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The Semantics of Evaluativity

Rett, J. (2015). Oxford University Press

Source Bibliography Paper

Rett derives the distribution of evaluativity across degree constructions, her Table 3.1, from two Neo-Gricean implicatures. A Quantity implicature strengthens the otherwise tautological positive construction, and the Marked Meaning Principle, after Horn's division of pragmatic labor, makes the marked, negative antonym evaluative in exactly the polar-invariant constructions, the equatives and degree questions in which its unmarked antonym has the same truth conditions.

Implementation notes

Antonym polarity is the adjective's Adjective.polarity, which acts on the comparison of its equative and comparative through the order dual, Polarity.negative • c = c.dual; negative antonyms are the marked members of their pairs (Bierwisch, Kennedy). The positive construction and the measure phrase have no polarity-parametrized semantics in the substrate, so their rows of IsPolarInvariant are the book's classification.

References

Polar (in)variance and markedness

L45–50
L52–54

The implicature derivation

L70–75

The book's contrasts

Chapter 1's How short is Adam? and Adam is as short as Doug are evaluative; their positive-antonym counterparts are not.

Polar variance grounded in the comparison semantics

Rett 2015b reduces polar (in)variance to mutual entailment of the antonyms' non-evaluative readings: the strengthened ("exactly") equatives of the two antonyms share truth conditions, so a truth-conditionally equivalent unmarked alternative exists and the Marked Meaning Principle can fire; the antonym comparatives exclude each other, so no such alternative exists. Degree questions pattern with the equative — both antonyms' true answers are the subject's actual measure.

The strengthened equatives of two antonyms, exactly as tall as and exactly as short as, are mutually entailing.

theorem exact_equative_antonym_invariantL129–136
{Entity : Type u_1} {D : Type u_2} [LinearOrder D] (μ : Entity → D) (a b : Entity) (p : Polarity) :
a ∈ μ ⁻¹' (p • Degree.Comparison.ge).interval (μ b) ∧ a ∉ μ ⁻¹' (p • Degree.Comparison.gt).interval (μ b) ↔ a ∈ μ ⁻¹' ((Polarity.negative * p) • Degree.Comparison.ge).interval (μ b) ∧ a ∉ μ ⁻¹' ((Polarity.negative * p) • Degree.Comparison.gt).interval (μ b)

Table 3.1

L153–162