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=====1.1.2.3. Reprise of Methods=====
=====1.1.2.3. Reprise of Methods=====
In summary, the whole array of methods will be typical of the top-down strategies used in artificial intelligence research (AIR), involving the conceptual and operational analysis of higher-order cognitive capacities with an eye toward the modeling, grounding, and support of these faculties in the form of effective computer programs. The toughest part of this discipline is in making sure that one does "come down", that is, in finding guarantees that the analytic reagents and synthetic apparatus that one applies are actually effective, reducing the "fat" of speculation into something that will wash.
In summary, the whole array of methods will be typical of the top-down strategies used in artificial intelligence research (AIR), involving the conceptual and operational analysis of higher-order cognitive capacities with an eye toward the modeling, grounding, and support of these faculties in the form of effective computer programs. The toughest part of this discipline is in making sure that one does "come down", that is, in finding guarantees that the analytic reagents and synthetic apparatus that one applies are actually effective, reducing the fat of speculation into something that will wash.
Finally, I ought to observe a hedge against betting too much on this or any neat arrangement of research stages. It should not be forgotten that the flourishing of inquiry evolves its own forms of organic integrity. No matter how one tries to tease them apart, the various tendrils of research tend to interleave and intertwine as they will.
Finally, I ought to observe a hedge against betting too much on this or any neat arrangement of research stages. It should not be forgotten that the flourishing of inquiry evolves its own forms of organic integrity. No matter how one tries to tease them apart, the various tendrils of research tend to interleave and intertwine as they will.
=====1.3.3.3. A Formalization of Discussion?=====
=====1.3.3.3. A Formalization of Discussion?=====
The previous section took the concept of "formalization" as an example of a topic that a writer might try to translate from informal to formal discussion, perhaps as a way of clarifying the general concept to an optimal degree, or perhaps as a way of communicating a particular concept of it to a reader. In either case the formalization process, that aims to translate a concept from informal to formal discussion, is itself mediated by a form of discussion: (1) that interpreters conduct as a part of their ongoing monologue with themselves, or (2) that a writer (speaker) conducts in real or imagined dialogue with a reader (hearer). In view of this, I see no harm in letting the concept of discussion be stretched to cover all attempted processes of formalization.
The previous section took the concept of ''formalization'' as an example of a topic that a writer might try to translate from informal to formal discussion, perhaps as a way of clarifying the general concept to an optimal degree, or perhaps as a way of communicating a particular concept of it to a reader. In either case the formalization process, that aims to translate a concept from informal to formal discussion, is itself mediated by a form of discussion: (1) that interpreters conduct as a part of their ongoing monologue with themselves, or (2) that a writer (speaker) conducts in real or imagined dialogue with a reader (hearer). In view of this, I see no harm in letting the concept of discussion be stretched to cover all attempted processes of formalization.
:: '''<code>F ⊆ D</code>'''
:: '''<code>F ⊆ D</code>'''
If this form of SOI-building narrative is truly intended to edify and educate, whether pursued in monologue or dialogue fashion, then its action cannot be forcibly to replace the meanings in practice a sign already has with others of an arbitrary nature, but freely to augment the options for meaning and powers for choice in the resulting SOI.
If this form of SOI-building narrative is truly intended to edify and educate, whether pursued in monologue or dialogue fashion, then its action cannot be forcibly to replace the meanings in practice a sign already has with others of an arbitrary nature, but freely to augment the options for meaning and powers for choice in the resulting SOI.
As conditions for the possibility of considerate but significant narration, there are a couple of requirements placed on the writer and the reader. Considerate narration, constructing a relation from SOI to SOI in a politic fashion, cannot operate in an infectious or addictive manner, invading a SOI like a virus or a trojan horse, but must transfer its communication into the control of the receiving SOI. Significant communication, in which the receiving SOI is augmented by options for meaning and powers for choice that it did not have before, requires a SOI on the reader's part that is "extensible" in non-trivial ways.
As conditions for the possibility of considerate but significant narration, there are a couple of requirements placed on the writer and the reader. Considerate narration, constructing a relation from SOI to SOI in a politic fashion, cannot operate in an infectious or addictive manner, invading a SOI like a virus or a trojan horse, but must transfer its communication into the control of the receiving SOI. Significant communication, in which the receiving SOI is augmented by options for meaning and powers for choice that it did not have before, requires a SOI on the reader's part that is ''extensible'' in non-trivial ways.
At this point, the discussion has touched on a topic, in one of its manifold aspects, that it will encounter repeatedly, under a variety of aspects, throughout this work. In recognition of this circumstance, and to prepare the way for future discussion, it seems like a good idea to note a few of the aliases that this protean topic can be found lurking under, and to notice the logical relationships that exist among its several different appearances.
At this point, the discussion has touched on a topic, in one of its manifold aspects, that it will encounter repeatedly, under a variety of aspects, throughout this work. In recognition of this circumstance, and to prepare the way for future discussion, it seems like a good idea to note a few of the aliases that this protean topic can be found lurking under, and to notice the logical relationships that exist among its several different appearances.
The ''syntactic domain'' or the ''sign system'' of their discussion is limited to the set of four signs {"Ann", "Bob", "I", "You"}.
The ''syntactic domain'' or the ''sign system'' of their discussion is limited to the set of four signs {"Ann", "Bob", "I", "You"}.
In their discussion, Ann and Bob are not only the passive objects of nominative and accusative references but also the active interpreters of the language that they use. The "system of interpretation" (SOI) associated with each language user can be represented in the form of an individual three-place relation called the ''[[sign relation]]'' of that interpreter.
In their discussion, Ann and Bob are not only the passive objects of nominative and accusative references but also the active interpreters of the language that they use. The ''system of interpretation'' (SOI) associated with each language user can be represented in the form of an individual three-place relation called the ''[[sign relation]]'' of that interpreter.
Understood in terms of its set-theoretic extension, a sign relation ''L'' is a subset of a cartesian product ''O''×''S''×''I''. Here, ''O'', ''S'', and ''I'' are three sets that are known as the ''object domain'', the ''sign domain'', and the ''interpretant domain'', respectively, of the sign relation ''L'' ⊆ ''O''×''S''×''I''. In general, the three domains of a sign relation can be any sets whatsoever, but the kinds of sign relations that are contemplated in a computational framework are usually constrained to having ''I'' ⊆ ''S''. In this case, interpretants are just a special variety of signs, and this makes it convenient to lump signs and interpretants together into a ''syntactic domain''. In the forthcoming examples, ''S'' and ''I'' are identical as sets, so the very same elements manifest themselves in two distinct roles of the sign relations in question. When it is necessary to refer to the whole set of objects and signs in the union of the domains ''O'', ''S'', and ''I'' for a given sign relation ''L'', one may call this the "world of ''L''" and write ''W'' = ''W''(''L'') = ''O'' ∪ ''S'' ∪ ''I''.
Understood in terms of its set-theoretic extension, a sign relation ''L'' is a subset of a cartesian product ''O''×''S''×''I''. Here, ''O'', ''S'', and ''I'' are three sets that are known as the ''object domain'', the ''sign domain'', and the ''interpretant domain'', respectively, of the sign relation ''L'' ⊆ ''O''×''S''×''I''. In general, the three domains of a sign relation can be any sets whatsoever, but the kinds of sign relations that are contemplated in a computational framework are usually constrained to having ''I'' ⊆ ''S''. In this case, interpretants are just a special variety of signs, and this makes it convenient to lump signs and interpretants together into a ''syntactic domain''. In the forthcoming examples, ''S'' and ''I'' are identical as sets, so the very same elements manifest themselves in two distinct roles of the sign relations in question. When it is necessary to refer to the whole set of objects and signs in the union of the domains ''O'', ''S'', and ''I'' for a given sign relation ''L'', one may call this the "world of ''L''" and write ''W'' = ''W''(''L'') = ''O'' ∪ ''S'' ∪ ''I''.
</pre>
</pre>
One aspect of semantics is concerned with the reference that a sign has to its object, which is called its "denotation". For signs in general, neither the existence nor the uniqueness of a denotation is guaranteed. Thus, the denotation of a sign can refer to a plural, a singular, or a vacuous number of objects. In the pragmatic theory of signs, these references are formalized as certain types of dyadic relations that are obtained by projection from the triadic sign relations.
One aspect of semantics is concerned with the reference that a sign has to its object, which is called its ''denotation''. For signs in general, neither the existence nor the uniqueness of a denotation is guaranteed. Thus, the denotation of a sign can refer to a plural, a singular, or a vacuous number of objects. In the pragmatic theory of signs, these references are formalized as certain types of dyadic relations that are obtained by projection from the triadic sign relations.
The dyadic relation that constitutes the "denotative component" of a sign relation L is denoted by "Den(L)". Information about the denotative component of semantics can be derived from L by taking its "dyadic projection" on the plane that is generated by the object domain and the sign domain, indicated by any one of the equivalent forms, "ProjOS(L)", "LOS", or "L12", and defined as follows:
The dyadic relation that constitutes the ''denotative component'' of a sign relation L is denoted by "Den(L)". Information about the denotative component of semantics can be derived from L by taking its ''dyadic projection'' on the plane that is generated by the object domain and the sign domain, indicated by any one of the equivalent forms, "ProjOS(L)", "LOS", or "L12", and defined as follows:
Den(L) = ProjOS(L) = LOS = {‹o, s› ? O?S : ‹o, s, i› ? L for some i ? I}.
Den(L) = ProjOS(L) = LOS = {‹o, s› ? O?S : ‹o, s, i› ? L for some i ? I}.
The other dyadic aspects of semantics that might be considered concern the reference that a sign has to its interpretant and the reference that an interpretant has to its object. As before, either type of reference can be multiple, unique, or empty in its collection of terminal points, and both can be formalized as different types of dyadic relations that are obtained as planar projections of the triadic sign relations.
The other dyadic aspects of semantics that might be considered concern the reference that a sign has to its interpretant and the reference that an interpretant has to its object. As before, either type of reference can be multiple, unique, or empty in its collection of terminal points, and both can be formalized as different types of dyadic relations that are obtained as planar projections of the triadic sign relations.
The connection that a sign makes to an interpretant is called its "connotation". In the general theory of sign relations, this aspect of semantics includes the references that a sign has to affects, concepts, impressions, intentions, mental ideas, and to the whole realm of an agent's mental states and allied activities, broadly encompassing intellectual associations, emotional impressions, motivational impulses, and real conduct. This complex ecosystem of references is unlikely ever to be mapped in much detail, much less completely formalized, but the tangible warp of its accumulated mass is commonly alluded to as the "connotative" import of language. Given a particular sign relation L, the dyadic relation that constitutes the "connotative component" of L is denoted by "Con(L)".
The connection that a sign makes to an interpretant is called its ''connotation''. In the general theory of sign relations, this aspect of semantics includes the references that a sign has to affects, concepts, impressions, intentions, mental ideas, and to the whole realm of an agent's mental states and allied activities, broadly encompassing intellectual associations, emotional impressions, motivational impulses, and real conduct. This complex ecosystem of references is unlikely ever to be mapped in much detail, much less completely formalized, but the tangible warp of its accumulated mass is commonly alluded to as the ''connotative'' import of language. Given a particular sign relation L, the dyadic relation that constitutes the ''connotative component'' of L is denoted by "Con(L)".
The bearing that an interpretant has toward a common object of its sign and itself has no standard name. If an interpretant is considered to be a sign in its own right, then its independent reference to an object can be taken as belonging to another moment of denotation, but this omits the mediational character of the whole transaction.
The bearing that an interpretant has toward a common object of its sign and itself has no standard name. If an interpretant is considered to be a sign in its own right, then its independent reference to an object can be taken as belonging to another moment of denotation, but this omits the mediational character of the whole transaction.
Given the service that interpretants supply in furnishing a locus for critical, reflective, and explanatory glosses on objective scenes and their descriptive texts, it is easy to regard them as "annotations" both of objects and of signs, but this function points in the opposite direction to what is needed in this connection. What does one call the inverse of the annotation function? More generally asked, what is the converse of the annotation relation?
Given the service that interpretants supply in furnishing a locus for critical, reflective, and explanatory glosses on objective scenes and their descriptive texts, it is easy to regard them as ''annotations'' both of objects and of signs, but this function points in the opposite direction to what is needed in this connection. What does one call the inverse of the annotation function? More generally asked, what is the converse of the annotation relation?
In light of these considerations, I find myself still experimenting with terms to suit this last-mentioned dimension of semantics. On a trial basis, I refer to it as the "ideational", the "intentional", or the "canonical" component of the sign relation, and I provisionally refer to the reference of an interpretant sign to its object as its "ideation", its "intention", or its "conation". Given a particular sign relation L, the dyadic relation that constitutes the "intentional component" of L is denoted by "Int(L)".
In light of these considerations, I find myself still experimenting with terms to suit this last-mentioned dimension of semantics. On a trial basis, I refer to it as the ''ideational'', the ''intentional'', or the ''canonical'' component of the sign relation, and I provisionally refer to the reference of an interpretant sign to its object as its ''ideation'', its ''intention'', or its ''conation''. Given a particular sign relation L, the dyadic relation that constitutes the ''intentional component'' of L is denoted by "Int(L)".
A full consideration of the connotative and intentional aspects of semantics would force a return to difficult questions about the true nature of the interpretant sign in the general theory of sign relations. It is best to defer these issues to a later discussion. Fortunately, omission of this material does not interfere with understanding the purely formal aspects of the present example.
A full consideration of the connotative and intentional aspects of semantics would force a return to difficult questions about the true nature of the interpretant sign in the general theory of sign relations. It is best to defer these issues to a later discussion. Fortunately, omission of this material does not interfere with understanding the purely formal aspects of the present example.
Con(L) = ProjSI(L) = LSI = {‹s, i› ? S?I : ‹o, s, i› ? L for some o ? O}.
Con(L) = ProjSI(L) = LSI = {‹s, i› ? S?I : ‹o, s, i› ? L for some o ? O}.
The intentional component of semantics for a sign relation L, or its "second moment of denotation", is adequately captured by its dyadic projection on the plane generated by the object domain and interpretant domain, defined as follows:
The intentional component of semantics for a sign relation L, or its ''second moment of denotation'', is adequately captured by its dyadic projection on the plane generated by the object domain and interpretant domain, defined as follows:
Int(L) = ProjOI(L) = LOI = {‹o, i› ? O?I : ‹o, s, i› ? L for some s ? S}.
Int(L) = ProjOI(L) = LOI = {‹o, i› ? O?I : ‹o, s, i› ? L for some s ? S}.
=====1.3.4.3. Semiotic Equivalence Relations=====
=====1.3.4.3. Semiotic Equivalence Relations=====
If one examines the sign relations L(A) and L(B) that are associated with the interpreters A and B, respectively, one observes that they have many contingent properties that are not possessed by sign relations in general. One nice property possessed by the sign relations L(A) and L(B) is that their connotative components ASI and BSI constitute a pair of equivalence relations on their common syntactic domain S = I. It is convenient to refer to such structures as "semiotic equivalence relations" (SER's) since they equate signs that mean the same thing to somebody. Each of the SER's, ASI, BSI ? S?I = S?S partitions the whole collection of signs into "semiotic equivalence classes" (SEC's). This makes for a strong form of representation in that the structure of the participants' common object domain is reflected or reconstructed, part for part, in the structure of each of their "semiotic partitions" (SEP's) of the syntactic domain.
