51.05.01 · linguistics / semantics-pragmatics

Semantics and pragmatics — meaning, truth, and use

shipped3 tiersLean: none

Anchor (Master): Montague 1974 Formal Philosophy (Yale); Austin 1962 How to Do Things with Words (Oxford); Grice 1975 Logic and Conversation; Sperber & Wilson 1986 Relevance (Blackwell)

Intuition Beginner

Semantics is the part of linguistics that studies what sentences mean. Pragmatics studies what speakers mean when they use those sentences. The two are distinct: a sentence can mean one thing while a speaker, in a particular situation, means something else with it.

Picture the dinner-table line "Can you pass the salt?" Taken as a question about ability, it asks whether you are physically capable of passing the salt. That is its literal, sentence meaning — the business of semantics. But no one at the table hears it as a question about ability. Everyone hears it as a request to pass the salt. That shift, from a yes/no question to a directive, is the business of pragmatics.

The unit builds on syntax 51.04.01, which gave the hidden tree-structure of a sentence. Semantics takes that tree as input and assigns it a meaning, rule by rule. Pragmatics then asks how context, intention, and use reshape that meaning in real conversation.

Visual Beginner

The dinner-table request and its two layers of meaning: a literal question about ability (the semantic layer) and an implied directive (the pragmatic layer), both carried by the very same string of words.

The same string of words carries both layers at once. Semantics fixes the literal layer; pragmatics supplies the rest from the surrounding context and the speaker's intention.

Worked example Beginner

Consider the dinner-table line "Can you pass the salt?" and trace it through both layers of meaning.

Step 1 — literal meaning (semantics). The sentence is a yes/no question about the addressee's ability to pass the salt. Its meaning is a request for information, answered by "yes" or "no". That is the literal, sentence-level content.

Step 2 — what the speaker means (pragmatics). The speaker already knows the addressee can pass the salt. So the literal question, if that were all, would be pointless. Grice's insight: because the addressee assumes the speaker is being cooperative, the addressee looks for a deeper intention — a request — and acts on it.

Step 3 — the inference. The addressee passes the salt without ever answering "yes". The request was never stated outright; it was implied. Meaning travelled from speaker to hearer through reasoning about intention, not through the literal words alone.

Check your understanding Beginner

Formal definition Intermediate+

Sense and reference. Following Frege ^{[Frege 1892]}, the meaning of an expression has two components. Its reference (Bedeutung) is the object it picks out in the world; its sense (Sinn) is the mode of presentation, the "way" the reference is given. "The morning star" and "the evening star" share a reference (the planet Venus) but differ in sense — which is why "The morning star is the evening star" is informative, while "The morning star is the morning star" is not. Sense accounts for cognitive value; reference accounts for the contribution to truth.

Compositionality. The principle of compositionality (the Fregean principle) states that the meaning of a complex expression is a function of the meanings of its parts and of the syntactic way they are combined ^{[Montague 1974]}. Given the syntactic tree of 51.04.01, a semantic rule assigns a denotation to each node from the denotations of its daughters: a transitive verb denotes a function from individuals to truth values, a noun phrase an individual or a quantifier, and composition proceeds bottom-up. This is what makes a finite lexicon adequate to unbounded sentencehood.

Truth-conditional semantics. A truth-conditional theory identifies the meaning of a declarative sentence with the conditions under which it is true ^{[Tarski semantics via 42.01.04]}. "Snow is white" is true exactly if snow is white; to grasp the meaning is to grasp those conditions. Formally, an interpretation $M$ assigns denotations to the lexicon and an extension $[[\cdot]]^{M, w}$ to every expression, relative to a possible world $w$ and an assignment of values to variables. Entailment is truth-preservation: $ϕ ⊨ ψ$ iff every world-assignment making $ϕ$ true makes $ψ$ true.

Pragmatics: what is conveyed but not encoded. Pragmatics studies meaning that depends on context and use. Entailment is a semantic consequence ("X killed Y" entails "Y is dead"). Presupposition is a background assumption taken for granted ("Sam no longer smokes" presupposes "Sam once smoked"). Implicature ^{[Grice 1975]} is what a speaker implies beyond what the sentence entails, recoverable by reasoning about cooperative intentions. Deixis ("I", "you", "here", "now", "this") comprises expressions whose reference is fixed by the context of utterance — by who speaks, where, and when.

