Fixing Frege (Princeton Monographs in Philosophy) by John P. Burgess

By John P. Burgess

The nice philosopher Gottlob Frege tried to supply a in simple terms logical origin for arithmetic. His procedure collapsed whilst Bertrand Russell found a contradiction in it. Thereafter, mathematicians and logicians, starting with Russell himself, grew to become in different instructions to seem for a framework for contemporary summary arithmetic. over the last couple of a long time, even if, logicians and philosophers have came upon that rather more is salvageable from the rubble of Frege's procedure than had formerly been assumed. quite a few repaired platforms were proposed, every one a constant concept allowing the advance of a good portion of arithmetic.

This booklet surveys the collection of equipment placed forth for solving Frege's method, in an try and make certain simply how a lot of arithmetic may be reconstructed in every one. John Burgess considers each proposed repair, each one with its specific philosophical merits and downsides. those platforms diversity from these slightly capable of reconstruct the rudiments of mathematics to those who cross well past the widely permitted axioms of set idea into the speculative realm of enormous cardinals. For the main half, Burgess unearths that makes an attempt to mend Frege do lower than marketed to restore his approach. This publication often is the benchmark opposed to which destiny analyses of the revival of Frege should be measured.

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