If one examines the sign relations L(A) and L(B) that are associated with the interpreters A and B, respectively, one observes that they have many contingent properties that are not possessed by sign relations in general. One nice property possessed by the sign relations L(A) and L(B) is that their connotative components ASI and BSI constitute a pair of equivalence relations on their common syntactic domain S = I. It is convenient to refer to such structures as ''semiotic equivalence relations'' (SER's) since they equate signs that mean the same thing to somebody. Each of the SER's, ASI, BSI ? S?I = S?S partitions the whole collection of signs into ''semiotic equivalence classes'' (SEC's). This makes for a strong form of representation in that the structure of the participants' common object domain is reflected or reconstructed, part for part, in the structure of each of their ''semiotic partitions'' (SEP's) of the syntactic domain.
The main trouble with this notion of semantics in the present situation is that the two semiotic partitions for A and B are not the same, indeed, they are orthogonal to each other. This makes it difficult to interpret either one of the partitions or equivalence relations on the syntactic domain as corresponding to any sort of objective structure or invariant reality, independent of the individual interpreter's point of view (POV).
The main trouble with this notion of semantics in the present situation is that the two semiotic partitions for A and B are not the same, indeed, they are orthogonal to each other. This makes it difficult to interpret either one of the partitions or equivalence relations on the syntactic domain as corresponding to any sort of objective structure or invariant reality, independent of the individual interpreter's point of view (POV).
</pre>
</pre>
To discuss these types of situations further, I introduce the square bracket notation "[x]E" for "the equivalence class of the element x under the equivalence relation E". A statement that the elements x and y are equivalent under E is called an "equation", and can be written in either one of two ways, as "[x]E = [y]E" or as "x =E y".
To discuss these types of situations further, I introduce the square bracket notation "[x]E" for ''the equivalence class of the element x under the equivalence relation E''. A statement that the elements x and y are equivalent under E is called an ''equation'', and can be written in either one of two ways, as "[x]E = [y]E" or as "x =E y".
In the application to sign relations I extend this notation in the following ways. When L is a sign relation whose "syntactic projection" or connotative component LSI is an equivalence relation on S, I write "[s]L" for "the equivalence class of s under LSI". A statement that the signs x and y are synonymous under a semiotic equivalence relation LSI is called a "semiotic equation" (SEQ), and can be written in either of the forms: "[x]L = [y]L" or "x =L y".
In the application to sign relations I extend this notation in the following ways. When L is a sign relation whose ''syntactic projection'' or connotative component LSI is an equivalence relation on S, I write "[s]L" for ''the equivalence class of s under LSI''. A statement that the signs x and y are synonymous under a semiotic equivalence relation LSI is called a ''semiotic equation'' (SEQ), and can be written in either of the forms: "[x]L = [y]L" or "x =L y".
In many situations there is one further adaptation of the square bracket notation that can be useful. Namely, when there is known to exist a particular triple ‹o, s, i› ? L, it is permissible to use "[o]L" to mean the same thing as "[s]L". These modifications are designed to make the notation for semiotic equivalence classes harmonize as well as possible with the frequent use of similar devices for the denotations of signs and expressions.
In many situations there is one further adaptation of the square bracket notation that can be useful. Namely, when there is known to exist a particular triple ‹o, s, i› ? L, it is permissible to use "[o]L" to mean the same thing as "[s]L". These modifications are designed to make the notation for semiotic equivalence classes harmonize as well as possible with the frequent use of similar devices for the denotations of signs and expressions.
It seems like a good idea to pause at this point and reflect on the state of understanding that has been reached. In order to motivate further developments it will be useful to inventory two types of shortfall in the present state of discussion, the first having to do with the defects of my present discussion in revealing the relevant attributes of even so simple an example as the one I used to begin, the second having to do with the defects that this species of example exhibits within the genus of sign relations it is intended to illustrate.
It seems like a good idea to pause at this point and reflect on the state of understanding that has been reached. In order to motivate further developments it will be useful to inventory two types of shortfall in the present state of discussion, the first having to do with the defects of my present discussion in revealing the relevant attributes of even so simple an example as the one I used to begin, the second having to do with the defects that this species of example exhibits within the genus of sign relations it is intended to illustrate.
As a general schema, I describe these respective limitations as the "rhetorical" and the "objective" defects that a discussion can have in addressing its intended object. The immediate concern is to remedy the insufficiencies of analysis that affect the treatment of the current case. The overarching task is to address the atypically simplistic features of this example as it falls within the class of sign relations that are relevant to actual inquiry.
As a general schema, I describe these respective limitations as the ''rhetorical'' and the ''objective'' defects that a discussion can have in addressing its intended object. The immediate concern is to remedy the insufficiencies of analysis that affect the treatment of the current case. The overarching task is to address the atypically simplistic features of this example as it falls within the class of sign relations that are relevant to actual inquiry.
The next few subsections will be concerned with the most problematic features of the A and B dialogue, especially with the sorts of difficulties that are clues to significant deficits in theory and technique, and that point out directions for future improvements.
The next few subsections will be concerned with the most problematic features of the A and B dialogue, especially with the sorts of difficulties that are clues to significant deficits in theory and technique, and that point out directions for future improvements.
The general character of this question can be expressed in the schematic terms that were used earlier to give a rough sketch of the modeling activity as a whole. How do the isolated SOI's of A and B relate to the interpretive framework that I am using to present them, and how does this IF operate, not only to objectify A and B as models of interpretation (MOI's), but simultaneously to embrace the present and the prospective SOI's of the current narrative, the implicit systems of interpretation that embody in turn the initial conditions and the final intentions of this whole discussion?
The general character of this question can be expressed in the schematic terms that were used earlier to give a rough sketch of the modeling activity as a whole. How do the isolated SOI's of A and B relate to the interpretive framework that I am using to present them, and how does this IF operate, not only to objectify A and B as models of interpretation (MOI's), but simultaneously to embrace the present and the prospective SOI's of the current narrative, the implicit systems of interpretation that embody in turn the initial conditions and the final intentions of this whole discussion?
One way to see how this issue arises in the discussion of A and B is to recognize that each table of a sign relation is a complex sign in itself, each of whose syntactic constituents plays the role of a simpler sign. In other words, there is nothing but text to be seen on the page. In comparison to what it represents, the table is like a sign relation that has undergone a step of "semantic ascent". It is as if the entire contents of the original sign relation have been transposed up a notch on the scale that registers levels of indirectness in reference, each item passing from a more objective to a more symbolic mode of presentation.
One way to see how this issue arises in the discussion of A and B is to recognize that each table of a sign relation is a complex sign in itself, each of whose syntactic constituents plays the role of a simpler sign. In other words, there is nothing but text to be seen on the page. In comparison to what it represents, the table is like a sign relation that has undergone a step of ''semantic ascent''. It is as if the entire contents of the original sign relation have been transposed up a notch on the scale that registers levels of indirectness in reference, each item passing from a more objective to a more symbolic mode of presentation.
Sign relations themselves, like any real objects of discussion, are either too abstract or too concrete to reside in the medium of communication, but can only find themselves represented there. The tables and graphs that are used to represent sign relations are themselves complex signs, involving a step of denotation to reach the sign relation intended. The intricacies of this step demand interpretive agents who are able, over and above executing all the rudimentary steps of denotation, to orchestrate the requisite kinds of concerted steps. This performance in turn requires a whole array of techniques to match the connotations of complex signs and to test their alternative styles of representation for semiotic equivalence. Analogous to the ways that matrices represent linear transformations and that multiplication tables represent group operations, a large part of the usefulness of these complex signs comes from the fact that they are not just conventional symbols for their objects but iconic representations of their structure.
Sign relations themselves, like any real objects of discussion, are either too abstract or too concrete to reside in the medium of communication, but can only find themselves represented there. The tables and graphs that are used to represent sign relations are themselves complex signs, involving a step of denotation to reach the sign relation intended. The intricacies of this step demand interpretive agents who are able, over and above executing all the rudimentary steps of denotation, to orchestrate the requisite kinds of concerted steps. This performance in turn requires a whole array of techniques to match the connotations of complex signs and to test their alternative styles of representation for semiotic equivalence. Analogous to the ways that matrices represent linear transformations and that multiplication tables represent group operations, a large part of the usefulness of these complex signs comes from the fact that they are not just conventional symbols for their objects but iconic representations of their structure.
=====1.3.4.7. Iconic Signs=====
=====1.3.4.7. Iconic Signs=====
In the pragmatic theory of signs, an "icon" is a sign that accomplishes its representation, including the projects of denotation and connotation, by virtue of properties that it shares with its object. In the case of relational tables and graphs, interpreted as iconic representations or analogous expressions of logical and mathematical objects, the pivotal properties are formal and abstract in character. Since a uniform translation through any dimension (of sight, of sound, or imagination) does not affect the structural properties of a configuration of signs in relation to each other, this may help to explain how tables and graphs, in spite of their semantic shiftiness, can succeed in representing sign relations without essential distortion.
In the pragmatic theory of signs, an ''icon'' is a sign that accomplishes its representation, including the projects of denotation and connotation, by virtue of properties that it shares with its object. In the case of relational tables and graphs, interpreted as iconic representations or analogous expressions of logical and mathematical objects, the pivotal properties are formal and abstract in character. Since a uniform translation through any dimension (of sight, of sound, or imagination) does not affect the structural properties of a configuration of signs in relation to each other, this may help to explain how tables and graphs, in spite of their semantic shiftiness, can succeed in representing sign relations without essential distortion.
Taking this unsuspecting introduction of iconic signs as a serendipitous lesson, an important principle can be lifted from their style of success. They bring the search for models of intellectual processes to look for classes of representation that do not lean too heavily on local idioms for devising labels but rather suspend their abstract formal structures in qualities of media that can best be preserved through a wide variety of global transformations. In time these ventures will lead this project to contemplate various forms of graphical abstraction as supplying possibly the most solid sites for pouring the foundations of formal expression.
Taking this unsuspecting introduction of iconic signs as a serendipitous lesson, an important principle can be lifted from their style of success. They bring the search for models of intellectual processes to look for classes of representation that do not lean too heavily on local idioms for devising labels but rather suspend their abstract formal structures in qualities of media that can best be preserved through a wide variety of global transformations. In time these ventures will lead this project to contemplate various forms of graphical abstraction as supplying possibly the most solid sites for pouring the foundations of formal expression.
What does appear in one of these Tables? It is not the objects that appear under the "Object" heading, but only the signs of these objects. It is not even the signs and interpretants themselves that appear under the "Sign" and "Interpretant" headings, but only the remoter signs of them that are formed by quotation. The unformalized sign relation in which these signs of objects, signs of signs, and signs of interpretants have their role as such is not the one Tabled, but another one that operates behind the scenes to bring its image and intent to the reader.
What does appear in one of these Tables? It is not the objects that appear under the ''Object'' heading, but only the signs of these objects. It is not even the signs and interpretants themselves that appear under the ''Sign'' and ''Interpretant'' headings, but only the remoter signs of them that are formed by quotation. The unformalized sign relation in which these signs of objects, signs of signs, and signs of interpretants have their role as such is not the one Tabled, but another one that operates behind the scenes to bring its image and intent to the reader.
To understand what the Table is meant to convey the reader has to participate in the informal and more accessory sign relation in order to follow its indications to the intended and more accessible sign relation. As logical or mathematical objects, the sign relations A and B do not exist in the medium of their Tables but are represented there by dint of the relevant structural properties that they share with these Tables. As fictional characters, the interpretive agents A and B do not exist in a uniquely literal sense but serve as typical literary figures to convey the intended formal account, standing in for concrete experiences with language use the likes of which are familiar to writer and reader alike.
To understand what the Table is meant to convey the reader has to participate in the informal and more accessory sign relation in order to follow its indications to the intended and more accessible sign relation. As logical or mathematical objects, the sign relations A and B do not exist in the medium of their Tables but are represented there by dint of the relevant structural properties that they share with these Tables. As fictional characters, the interpretive agents A and B do not exist in a uniquely literal sense but serve as typical literary figures to convey the intended formal account, standing in for concrete experiences with language use the likes of which are familiar to writer and reader alike.
=====1.3.4.9. Indexical Signs=====
=====1.3.4.9. Indexical Signs=====
In the pragmatic theory of signs, an "index" is a sign that achieves its representation of an object by virtue of an actual connection with it. Though real and objective, however, the indexical connection can be purely incidental and even a bit accidental. Its effectiveness depends only on the fact that an object in actual existence has many properties, definitive and derivative, any number of which can serve as its signs. Indices of an object reside among its more tangential sorts of attributes, its accidental or accessory features, which are really the properties of some but not all points in the locus of its existential actualization.
In the pragmatic theory of signs, an ''index'' is a sign that achieves its representation of an object by virtue of an actual connection with it. Though real and objective, however, the indexical connection can be purely incidental and even a bit accidental. Its effectiveness depends only on the fact that an object in actual existence has many properties, definitive and derivative, any number of which can serve as its signs. Indices of an object reside among its more tangential sorts of attributes, its accidental or accessory features, which are really the properties of some but not all points in the locus of its existential actualization.
Pronouns qualify as indices because their objective references cannot be traced without recovering further information about their actual context, not just their objective and syntactic contexts but the pragmatic context involved in their actualizing "situation of use" (SOU) or their realizing "instance of use" (IOU). To fulfill their duty to sense the reading of indices demands to be supplemented by a more determinate indication of their interpreter of reference, the agent that is responsible for putting them into active use at the moment in question.
Pronouns qualify as indices because their objective references cannot be traced without recovering further information about their actual context, not just their objective and syntactic contexts but the pragmatic context involved in their actualizing ''situation of use'' (SOU) or their realizing ''instance of use'' (IOU). To fulfill their duty to sense the reading of indices demands to be supplemented by a more determinate indication of their interpreter of reference, the agent that is responsible for putting them into active use at the moment in question.
Typical examples of indexical signs in programming languages are: (1) "variables", signs that need to be bound to a syntactic context or an instantiation frame in order to have a determinate meaning, and (2) "pointers", signs that serve particular interpreters operating relative to locally active environments as accessory addresses of modifiable memory contents. In any case something extra - some further information about the objective, syntactic, or interpretive context - must be added to the index in order to tell what it denotes.
Typical examples of indexical signs in programming languages are: (1) ''variables'', signs that need to be bound to a syntactic context or an instantiation frame in order to have a determinate meaning, and (2) ''pointers'', signs that serve particular interpreters operating relative to locally active environments as accessory addresses of modifiable memory contents. In any case something extra - some further information about the objective, syntactic, or interpretive context - must be added to the index in order to tell what it denotes.
If a real object can be regarded as a generic and permanent property that is shared by all of its specific and momentary instantiations, then it is possible to re-characterize indexical signs in the following terms: An index of an object is a property of an actual instance of that object. It is in this sense that indices are said to have actual but not essential connections to what they denote.
If a real object can be regarded as a generic and permanent property that is shared by all of its specific and momentary instantiations, then it is possible to re-characterize indexical signs in the following terms: An index of an object is a property of an actual instance of that object. It is in this sense that indices are said to have actual but not essential connections to what they denote.
