Davidson proposed that the meaning of a sentence is its truth-condition—what would have to be the case for the sentence to be true. A sentence is meaningful if we can specify its truth-conditions. Understanding 'Snow is white' requires knowing that it's true iff snow is white. Truth-conditional semantics provides a systematic, compositional account of meaning, where sentence meaning is determined by the meanings of parts and their mode of combination.
Consider simple examples ('Snow is white,' 'The cat is on the mat') and specify their truth-conditions formally. Then see how truth-conditions compose from parts. Explore the limits: some sentences (commands, questions, moral claims) seem to have no truth-conditions.
Truth-conditional semantics is about what sentences express psychologically—it's about what sentences are true under, an objective relational fact. All meaningful sentences have truth-conditions—this is contentious for imperatives, questions, and non-factual discourse.
You already understand reference determination — how names and terms latch onto things in the world. Davidson's truth-conditional semantics builds on this to answer the harder question: how does a whole sentence mean what it means? The key insight is that the meaning of a sentence just *is* the condition under which it is true. To understand "Snow is white" is to know that it is true if and only if snow is white. This seems trivially obvious — but Davidson's program makes it theoretically powerful by demanding that we explain, systematically, how the truth-condition of any sentence derives from the meanings of its parts.
The philosophical tool Davidson borrowed is Tarski's Convention T: an adequate theory of truth for a language must entail, for every sentence S, a biconditional of the form "'S' is true if and only if p" — where p is the translation of S into the language we're using to do theory. For English, this gives us: "'Snow is white' is true iff snow is white." Tarski intended this for formal languages; Davidson proposed using it as the core of a meaning theory for natural language. The radical idea is that knowing the meaning of a sentence is knowing its T-sentence: the biconditional that specifies under what worldly conditions the sentence holds. There is no further semantic entity — no meaning-object, no proposition in some Platonic realm — that the sentence "expresses." Meaning is fully explained by truth-conditions.
The payoff is compositionality. The truth-condition of a complex sentence is systematically derived from the truth-conditions of its parts and how they are combined. "The cat is on the mat" is true iff the individual referred to by "the cat" stands in the on-the-mat relation to the object referred to by "the mat." The semantics unfolds recursively: sentences build from predicates and names according to rules that preserve the truth-conditional output. This is why Davidson's framework plugs directly into the compositionality principle — the systematicity of language is explained by the compositional structure of truth-conditions.
The limits of the framework are instructive. Imperatives ("Close the door!"), questions ("Is the cat on the mat?"), and arguably moral claims ("You ought to keep your promise") don't seem to be true or false in the same way — they are not straightforwardly truth-apt. A strict truth-conditional semanticist must either extend the framework creatively, argue these reduce to truth-apt forms, or concede they fall outside the theory's scope. The boundary between semantics and pragmatics also comes under pressure: much of what a sentence communicates is not captured by its truth-condition alone — implicatures, presuppositions, and context-dependence all require additional explanation. Davidson's framework gives you the foundation; these challenges push you toward the frontiers of philosophy of language.
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