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covert platonism

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Chapter 10 - Logics and worlds
from Part II - History and Authors
- By Ermanno Bencivenga
Edited by Penelope Rush, University of Tasmania
Book:

The Metaphysics of Logic

Published online:

05 October 2014

Print publication:

16 October 2014, pp 178-188
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Summary

Wittgenstein's thought on mathematics had undergone a major, if often undetected, change. The idea that adopting an algorithm like "plus" determines in some physical, mental, or metaphysical way one's response to infinitely many exercises is nothing but covert Platonism, in many ways worse than the Platonism of objects. Wittgenstein agrees entirely with the Intuitionist critique of the law of excluded middle. For the Goldbach conjecture to be true in the sense of classical mathematics, we have to say that the operations of arithmetic determine in advance that every even number, no matter how large, can be partitioned into two primes. The law of excluded middle cannot be regarded as a hardened regularity in cases in which it is applied it to a putative infinite totality. But precisely because of this, there is no direct comparison possible between empirical observations and mathematical theorems in this type of proof.

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Chapter 10 - Logics and worlds

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Chapter 10 - Logics and worlds

Summary