Saying that an index is a property of an instance of an object almost makes it sound as though the relation of an index to what it denotes could be defined in purely objective terms, as a product of the two dyadic relations, "property of" and "instance of", and independently of any particular interpreter. But jumping to this conclusion would only produce an approximation to the truth, or a likely story, one that provokes the rejoinders: "In whose approach?" or "Likely to whom?"
Saying that an index is a property of an instance of an object almost makes it sound as though the relation of an index to what it denotes could be defined in purely objective terms, as a product of the two dyadic relations, ''property of'' and ''instance of'', and independently of any particular interpreter. But jumping to this conclusion would only produce an approximation to the truth, or a likely story, one that provokes the rejoinders: ''In whose approach?'' or ''Likely to whom?''
Taking up these challenges provides a clue as to how a sign relation can appear to be "nearly objective", "moderately independent", or "relatively composite", all within the medium of a particular framework for analysis and interpretation. Careful inspection of the context of definition reveals that it is not really the supposedly frame-free relations of properties and instances that suffice to compose the indexical connection. It is not enough that the separate links exist in principle to make something a property of an instance of something. In order to constitute a genuine sign relation, indexical or otherwise, each link must be recognized to exist by one and the same interpreter.
Taking up these challenges provides a clue as to how a sign relation can appear to be ''nearly objective'', ''moderately independent'', or ''relatively composite'', all within the medium of a particular framework for analysis and interpretation. Careful inspection of the context of definition reveals that it is not really the supposedly frame-free relations of properties and instances that suffice to compose the indexical connection. It is not enough that the separate links exist in principle to make something a property of an instance of something. In order to constitute a genuine sign relation, indexical or otherwise, each link must be recognized to exist by one and the same interpreter.
From this point of view, the object is considered to be something in the external world and the index is considered to be something that touches on the interpreter's experience, both of which subsume, though perhaps in different senses, the object instance (OI) that mediates their actual connection. Although the respective subsumptions, of OI to object and of OI to index, can appear to fall at first glance only within the reach of divergent senses, both must appeal for their eventual realization to a common sense, one that rests within the grasp of a single interpreter. Apparently then, the object instance is the sort of entity that can contribute to generating both the object and the experience, in this way connecting the diverse abstractions called "objects" and "indices".
From this point of view, the object is considered to be something in the external world and the index is considered to be something that touches on the interpreter's experience, both of which subsume, though perhaps in different senses, the object instance (OI) that mediates their actual connection. Although the respective subsumptions, of OI to object and of OI to index, can appear to fall at first glance only within the reach of divergent senses, both must appeal for their eventual realization to a common sense, one that rests within the grasp of a single interpreter. Apparently then, the object instance is the sort of entity that can contribute to generating both the object and the experience, in this way connecting the diverse abstractions called ''objects'' and ''indices''.
If a suitable framework of object instances can be found to rationalize an interpreter's experience with objects, then the actual connection that subsists between an object and its index becomes in this framework precisely the connection that exists between two properties of the same object instance, or between two sets intersecting in a common element. Relative to the appropriate framework, the actual connections needed to explain a global indexing operation can be identified, point for point, with the collective function of those joint instances or common elements.
If a suitable framework of object instances can be found to rationalize an interpreter's experience with objects, then the actual connection that subsists between an object and its index becomes in this framework precisely the connection that exists between two properties of the same object instance, or between two sets intersecting in a common element. Relative to the appropriate framework, the actual connections needed to explain a global indexing operation can be identified, point for point, with the collective function of those joint instances or common elements.
However, experience leads me to believe that forms of analysis are too peculiar to persons and communities, too dependent on their particular experiences and traditions, and overall too much bound to interpretive constitutions of learning and culture to ever be justly established as invariants of nature. In the end, or rather, by way of appeal to the many courts of final opinion, to invoke any particular form of analysis, no matter whether it is baseless or well-founded, is just another way of referring judgment to a particular interpreter, a contingent IF or a self-serving SOI. Consequently, every form of arbitration retains an irreducibly arbitrary element, and the best policy remains what it has always been, to maintain an honest index of that fact.
However, experience leads me to believe that forms of analysis are too peculiar to persons and communities, too dependent on their particular experiences and traditions, and overall too much bound to interpretive constitutions of learning and culture to ever be justly established as invariants of nature. In the end, or rather, by way of appeal to the many courts of final opinion, to invoke any particular form of analysis, no matter whether it is baseless or well-founded, is just another way of referring judgment to a particular interpreter, a contingent IF or a self-serving SOI. Consequently, every form of arbitration retains an irreducibly arbitrary element, and the best policy remains what it has always been, to maintain an honest index of that fact.
Therefore, I consider any supposed form of "ontological descent" to be, more likely, just one among many possible forms of "semantic descent", each one of which details a particular way to reformulate objects as signs of more determinate objects, and every one of which operates with respect to its assumed form of analysis or its tacit analytic framework.
Therefore, I consider any supposed form of ''ontological descent'' to be, more likely, just one among many possible forms of ''semantic descent'', each one of which details a particular way to reformulate objects as signs of more determinate objects, and every one of which operates with respect to its assumed form of analysis or its tacit analytic framework.
=====1.3.4.10. Sundry Problems=====
=====1.3.4.10. Sundry Problems=====
There are moments in the development of an analytic discussion when a thing initially described as a single object under a single sign needs to be reformulated as a congeries extending over more determinate objects. If the usage of the original singular sign is preserved, as it often is, then the multitude of new instances that one comes to fathom beneath the old object's superficial appearance gradually serve to reconstitute the singular sign's denotation in the fashion of a plural reference.
There are moments in the development of an analytic discussion when a thing initially described as a single object under a single sign needs to be reformulated as a congeries extending over more determinate objects. If the usage of the original singular sign is preserved, as it often is, then the multitude of new instances that one comes to fathom beneath the old object's superficial appearance gradually serve to reconstitute the singular sign's denotation in the fashion of a plural reference.
One such moment was reached in the preceding subsection, where the topics opened up by indexical signs invited the discussion to begin addressing much wider areas of concern. Eventually, to account for the effective operation of indexical signs I will have to invoke the concept of a "real object" and pursue the analysis of ostensible objects in terms of still more objective things. These are the extended multitudes of increasingly determinate objects that I will variously refer to as the actualizations, instantiations, realizations, etc. of objects, and on occasion (and not without reason) the "objects of objects" (OOO's).
One such moment was reached in the preceding subsection, where the topics opened up by indexical signs invited the discussion to begin addressing much wider areas of concern. Eventually, to account for the effective operation of indexical signs I will have to invoke the concept of a ''real object'' and pursue the analysis of ostensible objects in terms of still more objective things. These are the extended multitudes of increasingly determinate objects that I will variously refer to as the actualizations, instantiations, realizations, etc. of objects, and on occasion (and not without reason) the ''objects of objects'' (OOO's).
Another such moment will arrive when I turn to developing suitable embodiments of sign relations within dynamically realistic systems. In order to implement interpreters as state transition systems, I will have to justify the idea that dynamic states are the "real signs" and proceed to reconstitute the customary types of signs as abstractions from still more significant tokens. These are the immediate occasions of sign-using transactions that I will tender as "situations of use" (SOU's) or "instances of use" (IOU's), plus the states and motions of dynamic systems that solely are able to realize these uses and discharge the obligations they incur to reality.
Another such moment will arrive when I turn to developing suitable embodiments of sign relations within dynamically realistic systems. In order to implement interpreters as state transition systems, I will have to justify the idea that dynamic states are the ''real signs'' and proceed to reconstitute the customary types of signs as abstractions from still more significant tokens. These are the immediate occasions of sign-using transactions that I will tender as ''situations of use'' (SOU's) or ''instances of use'' (IOU's), plus the states and motions of dynamic systems that solely are able to realize these uses and discharge the obligations they incur to reality.
In every case, working within the framework of systems theory will lead this discussion toward systems and conditions of systems as the ultimate objects of investigation, implicated as the ends of both synthetic and analytic proceedings. Sign relations, initially formulated as relations among three arbitrary sets, will gradually have their original substrates replaced with three systems, the object, sign, and interpretant systems.
In every case, working within the framework of systems theory will lead this discussion toward systems and conditions of systems as the ultimate objects of investigation, implicated as the ends of both synthetic and analytic proceedings. Sign relations, initially formulated as relations among three arbitrary sets, will gradually have their original substrates replaced with three systems, the object, sign, and interpretant systems.
Since the roles of a sign relation are formally and pragmatically defined, they do not depend on the material aspects or the essential attributes of elements or domains. Therefore, it is conceivable that the very same system could appear in all three roles, and from this possibility arises much of the ensuing complications of the subject.
Since the roles of a sign relation are formally and pragmatically defined, they do not depend on the material aspects or the essential attributes of elements or domains. Therefore, it is conceivable that the very same system could appear in all three roles, and from this possibility arises much of the ensuing complications of the subject.
A related source of conceptual turbulence stems from the circumstance that, even though a certain aesthetic dynamics attracts the mind toward sign relational systems that are capable of reflecting on, commenting on, and thus "counter-rolling" their own behavior, it is still important to distinguish in every active instance the part of the system that is doing the discussing from the part of the system that is being discussed. To do this, interpreters need two things: (1) the senses to discern the essential tensions that typically prevail between the formal pole and the informal arena, and (2) the language to articulate, aside from their potential roles, the moment by moment placement of dynamic elements and systematic components with respect to this field of polarities.
A related source of conceptual turbulence stems from the circumstance that, even though a certain aesthetic dynamics attracts the mind toward sign relational systems that are capable of reflecting on, commenting on, and thus ''counter-rolling'' their own behavior, it is still important to distinguish in every active instance the part of the system that is doing the discussing from the part of the system that is being discussed. To do this, interpreters need two things: (1) the senses to discern the essential tensions that typically prevail between the formal pole and the informal arena, and (2) the language to articulate, aside from their potential roles, the moment by moment placement of dynamic elements and systematic components with respect to this field of polarities.
=====1.3.4.11. Review & Prospect=====
=====1.3.4.11. Review & Prospect=====
In the pragmatic account of things, thoughts are just signs in the mind of their thinker, so every object of a thought is the object of a sign, though perhaps in a sign relation that has not been fully formalized. Considered on these grounds, the search for a satisfactory context in which to explain the actions and effects of signs turns into a recursive process that potentially calls on ever higher levels of properties and ever deeper levels of instances that are found to stem from whatever objects instigated the search.
In the pragmatic account of things, thoughts are just signs in the mind of their thinker, so every object of a thought is the object of a sign, though perhaps in a sign relation that has not been fully formalized. Considered on these grounds, the search for a satisfactory context in which to explain the actions and effects of signs turns into a recursive process that potentially calls on ever higher levels of properties and ever deeper levels of instances that are found to stem from whatever objects instigated the search.
To make it serve as a paradigm for future developments, I repeat the basic pattern that has been observed with a slightly different emphasis. In order to explain the operation of icons and indices in a particular discussion, it is necessary to invoke the abstract properties of objects and the actual instances of objects, where by "objects" one initially comprehends a limited collection of objects of thought under discussion. If these properties and instances are themselves regarded as potential objects of thought, and if they are conceived to be definitively other than the objects whose properties and instances they happen to be, then every initial collection of objects is forced to expand on further consideration, in this way pointing to a world of objects of thought that extends in two directions beyond the originating frame of discussion.
To make it serve as a paradigm for future developments, I repeat the basic pattern that has been observed with a slightly different emphasis. In order to explain the operation of icons and indices in a particular discussion, it is necessary to invoke the abstract properties of objects and the actual instances of objects, where by ''objects'' one initially comprehends a limited collection of objects of thought under discussion. If these properties and instances are themselves regarded as potential objects of thought, and if they are conceived to be definitively other than the objects whose properties and instances they happen to be, then every initial collection of objects is forced to expand on further consideration, in this way pointing to a world of objects of thought that extends in two directions beyond the originating frame of discussion.
Can this manner of recursively searching for explanation be established as well-founded? In order to organize the expanding circle of thoughts and the growing wealth of objects that are envisioned within its scheme, it helps to introduce a set of organizing conceptions. Doing this will be the business of the next four Subsections.
Can this manner of recursively searching for explanation be established as well-founded? In order to organize the expanding circle of thoughts and the growing wealth of objects that are envisioned within its scheme, it helps to introduce a set of organizing conceptions. Doing this will be the business of the next four Subsections.
In accounting for the special characters of icons and indices that arose in previous discussions, it was necessary to open the domain of objects coming under formal consideration to include unspecified numbers of properties and instances of whatever objects were initially set down. This is a general phenomenon, affecting every motion toward explanation whether pursued by analytic or synthetic means. What it calls for in practice is a way of organizing growing domains of objects, without having to specify in advance all the objects there are.
In accounting for the special characters of icons and indices that arose in previous discussions, it was necessary to open the domain of objects coming under formal consideration to include unspecified numbers of properties and instances of whatever objects were initially set down. This is a general phenomenon, affecting every motion toward explanation whether pursued by analytic or synthetic means. What it calls for in practice is a way of organizing growing domains of objects, without having to specify in advance all the objects there are.
This subsection presents the "objective project" (OP) that I plan to take up for investigating the forms of sign relations, and it outlines three "objective levels" (OL's) of formulation that guide the analytic and synthetic study of interpretive structure and regulate the prospective stages of implementing this plan in particular cases. The main purpose of these schematic conceptions is organizational, to provide a conceptual architecture for the burgeoning hierarchies of objects that arise in the generative processes of inquiry.
This subsection presents the ''objective project'' (OP) that I plan to take up for investigating the forms of sign relations, and it outlines three ''objective levels'' (OL's) of formulation that guide the analytic and synthetic study of interpretive structure and regulate the prospective stages of implementing this plan in particular cases. The main purpose of these schematic conceptions is organizational, to provide a conceptual architecture for the burgeoning hierarchies of objects that arise in the generative processes of inquiry.
In the immediate context the objective project and the three levels of objective description are presented in broad terms. In the process of surveying a variety of problems that serve to instigate efforts in this general direction, I explore the prospects of a particular "organon", or "instrumental scheme for the analysis and synthesis of objects", that is intended to address these issues, and I give an overview of its design. In interpreting the sense of the word "objective" as it is used in this application, it may help to regard this objective project in the light of a telescopic analogy, with an "objective" being "a lens or system of lenses that forms an image of an object" (Webster's).
In the immediate context the objective project and the three levels of objective description are presented in broad terms. In the process of surveying a variety of problems that serve to instigate efforts in this general direction, I explore the prospects of a particular ''organon'', or ''instrumental scheme for the analysis and synthesis of objects'', that is intended to address these issues, and I give an overview of its design. In interpreting the sense of the word ''objective'' as it is used in this application, it may help to regard this objective project in the light of a telescopic analogy, with an ''objective'' being "a lens or system of lenses that forms an image of an object" (Webster's).
In the next three subsections after this one the focus returns to the separate levels of object structure, starting with the highest level of specification and treating the supporting levels in order of increasing detail. At each stage, the developing tools are applied to the analysis of concrete problems that arise in trying to clarify the structure and function of sign relations. For the present task, elaborations of this perspective are kept within the bounds of what is essential to deal with the example of A and B.
