Bypassing Lewis’ Triviality Results. A Kripke-Style Partial Semantics for Compounds of Adams’ Conditionals [Special Issue]
Issue: Issue 12 • Author/s: Alberto Mura
Topics: Epistemology, Metaphysics, Philosophical logic, Philosophy of language
According to Lewis’ Triviality Results (LTR), conditionals cannot satisfy the equation (E) P(C if A) = P(C | A), except in trivial cases. Ernst Adams (1975), however, provided a probabilistic semantics for the so-called simple conditionals that also satisfies equation (E) and provides a probabilistic counterpart of logical consequence (called p-entailment). Adams’ probabilistic semantics is coextensive to Stalnaker-Thomason’s (1970) and Lewis’ (1973) semantics as far as simple conditionals are concerned. A theorem, proved in McGee 1981, shows that no truth-functional many-valued logic allows a relation of logical consequence coextensive with…