The semantics/pragmatics boundary — competing positions

The boundary itself is contested. At least three positions deserve to be on the table. (i) Literalism / truth-conditionalism (the classic Gricean picture) holds that semantics is autonomous truth-conditional meaning and that pragmatics is a separate inferential layer on top: the sentence has a fixed literal content, and context only supplements it to recover what the speaker meant. (ii) Contextualism / relevance theory ^{[Sperber & Wilson 1986]} holds that literal content is typically incomplete and is enriched to a truth-evaluable proposition only by pragmatic processing, so the boundary is porous and "what is said" is itself pragmatically constructed; relevance theory replaces Grice's four maxims with a single principle of optimal relevance. (iii) Indexicalism (Stanley 2000) localises the enrichment to hidden indexical variables in the logical form, defending a near-minimal proposition against radical contextualism. The dispute is live; this unit teaches all three.

Counterexamples to common slips

Reference is not meaning. Two expressions with the same reference ("Hesperus", "Phosphorus") can differ in meaning; identity of reference does not imply identity of sense.
Entailment is not implicature. Implicatures are cancelable ("She's a philosopher; she's poor — but I don't mean to imply philosophers are poor") without contradiction; entailments are not ("X killed Y, but Y is not dead" is contradictory, not a cancellation).
Literal meaning is not always complete. "It's raining" does not specify a place or time; the full proposition requires pragmatic enrichment, which is the contextualist's main evidence.

Linguistic theory Intermediate+

Compositional semantics (Montague). Montague grammar ^{[Montague 1974]} realises compositionality in full formal detail by translating a fragment of English into a typed intensional logic $IL$ and interpreting the result by $λ$ -calculus function application. A common noun like "donkey" has type $⟨ e, t ⟩$ (a function from individuals to truth values); a determiner like "every" is a quantifier of type $⟨⟨ e, t ⟩, ⟨⟨ e, t ⟩, t ⟩⟩$ , so "every donkey" denotes the set of properties that donkeys have. The sentence "Every donkey walks" translates to $\forall x [donkey (x) \to walk (x)]$ . Quantifier scope ambiguity ("Every farmer owns a donkey") falls out as different derivation orders, exactly as constituency predicted on the syntactic side.

Speech acts (Austin, Searle). Austin's founding move ^{[Austin 1962]} was to notice that some utterances do not describe the world but change it: "I now pronounce you married", "I promise to pay", "You're fired". These performatives are not true or false but felicitous or infelicitous, depending on whether their felicity conditions hold (proper authority, appropriate procedure, sincere participants). Generalising, every utterance performs three acts: the locutionary act (producing the words with sense and reference), the illocutionary act (the force — asserting, ordering, promising, asking), and the perlocutionary act (the effect produced — persuading, frightening, amusing). Searle (1969) taxonomised illocutionary points into assertives, directives, commissives, expressives, and declarations.

The Gricean cooperative principle. Grice ^{[Grice 1975]} proposed that conversation is a cooperative enterprise governed by a cooperative principle — "make your conversational contribution such as is required" — backed by four maxims: Quantity (be as informative as required, neither more nor less), Quality (try to make your contribution true), Relation (be relevant), and Manner (be clear, brief, orderly). When a maxim appears to be flouted, the hearer, assuming cooperation, infers an implicature that restores sense. "There's a garage over there", said to a stranded driver, literally asserts a fact about geography yet implicates that help is at hand. Gricean implicatures are calculable (reconstructable by overt reasoning), cancelable (deniable without contradiction), and non-detachable (surviving paraphrase).

Relevance theory and cognitive semantics. Sperber and Wilson ^{[Sperber & Wilson 1986]} reduce the maxims to one principle of relevance: every utterance conveys a presumption of adequate cognitive effects for the minimum processing effort. On this view implicature is not maxim-violation but ordinary inference to the speaker's informative intention. Cognitive and conceptual semantics (Langacker, Lakoff, Talmy) reject the truth-conditional package altogether: meaning is conceptualisation, truth is a peripheral special case, and metaphor, frames, and image-schemas structure the lexicon. These positions sit on the non-formal wing of the field.