In the next three subsections after this one the focus returns to the separate levels of object structure, starting with the highest level of specification and treating the supporting levels in order of increasing detail. At each stage, the developing tools are applied to the analysis of concrete problems that arise in trying to clarify the structure and function of sign relations. For the present task, elaborations of this perspective are kept within the bounds of what is essential to deal with the example of A and B.
At this point, I need to apologize in advance for a introducing a certain difficulty of terminology, but the underlying issue it raises can no longer be avoided. To wit, I am forced to use the word "objective" in a way that conflicts with several traditions of interpretation, going so seriously against the grain of prevailing connotations that it will probably sound like a joke to many readers. Nevertheless, it is a definite "motive of consistency" (MOC) that requires me to do this.
At this point, I need to apologize in advance for a introducing a certain difficulty of terminology, but the underlying issue it raises can no longer be avoided. To wit, I am forced to use the word ''objective'' in a way that conflicts with several traditions of interpretation, going so seriously against the grain of prevailing connotations that it will probably sound like a joke to many readers. Nevertheless, it is a definite ''motive of consistency'' (MOC) that requires me to do this.
As always, my use of the word "object" derives from the stock of the Greek root "pragma", which captures all the senses needed to suggest the stability of concern and the dedication to purpose that are forever bound up in the constitution of objects and the institution of objectives. What it implies is that every object, objective, or objectivity is always somebody's object, objective, or objectivity.
As always, my use of the word ''object'' derives from the stock of the Greek root ''pragma'', which captures all the senses needed to suggest the stability of concern and the dedication to purpose that are forever bound up in the constitution of objects and the institution of objectives. What it implies is that every object, objective, or objectivity is always somebody's object, objective, or objectivity.
In other words, objectivity is always a matter of interpretation. It is concerned with and quantified by the magnitude of the consensus that a matter is bound to have at the end of inquiry, but in no way does this diminish or dismiss the fact that the fated determination is something on which any particular collection of current opinions are granted to differ. In principle, there begins to be a degree of objectivity as soon as something becomes an object to somebody, and the issue of whether this objective waxes or wanes in time is bound up with the number of observers that are destined to concur on it.
In other words, objectivity is always a matter of interpretation. It is concerned with and quantified by the magnitude of the consensus that a matter is bound to have at the end of inquiry, but in no way does this diminish or dismiss the fact that the fated determination is something on which any particular collection of current opinions are granted to differ. In principle, there begins to be a degree of objectivity as soon as something becomes an object to somebody, and the issue of whether this objective waxes or wanes in time is bound up with the number of observers that are destined to concur on it.
The critical question is not whether a thing is an object of thought and discussion, but what sort of thought and discussion it is an object of. How does one determine the character of this thought and discussion? And should this query be construed as a task of finding or of making? Whether it appeals to arts of acquisition, production, or discernment, and however one expects to decide or decode the conduct it requires, the character of the thought and discussion in view is sized up and riddled out in turn by looking at the whole domain of objects and the pattern of relations among them that it actively charts and encompasses. This makes what is usually called "subjectivity" a special case of what I must call "objectivity", since the interpretive and perspectival elements are ab initio operative and cannot be eliminated from any conceivable form of discernment, including their own.
The critical question is not whether a thing is an object of thought and discussion, but what sort of thought and discussion it is an object of. How does one determine the character of this thought and discussion? And should this query be construed as a task of finding or of making? Whether it appeals to arts of acquisition, production, or discernment, and however one expects to decide or decode the conduct it requires, the character of the thought and discussion in view is sized up and riddled out in turn by looking at the whole domain of objects and the pattern of relations among them that it actively charts and encompasses. This makes what is usually called ''subjectivity'' a special case of what I must call ''objectivity'', since the interpretive and perspectival elements are ab initio operative and cannot be eliminated from any conceivable form of discernment, including their own.
Consequently, analyses of objects and syntheses of objects are always analyses and syntheses to somebody. Both modes of approaching the constitutions of objects lead to the sorts of approximation that are appropriate to particular agents and able to be appropriated by whole communities of interpretation. By way of relief, on occasions when this motive of consistency hobbles discussion too severely, I will resort to using chimeras like "object-analytic" and "object-synthetic", paying the price of biasing the constitution of objects in one direction or another.
Consequently, analyses of objects and syntheses of objects are always analyses and syntheses to somebody. Both modes of approaching the constitutions of objects lead to the sorts of approximation that are appropriate to particular agents and able to be appropriated by whole communities of interpretation. By way of relief, on occasions when this motive of consistency hobbles discussion too severely, I will resort to using chimeras like ''object-analytic'' and ''object-synthetic'', paying the price of biasing the constitution of objects in one direction or another.
In this project I would like to treat the difference between construction and deconstruction as being more or less synonymous with the contrast between synthesis and analysis, but doing this without the introduction of too much distortion requires the intervention of a further distinction. Therefore, let it be recognized that all orientations to the constitutions of objects can be pursued in both "regimented" and "radical" fashions.
In this project I would like to treat the difference between construction and deconstruction as being more or less synonymous with the contrast between synthesis and analysis, but doing this without the introduction of too much distortion requires the intervention of a further distinction. Therefore, let it be recognized that all orientations to the constitutions of objects can be pursued in both ''regimented'' and ''radical'' fashions.
In the weaker senses of the terms, analysis and synthesis work within a preset and limited regime of objects, construing each object as being composed from a fixed inventory of stock constituents. In the stronger senses, contracting for the application of these terms places a more strenuous demand on the would-be construer.
In the weaker senses of the terms, analysis and synthesis work within a preset and limited regime of objects, construing each object as being composed from a fixed inventory of stock constituents. In the stronger senses, contracting for the application of these terms places a more strenuous demand on the would-be construer.
A radical form of analysis, in order to discern the contrasting intentions in everything construed as an object, requires interpreters to leave or at least re-place objects within the contexts of their live acquaintance, to reflect on their own motives and motifs for construing and employing objects in the ways they do, and to deconstruct how their own aims and biases enter into the form and use of objects.
A radical form of analysis, in order to discern the contrasting intentions in everything construed as an object, requires interpreters to leave or at least re-place objects within the contexts of their live acquaintance, to reflect on their own motives and motifs for construing and employing objects in the ways they do, and to deconstruct how their own aims and biases enter into the form and use of objects.
A radical form of synthesis, in order to integrate ideas and information devolving from entirely different "frameworks of interpretation" (FOI's), requires interpreters to reconstruct isolated concepts and descriptions on a mutually compatible basis and to use means of composition that can constitute a medium for common sensibilities.
A radical form of synthesis, in order to integrate ideas and information devolving from entirely different ''frameworks of interpretation'' (FOI's), requires interpreters to reconstruct isolated concepts and descriptions on a mutually compatible basis and to use means of composition that can constitute a medium for common sensibilities.
Thus, the radical project in all of these directions demands forms of interpretation, analysis, synthesis that can reflect a measure of light on the initially unstated assumptions of their prospective agents.
Thus, the radical project in all of these directions demands forms of interpretation, analysis, synthesis that can reflect a measure of light on the initially unstated assumptions of their prospective agents.
The foregoing considerations lead up to the organizing conception of an "objective framework" (OF), in which objects can be analyzed into sets of constituent objects, perhaps proceeding recursively to some limiting level where the fundamental objects of thought are thought to rest. If an OF is felt to be completely unique and uniquely complete, then people tend to regard it as constituting a veritable "ontology", but I will not be able to go that far. The recognition of plural and fallible perspectives that goes with pragmatic forms of thinking does not see itself falling into line any time soon with any one or only one ontology.
The foregoing considerations lead up to the organizing conception of an ''objective framework'' (OF), in which objects can be analyzed into sets of constituent objects, perhaps proceeding recursively to some limiting level where the fundamental objects of thought are thought to rest. If an OF is felt to be completely unique and uniquely complete, then people tend to regard it as constituting a veritable ''ontology'', but I will not be able to go that far. The recognition of plural and fallible perspectives that goes with pragmatic forms of thinking does not see itself falling into line any time soon with any one or only one ontology.
On the opposite score, there is no reason to deny the possibility that a unique and complete OF exists. Indeed, the hope that such a standpoint does exist often provides inquiry with a beneficial regulative principle or a heuristic hypothesis to work on. It merely happens, for the run of finitely informed creatures (FIC's) at any rate, that the existence of an ideal framework is something to be established after the fact, at least nearer toward the end of inquiry than the present time marks.
On the opposite score, there is no reason to deny the possibility that a unique and complete OF exists. Indeed, the hope that such a standpoint does exist often provides inquiry with a beneficial regulative principle or a heuristic hypothesis to work on. It merely happens, for the run of finitely informed creatures (FIC's) at any rate, that the existence of an ideal framework is something to be established after the fact, at least nearer toward the end of inquiry than the present time marks.
In this project, an OF embodies one or more "objective genres" (OG's), also called "forms of analysis" (FOA's) or "forms of synthesis" (FOS's), each of which delivers its own rendition of a "great chain of being" for all the objects under its purview. In effect, each OG develops its own version of an "ontological hierarchy" (OH), designed independently of the others to capture an aspect of structure in its objective domain.
In this project, an OF embodies one or more ''objective genres'' (OG's), also called ''forms of analysis'' (FOA's) or ''forms of synthesis'' (FOS's), each of which delivers its own rendition of a ''great chain of being'' for all the objects under its purview. In effect, each OG develops its own version of an ''ontological hierarchy'' (OH), designed independently of the others to capture an aspect of structure in its objective domain.
For now, the level of an OF operates as a catch-all, giving the projected discussion the elbow room it needs to range over an unspecified variety of different OG's and to place the particular OG's of active interest in a running context of comparative evaluations and developmental options.
For now, the level of an OF operates as a catch-all, giving the projected discussion the elbow room it needs to range over an unspecified variety of different OG's and to place the particular OG's of active interest in a running context of comparative evaluations and developmental options.
Any given OG can appear under the alias of a "form of analysis" (FOA) or a "form of synthesis" (FOS), depending on the direction of prevailing interest. A notion frequently invoked for the same purpose is that of an "ontological hierarchy" (OH), but I will use this only provisionally, and only so long as it is clear that alternative ontologies can always be proposed for the same space of objects.
Any given OG can appear under the alias of a ''form of analysis'' (FOA) or a ''form of synthesis'' (FOS), depending on the direction of prevailing interest. A notion frequently invoked for the same purpose is that of an ''ontological hierarchy'' (OH), but I will use this only provisionally, and only so long as it is clear that alternative ontologies can always be proposed for the same space of objects.
An OG embodies many "objective motives" or "objective motifs" (OM's). If an OG constitutes a genus, or generic pattern of object structure, then the OM's amount to its specific and individual exemplars. Thus, an OM can appear in the guise of a particular instance, trial, or "run" of the general form of analytic or synthetic procedure that accords with the protocols of a given OG.
An OG embodies many ''objective motives'' or ''objective motifs'' (OM's). If an OG constitutes a genus, or generic pattern of object structure, then the OM's amount to its specific and individual exemplars. Thus, an OM can appear in the guise of a particular instance, trial, or "run" of the general form of analytic or synthetic procedure that accords with the protocols of a given OG.
In order to provide a way of talking about objective points of view in general without having to specify a particular level, I will use the term "objective concern" (OC) to cover any individual OF, OG, or OM.
In order to provide a way of talking about objective points of view in general without having to specify a particular level, I will use the term ''objective concern'' (OC) to cover any individual OF, OG, or OM.
An OG, in its general way, or an OM, in its individual way, begins by relating each object in its purview to a unique set of further objects, called the "components", "constituents", "effects", "ingredients", or "instances" of that object with respect to that "objective concern" (OC). As long as discussion remains fixed to what is visible within the scope of a particular OC, the collected effects of each object in view constitute its "active ingredients", supplying it with a unique decomposition that defines it to a degree sufficient for all purposes conceivable within that discussion.
An OG, in its general way, or an OM, in its individual way, begins by relating each object in its purview to a unique set of further objects, called the ''components'', ''constituents'', ''effects'', ''ingredients'', or ''instances'' of that object with respect to that ''objective concern'' (OC). As long as discussion remains fixed to what is visible within the scope of a particular OC, the collected effects of each object in view constitute its ''active ingredients'', supplying it with a unique decomposition that defines it to a degree sufficient for all purposes conceivable within that discussion.
Contemplated from an outside perspective, however, the status of these effects as the "defining unique determinants" (DUD's) of each object under examination is something to be questioned. The supposed constituents of an object that are obvious with respect to one OC can be regarded with suspicion from the points of view of alternative OC's, and their apparent status as rock-bottom substantives can find itself reconstituted in the guise of provisional placeholders (placebos or excipients) that precipitately index the potential operation of more subtly active ingredients.
Contemplated from an outside perspective, however, the status of these effects as the ''defining unique determinants'' (DUD's) of each object under examination is something to be questioned. The supposed constituents of an object that are obvious with respect to one OC can be regarded with suspicion from the points of view of alternative OC's, and their apparent status as rock-bottom substantives can find itself reconstituted in the guise of provisional placeholders (placebos or excipients) that precipitately index the potential operation of more subtly active ingredients.
If a single OG could be unique and the realization of every object in it could be complete, then there might be some basis for saying that the elements of objects and the extensions of objects are known, and thus that the very "objects of objects" (OOO's) are determined by its plan. In practice, however, it takes a diversity of overlapping and not entirely systematic OG's to make up a moderately useful OF.
If a single OG could be unique and the realization of every object in it could be complete, then there might be some basis for saying that the elements of objects and the extensions of objects are known, and thus that the very ''objects of objects'' (OOO's) are determined by its plan. In practice, however, it takes a diversity of overlapping and not entirely systematic OG's to make up a moderately useful OF.
What gives an OG a definite constitution is the naming of a space of objects that falls under its purview and the setting down of a system of axioms that affects its generating relations.
What gives an OG a definite constitution is the naming of a space of objects that falls under its purview and the setting down of a system of axioms that affects its generating relations.
What gives an OM a determinate character from moment to moment is the particular selection of objects and linkages from its governing OG that it can say it has appropriated, apprehended, or actualized, that is, the portion of its OG that it can say actually belongs to it, and whether they make up a lot or a little, the roles it can say it has made its own.
What gives an OM a determinate character from moment to moment is the particular selection of objects and linkages from its governing OG that it can say it has appropriated, apprehended, or actualized, that is, the portion of its OG that it can say actually belongs to it, and whether they make up a lot or a little, the roles it can say it has made its own.
In setting out the preceding characterization, I have reiterated what is likely to seem like an anthropomorphism, prefacing each requirement of the candidate OM with the qualification "it can say". This is done in order to emphasize that an OM's command of a share of its OG is partly a function of the interpretive effability that it brings to bear on the object domain and partly a matter of the expressive power that it is able to dictate over its own development.
In setting out the preceding characterization, I have reiterated what is likely to seem like an anthropomorphism, prefacing each requirement of the candidate OM with the qualification ''it can say''. This is done in order to emphasize that an OM's command of a share of its OG is partly a function of the interpretive effability that it brings to bear on the object domain and partly a matter of the expressive power that it is able to dictate over its own development.
