NOTE-608: The Semantics of Definite and Indefinite Noun Phrases

Contribution

Before this work, the indefinite article was analysed as an existential quantifier (Russell), and its use as an antecedent for pronouns outside its scope (“A dog came in. It lay down”; “Every man who owns a donkey beats it”) was handled by text-wide binding (Geach, Egli, Smaby), pragmatic salience (Grice, Kripke, Lewis), pronouns as definite descriptions (Evans, Cooper, Parsons) or an ambiguity hypothesis (Strawson, Chastain). Heim argues each fails somewhere and proposes that indefinites have no quantificational force at all: they are variables bound by whatever operator is nearest. She then gives a second, better-motivated version in which sentence meanings are file change potentials, and in which definiteness is a single felicity condition. Kamp’s discourse representation theory reached closely similar ideas independently in the same period; Heim says so and does not compare the two.

Key insight

An utterance does not just narrow down the ways the world might be; it also opens and updates “cards” for the things talked about. An indefinite opens a new card; a definite or pronoun must find an old one. That one difference explains why indefinites seem to quantify (a new card can be filled by anything that fits, so truth comes out existential, or universal under “every” and “always”), why definites seem to refer (they are tied to a card already in the common ground, by mention or by salience), and why two sentences with the same truth conditions can differ in what a following pronoun can pick up.

Assumptions

• Logical form: syntactic structures are mapped by construal rules (NP-indexing, NP-prefixing, quantifier construal) to indexed, tripartite operator structures [Q, restrictor, nuclear scope]. In ch. II there are also obligatory rules of existential closure and quantifier indexing and a Novelty Condition; ch. III removes them.
• Extensional semantics for most of the work; modals and conditionals get an intensional treatment after Kratzer (modal base, ordering source) in ch. II §4.
• Singular NPs only (“the limitation to singular NPs will in fact be maintained throughout”); plurals, generics and specific indefinites are set aside or only sketched.
• Assertion only: the file change described is the essential effect of assertions, following Stalnaker, and only when not rejected.
• Common ground idealised: all participants presuppose the same things (“nondefective” contexts).
• Principle (B): a file constrains the n-th member of its satisfying sequences only if it has a card n.

Key results

• Ch. I. Counterexamples to each rival: the marble pair (21a/b) and “John has a spouse / John is married. She is nice” (truth-conditionally equivalent, different anaphoric potential) against salience accounts; “If someone is in Athens, he is not in Rhodes” and the sage-plant sentences against uniqueness in E-type accounts; most and in most cases against Egli’s and Smaby’s exportation rules. Common conclusion: (a) indefinites are existential quantifiers, (b) they obey the same scope islands as other quantifiers, (c) pronouns are bound or referential — cannot all be true.
• Ch. II §1–3. Lewis’s adverbs of quantification are unselective and bind all free variables in their restrictor; Heim adds that the free variables come from indefinites. Satisfaction semantics for indexed logical forms; existential closure at text level and in nuclear scopes; a Novelty Condition (an indefinite may not be coindexed with any NP to its left).
• Ch. II §4. Bare conditionals contain an unpronounced necessity operator restricted by the if-clause; under realistic modal bases and ordering sources, “If a man owns a donkey, he beats it” entails the universal ∀x∀y((man x ∧ donkey y ∧ own x y) → beat x y) but can say more (dispositions). Generic indefinites restrict an invisible operator, with non-realistic (stereotypical) ordering left open.
• Ch. II §5–7. Indefinites can be anaphorically related to pronouns outside their scope, like names and unlike every/no NPs; scope islands and weak crossover are accommodated; Karttunen’s “discourse referents” and their lifespans are reconstructed as indices and operator scopes, explaining why negation, quantifiers, modals and attitude verbs all close off discourse referents. Specific indefinites and Karttunen’s extended referents (“You must write a letter… It has to be sent by airmail”) remain unexplained.
• Ch. II §8. Definiteness = three independent properties: no operator indexing, no Novelty Condition, presupposed descriptive content.
• Ch. III §1. Principle (A): Sat(F + φ) = Sat(F) ∩ {a : a sat φ}. Files versus Stalnaker’s context sets: a file determines a world set (the context set), but files with the same world set can evolve differently under the same utterance, so the common ground needs more structure than a set of worlds.
• Ch. III §2. Novelty-Familiarity Condition: indefinite index ∉ Dom(F), definite index ∈ Dom(F), else infelicitous; deixis is reading a card created by salience. Felicity of a complex formula = felicity of every elementary update step, which projects presuppositions without a separate projection rule.
• Ch. III §3. Truth criterion (C): φ is true w.r.t. F if F + φ is true, false if F is true and F + φ false. Free indefinites get existential truth conditions from this (proved for the woman–dog example), so text-level existential closure is unnecessary; (C’) for false files is left vague.
• Ch. III §4. File change rules for universal quantification and negation in three and two steps; selection indices replaced by reference to Dom(F), and nuclear-scope existential closure built into the interpretation rule. Final rules (I)–(IV).
• Ch. III §5. Extended Novelty-Familiarity Condition (familiar card and entailed descriptive content); accommodation with “bridging” to existing cards; global accommodation preferred to local; paycheck pronouns and “prominence by proxy”; information-preserving accommodation licenses the Karttunen cases with know and with modal subordination (pp. 392–394).
• Ch. III §6. Four arguments for file change semantics: conjunction is privileged, presupposition projection, accommodation interleaved with interpretation, and a single principle of definiteness.

