Logical consequence and conditionals from a dialetheic perspective

Massimiliano Carrara, Enrico Martino

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 provable. 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 which only resorts to na ̈ıve 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 prove problematic.


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