[FOM] Book on model theory and the philosophy of mathematical practice

John Baldwin jbaldwin at uic.edu
Sun Aug 30 21:44:56 EDT 2015

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 mathematiciansmay 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.

Claim 0.0.1. (1) Formalization of specifi c mathematical areas is a tool
for studying mathematics itself as well as issues in the philosophy of math-
ematics (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

(3) The choice of vocabulary and logic appropriate to the particular topic
central to the success of a formalization. The logic which has been most
important for the study of mathematical practice is first order logic


Comments on fom or privately are very welcome.

John T. Baldwin
Professor Emeritus
Department of Mathematics, Statistics,
and Computer Science M/C 249
jbaldwin at uic.edu
851 S. Morgan
Chicago IL
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