of its reactive bearing, that is, wholly in terms of how it reacts to the application of a method, one can try to describe it in terms that appear to be more its own, its independent, natural, observational, perceptual, or "proper" features. What the "proper" or "object-oriented" features are and whether they can be distinguished in the end from "reactive" or "method-oriented" features are questions that cannot be answered in the early phases of an investigation.
| + | But let me just point out at this point some of |
| | + | the reasons why I have found the prerequisite |
| | + | of an inquiry into inquiry to be inescapable. |
| | | | |
| − | Example 2.
| + | Let us entertain the idea, for the sake of getting the inquiry started, |
| | + | if nothing else, that it is admissible to use a word like "inquiry" as |
| | + | an initially indefinite indicator of an ostensible object of inquiry. |
| | + | If we ever again find ourselves being puzzled how our reasoning can |
| | + | chastize its own entailments this way, we may remind ourselves of |
| | + | that fine old line between our "logica docens' (logic as taught) |
| | + | and our "logica utens" (logic as used). With this distinction |
| | + | in mind, we can dispell the initial puzzlement by saying that |
| | + | we are using a capacity for inquiry that we do not know how |
| | + | to formalize yet in order to examine the forms of inquiry |
| | + | that various thinkers have been able, at least partially, |
| | + | to formalize. |
| | | | |
| − | Suppose I find myself reasoning as follows:
| + | The dilemma that we face has the following structure: |
| | | | |
| − | If the current world (C) is a blessed world (B), | + | If we recommend to all a method of inquiry that |
| | + | we ourselves do not use in a pinch, precisely |
| | + | in a pinch where we need to study an issue |
| | + | as important as the nature of inquiry, |
| | + | then who would take our advice? |
| | | | |
| − | then it is a world in which my method works (A).
| + | So it seems that there is no choice |
| | + | but to study inquiry, the pragma, |
| | + | by way of inquiry, the praxis, |
| | + | that is to say, recursively. |
| | | | |
| − | Here, I call to mind an independent property of being, B, that a world or a situation can have, and I use it as a middle term to reason along the lines of the following scheme:
| + | Incidentally, many variations on this theme are |
| − | | + | thoroughly developed in Peirce's "Lectures" of |
| − | I express my inquiry by questioning the possibility of a certain Fact, that is, by interrogating the following statement:
| + | 1865 and 1866 and recapitulated in his early |
| − | | + | study "On a New List of Categories" (1867). |
| − | "The current world is amenable." (C =?> A)
| |
| − | | |
| − | I have in the back of my mind a general Rule:
| |
| − | | |
| − | "What is blessed, is amenable." (B => A)
| |
| − | | |
| − | I reason my way back from the interrogated Fact and the assumed Rule to guess that I ought to contemplate the chances of the following Case:
| |
| − | | |
| − | "The current world is blessed." (C =?> B)
| |
| − | | |
| − | Altogether, the argument that underlies the current question of method falls into line with the following example of abductive reasoning:
| |
| − | | |
| − | I hope that C is A, so I guess I hope that C is B.
| |
| − | | |
| − | To proceed with the application of a given method on the basis of such a piece of reasoning is tantamount to the faith, the hope, or the wish that there is already the right kind of justice in the world that would make the prejudices of one's favorite method turn out to be right, that one is just lucky enough to be playing in accord with a pre-established harmony. If such a confidence is all that allows one to go on inquiring, then there is no harm in assuming it, so long as one reserves the right to question every particular of its grant, should the occasion arise.
| |
| − | | |
| − | If one abstracts from the specific content of this example and examines its underlying structure, it reveals itself as the pattern of abductive reasoning that occurs in relating complex questions to simpler questions or in reducing difficult problems to easier problems. Furthermore, the iteration of this basic kind of step motivates a downward recursion from questions of fact to questions of cases, in a hopeful search for a level of cases where most of the answers are already known.
| |
| − | | |
| − | The previous examples of inquiry into method are not very satisfactory. Indeed, their schematic forms have an absurdly sketchy character about them, and they fail to convey the realistic sorts of problems that are usually involved in reasoning about the choice of a method. The first example characterizes a situation wholly in terms of a selected method. The second example characterizes a situation in terms of a property that is nominally independent of the method chosen, but the ad hoc character of this property remains obvious. In order to reason "properly" about the choice of method, it is necessary to contemplate properties of the methods themselves, and not just the situations in which they are used.
| |
| − | | |
| − | Example 3.
| |
| − | | |
| − | If I reason that scientific method is wise because wise people use it, then I am making the hypothesis that they use it because they are wise. Here, my reasoning can be explained according to the following pattern:
| |
| − | | |
| − | I observe a fact:
| |
| − | | |
| − | "A certain conduct is done by wise people." (C => X)
| |
| − | | |
| − | I have in mind a rule:
| |
| − | | |
| − | "If a wise act, then done by wise people." (A => X)
| |
| − | | |
| − | I abduce the case:
| |
| − | | |
| − | "A certain conduct is a wise act." (C => A)
| |
| − | | |
| − | Example 4.
| |
| − | | |
| − | If I reason that scientific method is a good method on account of the fact that it works for now, then I am guessing that it works for now precisely because it is good.
| |
| − | | |
| − | I observe a fact:
| |
| − | | |
| − | "Scientific method works for now." (C => X)
| |
| − | | |
| − | I have in mind a rule:
| |
| − | | |
| − | "What is good, works for now." (A => X)
| |
| − | | |
| − | I abduce the case:
| |
| − | | |
| − | "Scientific method is good." (C => A)
| |
| − | | |
| − | As always, the abductive argument is extremely fallible. The fact that scientific method works for now can be one of its accidental features, and not due to any essential goodness that it might be thought to have.
| |
| − | | |
| − | Finally, it is useful to consider an important variation on this style of argument, one that exhibits its close relation to reasoning by analogy or inference from example. Suppose that the above argument is presented in the following manner:
| |
| − | | |
| − | Scientific method (C) has many of the features that a good method needs to have, for instance, it works for now (X), so I reason that it has all of the features of a good method, in short, that it is a good method (A).
| |
| − | | |
| − | So far, the underlying argument is exactly the same. In particular, it is important to notice that the abductive argument does not depend on the prior establishment of any known cases of good methods. As of yet, the phrase "good method" is a purely hypothetical description, a term that could easily turn out to be vacuous. One has in mind a number of properties that one thinks a good method ought to have, but who knows if there is any thing that would satisfy all of these requirements? There may be some sort of subtle contradiction that is involved in the very juxtaposition of the terms "good" and "method". In sum, it can happen that scientific method is the very first method that is being considered for membership in the class of good methods, and so it is still unknown whether the class labeled "good methods" is empty or not.
| |
| − | | |
| − | But what if an example of a good method is already known to exist, one that has all of the commonly accepted properties that appear to define what a good method ought to be? In this case, the abductive argument acquires the additional strength of an argument from analogy.
| |
| − | | |
| − | =====1.4.3.4 Analogical Reasoning=====
| |
| − | | |
| − | The classical treatment of analogical reasoning by Aristotle explains it as a combination of induction and deduction. More recently, C.S. Peirce gave two different ways of viewing the use of analogy, analyzing it into complex patterns of reasoning that involve all three types of inference. In the appropriate place, it will be useful to consider these alternative accounts of analogy in detail. At the present point, it is more useful to illustrate the different versions of analogical reasoning as they bear on the topic of choosing a method.
| |
| − | | |
| − | The next example, ostensibly concerned with reasoning about a choice of method, is still too artificial to be taken seriously for this purpose, but it does serve to illustrate Aristotle's analysis of analogical reasoning as a mixed mode of inference, involving inductive and deductive phases.
| |
| − | | |
| − | Example 5.
| |
| − | | |
| − | Suppose I reason as follows. I think I can establish it as a fact that scientific method is a good method by taking it as a case of a method that always works and by using a rule that what always works is good. I think I can establish this rule, in turn, by pointing to one or more examples of methods that share the criterial property of always working and that are already acknowledged to be good. In form, this pattern of reasoning works by noticing examples of good methods, by identifying a reason why they are good, in other words, by finding a property of the examples that seems sufficient to prove them good, and by noticing that the method in question is similar to these examples precisely in the sense that it has in common this cause, criterion, property, or reason.
| |
| − | | |
| − | In this situation, I am said to be reasoning by way of analogy, example, or paradigm. That is, I am drawing a conclusion about the main subject of discussion by way of its likeness to similar examples. These cases are like the main subject in the possession of a certain property, and the relation of this critical feature to the consequential feature of interest is assumed to be conclusive. The examples that exhibit the criterial property are sometimes known as "analogues" or "paradigms". For many purposes, one can imagine that the whole weight of evidence present in a body of examples is represented by a single example of the type, an exemplary or typical case, in short, an archetype or epitome. With this in mind, the overall argument can be presented as follows:
| |
| − | | |
| − | Suppose that there is an exemplary method (E) that I already know to be a good method (A). Then it pays to examine the other properties of the exemplary method, in hopes of finding a property (B) that explains why it is good. If scientific method (C) shares this property, then it can serve to establish that scientific method is good.
| |
| − | | |
| − | The first part of the argument is the induction of a rule:
| |
| − | | |
| − | I notice the case:
| |
| − | | |
| − | "The exemplary method always works." (E => B)
| |
| − | | |
| − | I observe the fact:
| |
| − | | |
| − | "The exemplary method is a good method." (E => A)
| |
| − | | |
| − | I induce the rule:
| |
| − | | |
| − | "What always works, is good." (B => A)
| |
| − | | |
| − | The second part of the argument is the deduction of a fact:
| |
| − | | |
| − | I notice the case:
| |
| − | | |
| − | "Scientific method always works." (C => B)
| |
| − | | |
| − | I recall the rule:
| |
| − | | |
| − | "What always works, is good." (B => A)
| |
| − | | |
| − | I deduce the fact:
| |
| − | | |
| − | "Scientific method is good." (C => A)
| |
| − | | |
| − | Example 6.
| |
| − | | |
| − | | |
| − | | |
| − | Example 7.
| |
| − | | |
| − | Suppose that several examples (S1, S2, S3) of a good method are already known to exist, ones that have a number of the commonly accepted properties (P1, P2, P3) that appear to define what a good method is. Then the abductive argument acquires the additional strength of an argument from analogy.
| |
| − | | |
| − | The first part of the argument is the abduction of a case:
| |
| − | | |
| − | I observe a set of facts:
| |
| − | | |
| − | "Scientific method is P1, P2, P3." (C => P)
| |
| − | | |
| − | I recall a set of rules:
| |
| − | | |
| − | "Bona fide inquiry is P1, P2, P3." (B => P)
| |
| − | | |
| − | I abduce the case:
| |
| − | | |
| − | "Scientific method is bona fide inquiry." (C => B)
| |
| − | | |
| − | The second part of the argument is the induction of a rule:
| |
| − | | |
| − | I notice a set of cases:
| |
| − | | |
| − | "S1, S2, S3 exemplify bona fide inquiry." (S => B)
| |
| − | | |
| − | I observe a set of facts:
| |
| − | | |
| − | "S1, S2, S3 exemplify good method." (S => A)
| |
| − | | |
| − | I induce the rule:
| |
| − | | |
| − | "Bona fide inquiry is good method." (B => A)
| |
| − | | |
| − | The third part of the argument is the deduction of a fact:
| |
| − | | |
| − | I recall the case:
| |
| − | | |
| − | "Scientific method is bona fide inquiry." (C => B)
| |
| − | | |
| − | I recall the rule:
| |
| − | | |
| − | "Bona fide inquiry is good method." (B => A)
| |
| − | | |
| − | I deduce the fact:
| |
| − | | |
| − | "Scientfic method is good method." (C => A)
| |
| − | | |
| − | Now, logically and rationally in the purest sense, the argument by analogy to an example has no more force than the abductive argument, but, empirically and existentially, the example serves, not only as a model of the method to be emulated, but as an object of experimental variation and a source of further experience.
| |
| − | | |
| − | It is time to ask the question: Why do these examples continue to maintain their unrealistic character, their comical and even ridiculous appearance, in spite of all my continuing attempts to reform them in a sensible way? It is not merely their simplicity. A simple example can be telling, if it grasps the essence of the problem, that is, so long as it captures even a single essential feature or highlights even a single critical property of the thing that one seeks to understand. It is more likely due to the circumstance that I am describing agents, methods, and situations all in one piece, that is, without any analysis, articulation, or definition of what exactly constitutes the self, the scientific method, or the world in question. It is not completely useless to consider cases of this type, since many forms of automatic, customary, and unreflective practice are underlain by arguments that are not much better that this. Of course, on reflection, their "commedius" character becomes apparent, and all deny or laugh off the suggestion that they ever think this way, but that is just the way of reflection.
| |
| − | | |
| − | In order to improve the character of the discussion on this score ...
| |
| − | | |
| − | <pre>
| |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| |
| − | | |
| − | IDS. Additional Notes
| |
| − | | |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| |
| − | | |
| − | CFR. Note 78
| |
| − | | |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| |
| − | | |
| − | MW = Matthew West:
| |
| − | | |
| − | MW: Do you have a Cactus Manual all in one place please?
| |
| − | | |
| − | the documentation for my 'theme one' program
| |
| − | that I wrote up for my quant psy master's
| |
| − | contains the last thing like an official
| |
| − | manual that I wrote, also an expository
| |
| − | introduction to the cactus language and
| |
| − | its application to prop calc examples.
| |
| − | may still have an ancient ascii version,
| |
| − | or else the medieval 'word' doc, or i can
| |
| − | send the mac belle version by snail express
| |
| − | if you can vouchsafe me your postal address.
| |
| − | | |
| − | in the mean time, i append a few of the expositions that
| |
| − | i have outlined here/elsewhere over the last year on-line.
| |
| − | | |
| − | pre-scanning this whole mess'o'messages for you,
| |
| − | I find one that looks to me shortest & sweetest:
| |
| − | | |
| − | http://suo.ieee.org/email/msg05694.html
| |
| − | | |
| − | since this particular synopsis is mercifully short, i will copy it out here
| |
| − | and use it to explain surcatenation, along with a few other thing that i am
| |
| − | guessing might be puzzling at first sight about what in hey's going on here.
| |
| − | | |
| − | o~~~~~~~~~o~~~~~~~~~o~ARCHIVE~o~~~~~~~~~o~~~~~~~~~o
| |
| − | | |
| − | Reflective Extension of Logical Graphs (Ref Log)
| |
| − | | |
| − | Here is a formal introduction to the RefLog Syntax.
| |
| − | | |
| − | Formally speaking, we have the following set-up:
| |
| − | | |
| − | Set out the "alphabet of punctuation marks" $M$ = {" ", ",", "(", ")"}.
| |
| − | The elements of $M$ are vocalized as "blank, "comma", "links", "right".
| |
| − | | |
| − | 1. There is a parametric family of formal languages of character strings
| |
| − | such that, for each set $X$ of variable names $X$ = {"x_1", ..., "x_k"},
| |
| − | there is a formal language L($X$) over the alphabet A($X$) = $M$ |_| $X$.
| |
| − | The grammar can be given in gory detail, but most folks know it already.
| |
| − | | |
| − | | Examples. If $X$ = {"x", "y"}, then these are typical strings in L($X$):
| |
| − | |
| |
| − | | " ", "( )", "x", "y", "(x)", "(y)", "x y", "(x y)", "(x, y)", "((x)(y))", "((x, y))", ...
| |
| − | | |
| − | 2. There is a parallel family of formal languages of graphical structures,
| |
| − | generically known as "painted and rooted cacti" (PARC's), that exist in
| |
| − | a one-to-one correspondence with these string expressions, being more or
| |
| − | less roughly, at a suitable level of abstraction, their parse graphs as
| |
| − | data structures in the computer. The PARC's for the above formulas are:
| |
| − | | |
| − | | Examples.
| |
| − | | x y x y
| |
| − | | o o o---o
| |
| − | | x y x y x y \ / \ /
| |
| − | | o o o o o---o o o
| |
| − | | | x y | | x y | \ / | |
| |
| − | | @ @ @ @ @ @ @ @ @ @ @ ...
| |
| − | |
| |
| − | | " ", "( )", "x", "y", "(x)", "(y)", "x y", "(x y)", "(x, y)", "((x)(y))", "((x, y))", ...
| |
| − | | |
| − | Together, these two families of formal languages constitute a system
| |
| − | that is called the "reflective extension of logical graphs" (Ref Log).
| |
| − | | |
| − | Strictly speaking, Ref Log is an abstract or "uninterpreted" formal system,
| |
| − | but its expressions enjoy, as a rule, two dual interpretations that assign
| |
| − | them the meanings of propositions or sentences in "zeroth order logic" (ZOL),
| |
| − | to wit, what Peirce called the "alpha level" of his systems of logical graphs.
| |
| − | | |
| − | For example, the string expression "(x (y))" parses into the following graph:
| |
| − | | |
| − | | x y
| |
| − | | o---o
| |
| − | | |
| |
| − | | @
| |
| − | | |
| − | You can "deparse" the string off the graph by traversing
| |
| − | it like so, reading off the marks and varnames as you go.
| |
| − | | |
| − | | o---x->(--y---o
| |
| − | | ^ |
| |
| − | | | x ( y |
| |
| − | | | o-----o v
| |
| − | | | | ) )
| |
| − | | ( (|) )
| |
| − | | ^ | |
| |
| − | | | @ v
| |
| − | | |
| − | In the "existential" interpretation of RefLog,
| |
| − | in which I do my own thinking most of the time,
| |
| − | concatenation of expressions has the meaning of
| |
| − | logical conjunction, while "(x)" has the meaning
| |
| − | of "not x", and so the above string and graph have
| |
| − | a meaning of "x => y", "x implies y", "if x then y",
| |
| − | "not x without y", or anything else that's equivalent.
| |
| − | The blank expression is assigned the value of "true".
| |
| − | Hence, the expression "()" takes the value of "false".
| |
| − | The bracket expression "(x_1, x_2, ..., x_k)" is given
| |
| − | the meaning "Exactly one of the x_j is false, j=1..k".
| |
| − | Therefore, "((x_1),(x_2), ...,(x_k))" partitions the
| |
| − | universe of discourse, saying "Just one x_j is true".
| |
| − | | |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| |
| − | | |
| − | CFR. Note 83
| |
| − | | |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| |
| − | | |
| − | | Tantum ergo sacramentum
| |
| − | | veneremur cernui,
| |
| − | | et antiquum documentum
| |
| − | | novo cedat ritui,
| |
| − | | praestet fides supplementum
| |
| − | | sensuum defectui.
| |
| − | |
| |
| − | | So great therefore a sacrifice
| |
| − | | let us humbly adore
| |
| − | | and let the old law yield
| |
| − | | to the new rite;
| |
| − | | let faith supplement
| |
| − | | the shortcoming of the senses.
| |
| − | |
| |
| − | | Lyric by Thomas Aquinas,
| |
| − | | Music by Amadeus Mozart, KV 142 & 197.
| |
| − | | |
| − | The increasing ossification of asciification
| |
| − | is heaping up way too many old bones to bear.
| |
| − | So I am going to shift my anklage a bit, and
| |
| − | try out a new set of conventions for a while,
| |
| − | to see if I can lighten the overloading obit.
| |
| − | | |
| − | Let us try to reserve script and singly-underscored fake-fonts or formats
| |
| − | for the names of sets, as in the notations !O!, !S!, !I! that I will now
| |
| − | set aside and use from now on for the Object, Sign, Interpretant domains,
| |
| − | respectively, of an arbitrary sign relation !L! c !O! x !S! x !I!.
| |
| − | | |
| − | Among other benefits, this will serve to liberate the plain faced characters
| |
| − | for employment as the non-terminal symbols of our formal grammars, rendering
| |
| − | our formal grammatical productions far less $Capitalistic$, !Exclamatory!,
| |
| − | and overbearingly prescriptive than they be otherwise hell-bent to become.
| |
| − | | |
| − | So let me try out this new rite to see how it works out,
| |
| − | And I will not pause to rewrite the old law in its font,
| |
| − | But advise you solely of its transformed instantiations,
| |
| − | And fix my faith on imagination to sense the supplement.
| |
| − | | |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| |
| − | | |
| − | CFR. Note 92
| |
| − | | |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| |
| − | | |
| − | I need to try and say some things at his point about
| |
| − | why formal language theory is interesting and useful,
| |
| − | but all I have at the moment are random remembrances
| |
| − | and reflections that enter my mind from time to time.
| |
| − | | |
| − | In many ways, the study of formal languages and grammars
| |
| − | is a paradigm, more, a paragon, of the situation that we
| |
| − | face whenever we inquire into a complex reality, that is,
| |
| − | all of the ever-renewed sources of puzzling phenomena or
| |
| − | pressing problems that we call a world.
| |
| − | | |
| − | The archtypical place of formal language theory is well
| |
| − | understood in many quarters, and has been from the very
| |
| − | outset of its constellation as an independent viewpoint.
| |
| − | | |
| − | In this paradigmatic (analogical or exemplary) way of
| |
| − | understanding it, a formal language is the "data" and
| |
| − | a formal grammar is the "theory", and the question is,
| |
| − | as always, whether a theory accounts for and explains
| |
| − | the data, a "fitting" relationship that may be viewed
| |
| − | in many ways, for one, the way that a theory might be
| |
| − | said to "generate" the data, or perhaps better stated,
| |
| − | not just to "cook" in a precociously specious fashion
| |
| − | but more like to "regenerate" the form after the fact.
