Conditionals and Curry

Philosophical Studies 173 (10):2629-2647 (2016)

Authors
Daniel Nolan
University of Notre Dame
Abstract
Curry's paradox for "if.. then.." concerns the paradoxical features of sentences of the form "If this very sentence is true, then 2+2=5". Standard inference principles lead us to the conclusion that such conditionals have true consequents: so, for example, 2+2=5 after all. There has been a lot of technical work done on formal options for blocking Curry paradoxes while only compromising a little on the various central principles of logic and meaning that are under threat. Once we have a sense of the technical options, though, a philosophical choice remains. When dealing with puzzles in the logic of conditionals, a natural place to turn is independently motivated semantic theories of the behaviour of "if... then...". This paper argues that the closest-worlds approach outlined in Nolan 1997 offers a philosophically satisfying reason to deny conditional proof and so block the paradoxical Curry reasoning, and can give the verdict that standard Curry conditionals are false, along with related "contraction conditionals".
Keywords Curry paradox  Impossible Worlds  Paradox
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DOI 10.1007/s11098-016-0666-7
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References found in this work BETA

Counterfactuals.David K. Lewis - 1973 - Blackwell.
Truth.Paul Horwich - 1998 - Clarendon Press.
Outline of a Theory of Truth.Saul Kripke - 1975 - Journal of Philosophy 72 (19):690-716.

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Citations of this work BETA

Wierenga on Theism and Counterpossibles.Fabio Lampert - 2019 - Philosophical Studies 176 (3):693-707.
The Extent of Metaphysical Necessity.Daniel Nolan - 2011 - Philosophical Perspectives 25 (1):313-339.
Reflections on Routley's Ultralogic Program.Daniel Nolan - 2018 - Australasian Journal of Logic 15 (2):407-430.

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