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, 16:56, 15 January 2009→Propositions and Sentences: delete reconciled changes
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Introducing the realm of "values" is a stopgap measure that temporarily
−permits the discussion to avoid certain singularities in the embedding
−sign relation, and allowing the process of "evaluation" as a compromise
−mode of signification between connotation and denotation only manages to
−steer around a topic that eventually has to be mapped in full, but these
−strategies do allow the discussion to proceed a little further without
−having to answer questions that are too difficult to be settled fully
−or even tackled directly at this point. As far as the relations among
−connoting, denoting, and evaluing are concerned, it is possible that
−all of these constitute independent dimensions of significance that
−a sign might be able to enjoy, but since the notion of connotation
−is already generic enough to contain multitudes of subspecies, I am
−going to subsume, on a tentative basis, all of the conceivable modes
−of "evaluing" within the broader concept of connotation.
−With this degree of flexibility in mind, one can say that the sentence
−"f(x) = %1%" latently connotes what the sign "f(x)" patently connotes.
−Taken in abstraction, both syntactic entities fall into an equivalence
−class of signs that constitutes an abstract object, a thing of value
−that is "identified by" the sign "f(x)", and thus an object that might
−as well be "identified with" the value f(x).
−The upshot of this whole discussion of evaluation is that it allows one to
−rewrite the definitions of indicator functions and their fibers as follows:
−
<pre>
<pre>
−The "indicator function" or the "characteristic function" of a set Q c X,
The "indicator function" or the "characteristic function" of a set Q c X,
written "f_Q", is the map from X to the boolean domain %B% = {%0%, %1%}
written "f_Q", is the map from X to the boolean domain %B% = {%0%, %1%}