| |
| − | | |
| − | That's all that I can manage to express at the moment,
| |
| − | but maybe it will supply a grub-stake of motivational
| |
| − | victuals for the grueling labors of exploration ahead.
| |
| − | | |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| |
| − | | |
| − | IDS. Outline
| |
| − | | |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| |
| − | | |
| − | Inquiry Driven Systems
| |
| − | | |
| − | 1. Research Proposal
| |
| − | | |
| − | 1.1. Outline of the Project: Inquiry Into Inquiry
| |
| − | | |
| − | 1.1.1. Problem
| |
| − | | |
| − | 1.1.2. Method
| |
| − | | |
| − | 1.1.2.1. The Paradigmatic & Process-Analytic Phase
| |
| − | | |
| − | 1.1.2.2. The Paraphrastic & Faculty-Synthetic Phase
| |
| − | | |
| − | 1.1.2.3. Reprise of Methods
| |
| − | | |
| − | 1.1.3. Criterion
| |
| − | | |
| − | 1.1.4. Application
| |
| − | | |
| − | 1.2. Onus of the Project: No Way But Inquiry
| |
| − | | |
| − | 1.2.1. A Modulating Prelude
| |
| − | | |
| − | 1.2.2. A Fugitive Canon
| |
| − | | |
| − | | |
| − | | |
| − | 1.3. Option of the Project: A Way Up To Inquiry
| |
| − | | |
| − | 1.3.1. Initial Analysis of Inquiry Allegro Aperto
| |
| − | | |
| − | 1.3.2. Discussion of Discussion
| |
| − | | |
| − | 1.3.3. Discussion of Formalization: General Topics
| |
| − | | |
| − | 1.3.3.1. A Formal Charge
| |
| − | | |
| − | 1.3.3.2. A Formalization of Formalization?
| |
| − | | |
| − | 1.3.3.3. A Formalization of Discussion?
| |
| − | | |
| − | 1.3.3.4. A Concept of Formalization
| |
| − | | |
| − | 1.3.3.5. A Formal Approach
| |
| − | | |
| − | 1.3.3.6. A Formal Development
| |
| − | | |
| − | 1.3.3.7. A Formal Perasion
| |
| − | | |
| − | 1.3.4. Discussion of Formalization: Concrete Examples
| |
| − | | |
| − | 1.3.4.1. Formal Models: A Sketch
| |
| − | | |
| − | 1.3.4.2. Sign Relations: A Primer
| |
| − | | |
| − | 1.3.4.3. Semiotic Equivalence Relations
| |
| − | | |
| − | 1.3.4.4. Graphical Representations
| |
| − | | |
| − | 1.3.4.5. Taking Stock
| |
| − | | |
| − | 1.3.4.6. The "Meta" Question
| |
| − | | |
| − | 1.3.4.7. Iconic Signs
| |
| − | | |
| − | 1.3.4.8. The Conflict of Interpretations
| |
| − | | |
| − | 1.3.4.9. Indexical Signs
| |
| − | | |
| − | 1.3.4.10. Sundry Problems
| |
| − | | |
| − | 1.3.4.11. Review & Prospect
| |
| − | | |
| − | 1.3.4.12. Objective Plans & Levels
| |
| − | | |
| − | 1.3.4.13. Formalization of OF: Objective Levels
| |
| − | | |
| − | 1.3.4.14. Application of OF: Generic Level
| |
| − | | |
| − | 1.3.4.15. Application of OF: Motive Level
| |
| − | | |
| − | 1.3.4.16. The Integration of Frameworks
| |
| − | | |
| − | 1.3.4.17. Recapitulation: A Brush with Symbols
| |
| − | | |
| − | 1.3.4.18. C'est Moi
| |
| − | | |
| − | 1.3.4.19. Entr'acte
| |
| − | | |
| − | 1.3.5. Discussion of Formalization: Specific Objects
| |
| − | | |
| − | 1.3.5.1. The Will to Form
| |
| − | | |
| − | 1.3.5.2. The Forms of Reasoning
| |
| − | | |
| − | 1.3.5.3. A Fork in the Road
| |
| − | | |
| − | 1.3.5.4. A Forged Bond
| |
| − | | |
| − | 1.3.5.5. A Formal Account
| |
| − | | |
| − | 1.3.5.6. Analogs, Icons, Models, Surrogates
| |
| − | | |
| − | 1.3.5.7. Steps & Tests of Formalization
| |
| − | | |
| − | 1.3.5.8. Puck, the Ref
| |
| − | | |
| − | 1.3.5.9. Partial Formalizations
| |
| − | | |
| − | 1.3.5.10. A Formal Utility
| |
| − | | |
| − | 1.3.5.11. A Formal Aesthetic
| |
| − | | |
| − | 1.3.5.12. A Formal Apology
| |
| − | | |
| − | 1.3.5.13. A Formal Suspicion
| |
| − | | |
| − | 1.3.5.14. The Double Aspect of Concepts
| |
| − | | |
| − | 1.3.5.15. A Formal Permission
| |
| − | | |
| − | 1.3.5.16. A Formal Invention
| |
| − | | |
| − | 1.3.6. Recursion in Perpetuity
| |
| − | | |
| − | 1.3.7. Processus, Regressus, Progressus
| |
| − | | |
| − | 1.3.8. Rondeau Tempo di Menuetto
| |
| − | | |
| − | 1.3.9. Reconnaissance
| |
| − | | |
| − | 1.3.9.1. The Informal Context
| |
| − | | |
| − | 1.3.9.2. The Epitext
| |
| − | | |
| − | 1.3.9.3. The Formative Tension
| |
| − | | |
| − | 1.3.10. Recurring Themes
| |
| − | | |
| − | 1.3.10.1. Preliminary Notions
| |
| − | | |
| − | 1.3.10.2. Intermediary Notions
| |
| − | | |
| − | 1.3.10.3. Propositions & Sentences
| |
| − | | |
| − | 1.3.10.4. Empirical Types & Rational Types
| |
| − | | |
| − | 1.3.10.5. Articulate Sentences
| |
| − | | |
| − | 1.3.10.6. Stretching Principles
| |
| − | | |
| − | 1.3.10.7. Stretching Operations
| |
| − | | |
| − | 1.3.10.8. The Cactus Patch
| |
| − | | |
| − | 1.3.10.9. The Cactus Language: Syntax
| |
| − | | |
| − | 1.3.10.10. The Cactus Language: Stylistics
| |
| − | | |
| − | 1.3.10.11. The Cactus Language: Mechanics
| |
| − | | |
| − | 1.3.10.12. The Cactus Language: Semantics
| |
| − | | |
| − | 1.3.10.13. Stretching Exercises
| |
| − | | |
| − | 1.3.10.14. Syntactic Transformations
| |
| − | | |
| − | 1.3.10.15. Derived Equivalence Relations
| |
| − | | |
| − | 1.3.10.16. Digression on Derived Relations
| |
| − | | |
| − | | |
| − | | |
| − | 1.4. Outlook of the Project: All Ways Lead to Inquiry
| |
| − | | |
| − | 1.4.1. The Matrix of Inquiry
| |
| − | | |
| − | 1.4.1.1. Inquiry as Conduct
| |
| − | | |
| − | 1.4.1.2. Types of Conduct
| |
| − | | |
| − | 1.4.1.3. Perils of Inquiry
| |
| − | | |
| − | 1.4.1.4. Forms of Relations
| |
| − | | |
| − | 1.4.1.5. Models of Inquiry
| |
| − | | |
| − | 1.4.2. The Moment of Inquiry
| |
| − | | |
| − | 1.4.3. The Modes of Inquiry
| |
| − | | |
| − | 1.4.3.1. Deductive Reasoning
| |
| − | | |
| − | 1.4.3.2. Inductive Reasoning
| |
| − | | |
| − | 1.4.3.3. Abductive Reasoning
| |
| − | | |
| − | 1.4.3.4. Analogical Reasoning
| |
| − | | |
| − | | |
| − | | |
| − | 1.5.Obstacles to the Project: In the Way of Inquiry
| |
| − | | |
| − | 1.5.1. The Initial Unpleasantness
| |
| − | | |
| − | 1.5.2. The Justification Trap
| |
| − | | |
| − | 1.5.3. A Formal Apology
| |
| − | | |
| − | 1.5.3.1. Category Double-Takes
| |
| − | | |
| − | 1.5.3.2. Conceptual Extensions
| |
| − | | |
| − | 1.5.3.3. Explosional Recombinations
| |
| − | | |
| − | 1.5.3.4. Interpretive Frameworks
| |
| − | | |
| − | 1.5.4. A Material Exigency
| |
| − | | |
| − | 1.5.5. A Reconciliation of Accounts
| |
| − | | |
| − | 1.5.6. Objections to Reflexive Inquiry
| |
| − | | |
| − | 1.5.7. Empirical Considerations
| |
| − | | |
| − | 1.5.8. Computational Considerations
| |
| − | | |
| − | 1.5.8.1. A Form of Recursion
| |
| − | | |
| − | 1.5.8.2. A Power of Abstraction
| |
| − | | |
| − | | |
| − | | |
| − | 1.6. Orientation of the Project: A Way Into Inquiry
| |
| − | | |
| − | 1.6.1. Initial Description of Inquiry
| |
| − | | |
| − | 1.6.2. Terms of Analysis
| |
| − | | |
| − | 1.6.2.1. Digression on Signs
| |
| − | | |
| − | 1.6.2.2. Empirical Status of ID
| |
| − | | |
| − | 1.6.3. Expansion of Terms
| |
| − | | |
| − | 1.6.3.1. Agency
| |
| − | | |
| − | 1.6.3.2. Abstraction
| |
| − | | |
| − | 1.6.3.3. Analogy
| |
| − | | |
| − | 1.6.3.4. Accuracy
| |
| − | | |
| − | 1.6.3.5. Authenticity
| |
| − | | |
| − | 1.6.4. Anchoring Terms in Phenomena
| |
| − | | |
| − | 1.6.4.1. A Mistaken ID
| |
| − | | |
| − | 1.6.4.2. Phenomenology of Doubt
| |
| − | | |
| − | 1.6.4.3. Modalities of Knowledge
| |
| − | | |
| − | 1.6.5. Sets, Systems, & Substantive Agents
| |
| − | | |
| − | 1.6.6. Interpretive Systems
| |
| − | | |
| − | 1.6.6.1. Syntactic Systems
| |
| − | | |
| − | 1.6.6.2. Semantic Systems
| |
| − | | |
| − | 1.6.6.3. Pragmatic Systems
| |
| − | | |
| − | 1.6.7. Inquiry Driven Systems
| |
| − | | |
| − | 1.6.7.1. A Definition of Inquiry
| |
| − | | |
| − | 1.6.7.2. The Faculty of Inquiry
| |
| − | | |
| − | 1.6.7.3. A Definition of Determination
| |
| − | | |
| − | 1.6.7.4. A Definition of Definition
| |
| − | | |
| − | | |
| − | | |
| − | 1.7. Organization of the Project: A Way Through Inquiry
| |
| − | | |
| − | 1.7.1. The Problem: Inquiry Found as an Object of Study
| |
| − | | |
| − | 1.7.2. The Method: Inquiry Found as a Means of Study
| |
| − | | |
| − | 1.7.2.1. Conditions for the Possibility of Inquiry into Inquiry
| |
| − | | |
| − | 1.7.2.2. Conditions for the Success of Inquiry into Inquiry
| |
| − | | |
| − | 1.7.3. The Criterion: Inquiry in Search of a Sensible End
| |
| − | | |
| − | 1.7.3.1. The Irritation of Doubt, and The Scratch Test.
| |
| − | | |
| − | 1.7.3.2. Enabling Provision 1: The Scenes & Context of Inquiry.
| |
| − | | |
| − | 1.7.3.3. Enabling Provision 2: The Stages & Content of Inquiry.
| |
| − | | |
| − | 1.8. Objectives of the Project: Inquiry All the Way
| |
| − | | |
| − | 1.8.1. Substantial Objective
| |
| − | | |
| − | 1.8.1.1. Objective 1a: The Propositions as Types Analogy.
| |
| − | | |
| − | 1.8.1.2. Objective 1b: The Styles of Proof Development.
| |
| − | | |
| − | 1.8.1.3. Objective 1c: The Analysis of Interpreters, or A Problem with Authority.
| |
| − | | |
| − | 1.8.2. Instrumental Objective
| |
| − | | |
| − | 1.8.3. Coordination of Objectives
| |
| − | | |
| − | 1.8.4. Recapitulation: Da Capo, Al Segno
| |
| − | | |
| − | | |
| − | | |
| − | 2. Discussion of Inquiry
| |
| − | | |
| − | 2.1. Approaches to Inquiry
| |
| − | | |
| − | 2.1.1. The Classical Framework: Syllogistic Approaches
| |
| − | | |
| − | 2.1.2. The Pragmatic Framework: Sign-Theoretic Approaches
| |
| − | | |
| − | 2.1.3. The Dynamical Framework: System-Theoretic Approaches
| |
| − | | |
| − | 2.1.3.1. Inquiry & Computation
| |
| − | | |
| − | 2.1.3.2. Inquiry Driven Systems
| |
| − | | |
| − | 2.2. The Context of Inquiry
| |
| − | | |
| − | 2.2.1. The Field of Observation
| |
| − | | |
| − | 2.2.2. The Problem of Reflection
| |
| − | | |
| − | 2.2.3. The Problem of Reconstruction
| |
| − | | |
| − | 2.2.4. The Trivializing of Integration
| |
| − | | |
| − | 2.2.5. Tensions in the Field of Observation
| |
| − | | |
| − | 2.2.6. Problems of Representation & Communication
| |
| − | | |
| − | | |
| − | | |
| − | 2.3. The Conduct of Inquiry
| |
| − | | |
| − | 2.3.1. Introduction
| |
| − | | |
| − | 2.3.2. The Types of Reasoning
| |
| − | | |
| − | 2.3.2.1. Deduction
| |
| − | | |
| − | 2.3.2.2. Induction
| |
| − | | |
| − | 2.3.2.3. Abduction
| |
| − | | |
| − | 2.3.3. Hybrid Types of Inference
| |
| − | | |
| − | 2.3.3.1. Analogy
| |
| − | | |
| − | 2.3.3.2. Inquiry
| |
| − | | |
| − | 2.3.4. Details of Induction
| |
| − | | |
| − | 2.3.4.1. Learning
| |
| − | | |
| − | 2.3.4.2. Transfer
| |
| − | | |
| − | 2.3.4.3. Testing
| |
| − | | |
| − | 2.3.5. The Stages of Inquiry
| |
| − | | |
| − | | |
| − | | |
| − | 3. The Medium & Its Message
| |
| − | | |
| − | 3.1. Reflective Expression
| |
| − | | |
| − | 3.1.1. Casual Reflection
| |
| − | | |
| − | 3.1.1.1. Ostensibly Recursive Texts
| |
| − | | |
| − | 3.1.1.2. Analogical Recursion
| |
| − | | |
| − | 3.1.2. Conscious Reflection
| |
| − | | |
| − | 3.1.2.1. The Signal Moment
| |
| − | | |
| − | 3.1.2.2. The Symbolic Object
| |
| − | | |
| − | 3.1.2.3. The Endeavor to Communicate
| |
| − | | |
| − | 3.1.2.4. The Medium of Communication
| |
| − | | |
| − | 3.1.2.5. The Ark of Types: The Order of Things to Come.
| |
| − | | |
| − | 3.1.2.6. The Epitext
| |
| − | | |
| − | 3.1.2.7. The Context of Interpretation
| |
| − | | |
| − | 3.1.2.8. The Formative Tension
| |
| − | | |
| − | 3.1.2.9. The Vehicle of Communication: Reflection on the Scene, Reflection on the Self.
| |
| − | | |
| − | | |
| − | 3.1.2.10. (7)
| |
| − | | |
| − | 3.1.2.11. (6)
| |
| − | | |
| − | 3.1.2.12. Recursions: Possible, Actual, Necessary
| |
| − | | |
| − | 3.1.2.13. Ostensibly Recursive Texts
| |
| − | | |
| − | 3.1.2.14. (3)
| |
| − | | |
| − | 3.1.2.15. The Freedom of Interpretation
| |
| − | | |
| − | 3.1.2.16. The Eternal Return
| |
| − | | |
| − | 3.1.2.17. (1)
| |
| − | | |
| − | 3.1.2.18. Information in Formation
| |
| − | | |
| − | 3.1.2.19. Reflectively Indexical Texts
| |
| − | | |
| − | 3.1.2.20. (4)
| |
| − | | |
| − | 3.1.2.21. (5)
| |
| − | | |
| − | 3.1.2.22. (6)
| |
| − | | |
| − | 3.1.2.23. (7)
| |
| − | | |
| − | 3.1.2.24. (8)
| |
| − | | |
| − | 3.1.2.25. The Discursive Universe
| |
| − | | |
| − | 3.1.2.26. (7)
| |
| − | | |
| − | 3.1.2.27. (6)
| |
| − | | |
| − | 3.1.2.28. (5)
| |
| − | | |
| − | 3.1.2.29. (4)
| |
| − | | |
| − | 3.1.2.30. (3)
| |
| − | | |
| − | 3.1.2.31. (2)
| |
| − | | |
| − | 3.1.2.32. (1)
| |
| − | | |
| − | | |
| − | | |
| − | 3.2. Reflective Inquiry
| |
| − | | |
| − | 3.2.1. Integrity & Unity of Inquiry
| |
| − | | |
| − | 3.2.2. Apparitions & Allegations
| |
| − | | |
| − | 3.2.3. A Reflective Heuristic
| |
| − | | |
| − | 3.2.4. Either/Or: A Sense of Absence
| |
| − | | |
| − | 3.2.5. Apparent, Occasional, & Practical Necessity
| |
| − | | |
| − | 3.2.6. Approaches, Aspects, Exposures, Fronts
| |
| − | | |
| − | 3.2.7. Synthetic A Priori Truths
| |
| − | | |
| − | 3.2.8. Priorisms of Normative Sciences
| |
| − | | |
| − | 3.2.9. Principle of Rational Action
| |
| − | | |
| − | 3.2.10. The Pragmatic Cosmos
| |
| − | | |
| − | 3.2.11. Reflective Interpretive Frameworks
| |
| − | | |
| − | 3.2.11.1. Principals Versus Principles
| |
| − | | |
| − | 3.2.11.2. The Initial Description of Inquiry
| |
| − | | |
| − | 3.2.11.3. An Early Description of Interpretation
| |
| − | | |
| − | 3.2.11.4. Descriptions of the Mind
| |
| − | | |
| − | 3.2.11.5. Of Signs & the Mind
| |
| − | | |
| − | 3.2.11.6. Questions of Justification
| |
| − | | |
| − | 3.2.11.7. The Experience of Satisfaction
| |
| − | | |
| − | 3.2.11.8. An Organizational Difficulty
| |
| − | | |
| − | 3.2.11.9. Pragmatic Certainties
| |
| − | | |
| − | 3.2.11.10. Problems & Methods
| |
| − | | |
| − | | |
| − | | |
| − | 3.3. Reflection on Reflection
| |
| − | | |
| − | 3.4. Reflective Interpretive Frameworks
| |
| − | | |
| − | 3.4.1. The Phenomenology of Reflection
| |
| − | | |
| − | 3.4.2. A Candid Point of View
| |
| − | | |
| − | 3.4.3. A Projective Point of View
| |
| − | | |
| − | 3.4.4. A Formal Point of View
| |
| − | | |
| − | 3.4.5. Three Styles of Linguistic Usage
| |
| − | | |
| − | 3.4.6. Basic Notions of Group Theory
| |
| − | | |
| − | 3.4.7. Basic Notions of Formal Language Theory
| |
| − | | |
| − | 3.4.8. A Perspective on Computation
| |
| − | | |
| − | 3.4.9. Higher Order Sign Relations: Introduction
| |
| − | | |
| − | 3.4.10. Higher Order Sign Relations: Examples
| |
| − | | |
| − | 3.4.11. Higher Order Sign Relations: Application
| |
| − | | |
| − | 3.4.12. Issue 1: The Status of Signs
| |
| − | | |
| − | 3.4.13. Issue 2: The Status of Sets
| |
| − | | |
| − | 3.4.14. Issue 3: The Status of Variables
| |
| − | | |
| − | 3.4.15. Propositional Calculus
| |
| − | | |
| − | 3.4.16. Recursive Aspects
| |
| − | | |
| − | 3.4.17. Patterns of Self-Reference
| |
| − | | |
| − | 3.4.18. Practical Intuitions
| |
| − | | |
| − | 3.4.19. Examples of Self-Reference
| |
| − | | |
| − | 3.4.20. Three Views of Systems
| |
| − | | |
| − | 3.4.21. Building Bridges Between Representations
| |
| − | | |
| − | 3.4.22. Extensional Representations of Sign Relations
| |
| − | | |
| − | 3.4.23. Intensional Representations of Sign Relations
| |
| − | | |
| − | 3.4.24. Literal Intensional Representations
| |
| − | | |
| − | | |
| − | 3.4.25. Analytic Intensional Representations
| |
| − | | |
| − | 3.4.26. Differential Logic & Directed Graphs
| |
| − | | |
| − | 3.4.27. Differential Logic & Group Operations
| |
| − | | |
| − | 3.4.28. The Bridge: From Obstruction to Opportunity
| |
| − | | |
| − | 3.4.29. Projects of Representation
| |
| − | | |
| − | 3.4.30. Connected, Integrated, Reflective Symbols
| |
| − | | |
| − | 3.4.31. Generic Orders of Relations
| |
| − | | |
| − | 3.4.32. Partiality: Selective Operations
| |
| − | | |
| − | 3.4.33. Sign Relational Complexes
| |
| − | | |
| − | 3.4.34. Set-Theoretic Constructions
| |
| − | | |
| − | 3.4.35. Reducibility of Sign Relations
| |
| − | | |
| − | 3.4.36. Irreducibly Triadic Relations
| |
| − | | |
| − | 3.4.37. Propositional Types
| |
| − | | |
| − | 3.4.38. Considering the Source
| |
| − | | |
| − | 3.4.39. Prospective Indices: Pointers to Future Work
| |
| − | | |
| − | 3.4.40. Dynamic & Evaluative Frameworks
| |
| − | | |
| − | 3.4.41. Elective & Motive Forces
| |
| − | | |
| − | 3.4.42. Sign Processes: A Start
| |
| − | | |
| − | 3.4.43. Reflective Extensions
| |
| − | | |
| − | 3.4.44. Reflections on Closure
| |
| − | | |
| − | 3.4.45. Intelligence => Critical Reflection
| |
| − | | |
| − | 3.4.46. Looking Ahead
| |
| − | | |
| − | 3.4.47. Mutually Intelligible Codes
| |
| − | | |
| − | 3.4.48. Discourse Analysis: Ways & Means
| |
| − | | |
| − | 3.4.49. Combinations of Sign Relations
| |
| − | | |
| − | 3.4.50. Revisiting the Source
| |
| − | | |
| − | | |
| − | | |
| − | 3.5. Divertimento: Eternity in Love with the Creatures of Time
| |
| − | | |
| − | 3.5.1. Reflections on the Presentation of Examples
| |
| − | | |
| − | 3.5.2. Searching for Parameters
| |
| − | | |
| − | 3.5.3. Defect Analysis
| |
| − | | |
| − | 3.5.4. The Pragmatic Critique
| |
| − | | |
| − | 3.5.5. Pragmatic Operating Notions
| |
| − | | |
| − | 3.5.6. Defects of Presentation
| |
| − | | |
| − | 3.5.7. Dues to Process
| |
| − | | |
| − | 3.5.8. Duties to Purpose
| |
| − | | |
| − | | |
| − | | |
| − | 3.6. Computational Design Philosophy
| |
| − | | |
| − | 3.6.1. Intentional Objects & Attitudes
| |
| − | | |
| − | 3.6.2. Imperfect Design & Persistent Error
| |
| − | | |
| − | 3.6.3. Propositional Reasoning About Relations
| |
| − | | |
| − | 3.6.4. Dynamic & Evaluative Frameworks
| |
| − | | |
| − | 3.6.5. Discussion of Examples
| |
| − | | |
| − | 3.6.6. Information & Inquiry
| |
| − | | |
| − | | |
| − | | |
| − | 4. Overview of the Domain: Interpretive Inquiry
| |
| − | | |
| − | 4.1. Interpretive Bearings: Conceptual & Descriptive Frameworks
| |
| − | | |
| − | 4.1.1. Catwalks: Flexible Frameworks & Peripatetic Categories
| |
| − | | |
| − | 4.1.1.1. Eponymous Ancestors: The Precursors of Abstraction?