=====1.3.4.13. Formalization of OF : Objective Levels=====
=====1.3.4.13. Formalization of OF : Objective Levels=====
Aside from their indices, many of the Gj in G can be abstractly identical to each other. This would earn G the designation of a ''multi-family'' or a ''multi-set'' according to some usages, but I prefer to treat the index j as a concrete part of the indexed relation Gj, in this way distinguishing it from all other members of the indexed family G.
Aside from their indices, many of the Gj in G can be abstractly identical to each other. This would earn G the designation of a ''multi-family'' or a ''multi-set'' according to some usages, but I prefer to treat the index j as a concrete part of the indexed relation Gj, in this way distinguishing it from all other members of the indexed family G.
Ordinarily, it is desirable to avoid making individual mention of the separately indexed domains, Pj and Qj for all j ? J. Common strategies for getting around this trouble involve the introduction of additional domains, designed to encompass all the objects needed in given contexts. Toward this end, an adequate supply of intermediate domains, called the "rudiments of universal mediation" (RUM's), can be defined as follows:
Ordinarily, it is desirable to avoid making individual mention of the separately indexed domains, Pj and Qj for all j ? J. Common strategies for getting around this trouble involve the introduction of additional domains, designed to encompass all the objects needed in given contexts. Toward this end, an adequate supply of intermediate domains, called the ''rudiments of universal mediation'' (RUM's), can be defined as follows:
<pre>
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However, it serves a purpose of this project to preserve the individual indexing of relational domains for while longer, or at least to keep this usage available as an alternative formulation. Generally speaking, it is always possible in principle to form the union required by the RUI, or without loss of generality to assume the equality imposed by the RUE. The problem is that the unions and equalities invoked by these rubrics may not be effectively definable or testable in a computational context. Further, even when these sets or tests can be constructed or certified by some computational agent or another, the pertinent question at any interpretive moment is whether each collection or constraint is actively being apprehended or warranted by the particular interpreter charged with responsibility for it by the indicated assignment of domains.
However, it serves a purpose of this project to preserve the individual indexing of relational domains for while longer, or at least to keep this usage available as an alternative formulation. Generally speaking, it is always possible in principle to form the union required by the RUI, or without loss of generality to assume the equality imposed by the RUE. The problem is that the unions and equalities invoked by these rubrics may not be effectively definable or testable in a computational context. Further, even when these sets or tests can be constructed or certified by some computational agent or another, the pertinent question at any interpretive moment is whether each collection or constraint is actively being apprehended or warranted by the particular interpreter charged with responsibility for it by the indicated assignment of domains.
But an overall purpose of this formalism is to represent the objects and constituencies ''known to'' specific interpreters at definite moments of their interpretive proceedings, in other words, to depict the information about objective existence and constituent structure that is possessed, recognized, responded to, acted on, and followed up by concrete agents as they move through their immediate contexts of activity. Accordingly, keeping individual tabs on the relational domains Pj and Qj, though it does not solve this array of problems, does serve to mark the concern with particularity and to keep before the mind the issues of individual attention and responsibility that are appropriate to interpretive agents. In short, whether or not domains appear with explicit subscripts, one should always be ready to answer "Who subscribes to these domains?"
But an overall purpose of this formalism is to represent the objects and constituencies ''known to'' specific interpreters at definite moments of their interpretive proceedings, in other words, to depict the information about objective existence and constituent structure that is possessed, recognized, responded to, acted on, and followed up by concrete agents as they move through their immediate contexts of activity. Accordingly, keeping individual tabs on the relational domains Pj and Qj, though it does not solve this array of problems, does serve to mark the concern with particularity and to keep before the mind the issues of individual attention and responsibility that are appropriate to interpretive agents. In short, whether or not domains appear with explicit subscripts, one should always be ready to answer ''Who subscribes to these domains?''
It is important to emphasize that the index set J and the particular attachments of indices to dyadic relations are part and parcel to G, befitting the concrete character intended for the concept of an OG, which is expected to realistically embody in the character of each Gj both "a local habitation and a name". For this reason, among others, the Gj can safely be referred to as "individual dyadic relations" (IDR's). Since the classical notion of an "individual" as a "perfectly determinate entity" has no application in finite information contexts, it is safe to recycle this term to distinguish the "terminally informative particulars" (TIP's) that a concrete index j adds to its thematic object Gj, whether parenthetically or paraphatically.
It is important to emphasize that the index set J and the particular attachments of indices to dyadic relations are part and parcel to G, befitting the concrete character intended for the concept of an OG, which is expected to realistically embody in the character of each Gj both ''a local habitation and a name''. For this reason, among others, the Gj can safely be referred to as ''individual dyadic relations'' (IDR's). Since the classical notion of an ''individual'' as a ''perfectly determinate entity'' has no application in finite information contexts, it is safe to recycle this term to distinguish the ''terminally informative particulars'' (TIP's) that a concrete index j adds to its thematic object Gj, whether parenthetically or paraphatically.
Depending on the prevailing direction of interest in the genre G, "<" or ">", the same symbol is used equivocally for all the relations Gj. The Gj can be regarded as formalizing the OM's that make up the genre G, provided it is understood that the information corresponding to the parameter j constitutes an integral part of the "motive" or "motif" of Gj.
Depending on the prevailing direction of interest in the genre G, "<" or ">", the same symbol is used equivocally for all the relations Gj. The Gj can be regarded as formalizing the OM's that make up the genre G, provided it is understood that the information corresponding to the parameter j constitutes an integral part of the ''motive'' or ''motif'' of Gj.
In this formulation, G constitutes an "ontological hierarchy" (OH) of a plenary and potentiating type, one that determines the complete array of objects and relationships that are conceivably available and describably "effable" within a given discussion. Operating with reference to the global field of possibilities presented by G, each Gj corresponds to the specialized competence of a particular agent, selecting out the objects and links of the generic hierarchy that are known to, owing to, or owned by a given interpreter.
In this formulation, G constitutes an ''ontological hierarchy'' (OH) of a plenary and potentiating type, one that determines the complete array of objects and relationships that are conceivably available and describably ''effable'' within a given discussion. Operating with reference to the global field of possibilities presented by G, each Gj corresponds to the specialized competence of a particular agent, selecting out the objects and links of the generic hierarchy that are known to, owing to, or owned by a given interpreter.
Another way to formalize the defining structure of an OG can be posed in terms of a "relative membership relation" or a notion of "relative elementhood". The constitutional structure of a particular OG can be set up in a flexible manner by taking it in two stages, starting from the level of finer detail and working up to the big picture:
Another way to formalize the defining structure of an OG can be posed in terms of a ''relative membership relation'' or a notion of ''relative elementhood''. The constitutional structure of a particular OG can be set up in a flexible manner by taking it in two stages, starting from the level of finer detail and working up to the big picture:
1. Each OM is constituted by what it means to be an object within it. What constitutes an object in a given OM can be fixed as follows:
1. Each OM is constituted by what it means to be an object within it. What constitutes an object in a given OM can be fixed as follows:
ii. What is a property, quality, class, or set of what, relative to the OM in question.
ii. What is a property, quality, class, or set of what, relative to the OM in question.
2. The various OM's of a particular OG can be unified under its aegis by means of a single triadic relation, one that names an OM and a pair of objects and that holds when one object belongs to the other in the sense identified by the relevant OM. If it becomes absolutely essential to emphasize the relativity of elements, one may resort to calling them "relements", in this way jostling the mind to ask: "Relement to what?"
2. The various OM's of a particular OG can be unified under its aegis by means of a single triadic relation, one that names an OM and a pair of objects and that holds when one object belongs to the other in the sense identified by the relevant OM. If it becomes absolutely essential to emphasize the relativity of elements, one may resort to calling them ''relements'', in this way jostling the mind to ask: ''Relement to what?''
The last and likely the best way one can choose to follow in order to form an objective genre G is to present it as a triadic relation:
The last and likely the best way one can choose to follow in order to form an objective genre G is to present it as a triadic relation:
G = {‹j, x, y›} ? JxXxX.
G = {‹j, x, y›} ? JxXxX.
For some reason the ultimately obvious method seldom presents itself exactly in this wise without diligent work on the part of the inquirer, or one who would arrogate the roles of both its former and its follower. Perhaps this has to do with the problematic role of "synthetic a priori" truths in constructive mathematics. Perhaps the mystery lies encrypted, no doubt buried in some obscure dead letter office, due to the obliterate indicia on the letters "P", "Q", and "X" inscribed above. No matter - at the moment there are far more pressing rounds to make.
For some reason the ultimately obvious method seldom presents itself exactly in this wise without diligent work on the part of the inquirer, or one who would arrogate the roles of both its former and its follower. Perhaps this has to do with the problematic role of ''synthetic a priori'' truths in constructive mathematics. Perhaps the mystery lies encrypted, no doubt buried in some obscure dead letter office, due to the obliterate indicia on the letters "P", "Q", and "X" inscribed above. No matter - at the moment there are far more pressing rounds to make.
Given a genre G whose OM's are indexed by a set J and whose objects form a set X, there is a triadic relation among an OM and a pair of objects that exists when the first object belongs to the second object according to that OM. This is called the "standing relation" of the OG, and it can be taken as one way of defining and establishing the genre. In the way that triadic relations usually give rise to dyadic operations, the associated "standing operation" of the OG can be thought of as a brand of assignment operation that makes one object belong to another in a certain sense, namely, in the sense indicated by the designated OM.
Given a genre G whose OM's are indexed by a set J and whose objects form a set X, there is a triadic relation among an OM and a pair of objects that exists when the first object belongs to the second object according to that OM. This is called the "standing relation" of the OG, and it can be taken as one way of defining and establishing the genre. In the way that triadic relations usually give rise to dyadic operations, the associated ''standing operation'' of the OG can be thought of as a brand of assignment operation that makes one object belong to another in a certain sense, namely, in the sense indicated by the designated OM.
There is a "partial converse" of the standing relation that transposes the order in which the two object domains are mentioned. This is called the "propping relation" of the OG, and it can be taken as an alternate way of defining the genre.
There is a ''partial converse'' of the standing relation that transposes the order in which the two object domains are mentioned. This is called the ''propping relation'' of the OG, and it can be taken as an alternate way of defining the genre.
G^ = {‹j, q, p› ? J?Q?P : ‹j, p, q› ? G}, or
G^ = {‹j, q, p› ? J?Q?P : ‹j, p, q› ? G}, or
The following conventions are useful for discussing the set-theoretic extensions of the staging relations and staging operations of an OG:
The following conventions are useful for discussing the set-theoretic extensions of the staging relations and staging operations of an OG:
1. The standing relation of an OG is denoted by the symbol ":<", pronounced "set-in", so that :< ? JxPxQ or :< ? J?X?X.
1. The standing relation of an OG is denoted by the symbol ":<", pronounced ''set-in'', so that :< ? JxPxQ or :< ? J?X?X.
2. The propping relation of an OG is denoted by the symbol ":>", pronounced "set-on", so that :> ? J?Q?P or :> ? J?X?X.
2. The propping relation of an OG is denoted by the symbol ":>", pronounced ''set-on'', so that :> ? J?Q?P or :> ? J?X?X.
Often one's level of interest in a genre is "purely generic". When the relevant genre is regarded as an indexed family of dyadic relations, G = {Gj}, then this generic interest is tantamount to having one's concern rest with the union of all the dyadic relations in the genre.
Often one's level of interest in a genre is ''purely generic''. When the relevant genre is regarded as an indexed family of dyadic relations, G = {Gj}, then this generic interest is tantamount to having one's concern rest with the union of all the dyadic relations in the genre.
UJG = Uj Gj = {‹x, y› ? X?X : ‹x, y› ? Gj for some j ? J}.
UJG = Uj Gj = {‹x, y› ? X?X : ‹x, y› ? Gj for some j ? J}.
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In making these free interpretations of genres and motifs, one needs to read them in a "logical" rather than a "cognitive" sense. A statement like "j thinks x an instance of y" should be understood as saying that "j is a thought with the logical import that x is an instance of y", and a statement like "j proposes y a property of x" should be taken to mean that "j is a proposition to the effect that y is a property of x".
In making these free interpretations of genres and motifs, one needs to read them in a ''logical'' rather than a ''cognitive'' sense. A statement like "j thinks x an instance of y" should be understood as saying that "j is a thought with the logical import that x is an instance of y", and a statement like "j proposes y a property of x" should be taken to mean that "j is a proposition to the effect that y is a property of x".
These cautions are necessary to forestall the problems of intentional attitudes and contexts, something I intend to clarify later on in this project. At present, I regard the well-known opacities of this subject as arising from the circumstance that cognitive glosses tend to impute an unspecified order of extra reflection to each construal of the basic predicates. The way I plan to approach this issue is through a detailed analysis of the cognitive capacity for reflective thought, to be developed to the extent possible in formal terms by using sign relational models.
These cautions are necessary to forestall the problems of intentional attitudes and contexts, something I intend to clarify later on in this project. At present, I regard the well-known opacities of this subject as arising from the circumstance that cognitive glosses tend to impute an unspecified order of extra reflection to each construal of the basic predicates. The way I plan to approach this issue is through a detailed analysis of the cognitive capacity for reflective thought, to be developed to the extent possible in formal terms by using sign relational models.
Given an ontological framework that can provide multiple perspectives and moving platforms for dealing with object structure, in other words, that can organize diverse hierarchies and developing orders of objects, attention can now return to the discussion of sign relations as models of intellectual processes.
Given an ontological framework that can provide multiple perspectives and moving platforms for dealing with object structure, in other words, that can organize diverse hierarchies and developing orders of objects, attention can now return to the discussion of sign relations as models of intellectual processes.
A principal aim of using sign relations as formal models is to be capable of analyzing complex activities that arise in nature and human domains. Proceeding by the opportunistic mode of "analysis by synthesis" (ABS), one generates likely constructions from a stock of favored, familiar, and well-understood sign relations, the supply of which hopefully grows with time, constantly matching their formal properties against the structures encountered in the "wilds" of natural phenomena and human conduct. When salient traits of both the freely generated products and the widely gathered phenomena coincide in enough points, then the details of the constructs one has built for oneself can help to articulate a plausible hypothesis as to how the observable appearances might be explained.
A principal aim of using sign relations as formal models is to be capable of analyzing complex activities that arise in nature and human domains. Proceeding by the opportunistic mode of ''analysis by synthesis'' (ABS), one generates likely constructions from a stock of favored, familiar, and well-understood sign relations, the supply of which hopefully grows with time, constantly matching their formal properties against the structures encountered in the "wilds" of natural phenomena and human conduct. When salient traits of both the freely generated products and the widely gathered phenomena coincide in enough points, then the details of the constructs one has built for oneself can help to articulate a plausible hypothesis as to how the observable appearances might be explained.
A principal difficulty of using sign relations for this purpose arises from the very power of productivity they bring to bear in the process, the capacity of triadic relations to generate a welter of what are bound to be mostly arbitrary structures, with only a scattered few hoping to show any promise, but the massive profusion of which exceeds from the outset any reason's ability to sort them out and test them in practice. And yet, as the phenomena of interest become more complex, the chances grow slimmer that adequate explanations will be found in any of the thinner haystacks. In this respect, sign relations inherit the basic proclivities of set theory, which can be so successful and succinct in presenting and clarifying the properties of already found materials and hard won formal insights, and yet so overwhelming to use as a tool of random exploration and discovery.
