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domains, and thus defined as follows:
domains, and thus defined as follows:
Con(L) = Proj_SI (L) = {<s, i> in S x I : <o, s, i> in L for some o in O}.
Con(L) = Proj_SI (L) = {< s, i> in S x I : <o, s, i> in L for some o in O}.
The intentional component of meaning for a sign relation L, or its
The intentional component of meaning for a sign relation L, or its
note of the "horizontal" versus the "vertical" versions of what
note of the "horizontal" versus the "vertical" versions of what
amounts to the same abstract principle.
amounts to the same abstract principle.
</pre>
==Where I Left Off In June 2004==
<pre>
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
a particular goal, object, or purpose, I frequently refer to
a particular goal, object, or purpose, I frequently refer to
as "Facts".
as "Facts".
</pre>
=====1.3.10.14. Syntactic Transformations (cont.)=====
1.3.10.14. Syntactic Transformations (cont.)
Besides linking rules together into extended sequences of equivalents,
Besides linking rules together into extended sequences of equivalents,
If X c U
If X c U
and u C U,
and u C U,
then the following statement is true:
then the following statement is true:
C1a. u C X <=> {X}(u) = 1. R3a=R3c
C1a. u C X <=> {X}(u) = 1. R3a=R3c
If X c U is fixed
If X c U is fixed
and u C U is varied,
and u C U is varied,
then the following are equivalent:
then the following are equivalent:
R4a. u C X.
R4a. u C X.
R4b. [u C X].
R4b. [u C X].
R4c. [u C X](u).
R4c. [u C X](u).
R4d. {X}(u).
R4d. {X}(u).
R4e. {X}(u) = 1.
R4e. {X}(u) = 1.
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 STR as follows:
about things in the universe U
about things in the universe U
and Pj is a proposition
and Pj is a proposition
about things in the universe U
about things in the universe U
such that:
such that:
L0a. [Sj] = Pj, for all j C J,
L0a. [Sj] = Pj, for all j C J,
then the following equations are true:
then the following equations are true:
L0b. [ConcJj Sj] = ConjJj [Sj] = ConjJj Pj.
L0b. [ConcJj Sj] = ConjJj [Sj] = ConjJj Pj.
L0c. [SurcJj Sj] = SurjJj [Sj] = SurjJj Pj.
L0c. [SurcJj Sj] = SurjJj [Sj] = SurjJj Pj.
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.
Logical Translation Rule 1
Logical Translation Rule 1
about things in the universe U
about things in the universe U
and P is a proposition : U -> B, such that:
and P is a proposition : U -> B, such that:
L1a. [S] = P,
L1a. [S] = P,
then the following equations hold:
then the following equations hold:
L1b00. [False] = () = 0 : U->B.
L1b00. [False] = () = 0 : U->B.
L1b01. [Not S] = ([S]) = (P) : U->B.
L1b01. [Not S] = ([S]) = (P) : U->B.
L1b10. [S] = [S] = P : U->B.
L1b10. [S] = [S] = P : U->B.
L1b11. [True] = (()) = 1 : U->B.
L1b11. [True] = (()) = 1 : U->B.
Geometric Translation Rule 1
Geometric Translation Rule 1
If X c U
If X c U
and P : U -> B, such that:
and P : U -> B, such that:
G1a. {X} = P,
G1a. {X} = P,
then the following equations hold:
then the following equations hold:
G1b00. {{}} = () = 0 : U->B.
G1b00. {{}} = () = 0 : U->B.
G1b10. {~X} = ({X}) = (P) : U->B.
G1b10. {~X} = ({X}) = (P) : U->B.
G1b01. {X} = {X} = P : U->B.
G1b01. {X} = {X} = P : U->B.
G1b11. {U} = (()) = 1 : U->B.
G1b11. {U} = (()) = 1 : U->B.
Logical Translation Rule 2
Logical Translation Rule 2
about things in the universe U
about things in the universe U
and P, Q are propositions: U -> B, such that:
and P, Q are propositions: U -> B, such that:
L2a. [S] = P and [T] = Q,
L2a. [S] = P and [T] = Q,
then the following equations hold:
then the following equations hold:
L2b00. [False] = () = 0 : U->B.
