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Title: Logical Consequence and Conditionals from a Dialetheic Perspective
Author(s): CARRARA, Massimiliano , MARTINO, Enrico
Journal: Logique et Analyse
Volume: 227    Date: 2014   
Pages: 359-378
DOI: 10.2143/LEA.227.0.3053510

Abstract :
Dialetheism holds the thesis that certain sentences are dialetheias, i.e. both true and false, and devises several strategies for avoiding trivialism, the (classical) consequence that >all sentences are true. Two such strategies are aimed at invalidating one of the most direct arguments for trivialism, viz. Curry’s Paradox: a proof that you will win the lottery, a proof that only resorts to naïve truth-principles, Conditional Proof (CP), modus ponens (MPP) and the standardly accepted structural rules. The first strategy simply consists in observing that the most well-known dialetheist logic, sometimes referred to as the Logic of Paradox (LP), invalidates MPP. The second strategy consists in rather taking one of the primary senses of ‘if’ to be captured by an entailment connective which does not validate CP. We argue that both strategies are problematic.

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