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There are numerous modalities of description and representation that are involved in linking the extensions and intensions of terms and concepts.  To facilitate the building of a suitable analytic and synthetic framework for this task, and to abbreviate future references to the categories of modalities that come into play, I will employ a set of technical notions, along with their aliases and acronyms, to be indicated next.

There are numerous modalities of description and representation that are involved in linking the extensions and intensions of terms and concepts.  To facilitate the building of a suitable analytic and synthetic framework for this task, and to abbreviate future references to the categories of modalities that come into play, I will employ a set of technical notions, along with their aliases and acronyms, to be indicated next.

First of all, I want to call attention to a ''mode of description'' or a ''category of representation'' that logically precedes all forms of extensional representation and intensional representation.  To do this, I introduce the notion of a ''project of representation'' and the mode or category of ''pre-tensional representation'' that contains the elements for attempting its actualization.

First of all, I want to call attention to a "mode of description" (MOD) or a "category of representation" (COR) that logically precedes all forms of "extensional representation" (ER) and "intensional representation" (IR).  To do this, I introduce the notion of a "project of representation" (POR) and the mode or category of "pretensional representation" (PR) that contains the elements for attempting its actualization.

A "project of representation" (POR), in the interval before its completion or its viability can be assured with any measurable degree of certainty, initiates a mode of description called a "prospective representation" or a "pretended representation" (PR).  Taken over time, the POR issues in a series of PR notices, a sequence of explicit expressions that constitute its "prospectus" or "pretension".  If the POR turns out to be feasible, and if all goes well with its realization, then the promises tendered by these notes can be redeemed in full.  Regarded from a retrospective vantage point, and ever contingent on the eventual success of the POR, what amounts to little more than a species of potentially attractive PR bulletins can be valued ultimately as a set of successive approximations to the intended concept and, further, to the objective reality intended.  It is only at this point that a piece of PR achieves the virtues of an "actual representation" (AR), embodying in its purported description a modicum of "actually resolved tension" (ART), and becoming amenable to formalization as a non degenerate example of a sign relation.  This tells how a POR develops in time under conditions ideal enough to achieve its aim.  Next, I describe the features of PR as a form of existence sub specie aeternitatis.

A ''project of representation'', in the interval before its completion or its viability can be assured with any measurable degree of certainty, initiates a mode of description called a ''prospective representation'' or a ''pretended representation''.  Taken over time, the project of representation issues in a series of prospective representation notices, a sequence of explicit expressions that constitute its ''prospectus'' or ''pretension''.  If the project of representation turns out to be feasible, and if all goes well with its realization, then the promises tendered by these notes can be redeemed in full.  Regarded from a retrospective vantage point, and ever contingent on the eventual success of the project of representation, what amounts to little more than a species of potentially attractive prospective representation bulletins can be valued ultimately as a set of successive approximations to the intended concept and, further, to the objective reality intended.  It is only at this point that a piece of prospective representation achieves the virtues of an ''actual representation'', embodying in its purported description a modicum of ''actually resolved tension'', and becoming amenable to formalization as a non-degenerate example of a sign relation.  This tells how a project of representation develops in time under conditions ideal enough to achieve its aim.  Next, I describe the features of prospective representation as a form of existence ''sub specie aeternitatis''.

Under the banner of PR parades an uncontrolled and wide ranging variety of pretended signs and prospective signs, entities with the alleged or apparent significance of signs, of likely stories that are potentially meaningful and useful as descriptions and representations, but the character of whose participation in a sign relation is yet to be judged and warranted.  A certain quality of PR marks the brand of significance that a candidate sign possesses before it is known for certain whether it will be genuine or spurious in its role as a sign, the meagre benefit of the doubt that can be granted any reputed sign before its character as an authentic sign has been tested in the performance of its assigned functions.

Under the banner of prospective representation parades an uncontrolled and wide-ranging variety of pretended signs and prospective signs, entities with the alleged or apparent significance of signs, of likely stories that are potentially meaningful and useful as descriptions and representations, but the character of whose participation in a sign relation is yet to be judged and warranted.  A certain quality of PR marks the brand of significance that a candidate sign possesses before it is known for certain whether it will be genuine or spurious in its role as a sign, the meagre benefit of the doubt that can be granted any reputed sign before its character as an authentic sign has been tested in the performance of its assigned functions.

The prospects and pretensions of PR are associated with a quality of tension that prevails on the scene of representation even before it is definite that objects have signs and signs have objects, an uncertain character that supervenes on the stage before one is sure that a "project of representation" (POR) will succeed in its intentions:  far enough for its extension to stretch over many determinate instances, or well enough for its intension to hold forth any distinctive properties.  This whole modality of allegation and aspiration, given the self described significance and uncertified self advertisement that signs in all their immature phases and developmental crises cannot help but affect, taken along with the valid ambitions of potential signs to become signs in fact, is a class of pretended and prospective meaning that it seems fitting to label as a category of "pretensional representation" (PR).

The prospects and pretensions of PR are associated with a quality of tension that prevails on the scene of representation even before it is definite that objects have signs and signs have objects, an uncertain character that supervenes on the stage before one is sure that a "project of representation" (POR) will succeed in its intentions:  far enough for its extension to stretch over many determinate instances, or well enough for its intension to hold forth any distinctive properties.  This whole modality of allegation and aspiration, given the self described significance and uncertified self advertisement that signs in all their immature phases and developmental crises cannot help but affect, taken along with the valid ambitions of potential signs to become signs in fact, is a class of pretended and prospective meaning that it seems fitting to label as a category of "pretensional representation" (PR).