Changes

===6.32. Partiality : Selective Operations===

===6.32. Partiality : Selective Operations===

One of the main subtasks of this project is to develop a computational framework for carrying out set-theoretic operations on abstractly represented classes and for reasoning about their indicated results.  This effort has the general aim of enabling one to articulate the structures of <math>n\!</math>-place relations and the special aim of allowing one to reflect theoretically on the properties and projections of sign relations.  A prototype system that makes a beginning in this direction has already been implemented, to which the current work contributes a major part of the design philosophy and technical documentation.  This section presents the rudiments of set-theoretic notation in a way that conforms to these goals, taking the development only so far as needed for immediate application to sign relations like <math>L(\text{A})\!</math> and <math>L(\text{B}).\!</math>

One of the main subtasks of this project is to develop a computational framework for carrying out set theoretic operations on abstractly represented classes and for reasoning about their indicated results.  This effort has the general aim of enabling one to articulate the structures of n place relations and the special aim of allowing one to reflect theoretically on the properties and projections of sign relations.  A prototype system that makes a beginning in this direction has already been implemented, to which the current work contributes a major part of the design philosophy and technical documentation.  This section presents the rudiments of set theoretic notation in a way that conforms to these goals, taking the development only so far as needed for immediate application to sign relations like A and B.

One of the most important design considerations that goes into building the requisite software system is how well it furthers certain lines of abstraction and generalization.  One of these dimensions of abstraction or directions of generalization is discussed in this section, where I attempt to unify its many appearances under the theme of "partiality".  This name is chosen to suggest the desired sense of abstract intention since the extensions of concepts that it favors and for which it leaves room are outgrowths of the limitation that finite signs and expressions can never provide more than partial information about the richness of individual detail that is always involved in any real object.  All in all, this modicum of tolerance for uncertainty is the very play in the wheels of determinism that provides a significant chance for luck to play a part in the finer steps toward finishing every real objective.

One of the most important design considerations that goes into building the requisite software system is how well it furthers certain lines of abstraction and generalization.  One of these dimensions of abstraction or directions of generalization is discussed in this section, where I attempt to unify its many appearances under the theme of ''partiality''.  This name is chosen to suggest the desired sense of abstract intention since the extensions of concepts that it favors and for which it leaves room are outgrowths of the limitation that finite signs and expressions can never provide more than partial information about the richness of individual detail that is always involved in any real object.  All in all, this modicum of tolerance for uncertainty is the very play in the wheels of determinism that provides a significant chance for luck to play a part in the finer steps toward finishing every real objective.

If one needs a slogan to entitle this form of propagation, it is only that "Necessity is the mother of invention".  In other words, it is precisely this lack of perfect information that yields the opportunity for novel forms of speciation to develop among finitely informed creatures (FICs), and just this need of perfect information that drives the evolving forms of independent determination and spontaneous creation in any area, no matter how well the arena is circumscribed by the restrictions of signs.

If one needs a slogan to charge this form of propagation, it is only that &ldquo;Necessity is the mother of invention.&rdquo; In other words, it is precisely this lack of perfect information that yields the opportunity for novel forms of speciation to develop among finitely informed creatures (FICs), and just this need of perfect information that drives the evolving forms of independent determination and spontaneous creation in any area, no matter how well the arena is circumscribed by the restrictions of signs.

In tracing the echoes of this theme, it is necessary to reflect on the circumstance that degenerate sign relations happen to be perfectly possible in practice, and it is desirable to provide a critical method that can address the facts of their flaws in theoretically insightful terms.  Relative to particular environments of interpretation, nothing proscribes the occurrence of sign relations that are defective in any of their various facets, namely:  (1) with signs that fail to denote or connote, (2) with interpretants that lack of being faithfully represented or reliably objectified, and (3) with objects that make no impression or remain ineffable in the preferred medium.

In tracing the echoes of this theme, it is necessary to reflect on the circumstance that degenerate sign relations happen to be perfectly possible in practice, and it is desirable to provide a critical method that can address the facts of their flaws in theoretically insightful terms.  Relative to particular environments of interpretation, nothing proscribes the occurrence of sign relations that are defective in any of their various facets, namely:  (1) with signs that fail to denote or connote, (2) with interpretants that lack of being faithfully represented or reliably objectified, and (3) with objects that make no impression or remain ineffable in the preferred medium.

A cursory examination of the topic of "partiality", as just surveyed, reveals two strains fixing how this "quality of murky" in general reigns.  This division depends on the disposition of n tuples as the individual elements that inhabit an n place relation.

A cursory examination of the topic of "partiality", as just surveyed, reveals two strains fixing how this "quality of murky" in general reigns.  This division depends on the disposition of n tuples as the individual elements that inhabit an n place relation.