| |
| − | | |
| − | 4.1.1.2 Reticles: Interpretive Flexibility as a Design Issue
| |
| − | | |
| − | 4.1.2. Heuristic Inclinations & Regulative Principles
| |
| − | | |
| − | 4.2. Features of Inquiry Driven Systems
| |
| − | | |
| − | 4.2.1. The Pragmatic Theory of Signs
| |
| − | | |
| − | 4.2.1.1. Sign Relations
| |
| − | | |
| − | 4.2.1.2. Types of Signs
| |
| − | | |
| − | 4.2.2. The Pragmatic Theory of Inquiry
| |
| − | | |
| − | 4.2.2.1. Abduction
| |
| − | | |
| − | 4.2.2.2. Deduction
| |
| − | | |
| − | 4.2.2.3. Induction
| |
| − | | |
| − | 4.3. Examples of Inquiry Driven Systems
| |
| − | | |
| − | 4.3.1. "Index": A Program for Learning Formal Languages
| |
| − | | |
| − | 4.3.2. "Study": A Program for Reasoning with Propositions
| |
| − | | |
| − | 5. Discussion & Development of Objectives
| |
| − | | |
| − | 5.1. Objective 1a: Propositions as Types
| |
| − | | |
| − | 5.2. Objective 1b: Proof Styles & Developments
| |
| − | | |
| − | 5.3. Objective 1c: Interpretation & Authority
| |
| − | | |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
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| − | | |
| − | IDS. References
| |
| − | | |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| |
| − | | |
| − | Aristotle, "On The Soul", in 'Aristotle, Volume 8',
| |
| − | W.S. Hett (trans.), Heinemann, London, UK, 1936, 1986.
| |
| − | | |
| − | Charniak, E. & McDermott, D.V.,
| |
| − | 'Introduction to Artificial Intelligence',
| |
| − | Addison-Wesley, Reading, MA, 1985.
| |
| − | | |
| − | 2. Charniak, E., Riesbeck, C.K., & McDermott, D.V. Artificial Intelligence Programming. Lawrence Erlbaum Associates, Hillsdale, NJ, 1980.
| |
| − | | |
| − | 3. Holland, J.H., Holyoak, K.J., Nisbett, R.E., & Thagard, P.R. Induction: Processes of Inference, Learning, and Discovery. MIT Press, Cambridge, MA, 1986.
| |
| − | | |
| − | 4. O'Rorke, P. Review of AAAI 1990 Spring Symposium on Automated Abduction. SIGART Bulletin, Vol. 1, No. 3. ACM Press, October 1990, p. 12-17.
| |
| − | | |
| − | 5. Pearl, J. Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Revised 2nd printing. Morgan Kaufmann, San Mateo, CA, 1991.
| |
| − | | |
| − | 6. Peng, Y. & Reggia, J.A. Abductive Inference Models for Diagnostic Problem-Solving. Springer-Verlag, New York, NY, 1990.
| |
| − | | |
| − | 7. Sowa, J.F. Conceptual Structures: Information Processing in Mind and Machine. Addison-Wesley, Reading, MA, 1984.
| |
| − | | |
| − | 8. Sowa, J.F. (ed.) Principles of Semantic Networks: Explorations in the Representation of Knowledge. Morgan Kaufmann, San Mateo, CA, 1991.
| |
| − | | |
| − | Dewey, J. (1991). How We Think. Buffalo, NY: Prometheus Books. Originally published 1910.
| |
| − | | |
| − | Shakespeare, Wm. (1988). William Shakespeare: The Complete Works. Compact Edition. S. Wells & G. Taylor (eds.). Oxford University Press, Oxford, UK.
| |
| − | | |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| |
| − | | |
| − | IDS. Email Format
| |
| − | | |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
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| − | | |
| − | | Document History
| |
| − | |
| |
| − | | Subject: Inquiry Driven Systems: An Inquiry Into Inquiry
| |
| − | | Contact: Jon Awbrey <jawbrey@oakland.edu>
| |
| − | | Version: Draft 10.00
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| − | | Created: 23 Jun 1996
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| − | | Revised: 02 Mar 2003
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| − | | Advisor: M.A. Zohdy
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| − | | Setting: Oakland University, Rochester, Michigan, USA
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| − | | |
| − | http://members.door.net/arisbe/menu/library/aboutcsp/awbrey/inquiry.htm
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| − | | |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
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| − | | |
| − | IDS. Incitatory Note 1
| |
| − | | |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
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| − | | |
| − | | Each ground-principle must be proved entirely
| |
| − | | by that same kind of inference which it supports.
| |
| − | |
| |
| − | | But we cannot arrive at any conclusion
| |
| − | | by mere deduction except about symbols.
| |
| − | |
| |
| − | | We cannot arrive at any conclusion
| |
| − | | by mere induction except about things.
| |
| − | |
| |
| − | | And we cannot arrive at any conclusion
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| − | | by mere hypothesis except about forms.
| |
| − | |
| |
| − | | C.S. Peirce, CE 1, page 290.
| |
| − | |
| |
| − | | Charles Sanders Peirce, "On the Logic of Science",
| |
| − | | Harvard University Lectures (1865), pages 161-302 in:
| |
| − | |'Writings of Charles S. Peirce: A Chronological Edition',
| |
| − | |'Volume 1, 1857-1866', Peirce Edition Project,
| |
| − | | Indiana University Press, Bloomington, IN, 1982.
| |
| − | | |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
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| − | | |
| − | IDS. Incitatory Note 2
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| − | | |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
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| − | | |
| − | | |
| − | | |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
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| − | | |
| − | IDS. Meditative Note 1
| |
| − | | |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| |
| − | | |
| − | I would like to start from a "common sense practical" (CSP) point of view,
| |
| − | and, indeed, never to lose sight of what appears evident from that station,
| |
| − | no matter how many levels of abstract remove and abstruse mention it might
| |
| − | become necessary to interpose along the way.
| |
| − | | |
| − | So let's examine this initial caltrop
| |
| − | "descriptive/normative/prescriptive"
| |
| − | from the CSP POV, if you will.
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| − | | |
| − | Reading "Descriptive" to mean "What it is",
| |
| − | while "Normative" means "What it oughta be",
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| − | and "Prescriptive" says "Make it so, or else",
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| − | I will have very little to say about the last,
| |
| − | and only be able to focus on the distinctions
| |
| − | that may exist among the first two dimensions.
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| − | | |
| − | From the beginning, from this point of view, difficult words,
| |
| − | like "inquiry", "logic", "truth", and so on, must be taken
| |
| − | as initially indexical, inchoately succeeding at little
| |
| − | more than pointing to a realm of experience that may
| |
| − | or may not be common to the e-mitter and re-mitter.
| |
| − | | |
| − | I suspect that this stanza is likely to be controversial,
| |
| − | so I'll pause at this point for the countrapunctal verse.
| |
| − | | |
| − | Or for a rest ...
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| − | | |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
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| − | | |
| − | IDS. Meditative Note 2
| |
| − | | |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| |
| − | | |
| − | So I may begin with an object and a sign in a tenuous relation,
| |
| − | with the subject matter indexed under the topic name "inquiry",
| |
| − | where the sign originates from a "just noticeable differential"
| |
| − | of information about the object, and not a single "figit" more.
| |
| − | Few would call this a foundation -- I only call it a beginning.
| |
| − | | |
| − | Yet another of many ...
| |
| − | | |
| − | But it does provide us with a clue to a signficant difference,
| |
| − | however much this difference is bound by this origin to raise
| |
| − | itself from egg, germ, seed, spore, or whatever it is that is
| |
| − | infinitesimal in its initial condition. In this disjointness
| |
| − | of an archetype where what begins, what leads, and what rules
| |
| − | are not so trivially identical to one another, one encounters
| |
| − | the brand of beginning that begins in the middle of the story,
| |
| − | and has no need of any other foundation but the medium itself.
| |
| − | | |
| − | ["sign-ficant" [stet]]
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| − | | |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
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| − | | |
| − | IDS. Meditative Note 3
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| − | | |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
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| − | | |
| − | | |
| − | | |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
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| − | | |
| − | IDS. Obligatory Note 1
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| − | | |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
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| − | | |
| − | While I remain compelled to remain silent on the status of the absolute fiat,
| |
| − | the irrelative notion of the unmotivated motion and the disinterested stance,
| |
| − | let me then turn to the other axes of description, descriptive vs. normative.
| |
| − | Axes of description, indeed, you can almost hear one branch of the recursion
| |
| − | already beginning to wind up its whine to the verge of a howl, but toss it a
| |
| − | sop and try to persevere in the quest.
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| − | | |
| − | In this view, I regard the very idea of a norm as invoking its due pragma --
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| − | aim, business, concern, desire, end, function, goal, intention, interest,
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| − | objective, purpose, its names are legion -- and the good sense of the
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| − | norm is simply to suggest what one ought to do, contingent, of course,
| |
| − | on one's motive to achieve that pragma.
| |
| − | | |
| − | If we keep in mind the kinds of "applied research task" (ART) that your
| |
| − | everyday artist, designer, engineer, mathematician, scientist, or other
| |
| − | type of technical worker has to carry out on an everyday basis, we note
| |
| − | how these axes of description can be used to frame their activities and
| |
| − | to depict their forms of conduct, without mistaking either the frame or
| |
| − | the picture for the object of the picture so framed. Nor does any body
| |
| − | imagine that the observer must flatten out into a single plane or align
| |
| − | with a single axis, in order to make a vantage of the frame so pictured.
| |
| − | | |
| − | Common sense practical wit tells us that effective action toward the
| |
| − | achievement of a desirable result will naturally depend on acquiring
| |
| − | good descriptions of the lay of the land in which we hope to advance.
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| − | | |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| |
| − | | |
| − | IDS. Obligatory Note 2
| |
| − | | |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| |
| − | | |
| − | | |
| − | | |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
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| − | | |
| − | IDS. Projective Note 1
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| − | | |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
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| − | | |
| − | Good morning. Thanks. I had a bad night.
| |
| − | I blame Bernard Morand, who wrote me this:
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| − | | |
| − | BM: But this looks as some God's view.
| |
| − | What about us, finite humans, occupied
| |
| − | in counting the instants of our lives?
| |
| − | And thus condemned to try to improve
| |
| − | the fate of our successors?
| |
| − | | |
| − | When you think of this in the future, and of course you may never,
| |
| − | you may blame him too, for in writing this he has "erged" me on
| |
| − | to return to my deserted dissertation work, into which I have
| |
| − | poured my life for lo! these too many years to count, truly,
| |
| − | if you stop to contemplate the fact that time is relative.
| |
| − | | |
| − | In that time I have come to the view that we really need
| |
| − | a good "theory of inquiry" (TOI), for all sorts of very
| |
| − | practical and crucial reasons, also, that we cannot get
| |
| − | a good TOI without its being, at one and the same time,
| |
| − | a good "theory of information" (TOI too), and also that
| |
| − | an integral constituent of TOI 1 and TOI 2 would have to
| |
| − | be a good "theory of representation and semiosis" (TORAS) --
| |
| − | "Bull!?", you say, well, so be it.
| |
| − | | |
| − | Further, I think that it is abundantly evident by now that
| |
| − | we will get no such good theories of signs or science from
| |
| − | the "establishment philosophy of science" (EPOS?) -- which
| |
| − | has managed to mince and to trash the best available tries
| |
| − | at such theories for over a hundred years now. But Hey! --
| |
| − | don't take my word for it -- waste a century of your own.
| |
| − | | |
| − | We just got our regular email back,
| |
| − | so I think that I can now get going --
| |
| − | Yes, I have lost the ability to think
| |
| − | if not literally writing 'to' somebody.
| |
| − | | |
| − | When it begins, it begins like this:
| |
| − | | |
| − | Why am I asking this question?
| |
| − | | |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| |
| − | | |
| − | IDS. Projective Note 2
| |
| − | | |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| |
| − | | |
| − | So we may rest assured that we do have a "subject matter", an empirical domain,
| |
| − | or a realm of experience that is indexed, however dimly, generally, or vaguely,
| |
| − | by the word "inquiry", and only the question how best to describe it remains
| |
| − | in doubt at this stage of the play. If we wanted to cast our net as widely
| |
| − | as possible, at the risk of anticipating a bounding hypothesis, we could
| |
| − | think of all the world's creatures bright and beautiful and of how they
| |
| − | conduct themselves when faced with some moment of uncertainty, where
| |
| − | their aim is to cope with a surprising phenomenon or to deal with
| |
| − | a problematic situation that meets them in the course of their
| |
| − | ever-ongoing struggles to live, to revive, and to thrive.
| |
| − | | |
| − | Now, neither the fact that we begin with a descriptive task,
| |
| − | nor the fact that it remains of interest for its own sake,
| |
| − | necessarily means that we must end there, for it is also
| |
| − | the means to a further end, of learning how to better
| |
| − | our own skill at inquiry, which means in our time
| |
| − | the building of tools that help with the task.
| |
| − | | |
| − | I hope I have made this sound as truly and
| |
| − | as trivially obvious as it ought to be.
| |
| − | | |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| |
| − | | |
| − | IDS. Reflective Note 1
| |
| − | | |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| |
| − | | |
| − | In reflecting on what in the world a "Theory of Inquiry" (TOI) might be,
| |
| − | it occurs to me that there are many different things that one might mean
| |
| − | by such a theory. It could just be any number of things that one asserts
| |
| − | or has a mind to assert about the ostensible subject matter. But it has
| |
| − | been my experience that one can assert pretty much whatever one chooses,
| |
| − | and others will choose to heed it or ignore it on many different grounds,
| |
| − | the grounds themselves being a matter of choice, conditioning, or custom.
| |
| − | | |
| − | But I am looking for theories that work, that is to say, theories that
| |
| − | are subject to probation through proof, probability, and programming.
| |
| − | | |
| − | Astute readers will have noticed that I've already attempted to finesse
| |
| − | a very important, and most likely "infinessible" issue, to wit, that of
| |
| − | the scruples dividing descriptive, normative, and prescriptive theories.
| |
| − | | |
| − | I will think about that, and get back to you.
| |
| − | | |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| |
| − | | |
| − | IDS. Reflective Note 2
| |
| − | | |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| |
| − | | |
| − | | How will I approach this problem about the nature of inquiry?
| |
| − | |
| |
| − | | The simplest answer is this:
| |
| − | |
| |
| − | | I will apply the method of inquiry to the problem of inquiry's nature.
| |
| − | |
| |
| − | | This is the most concise and comprehensive answer that I know, but
| |
| − | | it is likely to sound facetious at this point. On the other hand,
| |
| − | | if I did not actually use the method of inquiry that I describe
| |
| − | | as inquiry, how could the results possibly be taken seriously?
| |
| − | | Accordingly, the questions of methodological self-application
| |
| − | | and self-referential consistency will be found at the center
| |
| − | | of this research.
| |
| − | | |
| − | These lines image in compact form the crux of the problem,
| |
| − | the crucible of the method, and the character that marks
| |
| − | relation between the two, if indeed they really are two,
| |
| − | in a form whose extended development will wind its way
| |
| − | through many a later page of the present exposition.
| |
| − | | |
| − | But let me just point out at this point some of
| |
| − | the reasons why I have found the prerequisite
| |
| − | of an inquiry into inquiry to be inescapable.
| |
| − | | |
| − | Let us entertain the idea, for the sake of getting the inquiry started,
| |
| − | if nothing else, that it is admissible to use a word like "inquiry" as
| |
| − | an initially indefinite indicator of an ostensible object of inquiry.
| |
| − | If we ever again find ourselves being puzzled how our reasoning can
| |
| − | chastize its own entailments this way, we may remind ourselves of
| |
| − | that fine old line between our "logica docens' (logic as taught)
| |
| − | and our "logica utens" (logic as used). With this distinction
| |
| − | in mind, we can dispell the initial puzzlement by saying that
| |
| − | we are using a capacity for inquiry that we do not know how
| |
| − | to formalize yet in order to examine the forms of inquiry
| |
| − | that various thinkers have been able, at least partially,
| |
| − | to formalize.
| |
| − | | |
| − | The dilemma that we face has the following structure:
| |
| − | | |
| − | If we recommend to all a method of inquiry that
| |
| − | we ourselves do not use in a pinch, precisely
| |
| − | in a pinch where we need to study an issue
| |
| − | as important as the nature of inquiry,
| |
| − | then who would take our advice?
| |
| − | | |
| − | So it seems that there is no choice
| |
| − | but to study inquiry, the pragma,
| |
| − | by way of inquiry, the praxis,
| |
| − | that is to say, recursively.
| |
| − | | |
| − | Incidentally, many variations on this theme are | |
| − | thoroughly developed in Peirce's "Lectures" of | |
| − | 1865 and 1866 and recapitulated in his early | |
| − | study "On a New List of Categories" (1867). | |
| − | | |
| − | http://members.door.net/arisbe/menu/library/bycsp/newlist/nl-main.htm
| |
| − | | |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| |
| − | | |
| − | IDS. Reflective Note 3
| |
| − | | |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| |
| − | | |
| − | | |
| − | | |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| |
| − | | |
| − | IDS. Work Area
| |
| − | | |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| |
| − | | |
| − | From this point of view, inquiry is form of conduct,
| |
| − | an applied research task, like may others that we
| |
| − | have to carry out, and that can be done either
| |
| − | better or worse.
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| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
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| − | IDS. Outline
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| − | Inquiry Driven Systems
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| − | 1. Introduction
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| − | 1.1. Outline of the Project: Inquiry Into Inquiry
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| − | 1.1.1. Problem
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| − | 1.1.2. Method
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| − | 1.1.2.1. The Paradigmatic and Process-Analytic Phase
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| − | 1.1.2.2. The Paraphrastic and Faculty-Synthetic Phase
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| − | 1.1.2.3. Reprise of Methods
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| − | 1.1.3. Criterion
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| − | 1.1.4. Application
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| − | 1.2. Onus of the Project: No Way But Inquiry
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| − | 1.2.1. A Modulating Prelude
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| − | 1.2.2. A Fugitive Canon
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| − | 1.3. Opening of the Project: A Way Up To Inquiry
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| − | 1.3.1. Initial Analysis of Inquiry Allegro Aperto
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| − | 1.3.2. Discussion of Discussion
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| − | 1.3.3. Discussion of Formalization: General Topics
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| − | 1.3.3.1. A Formal Charge
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| − | 1.3.3.2. A Formalization of Formalization?
