A Logical Calculus of Meaning and Synonymy

In his development of formal semantics for natural language Montague [1970a]– Montague [1973], Richard Montague modeled the meaning (Frege’s sense) of a term A by its Carnap intension CI(A), the function which assigns to each state a, specifying a “possibleworld”, “time” and“context of use”, the denotationden(A)(a) of A in that state. Now this is surely not right: among other things, it makes “there are infinitelymany odd numbers” synonymouswith “there are infinitelymany prime numbers”, which it is not. At the other extreme, “structural” approaches to the modeling of meaning (like Russell’s propositions, Church [1946]–Church [1974] andCresswell [1985]) basically tell us nomore than that “the sense of a complex term A can be determined from the syntactic structure ofA and the senses or denotations of the basic constituent parts ofA”, without explaining how this “determination” is to take place. But, to oversimplifyDavidson’s eloquent criticism inDavidson [1967], Theaetetus and the property of flying do not (by themselves) amount to themeaning of “Theaetetus flies”: we would like to know just what kind of objects meanings are, and how the meaning of “Theaetetus flies” is determined by the meanings of ‘Theaetetus’ and ‘flying’. In Moschovakis [1994] I argued that the meaning of a term A can be faithfully modeled by its referential intension int(A), an (abstract, idealized, not necessarily implementable) algorithmwhich computes the denotation ofA. The basic technical tool in that paper was the Formal language of recursion FLR, for which the theory of referential intensions can be developed rigorously, and the applications to fragments of natural language were to come by “formalizing” (translating, rendering) them into FLR. Here I will develop the theory of referential intensions for the formal language Lar, which extends the typed ë-calculus and so can accommodate (via the work of Montague) reasonably large fragments of natural language. The claim thatmeanings are algorithms is a philosophical one, but this is primarily a paper in logic, not in the philosophy of language or in linguistics. Every discussion