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===6.29. Projects of Representation===

===6.29. Projects of Representation===

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.

Variant.  The point of pointing out the indirect character and the allusory nature of all prospective representation is to draw attention to the circumstance that intelligent agents of interpretation and inquiry have to be capable of waiting, trading, and acting on purported and potential representations.  To proceed at all from the conditions prevailing at the outset of inquiry, they have to lead off from the slightest inklings that a problematic phenomenon may disclose an objective reality that is a key to its resolution, to take their initial direction from uncertain signs that an object of value might be in the offing, and to open the bidding on a brand of improper symbols whose very qualifications as representations are required by the nature of interpretive inquiry to remain in question for much of the mean time taken up by the pursuit of the alleged objects.  It is part of the task that prospective representation is all these agents have to go on, …

Variant.  The point of pointing out the indirect character and the allusory nature of all prospective representation is to draw attention to the circumstance that intelligent agents of interpretation and inquiry have to be capable of waiting, trading, and acting on purported and potential representations.  To proceed at all from the conditions prevailing at the outset of inquiry, they have to lead off from the slightest inklings that a problematic phenomenon may disclose an objective reality that is a key to its resolution, to take their initial direction from uncertain signs that an object of value might be in the offing, and to open the bidding on a brand of improper symbols whose very qualifications as representations are required by the nature of interpretive inquiry to remain in question for much of the mean time taken up by the pursuit of the alleged objects.  It is part of the task that prospective representation is all these agents have to go on, …

Extensional descriptions of <math>n\!</math>-place relations are the kinds that can be presented in relational data tables, or at least initiated and partially illustrated in this form.  If an <math>n\!</math>-place relation is constituted as a ''finite information construction'', where the relation as a whole plus each of its elements is specified in discrete and finite terms, then the prospective tabulation can be carried out to completion, at least in principle, explicitly enumerating the ''elementary relations'' or the <math>n\!</math>-tuples of relational domain elements that enter into the relation.

Extensional descriptions of n place relations are the kinds that can be presented in relational data tables, or at least initiated and partially illustrated in this form.  If an n place relation is constituted as a "finite information construction" (FIC), where the relation as a whole plus each of its elements is specified in "finite and discrete" (FAD) terms, then the prospective tabulation can be carried out to completion, at least in principle, explicitly enumerating the "elementary relations" or the n tuples of relational domain elements that enter into the relation.

Extensional descriptions are so close to what one casually and commonly regards as "immediate experience" that the knowledge of a relation one gains by means of their indications is often not thought to lie in the medium of description at all.  The acquaintance with the character of an objective relation that extensional descriptions so successfully manage to record and convey is a type of impression that one often fails to reflect on as arriving through signs at all, and thus it can leave an impression of knowing its object that is susceptible to being confounded with a direct experience of the relation itself.

Extensional descriptions are so close to what one casually and commonly regards as &ldquo;immediate experience&rdquo; that the knowledge of a relation one gains by means of their indications is often not thought to lie in the medium of description at all.  The acquaintance with the character of an objective relation that extensional descriptions so successfully manage to record and convey is a type of impression that one often fails to reflect on as arriving through signs at all, and thus it can leave an impression of knowing its object that is susceptible to being confounded with a direct experience of the relation itself.

This does not have to be a bad thing in practice.  Indeed, it is a factor contributing to the success of extensional descriptions that an agent can usually afford to remain oblivious to the more indirect aspects of their interpretation, to proceed with impunity to take them at face value, and unless there is some obvious trouble to work on the assumption that they are in fact nothing more than what they seem to denote.  Thus, one often finds extensional presentations treated as though they arose from radically empirical sources of data, instituting fundamentally pure modes of "knowledge by acquaintance" and reputed to lie in meaningful contradistinction to every other type of representation, the rest falling into categories that grade them as mere "knowledge by description".  However, when it comes to the ends of deliberate design and analysis, the usual assumptions can no longer be relied on to justify their own usage, and they need to make themselves available for examination whenever the limits of their usefulness are called into question.

