Journal of Philosophical Logic 45 (1):65-72 (2016)

Andreas Fjellstad
University of Bergen
In the recent paper “Naive modus ponens”, Zardini presents some brief considerations against an approach to semantic paradoxes that rejects the transitivity of entailment. The problem with the approach is, according to Zardini, that the failure of a meta-inference closely resembling modus ponens clashes both with the logical idea of modus ponens as a valid inference and the semantic idea of the conditional as requiring that a true conditional cannot have true antecedent and false consequent. I respond on behalf of the non-transitive approach. I argue that the meta-inference in question is independent from the logical idea of modus ponens, and that the semantic idea of the conditional as formulated by Zardini is inadequate for his purposes because it is spelled out in a vocabulary not suitable for evaluating the adequacy of the conditional in semantics for non-transitive entailment. I proceed to generalize the semantic idea of the conditional and show that the most popular semantics for non-transitive entailment satisfies the new formulation
Keywords Non-classical logics  Non-transitive entailment  Semantic paradoxes  Conditionals  Modus ponens
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DOI 10.1007/s10992-015-9351-0
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References found in this work BETA

The Logic of Paradox.Graham Priest - 1979 - Journal of Philosophical Logic 8 (1):219 - 241.
Paradoxes and Failures of Cut.David Ripley - 2013 - Australasian Journal of Philosophy 91 (1):139 - 164.
Tolerant, Classical, Strict.Pablo Cobreros, Paul Egré, David Ripley & Robert van Rooij - 2012 - Journal of Philosophical Logic 41 (2):347-385.

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A Family of Metainferential Logics.Federico Matias Pailos - 2019 - Journal of Applied Non-Classical Logics 29 (1):97-120.
Must Good Reasoning Satisfy Cumulative Transitivity?Shyam Nair - 2019 - Philosophy and Phenomenological Research 98 (1):123-146.

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