Any proposition of the form ‘if p then q ’. The condition hypothesized, p, is called the antecedent of the conditional, and q the consequent. Various kinds of conditional have been distinguished. The weakest is that of material implication, merely telling us that either not-p, or q . Stronger conditionals include elements of modality, corresponding to the thought that ‘if p is true then q must be true’. Ordinary language is very flexible in its use of the conditional form, and there is controversy whether conditionals are better treated semantically, yielding different kinds of conditionals with different meanings, or pragmatically, in which case there should be one basic meaning, with surface differences arising from other implicatures . See also Adams's thesis, counterfactual conditional, material conditional, strict implication.
Philosophy dictionary. Academic. 2011.