This does not have to be a bad thing in practice.  Indeed, it is a factor contributing to the success of extensional descriptions that an agent can usually afford to remain oblivious to the more indirect aspects of their interpretation, to proceed with impunity to take them at face value, and unless there is some obvious trouble to work on the assumption that they are in fact nothing more than what they seem to denote.  Thus, one often finds extensional presentations treated as though they arose from radically empirical sources of data, instituting fundamentally pure modes of &ldquo;knowledge by acquaintance&rdquo; and reputed to lie in meaningful contradistinction to every other type of representation, the rest falling into categories that grade them as mere &ldquo;knowledge by description&rdquo;.  However, when it comes to the ends of deliberate design and analysis, the usual assumptions can no longer be relied on to justify their own usage, and they need to make themselves available for examination whenever the limits of their usefulness are called into question.

One of the purposes of introducing an explicit theory of sign relations into the present study of inquiry is to examine the status of this idea, namely, that it makes sense to posit an absolute distinction between knowledge by acquaintance and knowledge by description.  Pragmatic thinking begins with a certain amount of skepticism toward this notion, on account of the many illusions that appear to trace their origins to it, but overall it seeks to arrive at a language in which to examine the question thoroughly, and to devise a means for individual interpreters to make a clear choice for themselves, with respect to the possibly of their purposes being divergent in the mean time, one way or the other.

One of the purposes of introducing an explicit theory of sign relations into the present study of inquiry is to examine the status of this idea, namely, that it makes sense to posit an absolute distinction between knowledge by acquaintance and knowledge by description.  Pragmatic thinking begins with a certain amount of skepticism toward this notion, on account of the many illusions that appear to trace their origins to it, but overall it seeks to arrive at a language in which to examine the question thoroughly, and to devise a means for individual interpreters to make a clear choice for themselves, with respect to the possibly of their purposes being divergent in the mean time, one way or the other.

Whatever the outcome of these individual decisions, independent in principle no matter how they turn out in practice, and without forcing the preliminary acknowledgement of any unavoidable gulf or unbridgable abyss that might be imagined to separate the modalities of acquaintance and description, one nevertheless wants to preserve the practical uses of the comparative, interpretive, relative, and otherwise sufficiently qualified and circumspect orderings of data and descriptions along these lines that can be organized by individual interpreters and communities of interpretation.  It is for these reasons that I have taken the trouble to conduct this discussion in a way that diverts some attention toward its own casual context, and I hope that this strategy is able to reflect, or at least scatter, enough light back on the enfolding context of informal sign relations that it can dispell any inkling of an automatic distinction of this form, or at least to cast doubts on the remaining traces of its illusion.

Whatever the outcome of these individual decisions, independent in principle no matter how they turn out in practice, and without forcing the preliminary acknowledgement of any unavoidable gulf or unbridgeable abyss that might be imagined to separate the modalities of acquaintance and description, one nevertheless wants to preserve the practical uses of the comparative, interpretive, relative, and otherwise sufficiently qualified and circumspect orderings of data and descriptions along these lines that can be organized by individual interpreters and communities of interpretation.  It is for these reasons that I have taken the trouble to conduct this discussion in a way that diverts some attention toward its own casual context, and I hope that this strategy is able to reflect, or at least scatter, enough light back on the enfolding context of informal sign relations that it can dispel any inkling of an automatic distinction of this form, or at least to cast doubts on the remaining traces of its illusion.

For the rest of this section I restrict the discussion to sign relations of the type R c OxSxI and elementary sign relations of the form <o, s, i>.

For the rest of this section I restrict the discussion to sign relations of the type <math>L \subseteq O \times S \times I\!</math> and elementary sign relations of the form <math>(o, s, i) \in L.\!</math>

A "discussion of concrete examples" (DOCE), intended to serve as a preparatory treatment for approaching a significantly more complex area, is necessarily limited in its focus to isolated cases, in effect, to those that remain simple enough to be instructive in a preliminary approach to the topic.  This means that the observable properties of the initial examples, with respect to the class they are aimed to exemplify, will sort themselves into two kinds:  (1) their essential, generic, or genuine properties, and (2) their accidental, factitious, or spurious properties.

A "discussion of concrete examples" (DOCE), intended to serve as a preparatory treatment for approaching a significantly more complex area, is necessarily limited in its focus to isolated cases, in effect, to those that remain simple enough to be instructive in a preliminary approach to the topic.  This means that the observable properties of the initial examples, with respect to the class they are aimed to exemplify, will sort themselves into two kinds:  (1) their essential, generic, or genuine properties, and (2) their accidental, factitious, or spurious properties.