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