L2b00. [False] = () = 0 : U->B.
L2b01. [Neither S nor T] = ([S])([T]) = (P)(Q).
L2b01. [Neither S nor T] = ([S])([T]) = (P)(Q).
L2b02. [Not S, but T] = ([S])[T] = (P) Q.
L2b02. [Not S, but T] = ([S])[T] = (P) Q.
L2b03. [Not S] = ([S]) = (P).
L2b03. [Not S] = ([S]) = (P).
L2b04. [S and not T] = [S]([T]) = P (Q).
L2b04. [S and not T] = [S]([T]) = P (Q).
L2b05. [Not T] = ([T]) = (Q).
L2b05. [Not T] = ([T]) = (Q).
L2b06. [S or T, not both] = ([S], [T]) = (P, Q).
L2b06. [S or T, not both] = ([S], [T]) = (P, Q).
L2b07. [Not both S and T] = ([S].[T]) = (P Q).
L2b07. [Not both S and T] = ([S].[T]) = (P Q).
L2b08. [S and T] = [S].[T] = P.Q.
L2b08. [S and T] = [S].[T] = P.Q.
L2b09. [S <=> T] = (([S], [T])) = ((P, Q)).
L2b09. [S <=> T] = (([S], [T])) = ((P, Q)).
L2b10. [T] = [T] = Q.
L2b10. [T] = [T] = Q.
L2b11. [S => T] = ([S]([T])) = (P (Q)).
L2b11. [S => T] = ([S]([T])) = (P (Q)).
L2b12. [S] = [S] = P.
L2b12. [S] = [S] = P.
L2b13. [S <= T] = (([S]) [T]) = ((P) Q).
L2b13. [S <= T] = (([S]) [T]) = ((P) Q).
L2b14. [S or T] = (([S])([T])) = ((P)(Q)).
L2b14. [S or T] = (([S])([T])) = ((P)(Q)).
L2b15. [True] = (()) = 1 : U->B.
L2b15. [True] = (()) = 1 : U->B.
D4b. {<u, v> C UxB : v = [u C X]}
D4b. {< u, v> C UxB : v = [u C X]}
::
::
R5d. {<u, v> C UxB : v = [u C X]}
R5d. {< u, v> C UxB : v = [u C X]}
=
=
{<u, v> C UxB : v = [u C Y]}. :???
{< u, v> C UxB : v = [u C Y]}. :???
:D5b
:D5b
: {X} = {<u, v> C UxB : v = [S](u)}. :R
: {X} = {< u, v> C UxB : v = [S](u)}. :R
::
::
///
///
=====1.3.10.15 Derived Equivalence Relations=====
1.3.10.15 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.
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:
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}.
Equivalent expressions for this concept are recorded in Definition 8.
Equivalent expressions for this concept are recorded in Definition 8.
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}
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:
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}.
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.
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}
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:
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:
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}.
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.
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}
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:
1.3.10.16 Digression on Derived Relations
=====1.3.10.16 Digression on Derived 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.
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.
may seem.
may seem.
====1.4.1 The Matrix of Inquiry====
<pre>
| Thus when mothers have chidren suffering from sleeplessness,
| Thus when mothers have chidren suffering from sleeplessness,
| and want to lull them to rest, the treatment they apply is
| and want to lull them to rest, the treatment they apply is
| to give them, not quiet, but motion, for they rock them
| to give them, not quiet, but motion, for they rock them
| constantly in their arms; and instead of silence, they
| constantly in their arms; and instead of silence, they
| use a kind of crooning noise; and thus they literally
| use a kind of crooning noise; and thus they literally
| cast a spell upon the children (like the victims of
| cast a spell upon the children (like the victims of
| a Bacchic frenzy) by employing the combined movements
| a Bacchic frenzy) by employing the combined movements
| of dance and song as a remedy.
| of dance and song as a remedy.
|
|
| Plato, 'Laws', VII, 790D
| Plato, 'Laws', VII, 790D
</pre>
Try as I may, I've never seen a way to develop a theory of inquiry from nothing:
Try as I may, I've never seen a way to develop a theory of inquiry from nothing:
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
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.