Bridge. The compositional and inferential machinery developed here builds toward 20.12.01, where sense, reference, and intentionality become questions of philosophy of mind and language, and appears again in 42.01.04 pending, whose Tarskian satisfaction relation is the model-theoretic backbone of truth-conditional semantics. The foundational reason compositionality is forced on us is that a finite mind must derive unbounded meanings from a finite lexicon, this is exactly the demand that syntactic and semantic recursion satisfy in lockstep, the central insight is that meaning is computed over structure rather than over flat word-strings, and putting these together, the bridge is that the same typed $λ$ -calculus used to interpret natural language also underlies the proof theory and the denotational semantics studied in the computing curriculum.

Exercises Intermediate+

Exercise 6 (medium, symbolic).

For each of the following, classify it as an entailment, a presupposition, or an implicature of the sentence "Sam stopped smoking", and apply the cancellation test to justify your answer.

(a) Sam does not now smoke.
(b) Sam once smoked.
(c) Sam has resolved to change his habits.

Hint

Entailments cannot be cancelled; presuppositions survive negation; implicatures can be cancelled.

Answer

(a) Entailment. "Stopped" entails no longer doing it; "Sam stopped smoking, but Sam still smokes" is contradictory. (b) Presupposition. "Stopped" presupposes a prior habit; it survives negation ("Sam didn't stop smoking" still takes Sam once smoked for granted). (c) Implicature. A resolution is suggested but cancelable: "Sam stopped smoking — though not from any new resolution, just illness" is coherent.

Exercise 7 (hard, symbolic).

Using the Montague-style type assignment (common nouns and intransitive verbs have type $⟨ e, t ⟩$ , and "every" is a determiner mapping a restrictor and a nuclear scope to a truth value), give the logical-form translation of "Every donkey walks" and explain why compositionality forces the quantifier to take wide scope over the whole sentence.

Hint

"Every" binds the variable ranging over donkeys inside the scope "walks".

Answer

$\forall x [donkey (x) \to walk (x)]$ . The determiner "every" combines with the restrictor predicate $donkey : ⟨ e, t ⟩$ and the scope predicate $walk : ⟨ e, t ⟩$ to yield a truth value, which requires binding a single variable $x$ across both. Compositionality forces wide scope because the determiner's denotation is a second-order relation on the two properties; there is no place for $x$ to live other than as a binder over the entire nuclear scope, so the universal must outrank the predicate.

Exercise 8 (hard, symbolic).

Consider "It's raining", uttered in a context where no place or time has been named. State how a literalist and a contextualist analyse the proposition expressed, and identify the datum that most strongly favours the contextualist.

Hint

Ask whether the sentence, taken in isolation, already determines a complete truth-evaluable proposition.

Answer

The literalist holds that "It's raining" expresses a fixed minimal proposition (perhaps with a hidden location variable bound by a default), onto which the speaker's intended place and time are layered as pragmatic addition. The contextualist holds that the sentence underdetermines any truth-evaluable proposition until pragmatic enrichment supplies the location and time, so "what is said" is itself pragmatically constructed rather than merely supplemented. The strongest datum for the contextualist is that there is no fixed, context-independent truth value for the bare utterance: the same words are true in London now and false in Cairo an hour later, yet no linguistic item in the sentence fixes that — the proposition, not just the speaker's meaning, depends on context.

Lean formalization Intermediate+

lean_status: none. The truth-conditional core — compositionality as a homomorphism condition, intensional model theory, and Tarskian satisfaction — overlaps the model theory and Tarski semantics of 42.01.04 pending and is in principle formalisable in dependent type theory, but the bespoke Montague-style intensional layer, the compositional lexicon, and the treatment of indexicals and illocutionary force are not present in Mathlib. The pragmatic half — implicature, relevance, felicity — is inference over use and intention rather than a theorem-grade object, so it stays prose-first and evidence-gated rather than proof-gated.

Advanced results Master

Montague's universal thesis. Montague's striking claim ^{[Montague 1974]} was that "there is in my opinion no important theoretical difference between natural languages and the artificial languages of logicians." Universal Grammar (1970) gave a uniform algebraic framework: a language is an algebra of syntactic operations paired homomorphically with an algebra of semantic operations, and compositionality is precisely the homomorphism condition. The Proper Treatment of Quantification in Ordinary English (PTQ) instantiated this for a fragment of English, deriving scope, intensionality, and pronoun binding from a small set of translation rules plus $λ$ -abstraction and type-shifting.