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| − | 1.3.3.3. A Formalization of Discussion?
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| − | 1.3.3.4. A Concept of Formalization
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| − | 1.3.3.5. A Formal Approach
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| − | 1.3.3.6. A Formal Development
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| − | 1.3.3.7 A Formal Persuasion
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| − | 1.3.4. Discussion of Formalization: Concrete Examples
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| − | 1.3.4.1. Formal Models: A Sketch
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| − | 1.3.4.2. Sign Relations: A Primer
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| − | 1.3.4.3. Semiotic Equivalence Relations
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| − | 1.3.4.4. Graphical Representations
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| − | 1.3.4.5. Taking Stock
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| − | 1.3.4.6. The "Meta" Question
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| − | 1.3.4.7. Iconic Signs
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| − | 1.3.4.8. The Conflict of Interpretations
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| − | 1.3.4.9. Indexical Signs
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| − | 1.3.4.10. Sundry Problems
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| − | 1.3.4.11. Review and Prospect
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| − | 1.3.4.12. Objective Plans & Levels
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| − | 1.3.4.13. Formalization of OF: Objective Levels
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| − | 1.3.4.14. Application of OF: Generic Level
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| − | 1.3.4.15. Application of OF: Motive Level
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| − | 1.3.4.16. The Integration of Frameworks
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| − | 1.3.4.17. Recapitulation: A Brush with Symbols
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| − | 1.3.4.18. C'est Moi
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| − | 1.3.4.19. Entr'acte
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| − | 1.3.5 Discussion of Formalization: Specific Objects
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| − | 1.3.5.1 The Will to Form
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| − | 1.3.5.2 The Forms of Reasoning
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| − | 1.3.5.3 A Fork in the Road
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| − | 1.3.5.4 A Forged Bond
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| − | 1.3.5.5 A Formal Account
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| − | 1.3.5.6 Analogs, Icons, Models, Surrogates
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| − | 1.3.5.7 Steps and Tests of Formalization
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| − | 1.3.5.8 Puck, the Ref
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| − | 1.3.5.9 Partial Formalizations
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| − | 1.3.5.10 A Formal Utility
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| − | 1.3.5.11 A Formal Aesthetic
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| − | 1.3.5.12 A Formal Apology
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| − | 1.3.5.13 A Formal Suspicion
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| − | 1.3.5.14 The Double Aspect of Concepts
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| − | 1.3.5.15 A Formal Permission
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| − | 1.3.5.16 A Formal Invention
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| − | 1.3.6 Recursion in Perpetuity
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| − | 1.3.7 Processus, Regressus, Progressus
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| − | 1.3.8 Rondeau Tempo di Menuetto
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| − | 1.3.9 Reconnaissance
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| − | 1.3.9.1 The Informal Context
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| − | 1.3.9.2 The Epitext
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| − | 1.3.9.3 The Formative Tension
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| − | 1.3.10 Recurring Themes
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| − | 1.3.10.1 Preliminary Notions
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| − | 1.3.10.2 Intermediary Notions
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| − | 1.3.10.3 Propositions and Sentences
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| − | 1.3.10.4 Empirical Types and Rational Types
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| − | 1.3.10.5 Articulate Sentences
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| − | 1.3.10.6 Stretching Principles
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| − | 1.3.10.7 Stretching Operations
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| − | 1.3.10.8 The Cactus Patch
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| − | 1.3.10.9 The Cactus Language: Syntax
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| − | 1.3.10.10 The Cactus Language: Stylistics
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| − | 1.3.10.11 The Cactus Language: Mechanics
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| − | 1.3.10.12 The Cactus Language: Semantics
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| − | 1.3.10.13 Stretching Exercises
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| − | 1.3.10.14 Syntactic Transformations
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| − | 1.3.10.15 Derived Equivalence Relations
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| − | 1.3.10.16 Digression on Derived Relations
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| − | 1.4 Outlook of the Project: All Ways Lead to Inquiry
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| − | 1.4.1 The Matrix of Inquiry
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| − | 1.4.1.1 Inquiry as Conduct
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| − | 1.4.1.2 Types of Conduct
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| − | 1.4.1.3 Perils of Inquiry
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| − | 1.4.1.4 Forms of Relations
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| − | 1.4.1.5 Models of Inquiry
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| − | 1.4.2 The Moment of Inquiry
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| − | 1.4.3 The Modes of Inquiry
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| − | 1.4.3.1 Deductive Reasoning
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| − | 1.4.3.2 Inductive Reasoning
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| − | 1.4.3.3 Abductive Reasoning
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| − | 1.4.3.4 Analogical Reasoning
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| − | 1.5 Obstacles to the Project: In the Way of Inquiry
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| − | 1.5.1 The Initial Unpleasantness
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| − | 1.5.2 The Justification Trap
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| − | 1.5.3 A Formal Apology
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| − | 1.5.3.1 Category Double-Takes
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| − | 1.5.3.2 Conceptual Extensions
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| − | 1.5.3.3 Explosional Recombinations
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| − | 1.5.3.4 Interpretive Frameworks
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| − | 1.5.4 A Material Exigency
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| − | 1.5.5 A Reconciliation of Accounts
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| − | 1.5.6 Objections to Reflexive Inquiry
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| − | 1.5.7 Empirical Considerations
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| − | 1.5.8 Computational Considerations
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| − | 1.5.8.1 A Form of Recursion
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| − | 1.5.8.2 A Power of Abstraction
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| − | 1.6 Orientation of the Project: A Way Into Inquiry
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| − | 1.6.1 Initial Description of Inquiry
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| − | 1.6.2 Terms of Analysis
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| − | 1.6.2.1 Digression on Signs
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| − | 1.6.2.2 Empirical Status of ID
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| − | 1.6.3 Expansion of Terms
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| − | 1.6.3.1 Agency
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| − | 1.6.3.2 Abstraction
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| − | 1.6.3.3 Analogy
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| − | 1.6.3.4 Accuracy
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| − | 1.6.3.5 Authenticity
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| − | 1.6.4 Anchoring Terms in Phenomena
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| − | 1.6.4.1 A Mistaken ID
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| − | 1.6.4.2 Phenomenology of Doubt
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| − | 1.6.4.3 Modalities of Knowledge
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| − | 1.6.5 Sets, Systems, & Substantive Agents
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| − | 1.6.6 Interpretive Systems
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| − | 1.6.6.1 Syntactic Systems
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| − | 1.6.6.2 Semantic Systems
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| − | 1.6.6.3 Pragmatic Systems
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| − | 1.6.7 Inquiry Driven Systems
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| − | 1.6.7.1 A Definition of Inquiry
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| − | 1.6.7.2 The Faculty of Inquiry
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| − | 1.6.7.3 A Definition of Determination
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| − | 1.6.7.4 A Definition of Definition
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| − | 1.7 Organization of the Project: A Way Through Inquiry
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| − | 1.7.1 The Problem: Inquiry Found as an Object of Study
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| − | 1.7.2 The Method: Inquiry Found as a Means of Study
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| − | 1.7.2.1 Conditions for the Possibility
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| − | of Inquiry into Inquiry
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| − | 1.7.2.2 Conditions for the Success of Inquiry into Inquiry
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| − | 1.7.3 The Criterion: Inquiry in Search of a Sensible End
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| − | 1.7.3.1 The Irritation of Doubt, and The Scratch Test
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| − | 1.7.3.2 Enabling Provision 1: The Scenes & Context of Inquiry
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| − | 1.7.3.3 Enabling Provision 2: The Stages & Content of Inquiry
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| − | 1.8 Objectives of the Project: Inquiry All the Way
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| − | 1.8.1 Substantial Objective
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| − | 1.8.1.1 Objective 1a: The Propositions as Types Analogy
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| − | 1.8.1.2 Objective 1b: The Styles of Proof Development
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| − | 1.8.1.3 Objective 1c: The Analysis of Interpreters, or A Problem with Authority
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| − | 1.8.2 Instrumental Objective
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| − | 1.8.3 Coordination of Objectives
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| − | 1.8.4 Recapitulation -- Da Capo, Al Segno
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| − | 2. Discussion of Inquiry
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| − | 2.1 Approaches to Inquiry
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| − | 2.1.1 The Classical Framework: Syllogistic Approaches
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| − | 2.1.2 The Pragmatic Framework: Sign-Theoretic Approaches
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| − | 2.1.3 The Dynamical Framework: System-Theoretic Approaches
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| − | 2.1.3.1 Inquiry & Computation
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| − | 2.1.3.2 Inquiry Driven Systems
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| − | 2.2 The Context of Inquiry
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| − | 2.2.1 The Field of Observation
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| − | 2.2.2 The Problem of Reflection
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| − | 2.2.3 The Problem of Reconstruction
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| − | 2.2.4 The Trivializing of Integration
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| − | 2.2.5 Tensions in the Field of Observation
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| − | 2.2.6 Problems of Representation & Communication
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| − | 2.3 The Conduct of Inquiry
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| − | 2.3.1 Introduction
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| − | 2.3.2 The Types of Reasoning
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| − | 2.3.2.1 Deduction
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| − | 2.3.2.2 Induction
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| − | 2.3.2.3 Abduction
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| − | 2.3.3 Hybrid Types of Inference
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| − | 2.3.3.1 Analogy
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| − | 2.3.3.2 Inquiry
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| − | 2.3.4 Details of Induction
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| − | 2.3.4.1 Learning
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| − | 2.3.4.2 Transfer
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| − | 2.3.4.3 Testing
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| − | 2.3.5 The Stages of Inquiry
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| − | 3. The Medium & Its Message
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| − | 3.1 Reflective Expression
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| − | 3.1.1 Casual Reflection
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| − | 3.1.1.1 Ostensibly Recursive Texts
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| − | 3.1.1.2 Analogical Recursion
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| − | 3.1.2 Conscious Reflection
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| − | 3.1.2.1 The Signal Moment
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| − | 3.1.2.2 The Symbolic Object
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| − | 3.1.2.3 The Endeavor to Communicate
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| − | 3.1.2.4 The Medium of Communication
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| − | 3.1.2.5 The Ark of Types:
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| − | The Order of Things to Come.
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| − | 3.1.2.6 The Epitext
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| − | 3.1.2.7 The Context of Interpretation
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| − | 3.1.2.8 The Formative Tension
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| − | 3.1.2.9 The Vehicle of Communication:
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| − | Reflection on the Scene,
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| − | Reflection on the Self.
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| − | 3.1.2.10 (7)
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| − | 3.1.2.11 (6)
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| − | 3.1.2.12 Recursions: Possible, Actual, Necessary
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| − | 3.1.2.13 Ostensibly Recursive Texts
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| − | 3.1.2.14 (3)
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| − | 3.1.2.15 The Freedom of Interpretation
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| − | 3.1.2.16 The Eternal Return
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| − | 3.1.2.17 (1)
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| − | 3.1.2.18 Information in Formation
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| − | 3.1.2.19 Reflectively Indexical Texts
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| − | 3.1.2.20 (4)
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| − | 3.1.2.21 (5)
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| − | 3.1.2.22 (6)
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| − | 3.1.2.23 (7)
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| − | 3.1.2.24 (8)
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| − | 3.1.2.25 The Discursive Universe
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| − | 3.1.2.26 (7)
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| − | 3.1.2.27 (6)
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| − | 3.1.2.28 (5)
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| − | 3.1.2.29 (4)
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| − | 3.1.2.30 (3)
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| − | 3.1.2.31 (2)
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| − | 3.1.2.32 (1)
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| − | 3.2 Reflective Inquiry
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| − | 3.2.1 Integrity and Unity of Inquiry
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| − | 3.2.2 Apparitions & Allegations
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| − | 3.2.3 A Reflective Heuristic
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| − | 3.2.4 Either/Or: A Sense of Absence
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| − | 3.2.5 Apparent, Occasional, & Practical Necessity
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| − | 3.2.6 Approaches, Aspects, Exposures, Fronts
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| − | 3.2.7 Synthetic A Priori Truths
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| − | 3.2.8 Priorisms of Normative Sciences
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| − | 3.2.9 Principle of Rational Action
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| − | 3.2.10 The Pragmatic Cosmos
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| − | 3.2.11 Reflective Interpretive Frameworks
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| − | 3.2.11.1 Principals Versus Principles
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| − | 3.2.11.2 The Initial Description of Inquiry
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| − | 3.2.11.3 An Early Description of Interpretation
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| − | 3.2.11.4 Descriptions of the Mind
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| − | 3.2.11.5 Of Signs & the Mind
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| − | 3.2.11.6 Questions of Justification
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| − | 3.2.11.7 The Experience of Satisfaction
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| − | 3.2.11.8 An Organizational Difficulty
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| − | 3.2.11.9 Pragmatic Certainties
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| − | 3.2.11.10 Problems & Methods
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| − | 3.3 Reflection on Reflection
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| − | 3.4 Reflective Interpretive Frameworks
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| − | 3.4.1 The Phenomenology of Reflection
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| − | 3.4.2 A Candid Point of View
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| − | 3.4.3 A Projective Point of View
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| − | 3.4.4 A Formal Point of View
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| − | 3.4.5 Three Styles of Linguistic Usage
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| − | 3.4.6 Basic Notions of Group Theory
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| − | 3.4.7 Basic Notions of Formal Language Theory
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| − | 3.4.8 A Perspective on Computation
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| − | 3.4.9 Higher Order Sign Relations: Introduction
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| − | 3.4.10 Higher Order Sign Relations: Examples
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| − | 3.4.11 Higher Order Sign Relations: Application
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| − | 3.4.12 Issue 1: The Status of Signs
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| − | 3.4.13 Issue 2: The Status of Sets
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| − | 3.4.14 Issue 3: The Status of Variables
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| − | 3.4.15 Propositional Calculus
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| − | 3.4.16 Recursive Aspects
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| − | 3.4.17 Patterns of Self-Reference
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| − | 3.4.18 Practical Intuitions
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| − | 3.4.19 Examples of Self-Reference
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| − | 3.4.20 Three Views of Systems
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| − | 3.4.21 Building Bridges Between Representations
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| − | 3.4.22 Extensional Representations of Sign Relations
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| − | 3.4.23 Intensional Representations of Sign Relations
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| − | 3.4.24 Literal Intensional Representations
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| − | 3.4.25 Analytic Intensional Representations
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| − | 3.4.26 Differential Logic & Directed Graphs
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| − | 3.4.27 Differential Logic & Group Operations
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| − | 3.4.28 The Bridge: From Obstruction to Opportunity
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| − | 3.4.29 Projects of Representation
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| − | 3.4.30 Connected, Integrated, Reflective Symbols
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| − | 3.4.31 Generic Orders of Relations
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| − | 3.4.32 Partiality: Selective Operations
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| − | 3.4.33 Sign Relational Complexes
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| − | 3.4.34 Set-Theoretic Constructions
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| − | 3.4.35 Reducibility of Sign Relations
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| − | 3.4.36 Irreducibly Triadic Relations
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| − | 3.4.37 Propositional Types
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| − | 3.4.38 Considering the Source
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| − | 3.4.39 Prospective Indices: Pointers to Future Work
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| − | 3.4.40 Dynamic & Evaluative Frameworks
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| − | 3.4.41 Elective & Motive Forces
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| − | 3.4.42 Sign Processes: A Start
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| − | 3.4.43 Reflective Extensions
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| − | 3.4.44 Reflections on Closure
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| − | 3.4.45 Intelligence => Critical Reflection
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| − | 3.4.46 Looking Ahead
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| − | 3.4.47 Mutually Intelligible Codes
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| − | 3.4.48 Discourse Analysis: Ways & Means
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| − | 3.4.49 Combinations of Sign Relations
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| − | 3.4.50 Revisiting the Source
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| − | 3.5 Divertimento:
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| − | Eternity in Love with the Creatures of Time
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| − | 3.5.1 Reflections on the Presentation of Examples
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| − | 3.5.2 Searching for Parameters
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| − | 3.5.3 Defect Analysis
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| − | 3.5.4 The Pragmatic Critique
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| − | 3.5.5 Pragmatic Operating Notions
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| − | 3.5.6 Defects of Presentation
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| − | 3.5.7 Dues to Process
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| − | 3.5.8 Duties to Purpose
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| − | 3.6 Computational Design Philosophy
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| − | 3.6.1 Intentional Objects & Attitudes
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| − | 3.6.2 Imperfect Design & Persistent Error
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| − | 3.6.3 Propositional Reasoning About Relations
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| − | 3.6.4 Dynamic & Evaluative Frameworks
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| − | 3.6.5 Discussion of Examples
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| − | 3.6.6 Information & Inquiry
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| − | 4. Overview of the Domain: Interpretive Inquiry
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| − | 4.1 Interpretive Bearings: Conceptual & Descriptive Frameworks
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| − | 4.1.1 Catwalks: Flexible Frameworks & Peripatetic Categories
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| − | 4.1.1.1 Eponymous Ancestors:
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| − | The Precursors of Abstraction?
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| − | 4.1.1.2 Reticles:
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| − | Interpretive Flexibility as a Design Issue.
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| − | 4.1.2 Heuristic Inclinations & Regulative Principles
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| − | 4.2 Features of Inquiry Driven Systems
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| − | 4.2.1 The Pragmatic Theory of Signs
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| − | 4.2.1.1 Sign Relations
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| − | 4.2.1.2 Types of Signs
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| − | 4.2.2 The Pragmatic Theory of Inquiry
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| − | 4.2.2.1 Abduction
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| − | 4.2.2.2 Deduction
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| − | 4.2.2.3 Induction
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| − | 4.3 Examples of Inquiry Driven Systems
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| − | 4.3.1 "Index": A Program for Learning Formal Languages
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| − | 4.3.2 "Study": A Program for Reasoning with Propositions
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| − | 5. Discussion & Development of Objectives
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| − | 5.1 Objective 1a: Propositions as Types
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| − | 5.2 Objective 1b: Proof Styles & Developments
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| − | 5.3 Objective 1c: Interpretation & Authority
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| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
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| − | IDS. Inquiry Driven Systems -- Ontology List
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| − | 01. http://suo.ieee.org/ontology/msg04618.html
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| − | 02. http://suo.ieee.org/ontology/msg04621.html
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| − | 03. http://suo.ieee.org/ontology/msg04626.html
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| − | 04.
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| − | IDS. Inquiry Driven Systems -- Incitatory Notes
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| − | 01. http://suo.ieee.org/ontology/msg04637.html
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| − | 02.
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| − | | |
| − | IDS. Inquiry Driven Systems -- Meditative Notes
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| − | 01. http://suo.ieee.org/ontology/msg04622.html
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| − | 02. http://suo.ieee.org/ontology/msg04636.html
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| − | 03.
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| − | IDS. Inquiry Driven Systems -- Obligatory Notes
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| − | 01. http://suo.ieee.org/ontology/msg04623.html
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| − | 02.
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| − | IDS. Inquiry Driven Systems -- Projective Notes
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| − | 01. http://suo.ieee.org/ontology/msg04619.html
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| − | 02. http://suo.ieee.org/ontology/msg04625.html
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| − | 03.
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| − | IDS. Inquiry Driven Systems -- Reflective Notes
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| − | 01. http://suo.ieee.org/ontology/msg04620.html
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| − | 02. http://suo.ieee.org/ontology/msg04631.html
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| − | 03.
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| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
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| − | IDS. Inquiry Driven Systems -- Inquiry List
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| − | 01.
