John Baldwin on Model Theory and the Philosophy of Mathematical Practice

John T. Baldwin (Illinois-Chicago) has a draft of his book Formalism without Foundationalism: Model Theory and the Philosophy of Mathematical Practice. On, FOM he wrote:

Martin Davis posted a couple of days ago a message containing this sentence. “Gödel showed us that the wild infinite could not really be separated from the tame mathematical world where most mathematicians may prefer to pitch their tents.” This is an excuse for me to publicize my book in progress. Much of it is dedicated to the proposition that modern model theory provides a systematic way to separate the wild from the tame. More precisely, this book supports three main claims.
  1. Formalization of specific mathematical areas is a tool for studying mathematics itself as well as issues in the philosophy of mathematics (e.g. axiomatization, purity, categoricity and completeness).
  2. The systematic comparison of local formalizations of distinct areas is a tool for organizing and doing mathematics and the analysis of mathematical practice.
  3. The choice of vocabulary and logic appropriate to the particular topic are central to the success of a formalization. The logic which has been most important for the study of mathematical practice is first order logic

Contact him directly if you would like to see a draft.

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