Indicative Conditionals as Strict Conditionals

Iacona, Andrea

This paper is intended to show that, at least in a considerably wide class of cases, indicative conditionals are adequately formalized as strict conditionals. The first part of the paper outlines three arguments that support the strict conditional view, that is, three reasons for thinking that an indicative conditional is true just in case it is impossible that its antecedent is true and its consequent is false. The second part of the paper develops the strict conditional view and defends it from some foreseeable objections.

Let us assume that > stands for ‘if then’ as used in indicative sentences, and that 1 and 0 designate truth and falsity. According to the strict conditional view, the truth conditions of p > q are defined relative to a possible world w as follows: Definition 1: [p > q] = 1 in w if and only if, for every w′, either [p] = 0 in w′ or [q] = 1 in w′. As is natural to expect, the set of possible worlds over which ‘every’ ranges may vary from context to context, just as in any other quantified sentence. To say that p > q is true simpliciter is to say that p > q is true in the actual world.

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