Philosophy of Mathematics
Prof. M. D. Potter
Michaelmas Term 2011, Thursdays at 9 a.m. in LB1
Intended audience
This course is aimed principally at those doing Philosophical Logic in Part II, but other interested students are welcome to attend. Be warned, however, that some knowledge of logic will be assumed.
Context
Kant thought that to grasp the proposition 7+5=12 I must have an intuition of 7 and an intuition of 5. Frege thought this absurd, at least for large numbers. How, he asked, can I have an intuition (i.e. an immediate representation) of 100,000? Frege's alternative (called logicism) was to define numbers as logical objects and to show that arithmetical truths are really logical, thus removing the appeal to intuition. This project ran into severe technical difficulties (Russell's paradox, Gödel's incompleteness theorems), but has refused to roll over and die: forms of Frege's and Carnap's versions of logicism have been defended recently by Crispin Wright and Bob Hale (Frege), and Tom Ricketts and Warren Goldfarb (Carnap).
Synopsis
For anyone who misses a lecture the handout (if there is one) will be available here for downloading (from Cambridge web addresses only) shortly afterwards.
- Introduction
- Kant
- Frege (Grundlagen)
- Frege (Grundgesetze)
- Neo-Fregean logicism
- Dedekind and structuralism
- Russell (Principia)
- Ramsey
Reading
Michael Potter, Reason's Nearest Kin (Oxford University Press, 2000)
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This page was last updated on 2nd October 2011
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