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.
1.4.1 The Matrix of Inquiry
====1.4.1 The Matrix of Inquiry (2)====
<blockquote>
<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>
</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.
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.
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.
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=====
1.4.1.1 Inquiry as Conduct
First of all, inquiry is conceived to be a form of conduct.
First of all, inquiry is conceived to be a form of conduct.
This invokes the technical term "conduct", referring to the
This invokes the technical term "conduct", referring to the
species of prototypically human action that is both dynamic
species of prototypically human action that is both dynamic
and deliberate, or conceived to fall under a form of purposeful
and deliberate, or conceived to fall under a form of purposeful
control, usually conscious but possibly not. For the sake of
control, usually conscious but possibly not. For the sake of
clarity, it helps to seek a more formal definition of conduct,
clarity, it helps to seek a more formal definition of conduct,
one that expresses the concept in terms of abstract features
one that expresses the concept in terms of abstract features
rather than trying to suggest it by means of typical examples.
rather than trying to suggest it by means of typical examples.
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.
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.
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:
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.
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.
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.
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 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.
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.
1. Inquiry is a form of conduct.
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.
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.
to name the genus of which "conduct" names a species, and thus depicts
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.
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.
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.
the object with respect to the states? The states are conceived to be
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.
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.
relation to these states the object must be conceived to fall in time.
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.
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.
This makes the question of relative time a secular parameter of the
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:
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.
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.
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.
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 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.
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.
1. Inquiry is a form of conduct.
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.
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.
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.
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.
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 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.
=====1.4.1.2 Types of Conduct=====
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.
What names can be given to these two orders of conduct?
=====1.4.1.3 Perils of Inquiry=====
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?
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.
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.
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.
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.
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.
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.
=====1.4.1.4 Forms of Relations=====
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:
a description in terms of laws and values of the rules that
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.
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.
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:
1. Signs are special cases of states.
2. Signs and states are the same sorts of things.
3. States are special cases of signs.
Depending on how one answers this question, one is also choosing among the following options:
1. Sign relations are special cases of conduct relations.
2. Sign relations and conduct relations are the same sorts of things.
3. Conduct relations are special cases of sign relations.
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.
=====1.4.1.5 Models of Inquiry=====
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.
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.
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.
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".
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.
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.
With respect to these
With respect to this hypothetical
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.
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?
====1.4.2 The Moment of Inquiry====
1.4.1.2 Types of Conduct
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.
<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>
<p>(Plato, Laws, VII, 799C).</p>
</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.
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.
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.
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.
1.4.3 The Modes of Inquiry
====1.4.3 The Modes of Inquiry====
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.
<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>
<p>(Plato, Laws, VII, 799E-800A).</p>
</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.
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.
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.
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.
1.4.3.1 Deductive Reasoning
=====1.4.3.1 Deductive Reasoning=====
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.
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.
The "first figure" of the syllogism is explained as follows:
The "first figure" of the syllogism is explained as follows:
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.
<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>
<p>(Aristotle, Prior Analytics, 1.4).</p>
</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.
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.
The "second figure" of the syllogism is explained as follows:
The "second figure" of the syllogism is explained as follows:
<blockquote>
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).
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.
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.
The "third figure" of the syllogism is explained as follows:
The "third figure" of the syllogism is explained as follows:
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.
<blockquote>
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.
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 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.
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.
1.4.3.2 Inductive Reasoning
=====1.4.3.2 Inductive Reasoning=====
(Aristotle, Prior Analytics, 2.23).
(Aristotle, Prior Analytics, 2.23).
1.4.3.3 Abductive Reasoning
=====1.4.3.3 Abductive Reasoning=====
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).
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).
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.
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
=====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 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.
In order to improve the character of the discussion on this score ...
In order to improve the character of the discussion on this score ...
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