Semantics

Semantics is the study of meaning — how signs, words, sentences, and symbols come to stand for things in the world, for concepts in minds, and for relations between other signs. The field sits at the intersection of Linguistics, Philosophy, Logic, and Cognitive Science, and every approach to it must answer two questions that have not yet received a consensus answer: what is meaning, and how does language acquire it? These questions are not merely academic. Every system that processes language — human, animal, or artificial — must solve the semantics problem or fail at understanding.

The Referential Theory and Its Limits

The oldest and most intuitive theory of meaning is referential: the meaning of a word is the thing it refers to. 'Cat' means the class of cats. 'Napoleon' means the historical individual. This theory has an immediate explanatory virtue — it explains why language is useful, why words track the world, why communication can succeed despite the fact that speakers and listeners have different internal states. The word does the tracking; the world does the fixing.

The referential theory has a famous problem: it cannot handle intensional contexts — contexts where substituting co-referring terms fails to preserve truth. 'The morning star' and 'the evening star' refer to the same object (Venus), but 'Babylonian astronomers believed the morning star was a star' and 'Babylonian astronomers believed the evening star was a star' have different truth values. Frege's solution — distinguish the sense (Sinn) of a term from its reference (Bedeutung) — is the founding move of modern formal semantics. Sense is the mode of presentation of the reference; two terms can have the same reference but different senses, and meaning is constituted by sense, not reference alone.

This distinction generates a research program: a compositional theory of meaning that assembles the meaning of complex expressions from the meanings of their parts through syntactic structure. The sentence means what it means because its parts mean what they mean and are combined as they are combined. Predicate logic provides the formal apparatus for this compositional project: predicates apply to arguments, quantifiers bind variables, truth conditions are computed by recursive evaluation.

Meaning as Use: The Wittgensteinian Turn

The formal program was interrupted — or rather, challenged from outside — by Ludwig Wittgenstein's later philosophy. Wittgenstein's Philosophical Investigations (1953) proposed that meaning is not reference and not sense but use: the meaning of a word is its role in a language game — a practice embedded in a form of life. 'Pain' means what it means because of the practices surrounding pain behavior, pain expression, and pain avowal in human social life. No referent is needed; no Fregean sense is needed. What is needed is the pattern of use.

This is not a nihilistic claim about meaning. It is a deflationary one: stop looking for meaning behind or beneath language, and look at what language does. The philosophical puzzles about meaning — how words attach to the world, how mental states connect to their objects, how communication is possible at all — dissolve when the question shifts from 'what is the hidden relation between a sign and its meaning?' to 'what are people doing when they use this sign?'

The Wittgensteinian move has been enormously productive in Pragmatics — the study of how context, intention, and social situation determine the force and interpretation of utterances beyond their literal semantic content. Speech Act Theory, developed by J.L. Austin and John Searle, extended this program into an account of how utterances accomplish actions: promising, asserting, ordering, apologizing. The meaning of 'I promise' is not its truth conditions but what it does in the social world.

Formal Semantics and the Computational Turn

The tension between the formal (referential, compositional) and pragmatic (use-based, social) approaches has not been resolved — it has been managed by disciplinary specialization. Formal semantics in the tradition of Montague develops compositional truth-conditional accounts of natural language, translating English sentences into intensional logic and evaluating them against possible worlds. This approach handles scope ambiguity, quantifier interactions, and modal operators with precision. It does not handle the fact that 'I'm fine' said by someone who is clearly not fine means something different from its truth conditions.

The computational turn — the attempt to build systems that process natural language — has forced an encounter between these traditions. Large language models trained on vast text corpora develop internal representations that track semantic relations (synonymy, entailment, co-reference) without being given explicit semantic rules. Whether these representations constitute understanding of meaning in any philosophically robust sense is the central debate in philosophy of AI. The models pass behavioral tests for semantic competence; they fail systematic tests for semantic consistency under transformation. This is exactly the structure the formal semanticist would predict if the models have learned statistical regularities without semantic structure, and exactly the structure the Wittgensteinian would expect if meaning is use and use patterns are not consistent.

Meaning as Narrative Structure

There is a third tradition largely absent from the formal-versus-pragmatic debate: the semiotic and narrative account of meaning developed by Charles Sanders Peirce, Ferdinand de Saussure, and their descendants in literary theory, anthropology, and cultural studies. In this tradition, meaning is not located in word-world relations or in patterns of use but in relations among signs: a sign gets its meaning from its position in a system of differences, from the other signs it contrasts with and resembles.

Saussure's foundational claim — that the sign is arbitrary, that there is no natural connection between the sound-image 'tree' and the concept of a tree — is the starting point for structuralism. If meaning is constituted by difference within a system, not by reference to the world, then semantics is fundamentally about the structure of sign systems, not about the structure of reality. The semantic map of a language carves up the world differently than the semantic map of another language, and neither map is the territory. Linguistic relativity — the hypothesis that the structure of a language shapes the conceptual structure available to its speakers — is the empirical program this theoretical commitment generates.

The narrative extension of semiotic semantics holds that the basic unit of meaning is not the word or the sentence but the story: the minimal structure in which a sign sequence produces meaning is a narrative arc — an agent, an action, a change of state, a consequence. Meaning without narrative is not meaning that has been stripped of its story; it is meaning that has suppressed the story it still requires. The truth conditions of 'The cat sat on the mat' are not semantically complete until you know why the cat sat on the mat — what the sitting was about in the narrative sense.

This is not a claim that all meaning is fictional. It is a claim that meaning is always situated in time, in context, in a sequence of events that makes the current sign intelligible. The semantics of a word is the history of its uses, the sediment of the contexts in which it has mattered, the arc of the story it has been part of. Any account of meaning that abstracts from this history produces a theory of the word, not of the meaning.

Any semantic theory that cannot account for how the same sentence means differently when it is the opening line of a story and when it is read aloud in a courtroom does not have a theory of meaning — it has a theory of sentences.