Possible worlds: a critical analysis

Abstract

Frege has proposed to consider names as denoting objects, predicates as standing for concepts and sentences as denoting truth values. He was, however, aware that such denotation does not exhaust all what is to be said about meaning. Therefore he has urged that in addition to such denotation (Bedeutung) an expression has sense (Sinn). The sense is the way of presentation of denotation; hence the expressions Morning Star and Evening Star have identical denotations, but different senses. Carnap has proposed to replace Frege's distinction between Sinn and Bedeutung by the distinction between intension and extension. Extension is, according to Carnap, what is shared by every two expressions which can be truthfully declared equivalent; where equivalence means a bit different things for different grammatical categories. In the formalism of the classical logic, the equivalence of two terms T1 and T2 is expressed by the formula T1=T2, that of two sentences S1 and S2 is by the formula S1↔S2, and that of two unary predicates P1 and P2 by the formula ∀xP1(x)↔P2(x). Hence the extension of a term can be identified with the individual the term stands for, that of a statement with its truth value, and the one of a unary predicate with the class of individuals which fall under the predicate. This means that Carnap's intension is something quite close to Frege's sense. Carnap's intension is, on the other hand, not a mere reincarnation of Frege's sense. Frege has been never quite explicit with respect to the nature of sense, but his reluctance to speak about it quite explicitly was conscious and purposeful: Frege was convinced that the only entities that can be really talked about are objects, and sense was not an object for him. To speak about a sense we would have to name it, and hence make the sense into a denotation of an expression. Carnap's intension is, on the other hand, not an entity of a category essentially different from that of extension, it is only something that casts a finer net over the space of expressions. Carnap has defined both extension and intension as derivatives of an equivalence, as that what so-and-so related expressions share. However, while in the case of extension there has been suitable things that could be considered as reifications of such equivalence (namely individuals, truth values and classes of individuals), in the case of intensions no such candidates were at hand.

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