Living in a Material World: A Critical Notice of Suppose and Tell: The Semantics and Heuristics of Conditionals by Timothy Williamson

Extract

1. The material conditional

Barristers in England are obliged to follow the ‘cab rank rule’, according to which they must take any case offered to them, as long as they have time in their schedule and can agree on fees. This rule is designed to ensure that unpopular people and causes can get legal representation. In philosophy, by contrast, we know we need no structural rule to ensure that seemingly hopeless causes receive representation from the brightest minds. And so we find Timothy Williamson, who famously defended epistemicism about vagueness over a quarter of a century ago, turning in his new book to another unpopular cause, the view that the meaning of ‘if’ is given by the material conditional.

The material conditional view of ‘if’ is the idea that linguistic expressions of the form ‘if A, then C’ (which I'll write ‘A → C’) are false if A is true and C is false, and true otherwise. This makes A → C equivalent to ‘not A or C’ (‘¬ A ∨ C’). To take an example, ‘If Lena has wings, she is an angel’ is false, on the material conditional view, only if Lena has wings and is not an angel; the sentence also means the same as the sentence, ‘Either Lena has no wings or she's an angel’. The material conditional is, of course, the standard conditional connective in propositional and first-order logic. It is reasonable to hope that the material conditional might correspond to the natural language conditional, as this connection would strengthen the ties between natural language and logic.¹