Generalized quantifier theory. Barwise and Cooper (1981) ^{[Barwise & Cooper 1981]} reconstrued determiners as binary relations between sets: "most $A$ are $B$ " is true iff $∣ A \cap B ∣ > ∣ A ∖ B ∣$ . This predicts conservativity ("every dog barks" is equivalent to "every dog is a thing-that-barks") and extension as near-universal properties of natural-language determiners. The striking typological consequence is that some simple, definable determiners — for instance "more things than $A$ " (true of $B$ iff $∣ B ∣ > ∣ A ∣$ ) — are nowhere attested as single lexical items in any known human language, exactly because they fail conservativity.

Dynamic semantics and anaphora. Donkey sentences ("Every farmer who owns a donkey beats it") defeated early static Montague grammar, since the pronoun "it" ranges over donkeys introduced by an existential inside a relative clause. Heim (1982) and Kamp's Discourse Representation Theory (1981) replaced static truth-conditions with dynamic context-update: the meaning of a sentence is the change it effects in an information state. Presupposition projection and cross-sentential anaphora fall out, and the static, truth-conditional picture is recovered as the one-sentence special case.

The boundary, resolved and unresolved. Relevance theorists and contextualists (Travis; Searle's "literal meaning is a myth") argue that sentence meaning radically underdetermines what is said; truth-conditional pragmatists (Stanley 2000) defend a minimal, compositionally fixed proposition augmented by a small, closed set of context-parameters. The live empirical battlegrounds — scalar implicature (does "some" semantically mean "some and perhaps all", or "some but not all"?), the reference of demonstratives, and the proposition expressed by incomplete sentences like "It's raining" — are where the three boundary-positions of the Formal definition section are put to the test.

Synthesis. The compositionality, speech-act, and implicature theories developed here build toward 20.12.01, where intentionality, reference, and truth become questions of philosophy of mind and language, and appears again in 42.01.04 pending, whose model theory and Tarskian semantics supply the lattice on which truth-conditional semantics is built. The foundational reason the semantics/pragmatics boundary is contested is that meaning is simultaneously a property of sentences and a property of acts, this is exactly the dual nature that compositional semantics and speech-act theory each capture from one side, the pattern generalises to the dynamic and game-theoretic semantics that treat meaning as context-update, putting these together, the central insight is that to interpret an utterance is to reconstruct both what is said and what is done, and the bridge is that this reconstructive, inferential picture unifies linguistics with the philosophy of action and the model theory of formal logic.

Full proof set Master

Proposition (Conservativity of natural-language determiners). Let $D_{A} (B)$ denote the truth value of a determiner $D$ applied to a restrictor set $A$ and a nuclear-scope set $B$ in a fixed model. The standard determiners every, some, no, most, exactly three, and at least two are conservative: for all $A, B$ ,

D_{A} (B) ⟺ D_{A} (A \cap B) .

Proof. It suffices to note that for the listed determiners the truth of $D_{A} (B)$ depends only on how $B$ behaves inside $A$ . We verify each case.

every: $every_{A} (B)$ iff $A \subseteq B$ . For any $x \in A$ we have $x \in (A \cap B) \Leftrightarrow x \in B$ , so $A \subseteq B \Leftrightarrow A \subseteq (A \cap B) \Leftrightarrow every_{A} (A \cap B)$ .
some: $some_{A} (B)$ iff $A \cap B \neq = \emptyset$ . Since $A \cap (A \cap B) = A \cap B$ , we have $some_{A} (A \cap B)$ iff $A \cap B \neq = \emptyset$ , identical to the left-hand side.
no: $no_{A} (B)$ iff $A \cap B = \emptyset$ , and $A \cap (A \cap B) = A \cap B$ , so both sides coincide.
most: $most_{A} (B)$ iff $∣ A \cap B ∣ > ∣ A ∖ B ∣$ . Now $A \cap (A \cap B) = A \cap B$ and $A ∖ (A \cap B) = A ∖ B$ , so both arguments to "most" are unchanged by replacing $B$ with $A \cap B$ .
exactly three / at least two: each counts elements of $A$ that lie in $B$ ; since $A \cap (A \cap B) = A \cap B$ , the count is invariant under the replacement.

