Citation Milne P (2012) Indicative conditionals, conditional probabilities, and the "defective truth-table": A request for more experiments. Thinking and Reasoning, 18 (2), pp. 196-224. https://doi.org/10.1080/13546783.2012.670754
Abstract While there is now considerable experimental evidence that, on the one hand, participants assign to the indicative conditional as probability the conditional probability of consequent given antecedent and, on the other, they assign to the indicative conditional the "defective truth-table" in which a conditional with false antecedent is deemed neither true nor false, these findings do not in themselves establish which multi-premise inferences involving conditionals participants endorse. A natural extension of the truth-table semantics pronounces as valid numerous inference patterns that do seem to be part of ordinary usage. However, coupled with something the probability account gives us-namely that when conditional-free \phi entails conditional-free \psi, "if \phi then \psi" is a trivial, uninformative truth-we have enough logic to derive the paradoxes of material implication. It thus becomes a matter of some urgency to determine which inference patterns involving indicative conditionals participants do endorse. Only thus will we be able to arrive at a realistic, systematic semantics for the indicative conditional.
Keywords Indicative conditionals; Conditional probability; Defective truth-table; Inference; Material conditional
Journal Thinking and Reasoning: Volume 18, Issue 2