Scoring theories on Chemla (2009) #

Chemla's first experiment asks whether a sentence with a presupposition trigger in the scope of a quantifier over ten students suggests the universal inference, that every one of them satisfies the presupposition. The text reports the acceptance rates pooled over two groups of quantifiers, each and no on one side and the numerical quantifiers on the other, and the comparison is scored in four steps. The fact is the order of the two rates (observed). The parse of a sentence that every theory shares is the quantified clause (Q these students. trigger) (clause). A theory parses it into a clause of its own: the same clause, or the clause with the trigger's presupposition accommodated in the scope, where it joins the assertion and the clause presupposes nothing (accommodateScope). A theory that covers quantified clauses says which contexts accept its parse (Theory.acceptsClause). The linking hypothesis, that subjects endorse the inferences a theory predicts and endorse alike the inferences it predicts alike, turns the acceptance conditions into a predicted order of the two rates (predicted).

The verdicts hold of every theory that accepts a clause only where symmetric Transparency does and accepts every clause without a trigger: Schlenker's Transparency and local satisfaction, checked incrementally or symmetrically, and any theory under development with these two properties. With every presupposition accommodated in the context (Accommodation.global), such a theory predicts the universal inference from all five quantifiers, and so no difference between the groups, and it is wrong (verdict_global_of). Chemla's §4.1.2 considers an amendment: the universal presupposition is not accommodated after the numerical quantifiers. A parser can stipulate this sentence by sentence, at the cost of three stipulations (Accommodation.stipulated). The section and Appendix F suggest a rule instead: keep the presupposition in the context where transparency derives it in one step (Accommodation.oneStep). The rule parses every sentence as the stipulations do, without any of them (parse_oneStep), so the two give every theory the same verdict (verdict_stipulated_eq), and by the rule such a theory is right (verdict_oneStep_of).

A theory that accepts a clause wherever supervaluation defines it, the trigger being transparent at its assertion, predicts the universal inference from none of the quantifiers. Where four students satisfy both parts of the trigger and a fifth only its presupposition, every quantifier of the experiment takes one value however the other students are resolved. So it predicts no difference between the groups and is wrong wherever it accommodates (verdict_of_transparentAt), as Schlenker's Strong Kleene and supervaluationist accounts are on either version (Schlenker2009.QuantifiedClause.strongKleeneAcceptable_trigger_iff). A theory silent on quantified clauses is silent here (verdict_eq_silent).

The experiment scores a theory together with where it accommodates the presupposition (experiment1), since that is part of the theory, not of the fact. The registered accounts get their verdicts from the general theorems (verdict_experiment1).

Implementation notes #

A presupposition not accommodated in the context is accommodated in the scope, where the clause no longer presupposes it; §4.1.2 says only that it is weakened or not accommodated.
In every model the linking hypothesis consults, the restrictor denotes the ten students at every world.
The linking hypothesis reads a theory's inference off acceptance alone. A Strong Kleene sentence with no that is true as well as defined has every student satisfying the presupposition, an inference from the assertion together with the presupposition that the hypothesis does not consult.

Scoring theories on Chemla (2009) #

Implementation notes #

References #

Local accommodation #

Linking hypothesis and verdicts #

Parsers #

Predictions #

The registered accounts #