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| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
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| − | IDS. Email Label
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| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
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| − | | Title: Inquiry Driven Systems
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| − | | Author: Jon Awbrey <jawbrey@oakland.edu>
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| − | | Version: Draft 10.01
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| − | | Created: 23 Jun 1996
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| − | | Revised: 07 Apr 2003
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| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
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| − | IDS. Inquiry Driven Systems
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| − | SUO List -- 04 Jan 2001
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| − | | |
| − | 01. http://suo.ieee.org/email/msg02678.html
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| − | 02. http://suo.ieee.org/email/msg02679.html
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| − | 03. http://suo.ieee.org/email/msg02682.html
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| − | 04. http://suo.ieee.org/email/msg02685.html
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| − | 05. http://suo.ieee.org/email/msg02695.html
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| − | 06. http://suo.ieee.org/email/msg02697.html
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| − | 07. http://suo.ieee.org/email/msg02720.html
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| − | 08. http://suo.ieee.org/email/msg03943.html
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| − | | |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
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| − | | |
| − | IDS. Inquiry Driven Systems
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| − | | |
| − | Ontology List -- Jan-Aug 2001
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| − | | |
| − | Systems Engineering Interest Statement
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| − | | |
| − | 00. http://suo.ieee.org/ontology/thrd103.html#00272
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| − | 01. http://suo.ieee.org/ontology/msg00272.html
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| − | 02. http://suo.ieee.org/ontology/msg00273.html
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| − | 03. http://suo.ieee.org/ontology/msg00276.html
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| − | 04. http://suo.ieee.org/ontology/msg00279.html
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| − | 05. http://suo.ieee.org/ontology/msg00289.html
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| − | 06. http://suo.ieee.org/ontology/msg00291.html
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| − | 07. http://suo.ieee.org/ontology/msg00314.html
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| − | | |
| − | Inquiry Driven Systems Essay 1
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| − | | |
| − | 08. http://suo.ieee.org/ontology/msg01535.html
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| − | | |
| − | Systems Engineering Dissertation
| |
| − | | |
| − | 00. http://suo.ieee.org/ontology/thrd103.html#03071
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| − | 09. http://suo.ieee.org/ontology/msg03071.html
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| − | 10. http://suo.ieee.org/ontology/msg03136.html
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| − | | |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
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| − | | |
| − | IDS. Inquiry Driven Systems
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| − | | |
| − | Arisbe List -- Jan 2002
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| − | | |
| − | http://stderr.org/pipermail/arisbe/2002-January/thread.html#1247
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| − | | |
| − | Ontology List -- Jan 2002
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| − | | |
| − | http://suo.ieee.org/ontology/thrd36.html#03604
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| − | http://suo.ieee.org/ontology/msg03604.html
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| − | | |
| − | 1.3.4.5. Taking Stock
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| − | http://suo.ieee.org/ontology/msg03605.html
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| − | | |
| − | 1.3.4.6. The "Meta" Question
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| − | http://suo.ieee.org/ontology/msg03607.html
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| − | | |
| − | 1.3.4.7. Iconic Signs
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| − | http://suo.ieee.org/ontology/msg03608.html
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| − | | |
| − | 1.3.4.8. The Conflict of Interpretations
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| − | http://suo.ieee.org/ontology/msg03609.html
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| − | | |
| − | Comment
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| − | http://suo.ieee.org/ontology/msg03613.html
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| − | | |
| − | 1.3.4.9. Indexical Signs
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| − | http://suo.ieee.org/ontology/msg03610.html
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| − | | |
| − | 1.3.4.10. Sundry Problems
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| − | http://suo.ieee.org/ontology/msg03611.html
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| − | | |
| − | 1.3.4.11. Review and Prospect
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| − | http://suo.ieee.org/ontology/msg03614.html
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| − | | |
| − | 1.3.4.12. Objective Plans and Levels
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| − | http://suo.ieee.org/ontology/msg03615.html
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| − | http://suo.ieee.org/ontology/msg03616.html
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| − | | |
| − | 1.3.4.13. Formalization of OF: Objective Levels
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| − | http://suo.ieee.org/ontology/msg03617.html
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| − | http://suo.ieee.org/ontology/msg03618.html
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| − | http://suo.ieee.org/ontology/msg03619.html
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| − | | |
| − | 1.3.4.14. Application of OF: Generic Level
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| − | http://suo.ieee.org/ontology/msg03620.html
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| − | http://suo.ieee.org/ontology/msg03621.html
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| − | http://suo.ieee.org/ontology/msg03622.html
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| − | http://suo.ieee.org/ontology/msg03623.html
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| − | | |
| − | 1.3.4.15. Application of OF: Motive Level
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| − | http://suo.ieee.org/ontology/msg03624.html
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| − | | |
| − | Comment
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| − | http://suo.ieee.org/ontology/msg03625.html
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| − | http://suo.ieee.org/ontology/msg03626.html
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| − | | |
| − | 1.3.4.16. Integration of Frameworks
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| − | http://suo.ieee.org/ontology/msg03627.html
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| − | | |
| − | Comment
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| − | http://suo.ieee.org/ontology/msg03629.html
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| − | | |
| − | 1.3.4.17 Recapitulation: A Brush with Symbols
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| − | http://suo.ieee.org/ontology/msg03630.html
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| − | | |
| − | Comment
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| − | http://suo.ieee.org/ontology/msg03631.html
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| − | http://suo.ieee.org/ontology/msg03634.html
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| − | http://suo.ieee.org/ontology/msg03636.html
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| − | http://suo.ieee.org/ontology/msg03638.html
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| − | http://suo.ieee.org/ontology/msg03639.html
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| − | | |
| − | 1.3.4.18. C'est Moi
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| − | http://suo.ieee.org/ontology/msg03640.html
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| − | | |
| − | 1.3.4.19 Entr'acte
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| − | http://suo.ieee.org/ontology/msg03642.html
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| − | | |
| − | Comment
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| − | http://suo.ieee.org/ontology/msg03645.html
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| − | http://suo.ieee.org/ontology/msg03647.html
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| − | http://suo.ieee.org/ontology/msg03648.html
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| − | http://suo.ieee.org/ontology/msg03649.html
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| − | http://suo.ieee.org/ontology/msg03650.html
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| − | http://suo.ieee.org/ontology/msg03652.html
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| − | http://suo.ieee.org/ontology/msg03657.html
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| − | http://suo.ieee.org/ontology/msg03659.html
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| − | http://suo.ieee.org/ontology/msg03660.html
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| − | http://suo.ieee.org/ontology/msg03661.html
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| − | http://suo.ieee.org/ontology/msg03662.html
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| − | http://suo.ieee.org/ontology/msg03663.html
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| − | http://suo.ieee.org/ontology/msg03664.html
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| − | | |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
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| − | | |
| − | Inquiry Into Inquiry (I^3)
| |
| − | | |
| − | 01. http://suo.ieee.org/ontology/msg02959.html
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| − | 02. http://suo.ieee.org/ontology/msg02961.html
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| − | | |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| |
| − | | |
| − | JA: 1.3.10.3 Propositions & Sentences
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| − | 01: http://suo.ieee.org/email/msg07444.html
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| − | 02: http://suo.ieee.org/email/msg07409.html
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| − | 03: http://suo.ieee.org/email/msg07416.html
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| − | 04: http://suo.ieee.org/email/msg07435.html
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| − | 05: http://suo.ieee.org/email/msg07443.html
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| − | 06: http://suo.ieee.org/email/msg07449.html
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| − | | |
| − | JA: 1.3.10.4 Empirical Types & Rational Types
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| − | 07: http://suo.ieee.org/email/msg07455.html
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| − | | |
| − | JA: 1.3.10.5 Articulate Sentences
| |
| − | 08: http://suo.ieee.org/email/msg07459.html
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| − | 09: http://suo.ieee.org/email/msg07461.html
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| − | | |
| − | JA: 1.3.10.6 Stretching Principles
| |
| − | 10: http://suo.ieee.org/email/msg07466.html
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| − | 11: http://suo.ieee.org/email/msg07469.html
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| − | | |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| |
| − | | |
| − | IDS. Discussion Notes
| |
| − | | |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| |
| − | | |
| − | IDS. Discussion Note 0
| |
| − | | |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| |
| − | | |
| − | JA = Jon Awbrey
| |
| − | SZ = Steven Ericsson-Zenith
| |
| − | | |
| − | SZ: You generate a seemingly endless stream of "inquiry" -- some
| |
| − | of which seems to ramble and some of which is quite facinating.
| |
| − | | |
| − | SZ: Now you have started to torture me with Nietzsche :)
| |
| − | | |
| − | SZ: I catch just enough of the stream to want to keep watching but
| |
| − | I find I need a statement of systematic intent. I know it is
| |
| − | inquiry into inquiry but can you summarise for me in brief
| |
| − | where you want to go and how you intend to get there.
| |
| − | | |
| − | SZ: Are these the endless streets of Eurpoean cities in which we can
| |
| − | occassionally find ourself lost, or do we wander a US city that
| |
| − | has had the luxury of laying down a grid first?
| |
| − | | |
| − | This is the document formerly known as my dissertation proposal --
| |
| − | in a system engineering program that I returned to school to do
| |
| − | as a kind of capstone / 2nd childhood / unfinished symphony,
| |
| − | mostly from '91 to '99. The formal beginning of it can be
| |
| − | found starting here:
| |
| − | | |
| − | http://stderr.org/pipermail/inquiry/2004-May/thread.html#1434
| |
| − | | |
| − | But I think most folks on the SemioCom List had seen the earlier parts
| |
| − | a couple of years ago, so I started at a point where I was starting
| |
| − | to re-write some things slghtly clearer than the last time, I hope.
| |
| − | | |
| − | The immediate excuse/occasion of my thinking on this stuff again was
| |
| − | the intermittent/interminable discussion that Bernard and I have been
| |
| − | having on the nature of the "formalization arrow", plus many questions
| |
| − | about what would constitute non-trivial examples of sign relations or
| |
| − | truly significant applications of the pragmatic theory of signs, and
| |
| − | what kind of conceptual/software architecture it would take to support
| |
| − | thinking about this level of complexity. So I was trying to bring folks
| |
| − | up to date with the "state of my art" (SOMA) circa 1996 before I ventured
| |
| − | to return to those issues.
| |
| − | | |
| − | Don't worry overmuch about the Nietzsche -- the stuff that I put in epigraphs
| |
| − | is called the "epitext", and it is often intended to serve more as an exercise
| |
| − | in counterpoint, if not fugue, than as a statement of the main theme. Still,
| |
| − | Freddy Nightmare was being remarkably Apollonian in these passages, I think.
| |
| − | | |
| − | Back to N'Orleans ...
| |
| − | | |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| |
| − | | |
| − | IDS. Discussion Note 1
| |
| − | | |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| |
| − | | |
| − | JA = Jon Awbrey
| |
| − | BM = Bernard Morand
| |
| − | | |
| − | Re: IDS 118. http://stderr.org/pipermail/inquiry/2004-May/001557.html
| |
| − | In: IDS. http://stderr.org/pipermail/inquiry/2004-May/thread.html#1434
| |
| − | | |
| − | I will go ahead and start a reply but I have to be on the road
| |
| − | to memorial day visits with out of town family in a little while,
| |
| − | so I will continue later tonight.
| |
| − | | |
| − | I should explain that this document arose out of the communication
| |
| − | situation with my advisor, committee, and other professors over the
| |
| − | better part of a decade. These people had very good backgrounds in
| |
| − | computer science, (control and optimal) systems engineering, and also
| |
| − | mathematics. So they already had a sense of how scientific method and
| |
| − | the formal sciences work, a sense of how they are applied in practical
| |
| − | settings, and a sense of how one uses empirical and statistical methods
| |
| − | to test the fitness of these applications on a recurring, incrementally
| |
| − | self-correcting basis. So the train of inquiry is already in motion,
| |
| − | and does not wait at the station for a good theory of how it works.
| |
| − | No one is going to stop the train and fire up the boilers again
| |
| − | from scratch. If I think that C.S. Peirce would make a better
| |
| − | conductor or engineer for the locomotion of inquiry, and not
| |
| − | just another "featherbedder" philosophy of science, I have
| |
| − | to show what he contributes to what is already under way.
| |
| − | That is to be contrasted with the epi-cartesian method
| |
| − | of flagging down the train, tearing up the rails, and
| |
| − | trying to justify its existence and motivation from
| |
| − | a standstill.
| |
| − | | |
| − | At any rate, this is the problem that I continually faced
| |
| − | in trying to write this erstwhile dissertation proposal,
| |
| − | and it forced me to work in a very different way from
| |
| − | anything that I had ever tried before, for instance,
| |
| − | where I could pretend to begin by just writing down
| |
| − | a bunch of axiomatic definitions as if it were the
| |
| − | first day of creation, and then following up their
| |
| − | consequences as best I could. Instead of doing
| |
| − | that, I had to write my opera 'in medias res'.
| |
| − | | |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| |
| − | | |
| − | IDS. Discussion Note 2
| |
| − | | |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| |
| − | | |
| − | JA = Jon Awbrey
| |
| − | BM = Bernard Morand
| |
| − | | |
| − | Re: IDS 118. http://stderr.org/pipermail/inquiry/2004-May/001557.html
| |
| − | In: IDS. http://stderr.org/pipermail/inquiry/2004-May/thread.html#1434
| |
| − | | |
| − | JA: It is important to realize that a "sampling relation", to express it
| |
| − | roughly, is a special case of a sign relation. Aside from acting on
| |
| − | sign relations and creating an association between sign relations, a
| |
| − | sampling relation is also involved in a larger sign relation, at least,
| |
| − | it can be subsumed within a general order of sign relations that allows
| |
| − | sign relations themselves to be taken as the objects, the signs, and the
| |
| − | interpretants of what can be called a "higher order" (HO) sign relation.
| |
| − | Considered with respect to its full potential, its use, and its purpose,
| |
| − | a sampling relation does not fall outside the closure of sign relations.
| |
| − | To be precise, a sampling relation falls within the denotative component
| |
| − | of a higher order sign relation, since the sign relation sampled is the
| |
| − | object of study and the sample is taken as a sign of it.
| |
| − | | |
| − | BM: I was away for the last whole week and I could not read your previous notes.
| |
| − | This paragraph of what seems to be some prolegomena for further explanations
| |
| − | caught my attention. A "sampling relation" can be subsumed within a general
| |
| − | order of sign relations: well, you seem to define the sampling case as some
| |
| − | kind of reverted hypostatic abstraction.
| |
| − | | |
| − | I may have to wait for you to explain what you mean by
| |
| − | this "reverted hypostatic abstraction". In the meantime,
| |
| − | what I am trying to say is this: If we approach "inquiry"
| |
| − | as an empirical domain or a quasi-natural phenomenon, taking
| |
| − | the word "inquiry" as a pointer to a certain field of activity
| |
| − | going on in the world, then whatever theory of inquiry we may
| |
| − | form will be based on our local sample of experience with this
| |
| − | domain of practice. At least, this would be the starting gate
| |
| − | in any other empirical domain. So the object is "all inquiry"
| |
| − | and the sign is "our sample of experience with all inquiry".
| |
| − | Indeed, we will ask whether the sample is "representative"
| |
| − | of the object domain, and a sensible method will try to
| |
| − | take steps to ensure that it is. Recall that the
| |
| − | root "sem-" in Hippocrates, from whom Aristotle
| |
| − | learned to appreciate abductive or diagnostic
| |
| − | reasoning, connotes "sample" or "specimen".
| |
| − | | |
| − | BM: Or to refer to the replica device between a legisign and its
| |
| − | sinsigns. If this is really your intend, you are missing a
| |
| − | third, I think. Namely the fact that sampling involves to
| |
| − | my sense particularizing much more than singularizing a
| |
| − | general type.
| |
| − | | |
| − | Yes, we know that the sample is more particular than the object domain
| |
| − | of interest, and thus gives us partial information. Indeed, since the
| |
| − | notion of "inquiry" is a rational concept, the domain "inquiry" is not
| |
| − | bounded by any finite experience or by all human experience together.
| |
| − | Thus we have to take measures that give us confidence of collecting a
| |
| − | "fair", "representative", or "typical" sample. This is only possible
| |
| − | in the long run, of course. Our initial sample is likely to be wholly
| |
| − | opportunistic and thus full of biases and "partialities".
| |
| − | | |
| − | This was partly the point of reverting to Aristotle's 'Peri Psyche' --
| |
| − | we possess and exercise an aptitude for inquiry long before we have
| |
| − | reflected on it sufficiently to formalize or objectify the smallest
| |
| − | sample of it.
| |
| − | | |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| |
| − | | |
| − | IDS. Discussion Note 3
| |
| − | | |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| |
| − | | |
| − | JA = Jon Awbrey
| |
| − | BM = Bernard Morand
| |
| − | | |
| − | Re: IDS 118. http://stderr.org/pipermail/inquiry/2004-May/001557.html
| |
| − | In: IDS. http://stderr.org/pipermail/inquiry/2004-May/thread.html#1434
| |
| − | | |
| − | BM: Doing so, you surely get the benefit of applying the signhood properties
| |
| − | to sample relations because you assume from the beginning the idea that
| |
| − | they don't fall outside the closure of sign relations. This is the great
| |
| − | deductive machinery used in inquiry. But aren't you dismissing from the
| |
| − | start his other friends, induction and abduction? As your text appears
| |
| − | to be a basic framework in order to inquire into inquiry, this would be
| |
| − | a too severe restriction.
| |
| − | | |
| − | I am merely saying that we can learn about X in general
| |
| − | by looking at examples of X, whether X is "inquiries" or
| |
| − | "sign relations" or anything else. Reasoning by way of
| |
| − | examples, analogies, or "paradigms" was classified by
| |
| − | Aristotle as a mixed form of reasoning that combined
| |
| − | induction of a rule and deduction of a similar fact,
| |
| − | while Peirce gave a couple of different analyses of
| |
| − | analogy that involved all three types of reasoning.
| |
| − | So I do not know why you say it is all deductive.
| |
| − | If one took the definition of a sign relation on
| |
| − | the basis of an a priori dictate, or authority,
| |
| − | then it might be so, but all sorts of abstract
| |
| − | definitions turn out to be useless for a given
| |
| − | purpose, and so Peirce's definition of a sign
| |
| − | has to prove its usefulness in the effort to
| |
| − | understand the object phenomena in question.
| |
| − | | |
| − | BM: From another side, it would throw tychism out of the picture:
| |
| − | you know, these samples which have absolutely not any subsumers.
| |
| − | | |
| − | I did not understand this comment fully. But choosing
| |
| − | random samples is a favorite way of getting fair ones.
| |
| − | | |
| − | BM: Your precision in the last sentence of the paragraph doesn't make
| |
| − | it more convenient in restricting sample relation to fall into the
| |
| − | denotative component of HO. The term "component" would deserve to
| |
| − | be itself defined: a restriction onto the !O! x !S! columns in L?
| |
| − | | |
| − | I made what seems like a simple observation, and hardly a novel one
| |
| − | if one considers the etymology and a host of classical discussions.
| |
| − | What use we make of the observation is another thing. I agree that
| |
| − | the word "component" is very multi-purpose -- here I conformed to
| |
| − | the usage that refers to factors of a product as "components",
| |
| − | as distinct from the sense used in relational "composition".
| |
| − | I plead the poverty of language.
| |
| − | | |
| − | BM: While I think that the component idea is at work in
| |
| − | sign relations, splitting them into a denotative part
| |
| − | and into another (?) connotative part would amount to
| |
| − | presume the problem at hand already solved. Reference to
| |
| − | components opens the difficult question (at least for me)
| |
| − | of the effective properties of composition relationship.
| |
| − | | |
| − | I don't understand this. We are operating in a situation of
| |
| − | partial information. We have focal sign relations that we can
| |
| − | objectify enough to study in detail, learning at least something
| |
| − | about the properties and variety of sign relations, at least some
| |
| − | of which learning will apply to classes of sign relations beyond
| |
| − | our immediate focus, perhaps even a little to the sign relation
| |
| − | in which we are embedded when we consider the relation of these
| |
| − | focal sign relations to the general class. Some people would
| |
| − | call this a "hermeneutic circle", I think.
| |
| − | | |
| − | BM: In short, the sign relation sampled is not the object of study
| |
| − | if it is not at the same time its interpretant, I think (and
| |
| − | then the concept of model is just newly born!)
| |
| − | | |
| − | The objective class of interest is "all" sign relations.
| |
| − | The sample that we have under the microscope is taken to
| |
| − | provide us with information about the object domain of
| |
| − | all sign relations, which it can do by virtue of the
| |
| − | fact that it "represents" the object domain more or
| |
| − | less well. If we transform the sample in some way,
| |
| − | or act on the information that it provides, then
| |
| − | we generate an interpretant sign of the sample.
| |
| − | Yes, I agree with that. I will have to ask
| |
| − | what sense of the word "model" you mean in
| |
| − | this context, though.
| |
| − | | |
| − | BM: Finally, what does it mean for a sample to be TAKEN AS a sign of
| |
| − | some study? The difficulty seems to me that the answer presupposes
| |
| − | the whole semiosis theory itself. I am not arguing here against the
| |
| − | possibility of this method, I am just trying to say that it would be
| |
| − | inaccurate to pretend escaping its complexity as a starting point.
| |
| − | On the contrary, I think that to begin with the assumption of
| |
| − | complexity will end (perhaps) into simplicity.
| |
| − | | |
| − | Yes, there is a shade of difference between passive experience,
| |
| − | where we take the samples that come our way, willy nilly, and
| |
| − | active experimentation, where we contrive to gather samples
| |
| − | under more contrived or controlled conditions, but none of
| |
| − | these variations are unique to the theory of signs or the
| |
| − | theory of inquiry. I do not know how I can presuppose
| |
| − | something that I am still in the middle of supposing.
| |
| − | That is, I do not view the theory of sign relations
| |
| − | or the theory of inquiry as finished products that
| |
| − | I might presuppose, or what would be the point of
| |
| − | an inquiry into their nature? I do have my pet
| |
| − | hypotheses, of course, but they are uncertain.
| |
| − | | |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| |
| − | | |
| − | IDS. Discussion Note 4
| |
| − | | |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| |
| − | | |
| − | JA = Jon Awbrey
| |
| − | BM = Bernard Morand
| |
| − | | |
| − | Re: IDS Discuss 1. http://stderr.org/pipermail/inquiry/2004-May/001560.html
| |
| − | In: IDS Discuss. http://stderr.org/pipermail/inquiry/2004-May/thread.html#1560
| |
| − | | |
| − | JA: I should explain that this document arose out of the communication
| |
| − | situation with my advisor, committee, and other professors over the
| |
| − | better part of a decade. These people had very good backgrounds in
| |
| − | computer science, (control and optimal) systems engineering, and also
| |
| − | mathematics. So they already had a sense of how scientific method and
| |
| − | the formal sciences work, a sense of how they are applied in practical
| |
| − | settings, and a sense of how one uses empirical and statistical methods
| |
| − | to test the fitness of these applications on a recurring, incrementally
| |
| − | self-correcting basis. So the train of inquiry is already in motion,
| |
| − | and does not wait at the station for a good theory of how it works.
