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Philosophia Mathematica 2004 12(3):222-243; doi:10.1093/philmat/12.3.222
© 2004 by Oxford University Press
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© 2004 PHILOSOPHIA MATHEMATICA

Choice Principles and Constructive Logics{dagger}

DAVID DEDIVI*

*Department of Philosophy, University of Waterloo Waterloo, Ontario N2L 3G1 Canada. ddevidi{at}uwaterloo.ca

That choice principles ‘change the logic’ when added to constructive systems is significant for contemporary metaphysics. However, many are surprised by these results, having learned that the Axiom of Choice (AC) is constructively valid. Indeed, even among specialists there were, until recently, reasons for puzzlement-rival versions of Intuitionistic Type Theory, one where (AC) is valid, another where it implies classical logic. This paper accessibly explains the situation, puts the issues in a broader setting by considering other choice principles, and draws philosophical morals for the understanding of quantification, choice principles, and the prospects for constructivism.


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