A principal difficulty of using sign relations for this purpose arises from the very power of productivity they bring to bear in the process, the capacity of triadic relations to generate a welter of what are bound to be mostly arbitrary structures, with only a scattered few hoping to show any promise, but the massive profusion of which exceeds from the outset any reason's ability to sort them out and test them in practice. And yet, as the phenomena of interest become more complex, the chances grow slimmer that adequate explanations will be found in any of the thinner haystacks. In this respect, sign relations inherit the basic proclivities of set theory, which can be so successful and succinct in presenting and clarifying the properties of already found materials and hard won formal insights, and yet so overwhelming to use as a tool of random exploration and discovery.
Consequently, naturally occurring sign relations can be expected to fall into species or natural kinds, and to have special properties that make them keep on occurring in nature. Moreover, cultivated varieties of sign relations, the kinds that have been converted to social purposes and found to be viable in actual practice, will have identifiable and especially effective properties by virtue of which their signs are rendered significant.
Consequently, naturally occurring sign relations can be expected to fall into species or natural kinds, and to have special properties that make them keep on occurring in nature. Moreover, cultivated varieties of sign relations, the kinds that have been converted to social purposes and found to be viable in actual practice, will have identifiable and especially effective properties by virtue of which their signs are rendered significant.
In the pragmatic theory of sign relations, three natural kinds of signs are recognized, under the names of "icons", "indices", and "symbols". Examples of indexical or accessional signs figured significantly in the discussion of A and B, as illustrated by the pronouns "i" and "u" in S. Examples of iconic or analogical signs were also present, though keeping to the background, in the very form of the sign relation Tables that were used to schematize the whole activity of each interpreter. Examples of symbolic or conventional signs, of course, abide even more deeply in the background, pervading the whole context and making up the very fabric of this discussion.
In the pragmatic theory of sign relations, three natural kinds of signs are recognized, under the names of ''icons'', ''indices'', and ''symbols''. Examples of indexical or accessional signs figured significantly in the discussion of A and B, as illustrated by the pronouns "i" and "u" in S. Examples of iconic or analogical signs were also present, though keeping to the background, in the very form of the sign relation Tables that were used to schematize the whole activity of each interpreter. Examples of symbolic or conventional signs, of course, abide even more deeply in the background, pervading the whole context and making up the very fabric of this discussion.
In order to deal with the array of issues presented so far in this subsection, all of which have to do with controlling the generative power of sign relations to serve the specific purposes of understanding, I apply the previously introduced concept of an "objective genre" (OG). This is intended to be a determinate purpose or a deliberate pattern of analysis and synthesis that one can identify as being active at given moments in a discussion and that affects what one regards as the relevant structural properties of its objects.
In order to deal with the array of issues presented so far in this subsection, all of which have to do with controlling the generative power of sign relations to serve the specific purposes of understanding, I apply the previously introduced concept of an ''objective genre'' (OG). This is intended to be a determinate purpose or a deliberate pattern of analysis and synthesis that one can identify as being active at given moments in a discussion and that affects what one regards as the relevant structural properties of its objects.
In the remainder of this subsection the concept of an OG is used informally, and only to the extent needed for a pressing application, namely, to rationalize the natural kinds that are claimed for signs and to clarify an important contrast that exists between icons and indices.
In the remainder of this subsection the concept of an OG is used informally, and only to the extent needed for a pressing application, namely, to rationalize the natural kinds that are claimed for signs and to clarify an important contrast that exists between icons and indices.
The OG I apply here is called the genre of "properties and instances". One moves through its space, higher and lower in a particular ontology, by means of two dyadic relations, upward by taking a "property of" and downward by taking an "instance of" whatever object initially enters one's focus of attention. Each object of this OG is reckoned to be the unique common property of the set of objects that lie one step below it, objects that are in turn reckoned to be instances of the given object.
The OG I apply here is called the genre of ''properties and instances''. One moves through its space, higher and lower in a particular ontology, by means of two dyadic relations, upward by taking a ''property of'' and downward by taking an ''instance of'' whatever object initially enters one's focus of attention. Each object of this OG is reckoned to be the unique common property of the set of objects that lie one step below it, objects that are in turn reckoned to be instances of the given object.
Pretty much the same relational structures could be found in the genre or paradigm of "qualities and examples", but the use of "examples" here is polymorphous enough to include experiential, exegetic, and executable examples (EXE's). This points the way to a series of related genres, for example, the OG's of "principles and illustrations", "laws and existents", "precedents and exercises", and on to "lessons and experiences". All in all, in their turn, these modulations of the basic OG show a way to shift the foundations of ontological hierarchies toward bases in individual and systematic experience, and thus to put existentially dynamic rollers under the blocks of what seem to be essentially invariant pyramids.
Pretty much the same relational structures could be found in the genre or paradigm of ''qualities and examples'', but the use of ''examples'' here is polymorphous enough to include experiential, exegetic, and executable examples (EXE's). This points the way to a series of related genres, for example, the OG's of ''principles and illustrations'', ''laws and existents'', ''precedents and exercises'', and on to ''lessons and experiences''. All in all, in their turn, these modulations of the basic OG show a way to shift the foundations of ontological hierarchies toward bases in individual and systematic experience, and thus to put existentially dynamic rollers under the blocks of what seem to be essentially invariant pyramids.
Any object of these OG's can be contemplated in the light of two potential relationships, namely, with respect to its chances of being an "object quality" (OQ) or an "object example" (OE) of something else. In future references, abbreviated notations like "OG (Prop, Inst)" or "OG = ‹Prop, Inst›" will be used to specify particular genres, giving the intended interpretations of their generating relations { < , > }.
Any object of these OG's can be contemplated in the light of two potential relationships, namely, with respect to its chances of being an ''object quality'' (OQ) or an ''object example'' (OE) of something else. In future references, abbreviated notations like "OG (Prop, Inst)" or "OG = ‹Prop, Inst›" will be used to specify particular genres, giving the intended interpretations of their generating relations { < , > }.
With respect to this OG, I can now characterize icons and indices. Icons are signs by virtue of being instances of properties of objects. Indices are signs by virtue of being properties of instances of objects.
With respect to this OG, I can now characterize icons and indices. Icons are signs by virtue of being instances of properties of objects. Indices are signs by virtue of being properties of instances of objects.
For Indices: Obj (Sign) = Prop (Inst (Sign)).
For Indices: Obj (Sign) = Prop (Inst (Sign)).
In spite of the apparent duality between these patterns of composition, there is a significant asymmetry to be observed in the way that the insistent theme of realism interrupts the underlying genre. In order to understand this, it is necessary to note that the strain of pragmatic thinking I am using here takes its definition of "reality" from the word's original Scholastic sources, where the adjective "real" means "having properties". Taken in this sense, reality is necessary but not sufficient to "actuality", where "actual" means "existing in act and not merely potentially" (Webster's). To reiterate, actuality is sufficient but not necessary to reality. The distinction between the ideas is further pointed up by the fact that a potential can be real, and that its reality can be independent of any particular moment in which the power acts.
In spite of the apparent duality between these patterns of composition, there is a significant asymmetry to be observed in the way that the insistent theme of realism interrupts the underlying genre. In order to understand this, it is necessary to note that the strain of pragmatic thinking I am using here takes its definition of ''reality'' from the word's original Scholastic sources, where the adjective ''real'' means ''having properties''. Taken in this sense, reality is necessary but not sufficient to ''actuality'', where ''actual'' means "existing in act and not merely potentially" (Webster's). To reiterate, actuality is sufficient but not necessary to reality. The distinction between the ideas is further pointed up by the fact that a potential can be real, and that its reality can be independent of any particular moment in which the power acts.
These "angelic doctrines" would probably remain distant from the present concern, were it not for two points of connection:
These ''angelic doctrines'' would probably remain distant from the present concern, were it not for two points of connection:
1. Relative to the present genre, the distinction of reality, that can be granted to certain objects of thought and not to others, fulfills an analogous role to the distinction that singles out "sets" among "classes" in modern versions of set theory. Taking the membership relation "?" as a predecessor relation in a pre-designated hierarchy of classes, a class attains the status of a set, and by dint of this becomes an object of more determinate discussion, simply if it has successors. Pragmatic reality is distinguished from both the medieval and the modern versions, however, by the fact that its reality is always a reality to somebody. This is due to the circumstance that it takes both an abstract property and a concrete interpreter to establish the practical reality of an object.
1. Relative to the present genre, the distinction of reality, that can be granted to certain objects of thought and not to others, fulfills an analogous role to the distinction that singles out ''sets'' among ''classes'' in modern versions of set theory. Taking the membership relation "∈" as a predecessor relation in a pre-designated hierarchy of classes, a class attains the status of a set, and by dint of this becomes an object of more determinate discussion, simply if it has successors. Pragmatic reality is distinguished from both the medieval and the modern versions, however, by the fact that its reality is always a reality to somebody. This is due to the circumstance that it takes both an abstract property and a concrete interpreter to establish the practical reality of an object.
2. This project seeks articulations and implementations of intelligent activity within dynamically realistic systems. The individual stresses placed on articulation, implementation, actuality, dynamics, and reality collectively reinforce the importance of several issues:
2. This project seeks articulations and implementations of intelligent activity within dynamically realistic systems. The individual stresses placed on articulation, implementation, actuality, dynamics, and reality collectively reinforce the importance of several issues:
a. Systems theory, consistently pursued, eventually demands for its rationalization a distinct ontology, in which states of being and modes of action form the principal objects of thought, out of which the ordinary sorts of stably extended objects must be constructed. In the "grammar" of process philosophy, verbs and pronouns are more basic than nouns. In its influence on the course of this discussion, the emphasis on systematic action is tantamount to an objective genre that makes dynamic systems, their momentary states and their passing actions, become the ultimate objects of synthesis and analysis. Consequently, the drift of this inquiry will be turned toward conceiving actions, as traced out in the trajectories of systems, to be the primitive elements of construction, more fundamental in this objective genre than stationary objects extended in space. As a corollary, it expects to find that physical objects of the static variety have a derivative status in relation to the activities that orient agents, both organisms and organizations, toward purposeful objectives.
a. Systems theory, consistently pursued, eventually demands for its rationalization a distinct ontology, in which states of being and modes of action form the principal objects of thought, out of which the ordinary sorts of stably extended objects must be constructed. In the "grammar" of process philosophy, verbs and pronouns are more basic than nouns. In its influence on the course of this discussion, the emphasis on systematic action is tantamount to an objective genre that makes dynamic systems, their momentary states and their passing actions, become the ultimate objects of synthesis and analysis. Consequently, the drift of this inquiry will be turned toward conceiving actions, as traced out in the trajectories of systems, to be the primitive elements of construction, more fundamental in this objective genre than stationary objects extended in space. As a corollary, it expects to find that physical objects of the static variety have a derivative status in relation to the activities that orient agents, both organisms and organizations, toward purposeful objectives.
b. At root, the notion of "dynamics" is concerned with "power" in the sense of "potential". The brand of pragmatic thinking that I use in this work permits potential entities to be analyzed as real objects and conceptual objects to be constituted by the conception of their actual effects in practical instances. In the attempt to unify symbolic and dynamic approaches to intelligent systems (Upper and Lower Kingdoms?), there remains an insistent need to build conceptual bridges. A facility for relating objects to their actualizing instances and their instantiating actions lends many useful tools to an effort of this nature, in which the search for understanding cannot rest until each object and phenomenon has been reconstructed in terms of active occurrences and ways of being.
b. At root, the notion of ''dynamics'' is concerned with ''power'' in the sense of ''potential''. The brand of pragmatic thinking that I use in this work permits potential entities to be analyzed as real objects and conceptual objects to be constituted by the conception of their actual effects in practical instances. In the attempt to unify symbolic and dynamic approaches to intelligent systems (Upper and Lower Kingdoms?), there remains an insistent need to build conceptual bridges. A facility for relating objects to their actualizing instances and their instantiating actions lends many useful tools to an effort of this nature, in which the search for understanding cannot rest until each object and phenomenon has been reconstructed in terms of active occurrences and ways of being.
c. In prospect of form, it does not matter whether one takes this project as a task of analyzing and articulating the actualizations of intelligence that already exist in nature, or whether one views it as a goal of synthesizing and artificing the potentials for intelligence that have yet to be conceived in practice. From a formal perspective, the analysis and the synthesis are just reciprocal ways of tracing or retracing the same generic patterns of potential structure that determine actual form.
c. In prospect of form, it does not matter whether one takes this project as a task of analyzing and articulating the actualizations of intelligence that already exist in nature, or whether one views it as a goal of synthesizing and artificing the potentials for intelligence that have yet to be conceived in practice. From a formal perspective, the analysis and the synthesis are just reciprocal ways of tracing or retracing the same generic patterns of potential structure that determine actual form.
In sum: For icons a separate reality is optional, for indices a separate reality is obligatory. As often happens with a form of analysis, each term under the indicated sum appears to verge on indefinite expansion:
In sum: For icons a separate reality is optional, for indices a separate reality is obligatory. As often happens with a form of analysis, each term under the indicated sum appears to verge on indefinite expansion:
1. "For icons, the existence of a separate reality is optional." This means that the question of reality in the sign relation can depend on nothing more than the reality of each sign itself, on whether it has any property with respect to the OG in question. In effect, icons can rely on their own reality to faithfully provide a real object.
1. ''For icons, the existence of a separate reality is optional.'' This means that the question of reality in the sign relation can depend on nothing more than the reality of each sign itself, on whether it has any property with respect to the OG in question. In effect, icons can rely on their own reality to faithfully provide a real object.
2. "For indices, the existence of a separate reality is obligatory." And yet this reality need not affect the object of the sign. In essence, indices are satisfied with a basis in reality that need only reside in an actual object instance, one that establishes a real connection between the object and its index with regard to the OG in question.
2. ''For indices, the existence of a separate reality is obligatory.'' And yet this reality need not affect the object of the sign. In essence, indices are satisfied with a basis in reality that need only reside in an actual object instance, one that establishes a real connection between the object and its index with regard to the OG in question.
Finally, suppose that M and N are hypothetical sign relations intended to capture all the iconic and indexical relationships, respectively, that a typical object x enjoys within its genre G. A sign relation in which every sign has the same kind of relation to its object under an assumed form of analysis is appropriately called a "homogeneous sign relation". In particular, if H is a homogeneous sign relation in which every sign has either an iconic or an indexical relation to its object, then it is convenient to apply the corresponding adjective to the whole of H.
Finally, suppose that M and N are hypothetical sign relations intended to capture all the iconic and indexical relationships, respectively, that a typical object x enjoys within its genre G. A sign relation in which every sign has the same kind of relation to its object under an assumed form of analysis is appropriately called a ''homogeneous sign relation''. In particular, if H is a homogeneous sign relation in which every sign has either an iconic or an indexical relation to its object, then it is convenient to apply the corresponding adjective to the whole of H.
Typical sign relations of the iconic or indexical kind generate especially simple and remarkably stable sorts of interpretive processes. In arity, they could almost be classified as "approximately dyadic", since most of their interesting structure is wrapped up in their denotative aspects, while their connotative functions are relegated to the tangential role of preserving the directions of their denotative axes. In a metaphorical but true sense, iconic and indexical sign relations equip objective frameworks with "gyroscopes", helping them maintain their interpretive perspectives in a persistent orientation toward their objective world.