| |
| − | No one is going to stop the train and fire up the boilers again
| |
| − | from scratch. If I think that C.S. Peirce would make a better
| |
| − | conductor or engineer for the locomotion of inquiry, and not
| |
| − | just another "featherbedder" philosophy of science, I have
| |
| − | to show what he contributes to what is already under way.
| |
| − | That is to be contrasted with the epi-cartesian method
| |
| − | of flagging down the train, tearing up the rails, and
| |
| − | trying to justify its existence and motivation from
| |
| − | a standstill.
| |
| − | | |
| − | BM: Agreed on the whole and the details, Jon. Except my suspicion
| |
| − | for "empirical method" for which I prefer "experimental" but
| |
| − | we already discussed that.
| |
| − | | |
| − | Okay. Those are basically synonyms to me. But I make no
| |
| − | inference from "empirical" to "radically naive empiricism",
| |
| − | or anything like that. Indeed, one of the principal jobs of
| |
| − | this whole project, that began long before I started trying to
| |
| − | document what I had been doing all along, was to integrate the
| |
| − | empirical data-driven and rational concept-driven modes of work.
| |
| − | Perhaps we could agree just between us -- I have already given up
| |
| − | trying to convert the masses (= effete minds) -- that "empiricism"
| |
| − | and "rationalism" are the names of heuristic attitudes, angles of
| |
| − | approach to be adopted on alternate weekdays, not the brands of
| |
| − | jealous religions that demand a fear and trembling either-or.
| |
| − | | |
| − | But I admit that I still see a residue of difference
| |
| − | between passive and active experience that comes up
| |
| − | all the time in the actual practice of research.
| |
| − | It is why we have consent forms, for example.
| |
| − | I had been meaning for a while now to take
| |
| − | it up under a separate thread, entitled
| |
| − | the "Lessons Of Play" (LOP), but I am
| |
| − | not ready to say what I think yet.
| |
| − | | |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| |
| − | | |
| − | IDS. Discussion Note 5
| |
| − | | |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| |
| − | | |
| − | JA = Jon Awbrey
| |
| − | BM = Bernard Morand
| |
| − | | |
| − | Re: IDS Discuss 3. http://stderr.org/pipermail/inquiry/2004-May/001562.html
| |
| − | In: IDS Discuss. http://stderr.org/pipermail/inquiry/2004-May/thread.html#1560
| |
| − | | |
| − | BM: Doing so, you surely get the benefit of applying the signhood properties
| |
| − | to sample relations because you assume from the beginning the idea that
| |
| − | they don't fall outside the closure of sign relations. This is the great
| |
| − | deductive machinery used in inquiry. But aren't you dismissing from the
| |
| − | start his other friends, induction and abduction? As your text appears
| |
| − | to be a basic framework in order to inquire into inquiry, this would be
| |
| − | a too severe restriction.
| |
| − | | |
| − | JA: I am merely saying that we can learn about X in general
| |
| − | by looking at examples of X, whether X is "inquiries" or
| |
| − | "sign relations" or anything else.
| |
| − | | |
| − | BM: All the difficulty resides in the meaning of "example" I think.
| |
| − | From which place can we judge that x is an example of some
| |
| − | (partially determined) X? This will become even more
| |
| − | difficult when we will have to make a selection
| |
| − | between several candidates x_i for learning X.
| |
| − | | |
| − | That is why we begin with easy examples.
| |
| − | | |
| − | It looks like some kind of Zenoesque "impossibility
| |
| − | of getting out of the starting blocks" difficulty here --
| |
| − | before Achilles can take a step he has to take a semi-step,
| |
| − | before he can take a semi-step he has to take a demi-semi-step,
| |
| − | before he can take a demi-semi-step he has to take a hemi-demi-semi-step, ...
| |
| − | | |
| − | This is the influence of epi-cartesion thinking again,
| |
| − | and I used to be sorely afflicted with it, so I know,
| |
| − | but Peirce, and already Aristotle before him, gave us
| |
| − | the way out with the abductive step of making a guess.
| |
| − | We want to minimize our risk, of course, but there is
| |
| − | an irreducible minimum of uncertainty that has to be
| |
| − | tolerated if thought and action are not to remain in
| |
| − | a state of utter paralysis.
| |
| − | | |
| − | So, can we read Peirce's definition of a sign relation and
| |
| − | use it to pick out some concrete and simple examples of
| |
| − | sign relations, or not? It's not much use if we can't.
| |
| − | Can I point to some examples of "inquiry" that are so
| |
| − | clearly examples of what we want to talk about that
| |
| − | both I and my committee will agree that they fit
| |
| − | the general description? Yes, though I might
| |
| − | have to defer to their language to do so,
| |
| − | calling it "research" or "applications
| |
| − | of scientific method" just by way of
| |
| − | getting out of the starting blocks.
| |
| − | | |
| − | If we get good at thinking about the simple examples,
| |
| − | then it may be worth the trouble to try and tackle the
| |
| − | harder cases. From my experience, 3-adic relations are
| |
| − | so difficult to think about that it will take some help
| |
| − | from software e-virons before we get much better at it.
| |
| − | | |
| − | JA: Reasoning by way of examples, analogies, or "paradigms" was classified by
| |
| − | Aristotle as a mixed form of reasoning that combined induction of a rule
| |
| − | and deduction of a similar fact, while Peirce gave a couple of different
| |
| − | analyses of analogy that involved all three types of reasoning. So I do
| |
| − | not know why you say it is all deductive. If one took the definition of
| |
| − | a sign relation on the basis of an a priori dictate, or authority, then it
| |
| − | might be so, but all sorts of abstract definitions turn out to be useless
| |
| − | for a given purpose, and so Peirce's definition of a sign has to prove its
| |
| − | usefulness in the effort to understand the object phenomena in question.
| |
| − | | |
| − | BM: Agreed
| |
| − | | |
| − | BM: From another side, it would throw tychism out of the picture:
| |
| − | you know, these samples which have absolutely not any subsumers.
| |
| − | | |
| − | JA: I did not understand this comment fully. But choosing
| |
| − | random samples is a favorite way of getting fair ones.
| |
| − | | |
| − | BM: This is a very complex problem but it is at the heart of the question of
| |
| − | induction. You certainly know that we can't elaborate true (absolute)
| |
| − | random samples. It seems that we have to admit in consequence that
| |
| − | probabilities fall into the domain of mathematics. The sampling
| |
| − | procedures of statisticians fall into the domain of experimental
| |
| − | sciences and both have to be not confused.
| |
| − | | |
| − | Yes, there is no reason to expect that inquiry into inquiry
| |
| − | will be any less complex than inquiry into anything else,
| |
| − | but I sense that I may have misunderstood your comment.
| |
| − | | |
| − | There are, of course, complications arising here over the difference
| |
| − | between descriptive sciences and normative sciences and what mix of
| |
| − | the two a particular person wants to focus on. But later, maybe.
| |
| − | | |
| − | BM: Your precision in the last sentence of the paragraph doesn't make
| |
| − | it more convenient in restricting sample relation to fall into the
| |
| − | denotative component of HO. The term "component" would deserve to
| |
| − | be itself defined: a restriction onto the !O! x !S! columns in L?
| |
| − | | |
| − | JA: I made what seems like a simple observation, and hardly a novel one
| |
| − | if one considers the etymology and a host of classical discussions.
| |
| − | What use we make of the observation is another thing. I agree that
| |
| − | the word "component" is very multi-purpose -- here I conformed to
| |
| − | the usage that refers to factors of a product as "components",
| |
| − | as distinct from the sense used in relational "composition".
| |
| − | I plead the poverty of language.
| |
| − | | |
| − | BM: Hum. Could you expand a little bit? This is not very familiar to me.
| |
| − | In relational composition, why does the relations couldn't be seen as
| |
| − | the factors of a product?
| |
| − | | |
| − | All I can do here is note the variety of usage. People will often
| |
| − | call the domains in a cartesian product or a direct product by the
| |
| − | name of "components" and they will speak of the "decomposition" of
| |
| − | a space X into the form of a product X = X_1 x ... x X_k, but not
| |
| − | be thinking of functional composition or relational composition
| |
| − | when they say this. I don't know any way around this, except
| |
| − | to use adjectives in front of the ambiguous words whenever
| |
| − | there's a chance of confusion.
| |
| − | | |
| − | If I have a 2-adic relation L that happens to be a composite of
| |
| − | two other 2-adic relations, L = M o N, then I'd tend to say that
| |
| − | L factors into M and N, or that M o N is "a" decomposition of L,
| |
| − | but M and N are not "the" factors of L or "the" components of L,
| |
| − | because we have no "unique factorization" theorem for relations
| |
| − | in general. So maybe that explains the nuance of usage. Maybe.
| |
| − | | |
| − | BM: While I think that the component idea is at work in
| |
| − | sign relations, splitting them into a denotative part
| |
| − | and into another (?) connotative part would amount to
| |
| − | presume the problem at hand already solved. Reference to
| |
| − | components opens the difficult question (at least for me)
| |
| − | of the effective properties of composition relationship.
| |
| − | | |
| − | JA: I don't understand this. We are operating in a situation of
| |
| − | partial information. We have focal sign relations that we can
| |
| − | objectify enough to study in detail, learning at least something
| |
| − | about the properties and variety of sign relations, at least some
| |
| − | of which learning will apply to classes of sign relations beyond
| |
| − | our immediate focus, perhaps even a little to the sign relation
| |
| − | in which we are embedded when we consider the relation of these
| |
| − | focal sign relations to the general class. Some people would
| |
| − | call this a "hermeneutic circle", I think.
| |
| − | | |
| − | BM: Yes, this is the strategy of learning which amounts for me to what
| |
| − | I poorly call synthesis. But there is its opposite too, analysis
| |
| − | that goes backward and allows to explain facts. The whole secret
| |
| − | of the method is articulating both of them together. Proceeding
| |
| − | this way, there is no more circle but something like a spiral.
| |
| − | | |
| − | Yes, not all circles are vicious. I understand all these things
| |
| − | on the model of recursive descent down to some basis that is so
| |
| − | simple as to be immediate -- what we do in top-down programming
| |
| − | or stepwise refinement -- and a spiral is a good image of that.
| |
| − | | |
| − | BM: On this point I am actually reading a book from K-O Apel
| |
| − | "Expliquer-Comprendre: La controverse centrale des sciences
| |
| − | humaines". It is a very fine book the first chapters of which
| |
| − | are difficult to read but it's a very great illumination when
| |
| − | arriving at the middle of the book. It is a French translation
| |
| − | from German. I don't know if there is an English one.
| |
| − | | |
| − | I will see if I can find it.
| |
| − | | |
| − | BM: In short, the sign relation sampled is not the object of study
| |
| − | if it is not at the same time its interpretant, I think (and then
| |
| − | the concept of model is just newly born!)
| |
| − | | |
| − | JA: The objective class of interest is "all" sign relations.
| |
| − | The sample that we have under the microscope is taken to
| |
| − | provide us with information about the object domain of
| |
| − | all sign relations, which it can do by virtue of the
| |
| − | fact that it "represents" the object domain more or
| |
| − | less well. If we transform the sample in some way,
| |
| − | or act on the information that it provides, then
| |
| − | we generate an interpretant sign of the sample.
| |
| − | Yes, I agree with that. I will have to ask
| |
| − | what sense of the word "model" you mean in
| |
| − | this context, though.
| |
| − | | |
| − | BM: I think of it as a pure synonym for sign, in all contexts.
| |
| − | And as for the case of signs there are 10 or 66 cases of
| |
| − | models. This is just an intuition of mine, not a theorem :-)
| |
| − | | |
| − | BM: Finally, what does it mean for a sample to be TAKEN AS a sign of
| |
| − | some study? The difficulty seems to me that the answer presupposes
| |
| − | the whole semiosis theory itself. I am not arguing here against the
| |
| − | possibility of this method, I am just trying to say that it would be
| |
| − | inaccurate to pretend escaping its complexity as a starting point.
| |
| − | On the contrary, I think that to begin with the assumption of
| |
| − | complexity will end (perhaps) into simplicity.
| |
| | | | |
| − | JA: Yes, there is a shade of difference between passive experience,
| + | http://members.door.net/arisbe/menu/library/bycsp/newlist/nl-main.htm |
| − | where we take the samples that come our way, willy nilly, and
| + | </pre> |
| − | active experimentation, where we contrive to gather samples
| |
| − | under more contrived or controlled conditions, but none of
| |
| − | these variations are unique to the theory of signs or the
| |
| − | theory of inquiry. I do not know how I can presuppose
| |
| − | something that I am still in the middle of supposing.
| |
| − | That is, I do not view the theory of sign relations
| |
| − | or the theory of inquiry as finished products that
| |
| − | I might presuppose, or what would be the point of
| |
| − | an inquiry into their nature? I do have my pet
| |
| − | hypotheses, of course, but they are uncertain.
| |
| | | | |
| − | BM: Yes. However I would add the following amendment. What any individual
| + | ===IDS. Work Area=== |
| − | inquirer (you, me or him) necessarily presupposes is the totality of
| |
| − | the previous inquiries. As such they aren't personal hypotheses,
| |
| − | and they have to be rendered explicit. If it was not the case
| |
| − | inquiry couldn't grow. We need them in order to be able to
| |
| − | experiment with samples. Perhaps it is there that we are
| |
| − | quite departing the one from the other.
| |
| | | | |
| − | That's kind of what I mean by 'in medias res'. But now the distinction
| + | <pre> |
| − | between "consciously presuppose" and "unconsciously presuppose" raises
| + | From this point of view, inquiry is form of conduct, |
| − | its head. I recently had to invoke the term "quasi-belief" to discuss
| + | an applied research task, like many others that we |
| − | this issue. It can take a considerable effort of critical reflection
| + | have to carry out, and that can be done either |
| − | to recognize that we are acting just as if certain propositions hold.
| + | better or worse. |
| − | Again, consider Aristotle's 3-fold:
| + | </pre> |
| | | | |
| − | | Matter is potentiality (dynamis), while form is
| + | ==Document History== |
| − | | realization or actuality (entelecheia), and the
| |
| − | | word actuality is used in two senses, illustrated
| |
| − | | by the possession of knowledge (episteme) and the
| |
| − | | exercise of it (theorein).
| |
| − | | |
| − | I think that his reputation as dichotomous thinker is greatly exaggerated.
| |
| | | | |
| | + | <pre> |
| | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o | | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o |
| | | | |
| − | IDS. Discussion Note 6
| + | | Document History |
| − | | + | | |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| + | | Subject: Inquiry Driven Systems: An Inquiry Into Inquiry |
| − | | + | | Contact: Jon Awbrey <jawbrey@oakland.edu> |
| − | | + | | Version: Draft 10.00 |
| − | | + | | Created: 23 Jun 1996 |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| + | | Revised: 02 Mar 2003 |
| − | | + | | Advisor: M.A. Zohdy |
| − | Inquiry Driven Systems
| + | | Setting: Oakland University, Rochester, Michigan, USA |
| − | | |
| − | 1. Introduction
| |
| − | 1.1. Outline of the Project: Inquiry Into Inquiry
| |
| − | 1.1.1. Problem
| |
| − | 1.1.2. Method
| |
| − | 1.1.2.1. The Paradigmatic and Process-Analytic Phase
| |
| − | 1.1.2.2. The Paraphrastic and Faculty-Synthetic Phase
| |
| − | 1.1.2.3. Reprise of Methods
| |
| − | 1.1.3. Criterion
| |
| − | 1.1.4. Application
| |
| − | | |
| − | 1.2. Onus of the Project: No Way But Inquiry
| |
| − | 1.2.1. A Modulating Prelude
| |
| − | 1.2.2. A Fugitive Canon
| |
| − | | |
| − | 1.3. Opening of the Project: A Way Up To Inquiry
| |
| − | 1.3.1. Initial Analysis of Inquiry Allegro Aperto
| |
| − | 1.3.2. Discussion of Discussion
| |
| − | 1.3.3. Discussion of Formalization: General Topics
| |
| − | 1.3.3.1. A Formal Charge
| |
| − | 1.3.3.2. A Formalization of Formalization?
| |
| − | 1.3.3.3. A Formalization of Discussion?
