Finitism

[Paul Levy]

Dear all,
To reinforce Bill’s point, there’s no problem with a finitist claiming that addition is commutive, or that a system is consistent.  But they would not claim a priori that there’s a fact of the matter whether Goldbach’s conjecture is true, or whether PA is consistent.
My Philosophia Mathematica paper “The price of mathematical scepticism” includes a Bivalence Questionnaire that might be helpful for this dicussion.
https://www.cs.bham.ac.uk/~pbl/papers/allornothing.pdf
Best regards,
Paul




On 07/02/2023, 18:48, "WILLIAM TAIT" <williamtait at mac.com> wrote:
Many Contributions to the potential/actual infinite thread take finitism to include the view that a statement of the form ‘for all n P(n)’ cannot be meaningful finitistically. This surely expels Kronecker  from the ranks of the finitists, but , even more blatantly, Hilbert,, who wanted finitist consistency proofs—finitist proofs of statements of just this form.  ???

Bill Taitg

Sent from my iPad

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