Changes

As a way of resolving the discerned “tensions”, posed here to fall into “ex-” and “in-” kinds, the strategy just described affords a way of approaching the problem that is less like a bridge than a pole vault, taking its pivot on a fixed set of narrowly circumscribed sign relations to make a transit from extensional to intensional outlooks on their form.  With time and reflection, the logical depth of the supposed distinction, the “pretension” of maintaining a couple of separate but equal tensions in isolation from each other, does not withstand a persistent probing.  Accordingly, the gulf between the two realms can always be fathomed by a finitely informed creature, in fact, by the very form of interpreter that created the fault in the first place.  Consequently, converting the form of a transient vault into the substance of a usable bridge requires in adjunction only that initially pliable and ultimately tensile sorts of connecting lines be conducted along the tracery of the vault until the work of castling the gap can begin.

As a way of resolving the discerned “tensions”, posed here to fall into “ex-” and “in-” kinds, the strategy just described affords a way of approaching the problem that is less like a bridge than a pole vault, taking its pivot on a fixed set of narrowly circumscribed sign relations to make a transit from extensional to intensional outlooks on their form.  With time and reflection, the logical depth of the supposed distinction, the “pretension” of maintaining a couple of separate but equal tensions in isolation from each other, does not withstand a persistent probing.  Accordingly, the gulf between the two realms can always be fathomed by a finitely informed creature, in fact, by the very form of interpreter that created the fault in the first place.  Consequently, converting the form of a transient vault into the substance of a usable bridge requires in adjunction only that initially pliable and ultimately tensile sorts of connecting lines be conducted along the tracery of the vault until the work of castling the gap can begin.

In the pragmatic theory of signs, the word ''representation'' is a technical term that is synonymous with the word ''sign'', in other words, it applies to an entity in the most general category of things that can enter into sign relations in the roles of signs and interpretants.  In this usage the scope of the term ''representation'' includes all sorts of syntactic, descriptive, and conceptual entities, a range of options I will frequently find it convenient to suggest by drawing on a pair of stock phrases:  ''terms and concepts'' (TACs) in a conjunctive context versus ''terms or concepts'' (TOCs) in a disjunctive context.

In the pragmatic theory of signs, the word "representation" is a technical term that is synonymous with the word "sign", in other words, it applies to an entity in the most general category of things that can enter into sign relations in the roles of signs and interpretants.  Thus, in this usage the scope of the term "representation" includes all sorts of syntactic, descriptive, and conceptual entities, a range of options I will frequently find it convenient to suggest by drawing on a pair of stock phrases:  "terms and concepts" (TACs) in a conjuctive context, versus "terms or concepts" (TOCs) in a disjunctive context.

In mathematics, the word "representation" is commonly reserved for referring to a "homomorphism", that is, a linear transformation or a structure preserving mapping h: X >Y between mathematical "objects", that is, structure bearing spaces in a category of comparable domains.

In mathematics, the word ''representation'' is commonly reserved for referring to a ''homomorphism'', that is, a linear transformation or a structure-preserving mapping <math>h : X \to Y\!</math> between mathematical objects, that is, structure-bearing spaces in a category of comparable domains.

In keeping with the spirit of the current discussion, I will first present a set of examples that are designed to illustrate what I mean by an IR.  In general, an IR of any object is a sign, description, or concept that denotes, describes, or conceives its object in terms of its properties, that is, in terms of the logical attributes that the object possesses or the propositional features that the object is supposed to have.  If the object to be represented is a complex formal object like a sign relation, then there needs to be an IR of each elementary sign relation and an IR of the sign relation as a whole.

In keeping with the spirit of the current discussion, I will first present a set of examples that are designed to illustrate what I mean by an intensional representation.  In general, an intensional representation of any object is a sign, description, or concept that denotes, describes, or conceives its object in terms of its properties, that is, in terms of the logical attributes that the object possesses or the propositional features that the object is supposed to have.  If the object to be represented is a complex formal object like a sign relation, then there needs to be an intensional representation of each elementary sign relation and an intensional representation of the sign relation as a whole.

But first, before I try to tackle this project, it is advisable to seek a measure of theoretical advantage that I can bring to bear on the task.  This I can do by anchoring my focal outlook on sign relations within a more global consideration of n place relations.  Not only will this help with the conceptual recasting of A and B, but it will also support later stages of the present work, especially in the effort to build a collection of readily accessible linkages between the extensions and the intensions of each construct that I try to use, and ultimately of each concept and term that might conceivably find a use in inquiry.

But first, before I try to tackle this project, it is advisable to seek a measure of theoretical advantage that I can bring to bear on the task.  This I can do by anchoring my focal outlook on sign relations within a more global consideration of <math>n\!</math>-place relations.  Not only will this help with the conceptual recasting of <math>L(\text{A})\!</math> and <math>L(\text{B}),\!</math> but it will also support later stages of the present work, especially in the effort to build a collection of readily accessible linkages between the extensions and the intensions of each construct that I try to use, and ultimately of each concept and term that might conceivably find a use in inquiry.

===6.29. Projects of Representation===

===6.29. Projects of Representation===