Hence $D_{A} (B) \Leftrightarrow D_{A} (A \cap B)$ in every case. $\qed$

Remark. Conservativity is not forced by pure logic: the determiner "more things than $A$ ", defined by $D_{A} (B)$ iff $∣ B ∣ > ∣ A ∣$ , is perfectly well-formed yet non-conservative and is unattested as a simple determiner in any known language ^{[Barwise & Cooper 1981]}. The universal absence of such items is a substantive empirical generalisation that determiner theory predicts and that a purely logical vocabulary does not.

Proposition (Duality of every and some). In any model, $\neg every_{A} (B) ⟺ some_{A} (\overline{B})$ , where $\overline{B}$ is the complement of $B$ .

Proof. $\neg every_{A} (B)$ iff $\neg (A \subseteq B)$ iff there exists $x \in A$ with $x \in / B$ , i.e. $x \in A \cap \overline{B}$ , iff $some_{A} (\overline{B})$ . $\qed$

This duality is the semantic reflex of the classical quantifier law $\neg\forall x ϕ \Leftrightarrow \exists x \neg ϕ$ , recovered as the special case $A =$ the whole domain; it is the bridge by which the determiner algebra of natural language embeds into the first-order logic of 42.01.04 pending.

Connections Master

Syntax 51.04.01. The syntactic tree is the input over which semantic composition operates: each node receives a denotation built from its daughters, so the constituency decided in syntax fixes the predictions of any compositional semantic theory.
Philosophy of language 20.12.01. Sense and reference, truth, intentionality, and the speech-act/pragmatics distinction are continuous with the philosophical debate over meaning and reference pursued there at the level of metaphysics and the philosophy of mind.
Phonology 51.02.01. Prosody and intonation carry pragmatic force — the rising contour that turns a statement into a question, the stress that marks focus and presupposition — so the sound system is a channel for illocutionary and information-structure meaning.
Formal logic and Tarski semantics 42.01.04 pending. The truth-conditional core of this unit is the model-theoretic semantics developed there: Tarskian satisfaction, entailment as truth-preservation, and the quantifier duality proved above are all instances of that framework.

Historical & philosophical context Master

Modern semantics has two founding moments. Frege's "Über Sinn und Bedeutung" (1892) split meaning into sense and reference, solving the puzzle of how identity statements can be informative and fixing compositionality as the load-bearing principle of semantic theory ^{[Frege 1892]}. The early twentieth century then built truth-conditional semantics on that base: the logical positivists (Carnap) tied meaning to verification and to formal truth-conditions, and Tarski's (1933) model-theoretic definition of truth gave semantics the precise notion of satisfaction it still uses, developed formally in 42.01.04 pending.

Pragmatics emerged later, as philosophers noticed that meaning outruns truth-conditions. Austin's How to Do Things with Words (1962) revealed performative utterances and founded speech-act theory ^{[Austin 1962]}; Searle systematised it into a taxonomy of illocutionary forces. Grice's William James lectures, delivered in 1967 and anthologised in 1975, introduced the cooperative principle and the notion of conversational implicature, relocating much of "meaning" into rational inference about speaker intention ^{[Grice 1975]}.

The formal and the inferential wings then converged. Montague's papers of the late 1960s and early 1970s recast the whole field in type-theoretic terms, demonstrating that natural-language semantics could be as rigorous as the semantics of formal logic ^{[Montague 1974]}. Sperber and Wilson's Relevance (1986) reframed pragmatics around a single cognitive principle, arguing that the Gricean maxims collapse into one presumption of optimal relevance ^{[Sperber & Wilson 1986]}. The semantics/pragmatics boundary has been contested ever since Grice drew it: the literalist picture is defended by truth-conditional pragmatists and contested by contextualists and relevance theorists who hold that what is said is itself pragmatically constructed. The dispute is taught here as a live one, with multiple positions on the table rather than a single settled answer.

