Material Implication and Indicative Conditionals

Abstract

It has often been asked whether the truth-function known as material implication correctly accounts for conditionals in the indicative mood. After defining material implication and indicative conditionals (hereafter just “conditionals”), I will discuss why I believe the former does not always account for the latter. Defences for a material interpretation of conditionals by H. P. Grice and Frank Jackson will then be given.

A function is analogous to a machine which outputs something when something is input. The inputs and outputs of truth-functions are truth values: “true” or “false”. The symbol for material implication (‘⊃’) is thus formally defined: if the sentence before it (the antecedent) is true and the sentence after it (the consequent) is false, then the material implication is false; otherwise it is true. Conditionals are a complex sentence form; they are made up of sentences and can be either true or false (but not both). If A and B are any sentences, then “If A, then B” is the conditional form. The previous sentence is also a conditional (A and B can be complex sentences, like “The flag is raised and somebody is dead.”) As with material implication, A is the antecedent and B is the consequent.

Conditionals with synthetic antecedents and consequents will be considered, rather than conditionals with analytic antecedents or consequents. The subject in a synthetic sentence – like “the flag” in the sentence “The flag is raised” – does not somehow contain the predicate (here “is raised”). Contrast this with the analytic sentence “The white swan is white.” Since this cannot be false, we cannot speak of “If the white swan is white, then the white swan is white” having a false antecedent or consequent, which is crucial.