slingshot

The argument sometimes known as the Frege–Church argument that if a context is such that co-referring singular terms (names or descriptions) can be substituted for each other salva veritate, then sentences with the same truth-value can also be so substituted. This justifies semantic theory in holding that the reference of a sentence is its truth-value rather than anything more ‘fine-grained’ such as a situation or state of affairs. The argument works by manufacturing a definite description from a sentence, and substituting a co-referring definite description with another sentence of the same truth-value in it. Suppose two propositions p, q with the same truth-value. Then from ‘ p ’ we derive ‘(the number x such that 2 x = 6 & p ) = 3’; substituting for the referring term in parentheses we have ‘(the number x such that 2 x = 6 & q ) = 3’ from which we derive q . The attribution to Frege, based on some remarks in ‘On Sense and Reference’, is doubtful.