Typical sign relations of the iconic or indexical kind generate especially simple and remarkably stable sorts of interpretive processes. In arity, they could almost be classified as ''approximately dyadic'', since most of their interesting structure is wrapped up in their denotative aspects, while their connotative functions are relegated to the tangential role of preserving the directions of their denotative axes. In a metaphorical but true sense, iconic and indexical sign relations equip objective frameworks with "gyroscopes", helping them maintain their interpretive perspectives in a persistent orientation toward their objective world.
Of course, every form of sign relation still depends on the agency of a proper interpreter to bring it to life, and every species of sign process stays forever relative to the interpreters that actually bring it to term. But it is a rather special circumstance by means of which the actions of icons and indices are able to turn on the existence of independently meaningful properties and instances, as recognized within an objective framework, and this means that the interpretive associations of these signs are not always as idiosyncratic as they might otherwise be.
Of course, every form of sign relation still depends on the agency of a proper interpreter to bring it to life, and every species of sign process stays forever relative to the interpreters that actually bring it to term. But it is a rather special circumstance by means of which the actions of icons and indices are able to turn on the existence of independently meaningful properties and instances, as recognized within an objective framework, and this means that the interpretive associations of these signs are not always as idiosyncratic as they might otherwise be.
Turning to the language of objective concerns, what can now be said about the compositional structures of the iconic sign relation M and the indexical sign relation N? In preparation for this topic, a few additional steps must be taken to continue formalizing the concept of an objective genre and to begin developing a calculus for composing objective motifs.
Turning to the language of objective concerns, what can now be said about the compositional structures of the iconic sign relation M and the indexical sign relation N? In preparation for this topic, a few additional steps must be taken to continue formalizing the concept of an objective genre and to begin developing a calculus for composing objective motifs.
I recall the OG of "properties and instances" and introduce the symbols "<" and ">" for the converse pair of dyadic relations that generate it. Reverting to the convention I employ in formal discussions of applying relational operators on the right, it is convenient to express the relative terms "property of x" and "instance of x" by means of a case inflection on x, that is, as "x's property" and "x's instance", respectively. Described in this way, OG (Prop, Inst) = ‹ < , > ›, where:
I recall the OG of ''properties and instances'' and introduce the symbols "<" and ">" for the converse pair of dyadic relations that generate it. Reverting to the convention I employ in formal discussions of applying relational operators on the right, it is convenient to express the relative terms ''property of x'' and ''instance of x'' by means of a case inflection on x, that is, as ''x's property'' and ''x's instance'', respectively. Described in this way, OG (Prop, Inst) = ‹ < , > ›, where:
"x <" = "x's Property" = "Property of x" = "Object above x",
"x <" = "x's Property" = "Property of x" = "Object above x",
"x >" = "x's Instance" = "Instance of x" = "Object below x".
"x >" = "x's Instance" = "Instance of x" = "Object below x".
A symbol like "x <" or "x >", with extra spaces or dots being optional, is called a "catenation", where "x" is the "catenand" and "<" or ">" is the "catenator". Due to the fact that "<" and ">" indicate dyadic relations, the significance of these so-called "unsaturated" catenations can be rationalized as follows:
A symbol like "x <" or "x >", with extra spaces or dots being optional, is called a ''catenation'', where "x" is the ''catenand'' and "<" or ">" is the ''catenator''. Due to the fact that "<" and ">" indicate dyadic relations, the significance of these so-called ''unsaturated'' catenations can be rationalized as follows:
"x <" = "x is the Instance of what?" = "x's Property",
"x <" = "x is the Instance of what?" = "x's Property",
Now that an adequate variety of formal tools have been set in order and the workspace afforded by an objective framework has been rendered reasonably clear, the structural theory of sign relations can be pursued with greater precision. In support of this aim, the concept of an objective genre and the particular example provided by OG (Prop, Inst) have served to rough out the basic shapes of the more refined analytic instruments to be developed in this subsection.
Now that an adequate variety of formal tools have been set in order and the workspace afforded by an objective framework has been rendered reasonably clear, the structural theory of sign relations can be pursued with greater precision. In support of this aim, the concept of an objective genre and the particular example provided by OG (Prop, Inst) have served to rough out the basic shapes of the more refined analytic instruments to be developed in this subsection.
The notion of an "objective motive" or "objective motif" (OM) is intended to specialize or personalize the application of objective genres to take particular interpreters into account. For example, pursuing the pattern of OG (Prop, Inst), a prospective OM of this genre does not merely tell about the properties and instances that objects can have in general, it recognizes a particular arrangement of objects and supplies them with its own ontology, giving "a local habitation and a name" to the bunch. What matters to an OM is a particular collection of objects (of thought) and a personal selection of links that go from each object (of thought) to higher and lower objects (of thought), all things being relative to a subjective ontology or a live "hierarchy of thought" (HOT), one that is currently known to and actively pursued by a designated interpreter of those thoughts.
The notion of an ''objective motive'' or ''objective motif'' (OM) is intended to specialize or personalize the application of objective genres to take particular interpreters into account. For example, pursuing the pattern of OG (Prop, Inst), a prospective OM of this genre does not merely tell about the properties and instances that objects can have in general, it recognizes a particular arrangement of objects and supplies them with its own ontology, giving "a local habitation and a name" to the bunch. What matters to an OM is a particular collection of objects (of thought) and a personal selection of links that go from each object (of thought) to higher and lower objects (of thought), all things being relative to a subjective ontology or a live ''hierarchy of thought'' (HOT), one that is currently known to and actively pursued by a designated interpreter of those thoughts.
The cautionary details interspersed at critical points in the preceding paragraph are intended to keep this inquiry vigilant against a constant danger of using ontological language, namely, the illusion that one can analyze the being of any real object merely by articulating the grammar of one's own thoughts, that is, simply by parsing signs in the mind. As always, it is best to regard OG's and OM's as "filters" and "reticles", as transparent templates that are used to view a space, constituting the structures of objects only in one respect at a time, but never with any assurance of totality.
The cautionary details interspersed at critical points in the preceding paragraph are intended to keep this inquiry vigilant against a constant danger of using ontological language, namely, the illusion that one can analyze the being of any real object merely by articulating the grammar of one's own thoughts, that is, simply by parsing signs in the mind. As always, it is best to regard OG's and OM's as ''filters'' and ''reticles'', as transparent templates that are used to view a space, constituting the structures of objects only in one respect at a time, but never with any assurance of totality.
With these refinements, the use of dyadic projections to investigate sign relations can be combined with the perspective of objective motives to "factor the facets" or "decompose the components" of sign relations in a more systematic fashion. Given a homogeneous sign relation H of iconic or indexical type, the dyadic projections HOS and HOI can be analyzed as compound relations over the basis supplied by the Gj in G. As an application that is sufficiently important in its own right, the investigation of icons and indices continues to provide a useful testing ground for breaking in likely proposals of concepts and notation.
With these refinements, the use of dyadic projections to investigate sign relations can be combined with the perspective of objective motives to ''factor the facets'' or ''decompose the components'' of sign relations in a more systematic fashion. Given a homogeneous sign relation H of iconic or indexical type, the dyadic projections HOS and HOI can be analyzed as compound relations over the basis supplied by the Gj in G. As an application that is sufficiently important in its own right, the investigation of icons and indices continues to provide a useful testing ground for breaking in likely proposals of concepts and notation.
To pursue the analysis of icons and indices at the next stage of formalization, fix the OG of this discussion to have the type ‹ < , > ›, and let each sign relation under discussion be articulated in terms of an objective motif that tells what objects and signs, plus what mediating linkages through properties and instances, are assumed to be recognized by its interpreter.
To pursue the analysis of icons and indices at the next stage of formalization, fix the OG of this discussion to have the type ‹ < , > ›, and let each sign relation under discussion be articulated in terms of an objective motif that tells what objects and signs, plus what mediating linkages through properties and instances, are assumed to be recognized by its interpreter.
2. k thinks x an index of y if and only if there is an n such that k thinks x a property of n and k thinks n an instance of y.
2. k thinks x an index of y if and only if there is an n such that k thinks x a property of n and k thinks n an instance of y.
Readers who object to the anthropomorphism or the approximation of these statements can replace every occurrence of the verb "thinks" with the phrase "interprets...as", or even the circumlocution "acts in every formally relevant way as if", changing what must be changed elsewhere. For the moment, I am not concerned with the exact order of reflective sensitivity that goes into these interpretive linkages, but only with a rough outline of the pragmatic equivalence classes that are afforded by the potential conduct of their agents.
Readers who object to the anthropomorphism or the approximation of these statements can replace every occurrence of the verb ''thinks'' with the phrase ''interprets...as'', or even the circumlocution ''acts in every formally relevant way as if'', changing what must be changed elsewhere. For the moment, I am not concerned with the exact order of reflective sensitivity that goes into these interpretive linkages, but only with a rough outline of the pragmatic equivalence classes that are afforded by the potential conduct of their agents.
In the discussion of the dialogue between A and B, it was allowed that the same signs "A" and "B" could reference the different categories of things they name with a deliberate duality and a systematic ambiguity. Used informally as a part of the peripheral discussion, they indicate the entirety of the sign relations themselves. Used formally within the focal dialogue, they denote the objects of two particular sign relations. In just this way, or an elaboration of it, the signs "j" and "k" can have their meanings extended to encompass both the objective motifs (OM's) that inform and regulate experience and the object experiences (OE's) that fill out and substantiate their forms.
In the discussion of the dialogue between A and B, it was allowed that the same signs "A" and "B" could reference the different categories of things they name with a deliberate duality and a systematic ambiguity. Used informally as a part of the peripheral discussion, they indicate the entirety of the sign relations themselves. Used formally within the focal dialogue, they denote the objects of two particular sign relations. In just this way, or an elaboration of it, the signs "j" and "k" can have their meanings extended to encompass both the objective motifs (OM's) that inform and regulate experience and the object experiences (OE's) that fill out and substantiate their forms.
Integrating divergent IF's and reconciling their objectifications is, generally speaking, a very difficult maneuver to carry out successfully. Two factors that contribute to the near intractability of this task can be described and addressed as follows.
Integrating divergent IF's and reconciling their objectifications is, generally speaking, a very difficult maneuver to carry out successfully. Two factors that contribute to the near intractability of this task can be described and addressed as follows.
1. The trouble is partly due to the ossified taxonomies and obligatory tactics that come through time and training to inhabit the conceptual landscapes of agents, especially if they have spent the majority of their time operating according to a single IF. The IF informs their activity in ways they no longer have to think about, and thus rarely find a reason to modify. But it also inhibits their interpretive and practical conduct to the customary ways of seeing and doing things that are granted by that framework, and it restricts them to the "forms of intuition" that are suggested and sanctioned by the operative IF. Without critical reflection, or a mechanism to make amendments to its own constitution, an IF tends to operate behind the scenes of observation in such a way as to obliterate any inkling of flexibility in thought or practice and to obstruct every hint or threat (so perceived) of conceptual revision.
1. The trouble is partly due to the ossified taxonomies and obligatory tactics that come through time and training to inhabit the conceptual landscapes of agents, especially if they have spent the majority of their time operating according to a single IF. The IF informs their activity in ways they no longer have to think about, and thus rarely find a reason to modify. But it also inhibits their interpretive and practical conduct to the customary ways of seeing and doing things that are granted by that framework, and it restricts them to the ''forms of intuition'' that are suggested and sanctioned by the operative IF. Without critical reflection, or a mechanism to make amendments to its own constitution, an IF tends to operate behind the scenes of observation in such a way as to obliterate any inkling of flexibility in thought or practice and to obstruct every hint or threat (so perceived) of conceptual revision.
2. Apparently it is so much easier to devise techniques for taking things apart than it is to find ways of putting them back together that there seem to be only a few heuristic strategies of general application that are available to guide the work of integration. A few of the tools and materials needed for these constructions have been illustrated in concrete form throughout the presentation of examples in this section. An overall survey of their principles can be summed up as follows.
2. Apparently it is so much easier to devise techniques for taking things apart than it is to find ways of putting them back together that there seem to be only a few heuristic strategies of general application that are available to guide the work of integration. A few of the tools and materials needed for these constructions have been illustrated in concrete form throughout the presentation of examples in this section. An overall survey of their principles can be summed up as follows.
a. One integration heuristic is the "lattice" metaphor, also called the "partial order" or "common denominator" paradigm. When IF's can be objectified as OF's that are organized according to the principles of suitable orderings, then it is often possible to "lift" or extend these order properties to the space of frameworks themselves, and thereby to enable construction of the desired kinds of integrative frameworks as upper and lower bounds in the appropriate ordering.
a. One integration heuristic is the ''lattice'' metaphor, also called the ''partial order'' or ''common denominator'' paradigm. When IF's can be objectified as OF's that are organized according to the principles of suitable orderings, then it is often possible to ''lift'' or extend these order properties to the space of frameworks themselves, and thereby to enable construction of the desired kinds of integrative frameworks as upper and lower bounds in the appropriate ordering.
b. Another integration heuristic is the "mosaic" metaphor, also called the "stereoscopic" or "inverse projection" paradigm. This technique has been illustrated especially well by the methods used throughout this section to analyze the three-dimensional structures of sign relations. In fact, the picture of any sign relation offers a paradigm in microcosm for the macroscopic work of integration, showing how reductive aspects of structure can be projected from a shared but irreducible reality. The extent to which the "full-bodied" structure of a triadic sign relation can be reconstructed from its dyadic projections, although a limited extent in general, presents a near perfect epitome of the larger task in this situation, namely, to find an integrated framework that embodies the diverse facets of reality severally observed from inside the individual frameworks. Acting as gnomonic recipes for the higher order processes they limn and delimit, sign relations keep before the mind the ways in which a higher dimensional structure determines its fragmentary aspects but is not in general determined by them.
b. Another integration heuristic is the ''mosaic'' metaphor, also called the ''stereoscopic'' or ''inverse projection'' paradigm. This technique has been illustrated especially well by the methods used throughout this section to analyze the three-dimensional structures of sign relations. In fact, the picture of any sign relation offers a paradigm in microcosm for the macroscopic work of integration, showing how reductive aspects of structure can be projected from a shared but irreducible reality. The extent to which the ''full-bodied'' structure of a triadic sign relation can be reconstructed from its dyadic projections, although a limited extent in general, presents a near perfect epitome of the larger task in this situation, namely, to find an integrated framework that embodies the diverse facets of reality severally observed from inside the individual frameworks. Acting as gnomonic recipes for the higher order processes they limn and delimit, sign relations keep before the mind the ways in which a higher dimensional structure determines its fragmentary aspects but is not in general determined by them.
To express the nature of this integration task in logical terms, it combines elements of both proof theory and model theory, interweaving: (1) A phase that develops theories about the symbolic competence or "knowledge" of intelligent agents, using abstract formal systems to represent the theories and phenomenological data to constrain them; (2) A phase that seeks concrete models of these theories, looking to the kinds of mathematical structure that have a dynamic or system-theoretic interpretation, and compiling the constraints that a recursive conceptual analysis imposes on the ultimate elements of their construction.
