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