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**1 - 4**of**4**### Completeness vs. Incompleteness

"... Metamathematical results on formally undecidable propositions: ..."

### More on Putnam’s Models A Reply to Bellotti

"... 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 Putna ..."

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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

### Akihiro Kanamori Putnam’s Constructivization Argument

"... Abstract. We revisit Putnam’s constructivization argument from his Models and Real-ity, part of his model-theoretic argument against metaphysical realism. We set out how it was initially put, the commentary and criticisms, and how it can be specifically seen and cast, respecting its underlying logic ..."

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Abstract. We revisit Putnam’s constructivization argument from his Models and Real-ity, part of his model-theoretic argument against metaphysical realism. We set out how it was initially put, the commentary and criticisms, and how it can be specifically seen and cast, respecting its underlying logic and in light of Putnam’s contributions to mathematical logic.