Prevalence is always non-negative (derived from measure_nonneg).
Prevalence is at most 1 (derived from measure_le_one).
Traditional GEN is eliminable via threshold semantics for descriptive generics.
For any normalcy predicate (the hidden parameter in GEN), there exists
a threshold θ such that thresholdGeneric gives the same truth value.
Proof:
- If GEN = true, pick θ = -1. Since prevalence ≥ 0 > -1, threshold generic is true.
- If GEN = false, pick θ = 1. Since prevalence ≤ 1, threshold generic is false.
The "normalcy" parameter is (1) not observable (covert), (2) context-dependent (varies by property), and (3) potentially circular (defined to give right results). It can be replaced by observable prevalence plus uncertain threshold. The RSA model then explains how the threshold is inferred pragmatically from priors over prevalence.
Scope limitation (@cite{krifka-2013}): This result applies only to descriptive
generics (empirical generalizations like "Dogs bark"). Definitional generics
("A madrigal is polyphonic") operate on the interpretation index, restricting
admissible word meanings rather than possible worlds, and cannot be reduced to
prevalence thresholds. See Phenomena/Generics/Studies/Krifka2013.lean.
For any GEN configuration that evaluates to true, threshold semantics
can also produce true (with θ < 0).
For any GEN configuration that evaluates to false, threshold semantics
can also produce false (with θ = 1).
How RSA Explains Generic Judgments #
@cite{tessler-goodman-2019} @cite{krifka-etal-1995}
@cite{tessler-goodman-2019} go further than just showing GEN is eliminable. They explain WHY certain generics are judged true despite low prevalence.
The threshold θ is uncertain and integrated out:
P(generic true | prevalence p) = ∫ δ_{p > θ} · P(θ) dθ = p
With a uniform prior over θ, the probability a generic is true equals the prevalence. But the listener reasons about both prevalence and what the speaker meant:
L₁(p | generic) ∝ p · P(p)
The prior P(p) varies by property:
- "Lays eggs": bimodal prior (many at 0, some at ~50%)
- "Is female": unimodal prior (peak at 50%)
Same 50% prevalence, different judgments:
- "Robins lay eggs" true -- 50% is high relative to prior
- "Robins are female" false -- 50% is expected given prior
See Phenomena/Generics/Studies/TesslerGoodman2019.lean for the
full RSA implementation with prevalence priors.