To express the nature of this integration task in logical terms, it combines elements of both proof theory and model theory, interweaving: (1) A phase that develops theories about the symbolic competence or ''knowledge'' of intelligent agents, using abstract formal systems to represent the theories and phenomenological data to constrain them; (2) A phase that seeks concrete models of these theories, looking to the kinds of mathematical structure that have a dynamic or system-theoretic interpretation, and compiling the constraints that a recursive conceptual analysis imposes on the ultimate elements of their construction.
The set of sign relations {A, B} is an example of an extremely simple formal system, encapsulating aspects of the symbolic competence and the pragmatic performance that might be exhibited by potentially intelligent interpretive agents, however abstractly and partially given at this stage of description. The symbols of a formal system like {A, B} can be held subject to abstract constraints, having their meanings in relation to each other determined by definitions and axioms (for example, the laws defining an equivalence relation), making it possible to manipulate the resulting information by means of the inference rules in a proof system. This illustrates the "proof-theoretic" aspect of a symbol system.
The set of sign relations {A, B} is an example of an extremely simple formal system, encapsulating aspects of the symbolic competence and the pragmatic performance that might be exhibited by potentially intelligent interpretive agents, however abstractly and partially given at this stage of description. The symbols of a formal system like {A, B} can be held subject to abstract constraints, having their meanings in relation to each other determined by definitions and axioms (for example, the laws defining an equivalence relation), making it possible to manipulate the resulting information by means of the inference rules in a proof system. This illustrates the ''proof-theoretic'' aspect of a symbol system.
Suppose that a formal system like {A, B} is initially approached from a theoretical direction, in other words, by listing the abstract properties one thinks it ought to have. Then the existence of an extensional model that satisfies these constraints, as exhibited by the sign relation tables, demonstrates that one's theoretical description is logically consistent, even if the models that first come to mind are still a bit too abstractly symbolic and do not have all the dynamic concreteness that is demanded of system-theoretic interpretations. This amounts to the other side of the ledger, the "model-theoretic" aspect of a symbol system, at least insofar as the present account has dealt with it.
Suppose that a formal system like {A, B} is initially approached from a theoretical direction, in other words, by listing the abstract properties one thinks it ought to have. Then the existence of an extensional model that satisfies these constraints, as exhibited by the sign relation tables, demonstrates that one's theoretical description is logically consistent, even if the models that first come to mind are still a bit too abstractly symbolic and do not have all the dynamic concreteness that is demanded of system-theoretic interpretations. This amounts to the other side of the ledger, the ''model-theoretic'' aspect of a symbol system, at least insofar as the present account has dealt with it.
More is required of the modeler, however, in order to find the desired kinds of system-theoretic models (for example, state transition systems), and this brings the search for realizations of formal systems down to the toughest part of the exercise. Some of the problems that emerge were highlighted in the example of A and B. Although it is ordinarily possible to construct state transition systems in which the states of interpreters correspond relatively directly to the acceptations of the primitive signs given, the conflict of interpretations that develops between different interpreters from these prima facie implementations is a sign that there is something superficial about this approach.
More is required of the modeler, however, in order to find the desired kinds of system-theoretic models (for example, state transition systems), and this brings the search for realizations of formal systems down to the toughest part of the exercise. Some of the problems that emerge were highlighted in the example of A and B. Although it is ordinarily possible to construct state transition systems in which the states of interpreters correspond relatively directly to the acceptations of the primitive signs given, the conflict of interpretations that develops between different interpreters from these prima facie implementations is a sign that there is something superficial about this approach.
The integration of model-theoretic and proof-theoretic aspects of "physical symbol systems", besides being closely analogous to the integration of denotative and connotative aspects of sign relations, is also relevant to the job of integrating dynamic and symbolic frameworks for intelligent systems. This is so because the search for dynamic realizations of symbol systems is only a more pointed exercise in model theory, where the mathematical materials made available for modeling are further constrained by system-theoretic principles, like being able to say what the states are and how the transitions are determined.
The integration of model-theoretic and proof-theoretic aspects of ''physical symbol systems'', besides being closely analogous to the integration of denotative and connotative aspects of sign relations, is also relevant to the job of integrating dynamic and symbolic frameworks for intelligent systems. This is so because the search for dynamic realizations of symbol systems is only a more pointed exercise in model theory, where the mathematical materials made available for modeling are further constrained by system-theoretic principles, like being able to say what the states are and how the transitions are determined.
=====1.3.4.17. Recapitulation : A Brush with Symbols=====
=====1.3.4.17. Recapitulation : A Brush with Symbols=====
Pursuant to this particular way of setting out on the long-term quest, a more immediate goal of the current project is to understand the action of full-fledged symbols, insofar as they conduct themselves through the media of minds and quasi-minds. At this very point the quest is joined by the pragmatic investigations of signs and inquiry, which share this interest in chasing down symbols to their precursive lairs.
Pursuant to this particular way of setting out on the long-term quest, a more immediate goal of the current project is to understand the action of full-fledged symbols, insofar as they conduct themselves through the media of minds and quasi-minds. At this very point the quest is joined by the pragmatic investigations of signs and inquiry, which share this interest in chasing down symbols to their precursive lairs.
In the pragmatic theory of signs a "symbol" is a strangely insistent yet curiously indirect type of sign, one whose accordance with its object depends sheerly on the real possibility that it will be so interpreted. Taking on the nature of a bet, a symbol's prospective value trades on nothing more than the chance of acquiring the desired interpretant, and thus it can capitalize on the simple fact that what it proposes is not impossible. In this way it is possible to see that a formal principle is involved in the success of symbols. The elementary conceivability of a particular sign relation, the pure circumstance that renders it logically or mathematically possible, means that the formal constraint it places on its domains is always really and potentially there, awaiting its discovery and exploitation for the purposes of representation and communication.
In the pragmatic theory of signs a ''symbol'' is a strangely insistent yet curiously indirect type of sign, one whose accordance with its object depends sheerly on the real possibility that it will be so interpreted. Taking on the nature of a bet, a symbol's prospective value trades on nothing more than the chance of acquiring the desired interpretant, and thus it can capitalize on the simple fact that what it proposes is not impossible. In this way it is possible to see that a formal principle is involved in the success of symbols. The elementary conceivability of a particular sign relation, the pure circumstance that renders it logically or mathematically possible, means that the formal constraint it places on its domains is always really and potentially there, awaiting its discovery and exploitation for the purposes of representation and communication.
In this question about the symbol's capacity for meaning, then, is found another contact between the theory of signs and the logic of inquiry. As C.S. Peirce expressed it:
In this question about the symbol's capacity for meaning, then, is found another contact between the theory of signs and the logic of inquiry. As C.S. Peirce expressed it:
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A full explanation of these statements, linking scientific inference, symbolization, and information together in such an integral fashion, would require an excursion into the pragmatic theory of information that Peirce was already presenting in lectures at Harvard as early as 1865. For now, let it suffice to say that this anticipation of the information concept, fully recognizing the reality of its dimension, would not sound too remote from the varieties of "law abiding constraint exploitation" that have become increasingly familiar since the dawn of cybernetics.
A full explanation of these statements, linking scientific inference, symbolization, and information together in such an integral fashion, would require an excursion into the pragmatic theory of information that Peirce was already presenting in lectures at Harvard as early as 1865. For now, let it suffice to say that this anticipation of the information concept, fully recognizing the reality of its dimension, would not sound too remote from the varieties of ''law abiding constraint exploitation'' that have become increasingly familiar since the dawn of cybernetics.
But more than this, Peirce's notion of information supplies an array of missing links that joins together in one scheme the logical roles of terms, propositions, and arguments, the semantic functions of denotation and connotation, and the practical methodology needed to address and measure the quantitative dimensions of information. This is precisely the kind of linkage that I need in this project to integrate the dynamic and symbolic aspects of inquiry.
But more than this, Peirce's notion of information supplies an array of missing links that joins together in one scheme the logical roles of terms, propositions, and arguments, the semantic functions of denotation and connotation, and the practical methodology needed to address and measure the quantitative dimensions of information. This is precisely the kind of linkage that I need in this project to integrate the dynamic and symbolic aspects of inquiry.
Not by sheer coincidence, the task of understanding symbolic action, working up through icons and indices to the point of tackling symbols, is also one of the ultimate aims that the interpretive and objective frameworks being proposed here are intended to subserve.
Not by sheer coincidence, the task of understanding symbolic action, working up through icons and indices to the point of tackling symbols, is also one of the ultimate aims that the interpretive and objective frameworks being proposed here are intended to subserve.
An OF is a convenient stage for those works that have progressed far enough to make use of it, but in times of flux it must be remembered that an OF is only a hypostatic projection, that is, the virtual image, reified concept, or "phantom limb" of the IF that tentatively extends it.
An OF is a convenient stage for those works that have progressed far enough to make use of it, but in times of flux it must be remembered that an OF is only a hypostatic projection, that is, the virtual image, reified concept, or ''phantom limb'' of the IF that tentatively extends it.
When the IF and the OF sketched here have been developed far enough, I hope to tell wherein and whereof a sign is able, by its very character, to address itself to a purpose, one determined by its objective nature and determining, in a measure, that of its intended interpreter, to the extent that it makes the other wiser than the other would otherwise be.
When the IF and the OF sketched here have been developed far enough, I hope to tell wherein and whereof a sign is able, by its very character, to address itself to a purpose, one determined by its objective nature and determining, in a measure, that of its intended interpreter, to the extent that it makes the other wiser than the other would otherwise be.
=====1.3.4.18. C'est Moi=====
=====1.3.4.18. C'est Moi=====
From the emblem unfurled on a tapestry to tease out the working of its loom and spindle, a charge to bind these frameworks together is drawn by necessity from a single request: "To whom is the sign addressed?" The easy, all too easy answer comes "To whom it may concern", but this works more to put off the question than it acts as a genuine response. To say that a sign relation is intended for the use of its interpreter, unless one has ready an independent account of that agent's conduct, only rephrases the initial question about the end of interpretation.
From the emblem unfurled on a tapestry to tease out the working of its loom and spindle, a charge to bind these frameworks together is drawn by necessity from a single request: ''To whom is the sign addressed?'' The easy, all too easy answer comes ''To whom it may concern'', but this works more to put off the question than it acts as a genuine response. To say that a sign relation is intended for the use of its interpreter, unless one has ready an independent account of that agent's conduct, only rephrases the initial question about the end of interpretation.
The interpreter is an agency depicted over and above the sign relation, but in a very real sense it is simply identical with the whole of it. And so one is led to examine the relationship between the interpreter and the interpretant, the element falling within the sign relation to which the sign in actuality tends. The catch is that the whole of the intended sign relation is seldom known from the beginning of inquiry, and so the aimed for interpretant is often just as unknown as the rest.
The interpreter is an agency depicted over and above the sign relation, but in a very real sense it is simply identical with the whole of it. And so one is led to examine the relationship between the interpreter and the interpretant, the element falling within the sign relation to which the sign in actuality tends. The catch is that the whole of the intended sign relation is seldom known from the beginning of inquiry, and so the aimed for interpretant is often just as unknown as the rest.
These eventualities call for the elaboration of interpretive and objective frameworks in which not just the specious but the speculative purpose of a sign can be contemplated, permitting extensions of the initial data, through error and retrial, to satisfy emergent and recurring questions.
These eventualities call for the elaboration of interpretive and objective frameworks in which not just the specious but the speculative purpose of a sign can be contemplated, permitting extensions of the initial data, through error and retrial, to satisfy emergent and recurring questions.
At last, even with the needed frameworks only partly shored up, I can finally ravel up and tighten one thread of this rambling investigation. All this time, steadily rising to answer the challenge about the identity of the interpreter, "Who's there?", and the role of the interpretant, "Stand and unfold yourself", has been the ready and abiding state of a certain system of interpretation, developing its character and gradually evolving its meaning through a series of imputations and extensions. Namely, the MOI (the SOI experienced as an object) can answer for the interpreter, to whatever extent that conduct can be formalized, and the IM (the SOI experienced in action, in statu nascendi) can serve as a proxy for the momentary thrust of interpretive dynamics, to whatever degree that process can be explicated.
At last, even with the needed frameworks only partly shored up, I can finally ravel up and tighten one thread of this rambling investigation. All this time, steadily rising to answer the challenge about the identity of the interpreter, ''Who's there?'', and the role of the interpretant, ''Stand and unfold yourself'', has been the ready and abiding state of a certain system of interpretation, developing its character and gradually evolving its meaning through a series of imputations and extensions. Namely, the MOI (the SOI experienced as an object) can answer for the interpreter, to whatever extent that conduct can be formalized, and the IM (the SOI experienced in action, in statu nascendi) can serve as a proxy for the momentary thrust of interpretive dynamics, to whatever degree that process can be explicated.
To put a finer point on this result I can do no better at this stage of discussion than to recount the "metaphorical argument" that Peirce often used to illustrate the same conclusion.
To put a finer point on this result I can do no better at this stage of discussion than to recount the ''metaphorical argument'' that Peirce often used to illustrate the same conclusion.
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1. To prescribe a context of effective systems theory (C'EST), one that can provide for the computational formalization of each intuitively given interpreter as a determinate model of interpretation (MOI). An appropriate set of concepts and methods would deal with the generic constitutions of interpreters, converting paraphrastic and periphrastic descriptions of their interpretive practice into relatively complete and concrete specifications of sign relations.
1. To prescribe a context of effective systems theory (C'EST), one that can provide for the computational formalization of each intuitively given interpreter as a determinate model of interpretation (MOI). An appropriate set of concepts and methods would deal with the generic constitutions of interpreters, converting paraphrastic and periphrastic descriptions of their interpretive practice into relatively complete and concrete specifications of sign relations.
2. To prepare a fully dynamic basis for actualizing interpretants. This means that an interpretant addressed by the interpretation of a sign would not be left in the form of a detached token or abstract memory image to be processed by a hypothetical but largely nondescript interpreter, but realized as a definite type of state configuration in a qualitative dynamic system. To fathom what should be the symbolic analogue of a "state with momentum" has presented this project with difficulties both conceptual and terminological. So far in this project, I have attempted to approach the character of an active sign-theoretic state in terms of an "interpretive moment" (IM), "information state" (IS), "attended token" (AT), "situation of use" (SOU), or "instance of use" (IOU). A successful concept would capture the transient dispositions that drive interpreters to engage in specific forms of inquiry, defining their ongoing state of uncertainty with regard to objects and questions of immediate concern.
2. To prepare a fully dynamic basis for actualizing interpretants. This means that an interpretant addressed by the interpretation of a sign would not be left in the form of a detached token or abstract memory image to be processed by a hypothetical but largely nondescript interpreter, but realized as a definite type of state configuration in a qualitative dynamic system. To fathom what should be the symbolic analogue of a ''state with momentum'' has presented this project with difficulties both conceptual and terminological. So far in this project, I have attempted to approach the character of an active sign-theoretic state in terms of an ''interpretive moment'' (IM), ''information state'' (IS), ''attended token'' (AT), ''situation of use'' (SOU), or ''instance of use'' (IOU). A successful concept would capture the transient dispositions that drive interpreters to engage in specific forms of inquiry, defining their ongoing state of uncertainty with regard to objects and questions of immediate concern.
=====1.3.4.19. Entr'acte=====
=====1.3.4.19. Entr'acte=====