| |
| − | 1.3.3.4. A Concept of Formalization
| |
| − | 1.3.3.5. A Formal Approach
| |
| − | 1.3.3.6. A Formal Development
| |
| − | 1.3.3.7 A Formal Persuasion
| |
| − | 1.3.4. Discussion of Formalization: Concrete Examples
| |
| − | 1.3.4.1. Formal Models: A Sketch
| |
| − | 1.3.4.2. Sign Relations: A Primer
| |
| − | 1.3.4.3. Semiotic Equivalence Relations
| |
| − | 1.3.4.4. Graphical Representations
| |
| − | 1.3.4.5. Taking Stock
| |
| − | 1.3.4.6. The "Meta" Question
| |
| − | 1.3.4.7. Iconic Signs
| |
| − | 1.3.4.8. The Conflict of Interpretations
| |
| − | 1.3.4.9. Indexical Signs
| |
| − | 1.3.4.10. Sundry Problems
| |
| − | 1.3.4.11. Review and Prospect
| |
| − | 1.3.4.12. Objective Plans & Levels
| |
| − | 1.3.4.13. Formalization of OF: Objective Levels
| |
| − | 1.3.4.14. Application of OF: Generic Level
| |
| − | 1.3.4.15. Application of OF: Motive Level
| |
| − | 1.3.4.16. The Integration of Frameworks
| |
| − | 1.3.4.17. Recapitulation: A Brush with Symbols
| |
| − | 1.3.4.18. C'est Moi
| |
| − | 1.3.4.19. Entr'acte
| |
| − | | |
| − | 1.3.5 Discussion of Formalization: Specific Objects
| |
| − | 1.3.5.1 The Will to Form
| |
| − | 1.3.5.2 The Forms of Reasoning
| |
| − | 1.3.5.3 A Fork in the Road
| |
| − | 1.3.5.4 A Forged Bond
| |
| − | 1.3.5.5 A Formal Account
| |
| − | 1.3.5.6 Analogs, Icons, Models, Surrogates
| |
| − | 1.3.5.7 Steps and Tests of Formalization
| |
| − | 1.3.5.8 Puck, the Ref
| |
| − | 1.3.5.9 Partial Formalizations
| |
| − | 1.3.5.10 A Formal Utility
| |
| − | 1.3.5.11 A Formal Aesthetic
| |
| − | 1.3.5.12 A Formal Apology
| |
| − | 1.3.5.13 A Formal Suspicion
| |
| − | 1.3.5.14 The Double Aspect of Concepts
| |
| − | 1.3.5.15 A Formal Permission
| |
| − | 1.3.5.16 A Formal Invention
| |
| − | 1.3.6 Recursion in Perpetuity
| |
| − | 1.3.7 Processus, Regressus, Progressus
| |
| − | 1.3.8 Rondeau Tempo di Menuetto
| |
| − | 1.3.9 Reconnaissance
| |
| − | 1.3.9.1 The Informal Context
| |
| − | 1.3.9.2 The Epitext
| |
| − | 1.3.9.3 The Formative Tension
| |
| − | 1.3.10 Recurring Themes
| |
| − | 1.3.10.1 Preliminary Notions
| |
| − | 1.3.10.2 Intermediary Notions
| |
| − | 1.3.10.3 Propositions and Sentences
| |
| − | 1.3.10.4 Empirical Types and Rational Types
| |
| − | 1.3.10.5 Articulate Sentences
| |
| − | 1.3.10.6 Stretching Principles
| |
| − | 1.3.10.7 Stretching Operations
| |
| − | 1.3.10.8 The Cactus Patch
| |
| − | 1.3.10.9 The Cactus Language: Syntax
| |
| − | 1.3.10.10 The Cactus Language: Stylistics
| |
| − | 1.3.10.11 The Cactus Language: Mechanics
| |
| − | 1.3.10.12 The Cactus Language: Semantics
| |
| − | 1.3.10.13 Stretching Exercises
| |
| − | 1.3.10.14 Syntactic Transformations
| |
| − | 1.3.10.15 Derived Equivalence Relations
| |
| − | 1.3.10.16 Digression on Derived Relations
| |
| − | | |
| − | 1.4 Outlook of the Project: All Ways Lead to Inquiry
| |
| − | 1.4.1 The Matrix of Inquiry
| |
| − | 1.4.1.1 Inquiry as Conduct
| |
| − | 1.4.1.2 Types of Conduct
| |
| − | 1.4.1.3 Perils of Inquiry
| |
| − | 1.4.1.4 Forms of Relations
| |
| − | 1.4.1.5 Models of Inquiry
| |
| − | 1.4.2 The Moment of Inquiry
| |
| − | 1.4.3 The Modes of Inquiry
| |
| − | 1.4.3.1 Deductive Reasoning
| |
| − | 1.4.3.2 Inductive Reasoning
| |
| − | 1.4.3.3 Abductive Reasoning
| |
| − | 1.4.3.4 Analogical Reasoning
| |
| − | | |
| − | 1.5 Obstacles to the Project: In the Way of Inquiry
| |
| − | 1.5.1 The Initial Unpleasantness
| |
| − | 1.5.2 The Justification Trap
| |
| − | 1.5.3 A Formal Apology
| |
| − | 1.5.3.1 Category Double-Takes
| |
| − | 1.5.3.2 Conceptual Extensions
| |
| − | 1.5.3.3 Explosional Recombinations
| |
| − | 1.5.3.4 Interpretive Frameworks
| |
| − | 1.5.4 A Material Exigency
| |
| − | 1.5.5 A Reconciliation of Accounts
| |
| − | 1.5.6 Objections to Reflexive Inquiry
| |
| − | 1.5.7 Empirical Considerations
| |
| − | 1.5.8 Computational Considerations
| |
| − | 1.5.8.1 A Form of Recursion
| |
| − | 1.5.8.2 A Power of Abstraction
| |
| − | | |
| − | 1.6 Orientation of the Project: A Way Into Inquiry
| |
| − | 1.6.1 Initial Description of Inquiry
| |
| − | 1.6.2 Terms of Analysis
| |
| − | 1.6.2.1 Digression on Signs
| |
| − | 1.6.2.2 Empirical Status of ID
| |
| − | 1.6.3 Expansion of Terms
| |
| − | 1.6.3.1 Agency
| |
| − | 1.6.3.2 Abstraction
| |
| − | 1.6.3.3 Analogy
| |
| − | 1.6.3.4 Accuracy
| |
| − | 1.6.3.5 Authenticity
| |
| − | 1.6.4 Anchoring Terms in Phenomena
| |
| − | 1.6.4.1 A Mistaken ID
| |
| − | 1.6.4.2 Phenomenology of Doubt
| |
| − | 1.6.4.3 Modalities of Knowledge
| |
| − | 1.6.5 Sets, Systems, & Substantive Agents
| |
| − | 1.6.6 Interpretive Systems
| |
| − | 1.6.6.1 Syntactic Systems
| |
| − | 1.6.6.2 Semantic Systems
| |
| − | 1.6.6.3 Pragmatic Systems
| |
| − | 1.6.7 Inquiry Driven Systems
| |
| − | 1.6.7.1 A Definition of Inquiry
| |
| − | 1.6.7.2 The Faculty of Inquiry
| |
| − | 1.6.7.3 A Definition of Determination
| |
| − | 1.6.7.4 A Definition of Definition
| |
| − | | |
| − | 1.7 Organization of the Project: A Way Through Inquiry
| |
| − | 1.7.1 The Problem: Inquiry Found as an Object of Study
| |
| − | 1.7.2 The Method: Inquiry Found as a Means of Study
| |
| − | 1.7.2.1 Conditions for the Possibility
| |
| − | of Inquiry into Inquiry
| |
| − | 1.7.2.2 Conditions for the Success of Inquiry into Inquiry
| |
| − | 1.7.3 The Criterion: Inquiry in Search of a Sensible End
| |
| − | 1.7.3.1 The Irritation of Doubt, and The Scratch Test
| |
| − | 1.7.3.2 Enabling Provision 1: The Scenes & Context of Inquiry
| |
| − | 1.7.3.3 Enabling Provision 2: The Stages & Content of Inquiry
| |
| − | 1.8 Objectives of the Project: Inquiry All the Way
| |
| − | 1.8.1 Substantial Objective
| |
| − | 1.8.1.1 Objective 1a: The Propositions as Types Analogy
| |
| − | 1.8.1.2 Objective 1b: The Styles of Proof Development
| |
| − | 1.8.1.3 Objective 1c: The Analysis of Interpreters, or A Problem with Authority
| |
| − | 1.8.2 Instrumental Objective
| |
| − | 1.8.3 Coordination of Objectives
| |
| − | 1.8.4 Recapitulation -- Da Capo, Al Segno
| |
| − | | |
| − | 2. Discussion of Inquiry
| |
| − | 2.1 Approaches to Inquiry
| |
| − | 2.1.1 The Classical Framework: Syllogistic Approaches
| |
| − | 2.1.2 The Pragmatic Framework: Sign-Theoretic Approaches
| |
| − | 2.1.3 The Dynamical Framework: System-Theoretic Approaches
| |
| − | 2.1.3.1 Inquiry & Computation
| |
| − | 2.1.3.2 Inquiry Driven Systems
| |
| − | 2.2 The Context of Inquiry
| |
| − | 2.2.1 The Field of Observation
| |
| − | 2.2.2 The Problem of Reflection
| |
| − | 2.2.3 The Problem of Reconstruction
| |
| − | 2.2.4 The Trivializing of Integration
| |
| − | 2.2.5 Tensions in the Field of Observation
| |
| − | 2.2.6 Problems of Representation & Communication
| |
| − | | |
| − | 2.3 The Conduct of Inquiry
| |
| − | 2.3.1 Introduction
| |
| − | 2.3.2 The Types of Reasoning
| |
| − | 2.3.2.1 Deduction
| |
| − | 2.3.2.2 Induction
| |
| − | 2.3.2.3 Abduction
| |
| − | 2.3.3 Hybrid Types of Inference
| |
| − | 2.3.3.1 Analogy
| |
| − | 2.3.3.2 Inquiry
| |
| − | 2.3.4 Details of Induction
| |
| − | 2.3.4.1 Learning
| |
| − | 2.3.4.2 Transfer
| |
| − | 2.3.4.3 Testing
| |
| − | 2.3.5 The Stages of Inquiry
| |
| − | | |
| − | 3. The Medium & Its Message
| |
| − | 3.1 Reflective Expression
| |
| − | 3.1.1 Casual Reflection
| |
| − | 3.1.1.1 Ostensibly Recursive Texts
| |
| − | 3.1.1.2 Analogical Recursion
| |
| − | 3.1.2 Conscious Reflection
| |
| − | 3.1.2.1 The Signal Moment
| |
| − | 3.1.2.2 The Symbolic Object
| |
| − | 3.1.2.3 The Endeavor to Communicate
| |
| − | 3.1.2.4 The Medium of Communication
| |
| − | 3.1.2.5 The Ark of Types:
| |
| − | The Order of Things to Come.
| |
| − | 3.1.2.6 The Epitext
| |
| − | 3.1.2.7 The Context of Interpretation
| |
| − | 3.1.2.8 The Formative Tension
| |
| − | 3.1.2.9 The Vehicle of Communication:
| |
| − | Reflection on the Scene,
| |
| − | Reflection on the Self.
| |
| − | 3.1.2.10 (7)
| |
| − | 3.1.2.11 (6)
| |
| − | 3.1.2.12 Recursions: Possible, Actual, Necessary
| |
| − | 3.1.2.13 Ostensibly Recursive Texts
| |
| − | 3.1.2.14 (3)
| |
| − | 3.1.2.15 The Freedom of Interpretation
| |
| − | 3.1.2.16 The Eternal Return
| |
| − | 3.1.2.17 (1)
| |
| − | 3.1.2.18 Information in Formation
| |
| − | 3.1.2.19 Reflectively Indexical Texts
| |
| − | 3.1.2.20 (4)
| |
| − | 3.1.2.21 (5)
| |
| − | 3.1.2.22 (6)
| |
| − | 3.1.2.23 (7)
| |
| − | 3.1.2.24 (8)
| |
| − | 3.1.2.25 The Discursive Universe
| |
| − | 3.1.2.26 (7)
| |
| − | 3.1.2.27 (6)
| |
| − | 3.1.2.28 (5)
| |
| − | 3.1.2.29 (4)
| |
| − | 3.1.2.30 (3)
| |
| − | 3.1.2.31 (2)
| |
| − | 3.1.2.32 (1)
| |
| − | | |
| − | 3.2 Reflective Inquiry
| |
| − | 3.2.1 Integrity and Unity of Inquiry
| |
| − | 3.2.2 Apparitions & Allegations
| |
| − | 3.2.3 A Reflective Heuristic
| |
| − | 3.2.4 Either/Or: A Sense of Absence
| |
| − | 3.2.5 Apparent, Occasional, & Practical Necessity
| |
| − | 3.2.6 Approaches, Aspects, Exposures, Fronts
| |
| − | 3.2.7 Synthetic A Priori Truths
| |
| − | 3.2.8 Priorisms of Normative Sciences
| |
| − | 3.2.9 Principle of Rational Action
| |
| − | 3.2.10 The Pragmatic Cosmos
| |
| − | 3.2.11 Reflective Interpretive Frameworks
| |
| − | 3.2.11.1 Principals Versus Principles
| |
| − | 3.2.11.2 The Initial Description of Inquiry
| |
| − | 3.2.11.3 An Early Description of Interpretation
| |
| − | 3.2.11.4 Descriptions of the Mind
| |
| − | 3.2.11.5 Of Signs & the Mind
| |
| − | 3.2.11.6 Questions of Justification
| |
| − | 3.2.11.7 The Experience of Satisfaction
| |
| − | 3.2.11.8 An Organizational Difficulty
| |
| − | 3.2.11.9 Pragmatic Certainties
| |
| − | 3.2.11.10 Problems & Methods
| |
| − | | |
| − | 3.3 Reflection on Reflection
| |
| − | 3.4 Reflective Interpretive Frameworks
| |
| − | 3.4.1 The Phenomenology of Reflection
| |
| − | 3.4.2 A Candid Point of View
| |
| − | 3.4.3 A Projective Point of View
| |
| − | 3.4.4 A Formal Point of View
| |
| − | 3.4.5 Three Styles of Linguistic Usage
| |
| − | 3.4.6 Basic Notions of Group Theory
| |
| − | 3.4.7 Basic Notions of Formal Language Theory
| |
| − | 3.4.8 A Perspective on Computation
| |
| − | 3.4.9 Higher Order Sign Relations: Introduction
| |
| − | 3.4.10 Higher Order Sign Relations: Examples
| |
| − | 3.4.11 Higher Order Sign Relations: Application
| |
| − | 3.4.12 Issue 1: The Status of Signs
| |
| − | 3.4.13 Issue 2: The Status of Sets
| |
| − | 3.4.14 Issue 3: The Status of Variables
| |
| − | 3.4.15 Propositional Calculus
| |
| − | 3.4.16 Recursive Aspects
| |
| − | 3.4.17 Patterns of Self-Reference
| |
| − | 3.4.18 Practical Intuitions
| |
| − | 3.4.19 Examples of Self-Reference
| |
| − | 3.4.20 Three Views of Systems
| |
| − | 3.4.21 Building Bridges Between Representations
| |
| − | 3.4.22 Extensional Representations of Sign Relations
| |
| − | 3.4.23 Intensional Representations of Sign Relations
| |
| − | 3.4.24 Literal Intensional Representations
| |
| − | 3.4.25 Analytic Intensional Representations
| |
| − | 3.4.26 Differential Logic & Directed Graphs
| |
| − | 3.4.27 Differential Logic & Group Operations
| |
| − | 3.4.28 The Bridge: From Obstruction to Opportunity
| |
| − | 3.4.29 Projects of Representation
| |
| − | 3.4.30 Connected, Integrated, Reflective Symbols
| |
| − | 3.4.31 Generic Orders of Relations
| |
| − | 3.4.32 Partiality: Selective Operations
| |
| − | 3.4.33 Sign Relational Complexes
| |
| − | 3.4.34 Set-Theoretic Constructions
| |
| − | 3.4.35 Reducibility of Sign Relations
| |
| − | 3.4.36 Irreducibly Triadic Relations
| |
| − | 3.4.37 Propositional Types
| |
| − | 3.4.38 Considering the Source
| |
| − | 3.4.39 Prospective Indices: Pointers to Future Work
| |
| − | 3.4.40 Dynamic & Evaluative Frameworks
| |
| − | 3.4.41 Elective & Motive Forces
| |
| − | 3.4.42 Sign Processes: A Start
| |
| − | 3.4.43 Reflective Extensions
| |
| − | 3.4.44 Reflections on Closure
| |
| − | 3.4.45 Intelligence => Critical Reflection
| |
| − | 3.4.46 Looking Ahead
| |
| − | 3.4.47 Mutually Intelligible Codes
| |
| − | 3.4.48 Discourse Analysis: Ways & Means
| |
| − | 3.4.49 Combinations of Sign Relations
| |
| − | 3.4.50 Revisiting the Source
| |
| − | 3.5 Divertimento:
| |
| − | Eternity in Love with the Creatures of Time
| |
| − | 3.5.1 Reflections on the Presentation of Examples
| |
| − | 3.5.2 Searching for Parameters
| |
| − | 3.5.3 Defect Analysis
| |
| − | 3.5.4 The Pragmatic Critique
| |
| − | 3.5.5 Pragmatic Operating Notions
| |
| − | 3.5.6 Defects of Presentation
| |
| − | 3.5.7 Dues to Process
| |
| − | 3.5.8 Duties to Purpose
| |
| − | 3.6 Computational Design Philosophy
| |
| − | 3.6.1 Intentional Objects & Attitudes
| |
| − | 3.6.2 Imperfect Design & Persistent Error
| |
| − | 3.6.3 Propositional Reasoning About Relations
| |
| − | 3.6.4 Dynamic & Evaluative Frameworks
| |
| − | 3.6.5 Discussion of Examples
| |
| − | 3.6.6 Information & Inquiry
| |
| − | | |
| − | 4. Overview of the Domain: Interpretive Inquiry
| |
| − | 4.1 Interpretive Bearings: Conceptual & Descriptive Frameworks
| |
| − | 4.1.1 Catwalks: Flexible Frameworks & Peripatetic Categories
| |
| − | 4.1.1.1 Eponymous Ancestors:
| |
| − | The Precursors of Abstraction?
| |
| − | 4.1.1.2 Reticles:
| |
| − | Interpretive Flexibility as a Design Issue.
| |
| − | 4.1.2 Heuristic Inclinations & Regulative Principles
| |
| − | 4.2 Features of Inquiry Driven Systems
| |
| − | 4.2.1 The Pragmatic Theory of Signs
| |
| − | 4.2.1.1 Sign Relations
| |
| − | 4.2.1.2 Types of Signs
| |
| − | 4.2.2 The Pragmatic Theory of Inquiry
| |
| − | 4.2.2.1 Abduction
| |
| − | 4.2.2.2 Deduction
| |
| − | 4.2.2.3 Induction
| |
| − | 4.3 Examples of Inquiry Driven Systems
| |
| − | 4.3.1 "Index": A Program for Learning Formal Languages
| |
| − | 4.3.2 "Study": A Program for Reasoning with Propositions
| |
| − | 5. Discussion & Development of Objectives
| |
| − | 5.1 Objective 1a: Propositions as Types
| |
| − | 5.2 Objective 1b: Proof Styles & Developments
| |
| − | 5.3 Objective 1c: Interpretation & Authority
| |
| − | | |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| |
| − | | |
| − | Jon Awbrey, "Inquiry Driven Systems: Inquiry Into Inquiry"
| |
| − | IDS. http://stderr.org/pipermail/inquiry/2004-May/thread.html#1434
| |
| − | IDS. http://stderr.org/pipermail/inquiry/2004-May/thread.html#1564
| |
| − | IDS. http://stderr.org/pipermail/inquiry/2004-June/thread.html#1574
| |
| − | IDS. http://members.door.net/arisbe/menu/library/aboutcsp/awbrey/inquiry.htm
| |
| − | | |
| − | 1.3.4.12. Objective Plans and Levels
| |
| − | IDS 46. http://stderr.org/pipermail/inquiry/2004-May/001485.html
| |
| − | IDS 47. http://stderr.org/pipermail/inquiry/2004-May/001486.html
| |
| − | IDS 48. http://stderr.org/pipermail/inquiry/2004-May/001487.html
| |
| − | IDS 49. http://stderr.org/pipermail/inquiry/2004-May/001488.html
| |
| − | | |
| − | 1.3.4.13. Formalization of OF: Objective Levels
| |
| − | IDS 50. http://stderr.org/pipermail/inquiry/2004-May/001489.html
| |
| − | IDS 51. http://stderr.org/pipermail/inquiry/2004-May/001490.html
| |
| − | IDS 52. http://stderr.org/pipermail/inquiry/2004-May/001491.html
| |
| − | IDS 53. http://stderr.org/pipermail/inquiry/2004-May/001492.html
| |
| − | IDS 54. http://stderr.org/pipermail/inquiry/2004-May/001493.html
| |
| − | IDS 55. http://stderr.org/pipermail/inquiry/2004-May/001494.html
| |
| − | | |
| − | 1.3.4.14. Application of OF: Generic Level
| |
| − | IDS 56. http://stderr.org/pipermail/inquiry/2004-May/001495.html
| |
| − | IDS 57. http://stderr.org/pipermail/inquiry/2004-May/001496.html
| |
| − | IDS 58. http://stderr.org/pipermail/inquiry/2004-May/001497.html
| |
| − | IDS 59. http://stderr.org/pipermail/inquiry/2004-May/001498.html
| |
| − | IDS 60. http://stderr.org/pipermail/inquiry/2004-May/001499.html
| |
| − | IDS 61. http://stderr.org/pipermail/inquiry/2004-May/001500.html
| |
| − | IDS 62. http://stderr.org/pipermail/inquiry/2004-May/001501.html
| |
| − | IDS 63. http://stderr.org/pipermail/inquiry/2004-May/001502.html
| |
| − | | |
| − | 1.3.4.15. Application of OF: Motive Level
| |
| − | IDS 64. http://stderr.org/pipermail/inquiry/2004-May/001503.html
| |
| − | IDS 65. http://stderr.org/pipermail/inquiry/2004-May/001504.html
| |
| − | | |
| − | 1.3.4.16. The Integration of Frameworks
| |
| − | IDS 66. http://stderr.org/pipermail/inquiry/2004-May/001505.html
| |
| − | IDS 67. http://stderr.org/pipermail/inquiry/2004-May/001506.html
| |
| − | | |
| − | 1.3.4.17. Recapitulation: A Brush with Symbols
| |
| − | IDS 68. http://stderr.org/pipermail/inquiry/2004-May/001507.html
| |
| − | IDS 69. http://stderr.org/pipermail/inquiry/2004-May/001508.html
| |
| − | | |
| − | 1.3.4.18. C'est Moi
| |
| − | IDS 70. http://stderr.org/pipermail/inquiry/2004-May/001509.html
| |
| − | IDS 71. http://stderr.org/pipermail/inquiry/2004-May/001510.html
| |
| − | | |
| − | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
| |
| − | | |
| − | IDS. Inquiry Driven Systems -- 2004
| |
| − | | |
| − | 000. http://stderr.org/pipermail/inquiry/2004-May/thread.html#1434
| |
| − | 000. http://stderr.org/pipermail/inquiry/2004-May/thread.html#1564
| |
| − | 000. http://stderr.org/pipermail/inquiry/2004-June/thread.html#1574
| |
| − | | |
| − | 001. http://stderr.org/pipermail/inquiry/2004-May/001434.html
| |
| − | 002. http://stderr.org/pipermail/inquiry/2004-May/001435.html
| |
| − | 003. http://stderr.org/pipermail/inquiry/2004-May/001436.html
| |
| − | 004. http://stderr.org/pipermail/inquiry/2004-May/001437.html
| |
| − | 005. http://stderr.org/pipermail/inquiry/2004-May/001438.html
| |
| − | 006. http://stderr.org/pipermail/inquiry/2004-May/001439.html
| |
| − | 007. http://stderr.org/pipermail/inquiry/2004-May/001440.html
| |
| − | 008. http://stderr.org/pipermail/inquiry/2004-May/001441.html
| |
| − | 009. http://stderr.org/pipermail/inquiry/2004-May/001442.html
| |
| − | 010. http://stderr.org/pipermail/inquiry/2004-May/001443.html
| |
| − | 011. http://stderr.org/pipermail/inquiry/2004-May/001444.html
| |
| − | 012. http://stderr.org/pipermail/inquiry/2004-May/001448.html
| |
| − | 013. http://stderr.org/pipermail/inquiry/2004-May/001449.html
| |
| − | 014. http://stderr.org/pipermail/inquiry/2004-May/001450.html
| |
| − | 015. http://stderr.org/pipermail/inquiry/2004-May/001451.html
| |
| − | 016. http://stderr.org/pipermail/inquiry/2004-May/001452.html
| |
| − | 017. http://stderr.org/pipermail/inquiry/2004-May/001453.html
| |
| − | 018. http://stderr.org/pipermail/inquiry/2004-May/001454.html
| |
| − | 019. http://stderr.org/pipermail/inquiry/2004-May/001455.html
| |
| − | 020. http://stderr.org/pipermail/inquiry/2004-May/001457.html
| |
| − | 021. http://stderr.org/pipermail/inquiry/2004-May/001458.html
| |
| − | 022. http://stderr.org/pipermail/inquiry/2004-May/001459.html
| |
| − | 023. http://stderr.org/pipermail/inquiry/2004-May/001460.html
| |
| − | 024. http://stderr.org/pipermail/inquiry/2004-May/001461.html
| |
| − | 025. http://stderr.org/pipermail/inquiry/2004-May/001462.html
| |
| − | 026. http://stderr.org/pipermail/inquiry/2004-May/001463.html
| |
| − | 027. http://stderr.org/pipermail/inquiry/2004-May/001464.html
| |
| − | 028. http://stderr.org/pipermail/inquiry/2004-May/001465.html
| |
| − | 029. http://stderr.org/pipermail/inquiry/2004-May/001466.html
| |
| − | 030. http://stderr.org/pipermail/inquiry/2004-May/001467.html
| |
| − | 031. http://stderr.org/pipermail/inquiry/2004-May/001468.html
| |
| − | 032. http://stderr.org/pipermail/inquiry/2004-May/001469.html
| |
| − | 033. http://stderr.org/pipermail/inquiry/2004-May/001470.html
| |
| − | 034. http://stderr.org/pipermail/inquiry/2004-May/001471.html
| |
| − | 035. http://stderr.org/pipermail/inquiry/2004-May/001472.html
| |
| − | 036. http://stderr.org/pipermail/inquiry/2004-May/001473.html
| |
| − | 037. http://stderr.org/pipermail/inquiry/2004-May/001474.html
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| − | 038. http://stderr.org/pipermail/inquiry/2004-May/001475.html
| |
| − | 039. http://stderr.org/pipermail/inquiry/2004-May/001478.html
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| − | 040. http://stderr.org/pipermail/inquiry/2004-May/001479.html
| |
| − | 041. http://stderr.org/pipermail/inquiry/2004-May/001480.html
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| − | | |
| − | IDS. Inquiry Driven Systems -- Discussion
| |
| − | | |
| − | 00. http://stderr.org/pipermail/inquiry/2004-May/thread.html#1560
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| − | 00. http://stderr.org/pipermail/inquiry/2004-June/thread.html#1576
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| − | 06.
