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Knowing the meaning of a declarative sentence means knowing its truth conditions—what circumstances would make it true or false. This approach treats truth conditions as constitutive of semantic content and provides a systematic way to analyze complex sentences using model-theoretic semantics.
Study Tarski's T-biconditionals: 'Snow is white' is true iff snow is white. Work through how truth conditions compose for complex sentences with multiple operators.
Truth-conditional semantics does not reduce all meaning to truth conditions; imperatives, questions, and pragmatic content fall outside this framework. Not all meaningful discourse is truth-valued.
You already know from Davidson's truth-conditional semantics that meaning and truth are deeply connected: to understand a sentence is, at minimum, to know what circumstances would make it true or false. You also know from first-order semantics how to assign truth values to complex sentences—quantified formulas, negations, conjunctions—by recursively evaluating them in models. This topic brings those two strands together and asks: can we build a full theory of meaning for a natural language by specifying truth conditions systematically?
The starting point is Tarski's T-biconditional schema: "'Snow is white' is true if and only if snow is white." This looks trivial, but its systematic generalization is not. If you can specify, for *every* sentence of a language, the conditions under which it is true, you have given a truth theory for that language. Davidson's insight was that a truth theory of this form functions as a meaning theory: knowing the truth conditions of a sentence just *is* knowing what the sentence means. The semantic content of a sentence, on this view, is its truth condition—the set of possible situations that would make it true.
The compositional structure is what makes this tractable. You already know from first-order semantics that atomic sentences get their truth conditions from the reference of their names and the extensions of their predicates. Complex sentences build truth conditions compositionally: "P and Q" is true iff P is true and Q is true; "Not P" is true iff P is false; "There exists an x such that Fx" is true iff some object in the domain satisfies F. This principle of compositionality—meaning is a function of parts and structure—explains how we understand infinitely many sentences from a finite vocabulary: we learn the base cases and the rules for combining them.
Model-theoretic semantics, which you already have, provides the formal framework. A model specifies a domain of objects and an interpretation function assigning extensions to predicates and referents to names. A sentence is true in a model iff the world described by the model satisfies the sentence's truth conditions. Meaning, on the truth-conditional approach, becomes the function from models (or possible worlds) to truth values—the intension of the sentence. Knowing this function is knowing what the sentence means.
The limitations are real and instructive. Imperatives ("Close the door!") and questions ("Is it raining?") are not truth-apt in the ordinary sense, yet they are clearly meaningful. Indexicals complicate truth-conditions since the same sentence-type has different truth conditions depending on who utters it when. Pragmatic content—what speakers implicate beyond what they literally say—falls outside the truth-conditional theory of sentence meaning, requiring Gricean or other pragmatic supplements. These limitations do not refute the approach; they define the domain within which it succeeds, and understanding those boundaries is as important as mastering the framework itself.
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