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Analysis Advance Access originally published online on July 13, 2009
Analysis 2009 69(4):612-620; doi:10.1093/analys/anp089
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© The Author 2009. Published by Oxford University Press on behalf of The Analysis Trust. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Curry, Yablo and duality

Roy T. Cook

The University of Minnesota Minneapolis, MN, 55455 USA cookx432@umn.edu

The first 150 words of the full text of this article appear below.


   1. Introduction
 
The Liar paradox is (or involves, depending on one's definition of ‘paradox’) the directly self-referential Liar statement:

 This statement is false.

or (where T is a truth predicate):

{Lambda}: ~ T(<{Lambda}>)1

The argument that proceeds from the Liar statement and the relevant instance of the T-schema:
T(<{Lambda}>) {leftrightarrow} {Lambda}

to a contradiction is familiar. In recent years, a number of variations on the Liar paradox have arisen in the literature on semantic paradox. The two that will concern us here are the Curry paradox,2 and the Yablo paradox.3

The Curry paradox demonstrates that neither negation nor a falsity predicate is required in order to generate semantic paradoxes. Given any statement {Phi} whatsoever, we need merely consider the statement:

 If this statement is true, then {Phi}

or:

{Xi}: T(<{Xi}>) -> {Phi}

Here, via familiar reasoning, one can ‘prove’ {Phi} merely through consideration of statement {Xi} and the {Xi}-instance of the T-schema.

Interestingly, . . . [Full Text of this Article]


   2. The Dual Yablurry paradox
 

   3. The Yablurry paradox
 

   Appendix
 

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