issue with several of the arguments in that paper. 2 Here, I want to respond to Bellotti’s objections and to take the opportunity to make a few, somewhat more general remarks concerning the mathematical side of Putnam’s project. 1 Putnam and Bays Let me begin by recapping the the main lines of Putnam’s argument (or, at least, of the small portion of that argument which is under discussion here). In the first few pages of his 1980 paper, “Models and Reality,” Putnam tries to show that there is an “intended model ” for the language of set theory which satisfies the set-theoretic axiom V = L. 3 He begins by assuming that there are only two things which could play a role in fixing the intended model for set-theoretic language. First, there are what Putnam calls “theoretical constraints. ” These include the standard axioms of set theory (which the intended model must satisfy), as well as principles and theories from other branches of science (which the intended model must at least be compatible with). Second, there are “operational constraints. ” These are just the various empirical observations and measurements that we make in the course of scientific investigation. 4

1 Descriptive use of logic and Intended models 1 1.1 Standard models of arithmetic.......................... 1 1.2 Axiomatics and Formal theories......................... 3 1.3 Hintikka and the two uses of logic in mathematics.............. 5