Abstract:

Starting with Quine, and followed by Putnam, Feferman, Field and others, it has been argued that the only justification for mathematics is that it is used in physics (even though a great deal of mathematics has no use in physics). My own view, in agreement with David Lewis, is that mathematics needs no such justification. But if it does, it cannot be its uses in physics, which sometimes uses ‘mathematics’ that is mathematically false.

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