'Deduction' versus 'inference' and the denotation of conditional sentences

The paper defends a variant of the material implication approach to the meaning of conditional sentences against some arguments that are considered to be widely subscribed to and/or important in the philosophical, psychological and linguistic literature. These arguments are shown to be wrong, debatable, or to miss their aim if the truth conditions defining material implication are viewed as determining nothing but the denotation of conditional sentences and if the function of conditional sentences in deduction (logic) is focused on rather than in inferencing (reasoning). It is shown that some ‘paradoxes of material implication’ are due to inconsistent premises of deductions introduced by semantic relations between clauses constituting the premises, a fact which does not invalidate the approach. Other ‘paradoxes’ are shown to arise because they are based on uninformative deductions, violating a basic pragmatic principle. In addition, the paper introduces the distinction between the set of possible states of a mental model of the actual world and of alternative worlds. It is argued that material implication determines the denotation of an indicative conditional as a subset of the former set and the denotation of a subjunctive conditional as a subset of the latter set, thus unifying these two types of conditionals.