Claims

id	claim	strength	support
C1	Indefinites have no quantificational force of their own; it comes from the binding operator or from the truth definition	moderate	the analysis covers donkey sentences, adverbs of quantification, modals and conditionals (ch. II §1–4); argued, not proved unique
C2	Truth-conditionally equivalent sentences can differ in anaphoric potential, so meaning is not exhausted by truth conditions	strong (data)	marble pair, spouse/married, bicycle-owner (ch. I §1.3)
C3	E-type analyses with Russellian uniqueness give wrong truth conditions for donkey conditionals	strong for the cases given	Athens/Rhodes, sage plants (ch. I §2.3)
C4	A common ground must be finer than a set of worlds to predict how it changes	moderate	files with equal world sets diverge (ch. III §1.4); depends on treating open formulas as update units
C5	Definiteness reduces to familiarity with respect to the file (with descriptive content entailed)	moderate	derivation of binding, deixis/anaphora unity and narrow-scope definites (ch. III §2–5); accommodation is under-specified
C6	File change semantics solves the presupposition projection problem	weak here	one worked example; full treatment deferred to separate work
C7	Specific indefinites, weak crossover with indefinites and extended discourse referents are not explained	stated limitation	ch. II §5.4, §7

Method

Model-theoretic semantics of a fragment of English via indexed logical forms, tested against acceptability and truth-value judgements on constructed examples, with comparison to rival analyses case by case. In ch. III the interpretation is moved from satisfaction conditions to file change potentials and the construal component is simplified.

Concepts

• file: a common ground with a domain (card numbers) and a satisfaction set (sequences of individuals, per world).
• file change potential (F + φ): the function from files to files a logical form denotes.
• novel / familiar (w.r.t. a file): index not in / in Dom(F).
• Extended Novelty-Familiarity Condition: indefinites novel; definites familiar with descriptive content entailed by the file.
• accommodation: repairing a felicity failure by adding a card, linked to existing cards (“bridging”); global or local.
• unselective quantifier: an operator binding every free variable its restrictor introduces (after Lewis 1975).
• discourse referent: Karttunen’s notion, identified first with referential indices, then with file cards.
• prominence: the small set of recently handled cards a pronoun may use.

Connections

Built on Lewis’s “Adverbs of quantification” (1975) and “Scorekeeping in a language game” (1979, accommodation), Kratzer’s modality, Karttunen’s discourse referents and presupposition work, and Stalnaker’s “Assertion”, whose account of the common ground and of assertion’s essential effect (eliminating the possibilities incompatible with what is said, unless the assertion is rejected) it quotes and adopts, refining the context set into a file. Kamp (1981) is acknowledged as independent and closely similar; Hintikka and Carlson’s game-theoretical account is assessed at the end of ch. I. Veltman (LIT-818) later credits this work as one origin of update semantics.

Bearing on the record

• Source, with Veltman and Krifka, of THEORY-162: what an utterance does to a context is part of its meaning and is not fixed by its truth conditions. Heim’s anaphora pairs are the cleanest evidence for it read in the record.
• CLAIM-061 (proposition neither necessary nor sufficient for the communicative event): the marble and spouse pairs show, for anaphoric potential, that sameness of proposition does not fix what an utterance makes available for what follows. That is the “not sufficient” half, for a dimension (discourse referents) other than the footing and force the claim names.
• CLAIM-054 (interpretive and performative fidelity come apart): no direct bearing; Heim restricts herself to assertion.
• Stalnaker’s “Assertion” (LIT-811), unread here, is quoted in ch. III §1.4 (pp. 321, 323 of the essay), which is the record’s only first-hand access to its wording; Heim cites the volume as 1979.
• No instruction for ML practice; nothing for the anthology.

Limitations

• Singular NPs only; plurals, generics and specific indefinites are outside the theory or sketched.
• Accommodation’s conditions (bridging, global preference, prominence by proxy, information preservation) are described, not derived.
• Truth for utterances against false files, (C’), is vague by the author’s admission.
• The projection-problem claim rests on one example; the full treatment is deferred.
• The evidence is introspective judgement on constructed sentences.
• The author calls the dissertation “a rough draft” in the preface.

Open questions

• How a static rival (E-type or situation-based accounts, developed later) handles the marble and spouse contrasts without file change.
• The general conditions on accommodation, and why accommodated cards must be bridged.
• How Karttunen’s extended discourse referents (modal subordination) are licensed in general; pp. 392–394 give a sketch through information-preserving accommodation.