Wittgenstein and Formal Semantics: A Case Study on the Tractarian Notions of Truth-Conditions and Compositionality

Abstract

This paper argues that there are three reasons why we should regard Wittgenstein's Tractatus as a forerunner of formal semantics: Wittgenstein is convinced that we can apply formal notions to natural languages, that the meaning of a sentence is to be explained in terms of its truth-conditions and that language is compositional. These claims are also defended against the following three objections. First, the formal semantics defines truth-conditions using the language-metalanguage distinction, while Wittgenstein doesn't. He relies on the picture theory, which is not a formal notion. Secondly, the formal semanticists' ‘compositionality principle’ presupposes that the truth-conditions of complex sentences should be understood in terms of the truth-conditions of elementary ones, whereas Wittgenstein applies the notion of truth-conditions only to complex sentences. And, finally, that differently from the formal semanticists, Wittgenstein doesn't envisage recursive rules for the combination of the semantic primitives. The claim of this paper is that the first objection can be overcome by relating the picture theory to the pre-Tractarian principle of bipolarity, the second by relying on the famous distinction between what a sentence says and what it shows and the third by acknowledging that Wittgenstein, differently from the formal semanticists, works with propositional logic.