David Corfield intension

p. 145 of Ranta on Carnap intensional isomorphism.

IEP article on Carnap:

There are sentences which are neither extensional not intensional; for example, belief-sentences. Carnap’s example is “John believes that D”. Suppose that “John believes that D” is true; let A be a sentence equivalent to D and let B be a sentence L-equivalent to D. It is possible that the sentences “John believes that A” and “John believes that B” are false. In fact, John can believe that a sentence is true, but he can believe that a logically equivalent sentence is false. To explain belief-sentences, Carnap defines the notion of intensional isomorphism. In broad terms, two sentences are intensionally isomorphic if and only if their corresponding elements are L-equivalent. In the belief-sentence “John believes that D” we can substitute D with an intensionally isomorphic sentence C.

Mike Beaney, Carnap’s Conception of Explication

Consider the example that Carnap takes from Moore:

(B1) The concept brother is identical with the concept male sibling. (B2) The concept brother is identical with the concept brother. The first, Carnap writes, “is a sentence conveying fruitful information, although of a logical, not a factual, nature”, whilst the second is “quite trivial” (1947, 63). But if the two concepts are identical, how can this be? Carnap’s answer is to distinguish two notions of meaning, which is precisely the response that Frege gave to the paradox in his early and middle periods. (B1) and (B2) are ‘L-equivalent’, in Carnap’s terms, but differ in intensional structure, i.e., are not ‘intensionally isomorphic’. (B1) L-implies (B2), and vice versa, but (B1) and (B2) are built up in different ways out of their constituent ‘designators’. Langford, in his original discussion of the paradox, had suggested that the two expressions representing the analysandum and analysans in a correct and informative analysis were “cognitively equivalent in some appropriate sense” but not “synonymous” (1942, 326). According to Carnap, the notion of L-equivalence explicates cognitive or logical equivalence, and the notion of intensional isomorphism explicates synonymy (1947, 64).

What is hyperintensionality?