Bibliography Master

@article{Frege1892,
  author = {Frege, Gottlob},
  title = { \"{U}ber Sinn und Bedeutung },
  journal = {Zeitschrift f\"ur Philosophie und philosophische Kritik},
  year = {1892},
}

@book{Austin1962,
  author = {Austin, J. L.},
  title = {How to Do Things with Words},
  publisher = {Oxford University Press},
  year = {1962},
}

@incollection{Grice1975,
  author = {Grice, H. Paul},
  title = {Logic and Conversation},
  booktitle = {Syntax and Semantics 3: Speech Acts},
  editor = {Cole, Peter and Morgan, Jerry L.},
  publisher = {Academic Press},
  year = {1975},
}

@book{Montague1974,
  author = {Montague, Richard},
  title = {Formal Philosophy: Selected Papers of Richard Montague},
  editor = {Thomason, Richmond H.},
  publisher = {Yale University Press},
  year = {1974},
}

@book{SperberWilson1986,
  author = {Sperber, Dan and Wilson, Deirdre},
  title = {Relevance: Communication and Cognition},
  publisher = {Blackwell},
  year = {1986},
}

@book{Searle1969,
  author = {Searle, John R.},
  title = {Speech Acts: An Essay in the Philosophy of Language},
  publisher = {Cambridge University Press},
  year = {1969},
}

@book{Cruse2011,
  author = {Cruse, D. A.},
  title = {Meaning in Language: An Introduction to Semantics and Pragmatics},
  edition = {3},
  publisher = {Oxford University Press},
  year = {2011},
}

@book{Levinson2000,
  author = {Levinson, Stephen C.},
  title = {Pragmatics},
  publisher = {Cambridge University Press},
  year = {2000},
}

@article{BarwiseCooper1981,
  author = {Barwise, Jon and Cooper, Robin},
  title = {Generalized Quantifiers and Natural Language},
  journal = {Linguistics and Philosophy},
  volume = {4},
  year = {1981},
}

Prerequisites

51.04.01

Tier anchors

beginner: Cruse 2011 Meaning in Language (Oxford) Ch. 1–3 (plain English); Saeed 2016 Semantics (Wiley-Blackwell) Ch. 1–2
intermediate: Cruse 2011 Meaning in Language (Oxford) — sense, reference, sense relations; Levinson 2000 Pragmatics (Cambridge) — implicature, deixis, speech acts
master: Montague 1974 Formal Philosophy (Yale); Austin 1962 How to Do Things with Words (Oxford); Grice 1975 Logic and Conversation; Sperber & Wilson 1986 Relevance (Blackwell)

References

Frege — Uber Sinn und Bedeutung · Frege, G. (1892). Sense and reference; the morning-star/evening-star puzzle and the separation of cognitive value from reference. Zeitschrift fuer Philosophie und philosophische Kritik.
Austin — How to Do Things with Words · Austin, J. L. (1962). Constative vs performative utterances; locutionary, illocutionary, perlocutionary acts; felicity conditions. Oxford University Press.
Grice — Logic and Conversation · Grice, H. P. (1975). The cooperative principle; maxims of quantity, quality, relation, manner; conversational implicature and its cancellation. In Cole & Morgan (eds.), Syntax and Semantics 3. Academic Press.
Montague — Formal Philosophy · Montague, R. (1974). Universal Grammar; The Proper Treatment of Quantification in Ordinary English. Type-theoretic interpretation via intensional logic and lambda calculus. Yale University Press.
Sperber & Wilson — Relevance · Sperber, D. & Wilson, D. (1986/1995). Relevance theory; the cognitive and communicative principles of relevance; mutual manifestness. Blackwell.
Cruse — Meaning in Language · Cruse, D. A. (2011). Sense relations (synonymy, antonymy, hyponymy), reference, sentence meaning vs utterance meaning. Oxford University Press.
Levinson — Pragmatics · Levinson, S. C. (2000). Presupposition, entailment, implicature, deixis, speech acts, conversational structure. Cambridge University Press.
Barwise & Cooper — Generalized Quantifiers and Natural Language · Barwise, J. & Cooper, R. (1981). Determiners as relations between sets; conservativity and extension as universals. Linguistics and Philosophy 3.

Estimated time

beginner: 15m
intermediate: 40m
master: 90m