Definition
A conditional is an if...then statement: it asserts the consequent on the supposition of the antecedent, as in "if you heat water to 100 degrees Celsius at sea level, then it boils." Conditionals are everywhere in reasoning, prediction, and planning, which makes getting their logic right a central concern.
The trouble is that the ordinary-language conditional resists tidy formalisation. The classical material conditional captures part of its behaviour, but, as Priest shows, it also licenses inferences that strike every competent speaker as wrong.
Why it matters
How it works
Priest distinguishes several uses of if...then. Indicative conditionals concern what is actually the case; counterfactual conditionals — "if the match had been struck, it would have lit" — concern what would hold in a non-actual situation. No single truth-functional definition handles both, and the counterfactual plainly cannot be truth-functional at all, since its antecedent is known to be false.
The book treats the conditional as one of logic's hardest open problems. Competing accounts — the material conditional, relevance-logic conditionals, and possible-worlds analyses of counterfactuals — each capture some intuitions while violating others, which is exactly why the conditional remains a frontier rather than a settled topic.