Paper announcement: The Price of Mathematical Scepticism

[Paul Blain Levy]

Dear all,

I hope that this paper, which has been accepted for publication in Philosophia Mathematica, will be of interest to the list.

Best regards,
Paul

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The Price of Mathematical Scepticism

Preprint: www.cs.bham.ac.uk/~pbl/papers/allornothing.pdf <http://www.cs.bham.ac.uk/~pbl/papers/allornothing.pdf>

This paper argues that, insofar as we doubt the bivalence of the
 Continuum Hypothesis or the truth of the Axiom of Choice, we should
 also doubt the consistency of third-order arithmetic, both the 
 classical and intuitionistic versions.

 Underlying this argument is the following philosophical view.
 Mathematical belief springs from certain intuitions, each of which
 can be either accepted or doubted in its entirety, but not
 half-accepted.    Therefore, our beliefs about reality, bivalence,
 choice and consistency should all be aligned.
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