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Philosophy of Mathematics

Michaelmas Term 2014, Thursdays at 10 a.m. in Mill Lane LR5

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.

  1. Introduction
  2. Kant
  3. Frege (Grundlagen)
  4. Frege (Grundgesetze)
  5. Neo-Fregean logicism
  6. Dedekind and structuralism
  7. Russell (Principia)
  8. Ramsey

Reading

Michael Potter, Reason's Nearest Kin (Oxford University Press, 2000)