H. P. Grice, ""Si" and "If""

“SI” -- conditional Logic A conditional, or a conditional statement, is a complex sentence of the form: “if p then q.” Both p and q are statements, with p the antecedent and q the consequent. The logical relation between the antecedent and consequent is called implication. The converse of the conditional, that is, “if not q then not p,” is called the contrapositive. Conditionals are also called hypotheticals. In propositional logic, a conditional is generally symbolized as “p→q” or “p⊃q.” The major problem associated with conditionals is determining their truth condition. Most commonly a conditional is treated as a truthfunction such that “if p then q” is false if and only if p is true and q is false. This is called the material conditional or material implication. But there is a paradox associated with the material conditional that has led to a revision called the strict conditional, which claims that a conditional is true if and only if when p is true, q is necessarily true. There are, however, also problems associated with strict conditionals. A much-debated issue concerns the truth conditions of the counterfactuals in which the antecedent is false. For example, “If Kennedy had not been killed, he would have won the next election.” The problem of counterfactuals is also closely associated with the discussion of possible worlds. “A sentence of the form ‘If . . . then . . .’, where the blanks are to be filled with other sentences, is called a conditional.” Mates, Elementary Logic conditional duty, see prima facie duties conditional probability Logic The probability of an event e′ occurring after the occurrence of another event e. The value of this probability is determined by the effect of the probability of e on the probability of e′ before e occurred. A related notion is conditional proof. If B is deduced from a set of premises that includes A n, then in a deductive system we can infer from the remaining premises the conditional if A n then B. This rule of conditional proof is presented as the conjunction following: If A 1 . . . A n ◊B, then A 1 . . . A n−1◊ A n ⊃B. This rule is also called the rule of ⊃ introduction. “Crudely, the expected frequency of a kind of outcome, B, given that a kind of outcome, A, has occurred, is the probability of B conditional on A or the conditional probability of B given A.” Sklar, Philosophy of Physics