| |
| | | | |
| | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o | | o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o |
| | </pre> | | </pre> |
| | | | |
| − | ==Outline== | + | ===Inquiry List=== |
| | | | |
| − | <pre>
| + | * http://stderr.org/pipermail/inquiry/2004-May/thread.html#1434 |
| − | Inquiry Driven Systems (07 Apr 2003)
| + | * http://stderr.org/pipermail/inquiry/2004-May/thread.html#1564 |
| − | 1. Research Proposal
| + | * http://stderr.org/pipermail/inquiry/2004-June/thread.html#1574 |
| − | 1.1 Outline of the Project : Inquiry Driven Systems
| |
| − | 1.1.1 Problem
| |
| − | 1.1.2 Method
| |
| − | 1.1.2.1 The Paradigmatic & Process-Analytic Phase.
| |
| − | 1.1.2.2 The Paraphrastic & Faculty-Synthetic Phase.
| |
| − | 1.1.2.3 Reprise of Methods
| |
| − | 1.1.3 Criterion
| |
| − | 1.1.4 Application
| |
| − | 1.2 Onus of the Project : No Way But Inquiry
| |
| − | 1.2.1 A Modulating Prelude
| |
| − | 1.2.2 A Fugitive Canon
| |
| − | | |
| − | 1.3 Option of the Project : A Way Up To Inquiry
| |
| − | 1.3.1 Initial Analysis of Inquiry : Allegro Aperto
| |
| − | 1.3.2 Discussion of Discussion
| |
| − | 1.3.3 Discussion of Formalization : General Topics
| |
| − | 1.3.3.1 A Formal Charge
| |
| − | 1.3.3.2 A Formalization of Formalization?
| |
| − | 1.3.3.3 A Formalization of Discussion?
| |
| − | 1.3.3.4 A Concept of Formalization
| |
| − | 1.3.3.5 A Formal Approach
| |
| − | 1.3.3.6 A Formal Development
| |
| − | 1.3.3.7 A Formal Persuasion
| |
| − | 1.3.4 Discussion of Formalization : Concrete Examples
| |
| − | 1.3.4.1 Formal Models : A Sketch
| |
| − | 1.3.4.2 Sign Relations : A Primer
| |
| − | 1.3.4.3 Semiotic Equivalence Relations
| |
| − | 1.3.4.4 Graphical Representations
| |
| − | 1.3.4.5 Taking Stock
| |
| − | 1.3.4.6 The "Meta" Question
| |
| − | 1.3.4.7 Iconic Signs
| |
| − | 1.3.4.8 The Conflict of Interpretations
| |
| − | 1.3.4.9 Indexical Signs
| |
| − | 1.3.4.10 Sundry Problems
| |
| − | 1.3.4.11 Review & Prospect
| |
| − | 1.3.4.12 Objective Plans & Levels
| |
| − | 1.3.4.13 Formalization of OF : Objective Levels
| |
| − | 1.3.4.14 Application of OF : Generic Level
| |
| − | 1.3.4.15 Application of OF : Motive Level
| |
| − | 1.3.4.16 The Integration of Frameworks
| |
| − | 1.3.4.17 Recapitulation : A Brush with Symbols
| |
| − | 1.3.4.18 C'est Moi
| |
| − | 1.3.4.19 Entr'acte
| |
| − | 1.3.5 Discussion of Formalization : Specific Objects
| |
| − | 1.3.5.1 The Will to Form
| |
| − | 1.3.5.2 The Forms of Reasoning
| |
| − | 1.3.5.3 A Fork in the Road
| |
| − | 1.3.5.4 A Forged Bond
| |
| − | 1.3.5.5 A Formal Account
| |
| − | 1.3.5.6 Analogs, Icons, Models, Surrogates
| |
| − | 1.3.5.7 Steps & Tests of Formalization
| |
| − | 1.3.5.8 Puck, the Ref
| |
| − | 1.3.5.9 Partial Formalizations
| |
| − | 1.3.5.10 A Formal Utility
| |
| − | 1.3.5.11 A Formal Aesthetic
| |
| − | 1.3.5.12 A Formal Apology
| |
| − | 1.3.5.13 A Formal Suspicion
| |
| − | 1.3.5.14 The Double Aspect of Concepts
| |
| − | 1.3.5.15 A Formal Permission
| |
| − | 1.3.5.16 A Formal Invention
| |
| − | 1.3.6 Recursion in Perpetuity
| |
| − | 1.3.7 Processus, Regressus, Progressus
| |
| − | 1.3.8 Rondeau : Tempo di Menuetto
| |
| − | 1.3.9 Reconnaissance
| |
| − | 1.3.9.1 The Informal Context
| |
| − | 1.3.9.2 The Epitext
| |
| − | 1.3.9.3 The Formative Tension
| |
| − | 1.3.10 Recurring Themes
| |
| − | 1.3.10.1 Preliminary Notions
| |
| − | 1.3.10.2 Intermediary Notions
| |
| − | 1.3.10.3 Propositions & Sentences
| |
| − | 1.3.10.4 Empirical Types & Rational Types
| |
| − | 1.3.10.5 Articulate Sentences
| |
| − | 1.3.10.6 Stretching Principles
| |
| − | 1.3.10.7 Stretching Operations
| |
| − | 1.3.10.8 The Cactus Patch
| |
| − | 1.3.10.9 The Cactus Language : Syntax
| |
| − | 1.3.10.10 The Cactus Language : Stylistics
| |
| − | 1.3.10.11 The Cactus Language : Mechanics
| |
| − | 1.3.10.12 The Cactus Language : Semantics
| |
| − | 1.3.10.13 Stretching Exercises
| |
| − | 1.3.10.14 Syntactic Transformations
| |
| − | 1.3.10.15 Derived Equivalence Relations
| |
| − | 1.3.10.16 Digression on Derived Relations
| |
| − | | |
| − | 1.4 Outlook of the Project : All Ways Lead to Inquiry
| |
| − | 1.4.1 The Matrix of Inquiry
| |
| − | 1.4.1.1 Inquiry as Conduct
| |
| − | 1.4.1.2 Types of Conduct
| |
| − | 1.4.1.3 Perils of Inquiry
| |
| − | 1.4.1.4 Forms of Relations
| |
| − | 1.4.1.5 Models of Inquiry
| |
| − | 1.4.2 The Moment of Inquiry
| |
| − | 1.4.3 The Modes of Inquiry
| |
| − | 1.4.3.1 Deductive Reasoning
| |
| − | 1.4.3.2 Inductive Reasoning
| |
| − | 1.4.3.3 Abductive Reasoning
| |
| − | 1.4.3.4 Analogical Reasoning
| |
| − | ...
| |
| − | | |
| − | 1.5 Obstacles to the Project : In the Way of Inquiry
| |
| − | 1.5.1 The Initial Unpleasantness
| |
| − | 1.5.2 The Justification Trap
| |
| − | 1.5.3 A Formal Apology
| |
| − | 1.5.3.1 Category Double-Takes
| |
| − | 1.5.3.2 Conceptual Extensions
| |
| − | 1.5.3.3 Explosional Recombinations
| |
| − | 1.5.3.4 Interpretive Frameworks
| |
| − | 1.5.4 A Material Exigency
| |
| − | 1.5.5 A Reconciliation of Accounts
| |
| − | 1.5.6 Objections to Reflexive Inquiry
| |
| − | 1.5.7 Empirical Considerations
| |
| − | 1.5.8 Computational Considerations
| |
| − | 1.5.8.1 A Form of Recursion
| |
| − | 1.5.8.2 A Power of Abstraction
| |
| − | | |
| − | 1.6 Orientation of the Project : A Way Into Inquiry
| |
| − | 1.6.1 Initial Description of Inquiry
| |
| − | 1.6.2 Terms of Analysis
| |
| − | 1.6.2.1 Digression on Signs
| |
| − | 1.6.2.2 Empirical Status of ID
| |
| − | 1.6.3 Expansion of Terms
| |
| − | 1.6.3.1 Agency
| |
| − | 1.6.3.2 Abstraction
| |
| − | 1.6.3.3 Analogy
| |
| − | 1.6.3.4 Accuracy
| |
| − | 1.6.3.5 Authenticity
| |
| − | 1.6.4 Anchoring Terms in Phenomena
| |
| − | 1.6.4.1 A Mistaken ID
| |
| − | 1.6.4.2 Phenomenology of Doubt
| |
| − | 1.6.4.3 Modalities of Knowledge
| |
| − | 1.6.5 Sets, Systems, & Substantive Agents
| |
| − | 1.6.6 Interpretive Systems
| |
| − | 1.6.6.1 Syntactic Systems
| |
| − | 1.6.6.2 Semantic Systems
| |
| − | 1.6.6.3 Pragmatic Systems
| |
| − | 1.6.7 Inquiry Driven Systems
| |
| − | 1.6.7.1 A Definition of Inquiry
| |
| − | 1.6.7.2 The Faculty of Inquiry
| |
| − | 1.6.7.3 A Definition of Determination
| |
| − | 1.6.7.4 A Definition of Definition
| |
| − | | |
| − | 1.7 Organization of the Project : A Way Through Inquiry
| |
| − | 1.7.1 The Problem : Inquiry Found as an Object of Study
| |
| − | 1.7.2 The Method : Inquiry Found as a Means of Study
| |
| − | 1.7.2.1 Conditions for the Possibility
| |
| − | of Inquiry into Inquiry
| |
| − | 1.7.2.2 Conditions for the Success
| |
| − | of Inquiry into Inquiry
| |
| − | 1.7.3 The Criterion : Inquiry in Search of a Sensible End
| |
| − | 1.7.3.1 The Irritation of Doubt, and The Scratch Test.
| |
| − | 1.7.3.2 Enabling Provision 1 : The Scenes & Context of Inquiry.
| |
| − | 1.7.3.3 Enabling Provision 2 : The Stages & Content of Inquiry.
| |
| − | 1.8 Objectives of the Project : Inquiry All the Way
| |
| − | 1.8.1 Substantial Objective
| |
| − | 1.8.1.1 Objective 1a : The Propositions as Types Analogy.
| |
| − | 1.8.1.2 Objective 1b : The Styles of Proof Development.
| |
| − | 1.8.1.3 Objective 1c : The Analysis of Interpreters, or A Problem with Authority.
| |
| − | 1.8.2 Instrumental Objective
| |
| − | 1.8.3 Coordination of Objectives
| |
| − | 1.8.4 Recapitulation : Da Capo, Al Segno
| |
| − | | |
| − | 2. Discussion of Inquiry
| |
| − | 2.1 Approaches to Inquiry
| |
| − | 2.1.1 The Classical Framework : Syllogistic Approaches
| |
| − | 2.1.2 The Pragmatic Framework : Sign-Theoretic Approaches
| |
| − | 2.1.3 The Dynamical Framework : System-Theoretic Approaches
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| − | 2.1.3.1 Inquiry & Computation
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| − | 2.1.3.2 Inquiry Driven Systems
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| − | 2.2 The Context of Inquiry
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| − | 2.2.1 The Field of Observation
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| − | 2.2.2 The Problem of Reflection
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| − | 2.2.3 The Problem of Reconstruction
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| − | 2.2.4 The Trivializing of Integration
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| − | 2.2.5 Tensions in the Field of Observation
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| − | 2.2.6 Problems of Representation & Communication
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| − | 2.3 The Conduct of Inquiry
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| − | 2.3.1 Introduction
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| − | 2.3.2 The Types of Reasoning
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| − | 2.3.2.1 Deduction
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| − | 2.3.2.2 Induction
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| − | 2.3.2.3 Abduction
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| − | 2.3.3 Hybrid Types of Inference
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| − | 2.3.3.1 Analogy
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| − | 2.3.3.2 Inquiry
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| − | 2.3.4 Details of Induction
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| − | 2.3.4.1 Learning
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| − | 2.3.4.2 Transfer
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| − | 2.3.4.3 Testing
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| − | 2.3.5 The Stages of Inquiry
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| − | 3. The Medium & Its Message
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| − | 3.1 Reflective Expression
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| − | 3.1.1 Casual Reflection
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| − | 3.1.1.1 Ostensibly Recursive Texts
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| − | 3.1.1.2 Analogical Recursion
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| − | 3.1.2 Conscious Reflection
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| − | 3.1.2.1 The Signal Moment
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| − | 3.1.2.2 The Symbolic Object
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| − | 3.1.2.3 The Endeavor to Communicate
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| − | 3.1.2.4 The Medium of Communication
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| − | 3.1.2.5 The Ark of Types : The Order of Things to Come.
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| − | 3.1.2.6 The Epitext
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| − | 3.1.2.7 The Context of Interpretation
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| − | 3.1.2.8 The Formative Tension
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| − | 3.1.2.9 The Vehicle of Communication :
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| − | Reflection on the Scene,
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| − | Reflection on the Self.
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| − | 3.1.2.10 (7)
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| − | 3.1.2.11 (6)
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| − | 3.1.2.12 Recursions : Possible, Actual, Necessary
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| − | 3.1.2.13 Ostensibly Recursive Texts
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| − | 3.1.2.14 (3)
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| − | 3.1.2.15 The Freedom of Interpretation
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| − | 3.1.2.16 The Eternal Return
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| − | 3.1.2.17 (1)
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| − | 3.1.2.18 Information in Formation
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| − | 3.1.2.19 Reflectively Indexical Texts
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| − | 3.1.2.20 (4)
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| − | 3.1.2.21 (5)
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| − | 3.1.2.22 (6)
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| − | 3.1.2.23 (7)
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| − | 3.1.2.24 (8)
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| − | 3.1.2.25 The Discursive Universe
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| − | 3.1.2.26 (7)
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| − | 3.1.2.27 (6)
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| − | 3.1.2.28 (5)
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| − | 3.1.2.29 (4)
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| − | 3.1.2.30 (3)
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| − | 3.1.2.31 (2)
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| − | 3.1.2.32 (1)
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| − | 3.2 Reflective Inquiry
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| − | 3.2.1 Integrity & Unity of Inquiry
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| − | 3.2.2 Apparitions & Allegations
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| − | 3.2.3 A Reflective Heuristic
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| − | 3.2.4 Either/Or : A Sense of Absence
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| − | 3.2.5 Apparent, Occasional, & Practical Necessity
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| − | 3.2.6 Approaches, Aspects, Exposures, Fronts
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| − | 3.2.7 Synthetic A Priori Truths
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| − | 3.2.8 Priorisms of Normative Sciences
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| − | 3.2.9 Principle of Rational Action
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| − | 3.2.10 The Pragmatic Cosmos
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| − | 3.2.11 Reflective Interpretive Frameworks
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| − | 3.2.11.1 Principals Versus Principles
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| − | 3.2.11.2 The Initial Description of Inquiry
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| − | 3.2.11.3 An Early Description of Interpretation
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| − | 3.2.11.4 Descriptions of the Mind
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| − | 3.2.11.5 Of Signs & the Mind
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| − | 3.2.11.6 Questions of Justification
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| − | 3.2.11.7 The Experience of Satisfaction
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| − | 3.2.11.8 An Organizational Difficulty
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| − | 3.2.11.9 Pragmatic Certainties
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| − | 3.2.11.10 Problems & Methods
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| − | 3.3 Reflection on Reflection
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| − | 3.4 Reflective Interpretive Frameworks
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| − | 3.4.1 The Phenomenology of Reflection
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| − | 3.4.2 A Candid Point of View
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| − | 3.4.3 A Projective Point of View
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| − | 3.4.4 A Formal Point of View
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| − | 3.4.5 Three Styles of Linguistic Usage
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| − | 3.4.6 Basic Notions of Group Theory
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| − | 3.4.7 Basic Notions of Formal Language Theory
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| − | 3.4.8 A Perspective on Computation
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| − | 3.4.9 Higher Order Sign Relations : Introduction
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| − | 3.4.10 Higher Order Sign Relations : Examples
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| − | 3.4.11 Higher Order Sign Relations : Application
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| − | 3.4.12 Issue 1 : The Status of Signs
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| − | 3.4.13 Issue 2 : The Status of Sets
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| − | 3.4.14 Issue 3 : The Status of Variables
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| − | 3.4.15 Propositional Calculus
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| − | 3.4.16 Recursive Aspects
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| − | 3.4.17 Patterns of Self-Reference
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| − | 3.4.18 Practical Intuitions
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| − | 3.4.19 Examples of Self-Reference
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| − | 3.4.20 Three Views of Systems
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| − | 3.4.21 Building Bridges Between Representations
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| − | 3.4.22 Extensional Representations of Sign Relations
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| − | 3.4.23 Intensional Representations of Sign Relations
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| − | 3.4.24 Literal Intensional Representations
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| − | 3.4.25 Analytic Intensional Representations
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| − | 3.4.26 Differential Logic & Directed Graphs
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| − | 3.4.27 Differential Logic & Group Operations
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| − | 3.4.28 The Bridge : From Obstruction to Opportunity
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| − | 3.4.29 Projects of Representation
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| − | 3.4.30 Connected, Integrated, Reflective Symbols
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| − | 3.4.31 Generic Orders of Relations
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| − | 3.4.32 Partiality : Selective Operations
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| − | 3.4.33 Sign Relational Complexes
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| − | 3.4.34 Set-Theoretic Constructions
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| − | 3.4.35 Reducibility of Sign Relations
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| − | 3.4.36 Irreducibly Triadic Relations
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| − | 3.4.37 Propositional Types
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| − | 3.4.38 Considering the Source
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| − | 3.4.39 Prospective Indices : Pointers to Future Work
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| − | 3.4.40 Dynamic & Evaluative Frameworks
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| − | 3.4.41 Elective & Motive Forces
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| − | 3.4.42 Sign Processes : A Start
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| − | 3.4.43 Reflective Extensions
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| − | 3.4.44 Reflections on Closure
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| − | 3.4.45 Intelligence => Critical Reflection
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| − | 3.4.46 Looking Ahead
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| − | 3.4.47 Mutually Intelligible Codes
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| − | 3.4.48 Discourse Analysis : Ways & Means
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| − | 3.4.49 Combinations of Sign Relations
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| − | 3.4.50 Revisiting the Source
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| − | 3.5 Divertimento : Eternity in Love with the Creatures of Time
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| − | 3.5.1 Reflections on the Presentation of Examples
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| − | 3.5.2 Searching for Parameters
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| − | 3.5.3 Defect Analysis
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| − | 3.5.4 The Pragmatic Critique
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| − | 3.5.5 Pragmatic Operating Notions
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| − | 3.5.6 Defects of Presentation
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| − | 3.5.7 Dues to Process
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| − | 3.5.8 Duties to Purpose
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| − | 3.6 Computational Design Philosophy
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| − | 3.6.1 Intentional Objects & Attitudes
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| − | 3.6.2 Imperfect Design & Persistent Error
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| − | 3.6.3 Propositional Reasoning About Relations
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| − | 3.6.4 Dynamic & Evaluative Frameworks
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| − | 3.6.5 Discussion of Examples
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| − | 3.6.6 Information & Inquiry
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| − | 4. Overview of the Domain : Interpretive Inquiry
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| − | 4.1 Interpretive Bearings : Conceptual & Descriptive Frameworks
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| − | 4.1.1 Catwalks : Flexible Frameworks & Peripatetic Categories
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| − | 4.1.1.1 Eponymous Ancestors : The Precursors of Abstraction?
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| − | 4.1.1.2 Reticles : Interpretive Flexibility as a Design Issue.
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| − | 4.1.2 Heuristic Inclinations & Regulative Principles
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| − | 4.2 Features of Inquiry Driven Systems
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| − | 4.2.1 The Pragmatic Theory of Signs
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| − | 4.2.1.1 Sign Relations
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| − | 4.2.1.2 Types of Signs
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| − | 4.2.2 The Pragmatic Theory of Inquiry
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| − | 4.2.2.1 Abduction
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| − | 4.2.2.2 Deduction
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| − | 4.2.2.3 Induction
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| − | 4.3 Examples of Inquiry Driven Systems
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| − | 4.3.1 "Index" : A Program for Learning Formal Languages
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| − | 4.3.2 "Study" : A Program for Reasoning with Propositions
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| − | 5. Discussion & Development of Objectives
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| − | 5.1 Objective 1a : Propositions as Types
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| − | 5.2 Objective 1b : Proof Styles & Developments
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| − | 5.3 Objective 1c : Interpretation & Authority
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| − | </pre>
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