Elbourne (2026): Adjectives without syntactic categories #
@cite{elbourne-2026}
Published online: 12 March 2026, Natural Language & Linguistic Theory 44:17.
Adjectives are uniformly type ⟨et,et⟩ — functions from noun denotations to noun denotations. This eliminates Predicate Modification for adjective-noun combination (FA suffices) and supports the program of eliminating syntactic categories in favor of semantic types ("Meaning-Dependent Grammar", building on @cite{elbourne-2024}).
Key result #
Classification.lean already defines AdjMeaning W E = Property W E → Property W E, which IS the ⟨et,et⟩ type. The Kamp hierarchy there
(intersective, subsective, privative) classifies adjectives by meaning
postulates within that type — not by assigning different types to
different classes. The present file makes this explicit and adds
Elbourne's copula semantics.
Copula BE #
Elbourne's copula takes a tense relation R and an ⟨et,et⟩ adjective G,
applies G to the trivially true noun λt.λx. ⊤, and existentially
quantifies over a time satisfying R. This contrasts with
@cite{partee-1987}'s BE (a type-shifting operation ⟨⟨e,t⟩,t⟩ → ⟨e,t⟩
for nominal predication) — a different function for a different
construction.
Sections #
- ⟨et,et⟩ adjective meanings (intersective)
- Copula BE
- FA-sufficiency: FA on ⟨et,et⟩ = PM on ⟨e,t⟩; PM limitation
- "Fido was cute" derivation
- Connection to Classification hierarchy
- Former: non-subsective
AdjMeaning+ PM failure + end-to-end chain - Compulsory E_R: attributive-only adjectives
The trivially true noun meaning: λt.λx. ⊤.
The copula applies an ⟨et,et⟩ adjective to this to extract
the adjective's inherent content.
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Intersective ⟨et,et⟩ adjective: λN.λt.λx. N(t)(x) ∧ Q(t)(x).
@cite{elbourne-2026} (24b)/(59):
/cute/ :: λf⟨e,it⟩.λx.λt. f(x)(t) & cute(x)(t)
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- Phenomena.Copulas.Studies.Elbourne2026.intersective Q N t x = (N t x && Q t x)
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Applying an intersective adjective to the trivial noun recovers the underlying property Q. This is what the copula exploits.
Elbourne's copula BE.
Takes a tense relation R and an ⟨et,et⟩ adjective G, applies G
to the trivial noun, and existentially quantifies over a time
satisfying R.
@cite{elbourne-2026} (8)/(27c):
BE :: λR⟨i,it⟩.λG⟨eit,eit⟩.λx.λt. ∃t'(R(t')(t) & G(λy.λt''.⊤)(x)(t'))
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BE applied to an intersective adjective produces the expected
truth conditions: ∃t'. R(t',t) ∧ Q(t')(x).
Core theorem: FA on ⟨et,et⟩ adjective = PM on ⟨e,t⟩ property.
The LHS is the FA attributive derivation: an intersective ⟨et,et⟩ adjective applied to a noun via function application. The RHS is Predicate Modification: conjunction of the underlying adjective property with the noun. Since FA reproduces PM for intersective adjectives, PM is unnecessary for adjective-noun combination.
@cite{elbourne-2026} (25)–(26):
⟦cute donkey⟧ = λx.λt. donkey(x)(t) & cute(x)(t)
PM always produces intersective results: the composition
λN.λt.λx. A(t)(x) ∧ N(t)(x) satisfies Classification.isIntersective
with witness A. This means PM is too restrictive even for merely
subsective adjectives like skillful — not just non-subsective ones.
@cite{elbourne-2026} (p. 13): under ⟨e,t⟩, "a rule like Predicate Modification is presumably necessary; but this would impose the intersective semantics that we have just seen is inappropriate for merely subsective adjectives."
Corollary: PM always yields subsective results (A ∧ N entails
N). Follows from pm_always_intersective via the hierarchy
(intersective → subsective), but also provable directly.
Truth conditions for "Fido was cute":
∃t'(t' < t ∧ cute(Fido)(t')).
Step-by-step derivation (@cite{elbourne-2026} (28)–(30)):
⟦BE PAST⟧ = λG.λx.λt. ∃t'(t' < t ∧ G(⊤)(x)(t'))⟦[BE PAST] cute⟧ = λx.λt. ∃t'(t' < t ∧ cute(x)(t'))⟦Fido [[BE PAST] cute]⟧ = λt. ∃t'(t' < t ∧ cute(Fido)(t'))
Intersective ⟨et,et⟩ adjectives satisfy
Classification.isIntersective. The witness is the underlying
property Q.
Intersective ⟨et,et⟩ adjectives are subsective:
cute N entails N.
Attributive combination (FA on ⟨et,et⟩ adj + noun) and predicative extraction (copula applies adj to trivial noun) use the SAME adjective denotation. The copula adds tense; FA does not.
"cute donkey" (attributive) = intersective Q donkey
"Fido was cute" (predicative) uses intersective Q applied to ⊤
The adjective meaning intersective Q is identical in both.
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Non-subsective ⟨et,et⟩ adjective: former.
Computable over a finite list of time points via List.any.
formerAdj times ltb N t x = true iff some earlier time t'
satisfies ltb t' t ∧ N t' x and N t x = false.
@cite{elbourne-2026} (44)/(60):
λf⟨e,it⟩.λx.λt. ∃t'(< (t')(t) & f(x)(t') & ¬f(x)(t))
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formerAdj produces the expected truth value at (now, joe):
Joe is a former judge.
formerAdj is not subsective — connecting directly to
Classification.isSubsective. This is a genuine AdjMeaning,
so it integrates with the full Classification hierarchy.
No ⟨e,t⟩ adjective property, combined with judge via PM, can
yield a true result at (now, joe) — because judge(now)(joe)
is false and PM includes the noun in the conjunction.
Contrast with former_adj_holds: the ⟨et,et⟩ theory CAN
produce a true former judge result while judge is false.
End-to-end chain: the ⟨et,et⟩ theory strictly subsumes ⟨e,t⟩ + PM for adjective-noun composition.
- For intersective adjectives, FA on ⟨et,et⟩ reproduces PM
(
fa_eq_pm). - For non-subsective adjectives, ⟨et,et⟩ succeeds
(
former_adj_holds∧judge .now .joe = false). - For non-subsective adjectives, ⟨e,t⟩ + PM fails
(
pm_cannot_produce_former).
Applying formerAdj to the trivial noun gives false everywhere:
⊤ can never "formerly" hold (it always holds). The copula applies
adjectives to ⊤, so former in predicative position would be
vacuously false — a semantic reason for the attributive-only
restriction (complementing compulsory E_R in § 7).
Whether an adjective requires a noun argument (E_R feature status).
Under the ⟨et,et⟩ theory ALL adjectives are the same type; the attributive/predicative distinction is syntactic, not semantic.
- Optional E_R (
cute,tall): attributive or predicative. - Compulsory E_R (
former,mere,alleged): attributive only.
@cite{elbourne-2026} § 3.2: the copula derivation requires the adjective to appear WITHOUT an E_R feature; adjectives bearing compulsory E_R cannot be taken as argument by [BE PAST].
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