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BUNDER’S PARADOX

Published online by Cambridge University Press:  06 February 2019

MICHAEL CAIE
MICHAEL CAIE*
Affiliation:
Department of Philosophy, University of Toronto
*
*DEPARTMENT OF PHILOSOPHY UNIVERSITY OF TORONTO 170 ST. GEORGE STREET TORONTO, ON M5R 2M8, CANADA E-mail:[email protected]
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Abstract

Systems of illative logic are logical calculi formulated in the untyped λ-calculus supplemented with certain logical constants.1 In this short paper, I consider a paradox that arises in illative logic. I note two prima facie attractive ways of resolving the paradox. The first is well known to be consistent, and I briefly outline a now standard construction used by Scott and Aczel that establishes this. The second, however, has been thought to be inconsistent. I show that this isn’t so, by providing a nonempty class of models that establishes its consistency. I then provide an illative logic which is sound and complete for this class of models. I close by briefly noting some attractive features of the second resolution of this paradox.

Keywords

03A0203B02illative logiclambda calculuscombinatory logicparadoxes
Type
Research Article
Information
The Review of Symbolic Logic , Volume 13 , Issue 4 , December 2020 , pp. 829 - 844
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Copyright
Copyright © Association for Symbolic Logic 2019 

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