Two Flavors of Curry’s Paradox

Abstract

In this paper, we distinguish two versions of Curry's paradox: c-Curry, the standard conditional-Curry paradox, and v-Curry, a validity-involving version of Curry's paradox that isn't automatically solved by solving c-curry. A unified treatment of Curry's paradox thus calls for a unified treatment of both c-Curry and v-Curry. If, as is often thought, c-Curry paradox is to be solved via nonclassical logic, then v-Curry may require a lesson about the structure-indeed, the substructure-of the validity relation itself.

Paradox and Logical Revision. A Short Introduction

“…rules specifically governing the use of logical operators, suffice to solve the semantic paradoxes in general? The paradoxes of naïve logical properties suggest a negative answer to this question (Beall and Murzi 2013;Zardini 2013aZardini , 2014a.…”

“…follows on no assumptions via VD. This is the Validity Curry Paradox, or v-Curry, for short (Whittle 2004;Shapiro 2011;Beall and Murzi 2013).…”

Truthmaker Maximalism defended again

“…It is strange to object to Contraction, unless one has already assumed that M is analogous to the Liar. It is strange then that at the end of his article Milne says that there are two options: either to abandon Contraction or to assume that M is genuinely paradoxical; for the motivation to abandon Contraction lies in taking M to be genuinely paradoxical (Zardini 2011, Beall andMurzi 2013, Murzi and.…”

Non-classical Metatheory for Non-classical Logics

“…Stephen Schiffer argues ( [19] p224) that it is vague whether the principle of excluded middle is valid and that it is vague whether a standard Sorites argument is valid. On the other hand, considerations very similar to those responsible for the semantic paradoxes can lead one to think that there are similar paradoxes for a validity predicate (see [16]), or a consequence relation (see [1], [23].) Since in this case we should expect classical laws involving the validity predicate and consequence relation, to fail, we shouldn't expect to be able to give it a sound and complete axiomatisation -at least, not if we are using a classical theory of syntax.…”

“…Field argues that we can characterise the extension of his preferred non-classical consequence relation in a classical model theory, provided that one keeps in mind that this model theory does not contain the intended model. 1 As far as semantics is concerned, Field's non-classical object theory contains certain semantic notions such as a truth predicate or a satisfaction relation. However one might object that this is far from enough to do any serious semantics.…”