The intension of a referring expression e in a language is a partial function Ie that assigns to a world w the referent Ie(w) of e there, when there is a referent of e in w. Thus, the intension of "the tallest woman" is a partial function that assigns to w the tallest woman in w.
The intension of a unary predicate P is a partial function IP that assigns to a world w the extension IP(w) of P at w, i.e., the set of all satisfiers of P there.
Intensions are meant to capture the semantic features of terms, with respect to intensional semantics. Now let e be the referring expression:
- The set of even integers.
- is an even integer.
A longshot: Perhaps something like this led Frege to his weird "The concept horse is not a concept" claim.
Literature on the concept horse paradox suggests the following line of thought:
ReplyDelete(1) The referent of 'the concept horse' is not a concept.
(2) The referent of 'the concept horse' = the concept horse.
(3) So, the concept horse is not a concept.
(1) follows from Frege's type-theory and syntax-semantics isomorphism: noun phrases must refer to objects; no object is a concept.
One might interpret (2) just as an identity claim. Alternatively, it might be, for Frege, the claim that 'The referent of 'the concept horse'' and 'the concept horse' co-refer, and so, via Frege's so-called "Reference Principle", they must be intersubstitutable salva veritate.
Yeah, but this raises the question why not just take this to provide a counterexample to the thesis that concepts are not objects, or to the thesis that only objects are referred to.
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