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A conditional statement whose antecedent [see below] is known (or, at least, believed) to be contrary to fact. Thus, for example, “If George W. Bush had been born in Idaho, then he would never have become President.”

Unlike material implications [see below], counterfactuals are not made true by the falsity of their antecedents. Although they are not truth-functional [see below] statements, counterfactuals may be significant for the analysis of scientific hypotheses.

[antecedent - The element that states the prior condition in any conditional statement. For example, "It doesn't rain" is the antecedent in both

"If it doesn't rain, then we'll have a picnic." and

"It will reach ninety degrees today if it doesn't rain."

In a true material implication, the truth of its antecedent is incompatible with the falsity of its consequent.]

[material implication - The logical relationship between any two propositions such that either the first is false or the second is true. See implication.]

[truth functional - A compound statement or connective is truth-functional if its truth or meaning is wholly determined by the possible combinations of truth-value of its component statements.]

(Via Philosophical Dictionary)

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