A meta-analytic review of thinking about what is true, possible, and irrelevant in reasoning from or reasoning about conditional propositions

Truth-table tasks probe for interpretations of if A then C conditionals by having people evaluate both true-antecedent cases (A and C, A and not-C) and false-antecedent cases, (not-A and C, not-A and not-C). Do these make the rule true or false, or are they irrelevant to the rule? Alternatively, are these cases possible or impossible when one assumes the rule is true? We present meta-analyses correcting the erroneous generalisation that false-antecedent cases are judged irrelevant by most people. Irrelevant judgement of a false-antecedent is only a modal response in a specific minority of cases (implicit “not-A and not-2” cases, e.g., “the letter is a B and the number is a 7” vis-à-vis “if A then 2”). Given that arguments against mental-models theory (e.g., Johnson-Laird & Byrne, 2002) are thus based on a mistaken idea about the “facts”, they require critical analysis. A reconsideration of the theory indicates that it accounts for all benchmark phenomena in truth-table tasks and even yields new predictions. The theory implies that a single case that does make the rule false does not make it true but is not irrelevant either. Such cases are consistent with the rule and corroborate it. Specific meta-analyses confirm the resulting prediction that “consistent” response rates are higher than “true” response rates, which goes at the cost of the irrelevant responses.