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, 03:05, 15 January 2009→Propositions and Sentences: delete reconciled text
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The sign "f(x)" manifestly names the value f(x).
−This is a value that can be seen in many lights.
−It is, at turns:
−1. The value that the proposition f has at the point x,
− in other words, the value that f bears at the point x
− where f is being evaluated, the value that f takes on
− with respect to the argument or the object x that the
− whole proposition is taken to be about.
−2. The value that the proposition f not only takes up at
− the point x, but that it carries, conveys, transfers,
− or transports into the setting "{x in X : ... }" or
− into any other context of discourse where f is meant
− to be evaluated.
−3. The value that the sign "f(x)" has in the context where it is placed,
− that it stands for in the context where it stands, and that it continues
− to stand for in this context just so long as the same proposition f and the
− same object x are borne in mind.
−4. The value that the sign "f(x)" represents to its full interpretive context
− as being its own logical interpretant, namely, the value that it signifies
− as its canonical connotation to any interpreter of the sign that is cognizant
− of the context in which it appears.
−The sentence "f(x) = %1%" indirectly names what the sign "f(x)"
−more directly names, that is, the value f(x). In other words,
−the sentence "f(x) = %1%" has the same value to its interpretive
−context that the sign "f(x)" imparts to any comparable context,
−each by way of its respective evaluation for the same x in X.
−What is the relation among connoting, denoting, and "evaluing", where
−the last term is coined to describe all the ways of bearing, conveying,
−developing, or evolving a value in, to, or into an interpretive context?
−In other words, when a sign is evaluated to a particular value, one can
−say that the sign "evalues" that value, using the verb in a way that is
−categorically analogous or grammatically conjugate to the times when one
−says that a sign "connotes" an idea or that a sign "denotes" an object.
−This does little more than provide the discussion with a "weasel word",
−a term that is designed to avoid the main issue, to put off deciding the
−exact relation between formal signs and formal values, and ultimately to
−finesse the question about the nature of formal values, whether they are
−more akin to conceptual signs and figurative ideas or to the kinds of
−literal objects and platonic ideas that are independent of the mind.
−These questions are confounded by the presence of certain peculiarities in
−formal discussions, especially by the fact that an equivalence class of signs
−is tantamount to a formal object. This has the effect of allowing an abstract
−connotation to work as a formal denotation. In other words, if the purpose of
−a sign is merely to lead its interpreter up to a sign in an equivalence class
−of signs, then it follows that this equivalence class is the object of the
−sign, that connotation can achieve denotation, at least, to some degree,
−and that the interpretant domain collapses with the object domain,
−at least, in some respect, all things being relative to the
−sign relation that embeds the discussion.
−
<pre>
<pre>
−Introducing the realm of "values" is a stopgap measure that temporarily
Introducing the realm of "values" is a stopgap measure that temporarily
permits the discussion to avoid certain singularities in the embedding
permits the discussion to avoid certain singularities in the embedding
