An even simpler defense of the material implication (Draft)

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Lee Archie argued that if any truth-values are consistently assigned to a natural language conditional for which modus ponens and modus tollens are valid argument forms and affirming the consequent is invalid, this conditional will have the same truth-conditions of a material implication. This argument is simple and it requires few and relatively uncontroversial assumptions. We show that it is possible to extend ArchieĀ“s argument to three and five-valued logics and still vindicate the same conclusion. This defense is simpler because it requires fewer assumptions: even if you do not believe in bivalence and the classical negation operator you still have good reasons to accept that natural language conditionals and the material implication are logically equivalent.
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First archival date: 2013-06-25
Latest version: 2 (2013-07-04)
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