Changes

This is where higher order sign relations come in, making it possible to formalize sign relations that describe themselves and other sign relations, and thus enabling one to conceive of inquiries that inquire into themselves and other inquiries, at least in part.  It is useful to approach these topics in a couple of stages, at first, by describing sign relations that describe other sign relations, and then, by describing sign relations that describe themselves.  Although the implicit aim, or naive hope, is always to make these descriptions as complete as possible, it has to be recognized that partial success is all that is likely to be realized in practice.  It seems to be something between rare and impossible that a non-trivial sign relation could completely describe itself with respect to every facet of its being and in all the ways that it does in fact exist.

This is where higher order sign relations come in, making it possible to formalize sign relations that describe themselves and other sign relations, and thus enabling one to conceive of inquiries that inquire into themselves and other inquiries, at least in part.  It is useful to approach these topics in a couple of stages, at first, by describing sign relations that describe other sign relations, and then, by describing sign relations that describe themselves.  Although the implicit aim, or naive hope, is always to make these descriptions as complete as possible, it has to be recognized that partial success is all that is likely to be realized in practice.  It seems to be something between rare and impossible that a non-trivial sign relation could completely describe itself with respect to every facet of its being and in all the ways that it does in fact exist.

Nevertheless, partially self-describing sign relations and partially self-documenting data structures do arise in practice, and so it is incumbent on this inquiry to look into the question of how they usually develop.  That is, how does a sign get itself interpreted in a sign relation in such a way that it acts as a partial self-description of that selfsame sign relation?  There appear to be two main ways that this can happen.  Occasionally, it develops through the reflective operation or insightful turn of ''retracting projections'', that is, by recognizing that a feature attributed to others is also (or primarily) an aspect of oneself.  More commonly, partially self-describing sign relations are encountered already in place, as when a higher order sign relation has signs that describe lower orders, partial aspects, or previous stages of itself.

Nevertheless, "partially self describing" (PSD) sign relations and "partially self documenting" (PSD) data structures do arise in practice, and so it is incumbent on this inquiry to look into the question of how they usually develop.  That is, how does a sign get itself interpreted in a sign relation in such a way that it acts as a partial self description of that selfsame sign relation?  There appear to be two main ways that this can happen.  Occasionally, it develops through the reflective operation or insightful turn of "retracting projections", that is, by recognizing that a feature attributed to others is also (or primarily) an aspect of oneself.  More commonly, PSD sign relations are encountered already in place, as when a HO sign relation has signs that describe lower orders, partial aspects, or previous stages of itself.

A further reduction in the number of different kinds of signs to worry about can be achieved by means of a special technique — some may call it an "artful dodge" — for referring indifferently to the elements of a set without referring to the set itself.  Under the designation of a "plural indefinite reference" (PIR) is included all the various ways of dealing with denominations, multiple denotations, collective references, or objective multitudes that avail themselves of this trick.

A further reduction in the number of different kinds of signs to worry about can be achieved by means of a special technique — some may call it an “artful dodge” — for referring indifferently to the elements of a set without referring to the set itself.  Under the designation of a ''plural indefinite reference'' (PIR) is included all the various ways of dealing with denominations, multiple denotations, collective references, or objective multitudes that avail themselves of this trick.

By way of definition, a sign q in a sign relation R c OxSxI is said to be, to constitute, or to make a PIR to (every element in) a set of objects, X c O, if and only if q denotes every element of X.  This relationship can be expressed in a succinct formula by making use of one additional definition.

By way of definition, a sign q in a sign relation R c OxSxI is said to be, to constitute, or to make a PIR to (every element in) a set of objects, X c O, if and only if q denotes every element of X.  This relationship can be expressed in a succinct formula by making use of one additional definition.