Del Pinal, Bassi & Sauerland (2024): free choice and presuppositional exhaustification #
[DPBS24] derive free choice with pex^{IE+II}
(Exhaustification.Presuppositional.pexIEII), which asserts its prejacent and
presupposes the negation of the innocently excludable alternatives together with
homogeneity over the innocently includable ones. On ◇(p ∨ q) this is (14): the
presupposed ◇p ↔ ◇q with the asserted disjunction entails ◇p ∧ ◇q (pex_fc), and the
same structure gives double prohibition under negation (16) (pex_double_prohibition) and,
with the necessity alternatives relabelled, negative free choice (19a)–(20)
(pex_negative_fc, pex_double_requirement). The split is what flat exh^{IE+II}
lacks, and the paper's embedded puzzles turn on it. Under a negative factive (§3), the
factive presupposes the whole pex output, so free choice is presupposed
(fc_presupposed_under_neg_factive), while the assertion denies belief in the bare
prejacent, which denies belief in either disjunct (pex_unaware_target); a flat exh
complement yields only denial of belief in the exhaustified conjunction, which a believer
in free choice can satisfy (exh_unaware_too_weak). In a disjunction (§4) the homogeneity
presupposition of the second disjunct is filtered in its local context
([Sch09a]) and free choice follows there (filtering_fc), whereas flat exh
leaves nothing to project (exh_filtering_trivial). Under quantifiers (§5.1) universal
projection of the presupposition gives universal, universal-negative, and existential
free choice, (62), (63), (75) (universal_fc, universal_negative_fc, existential_fc),
and under exactly one (§5.2) the salient readings of (76)–(77) of
[GRS20] (exactly_one_fc, exactly_one_double_prohibition).
The five-world model and alternative set are [BLF20]'s.
pex^{IE+II} on ◇(p ∨ q) (§2) #
(14): pex^{IE+II}[◇(p ∨ q)] on the five-world model.
Equations
Instances For
(14): the presupposed homogeneity ◇p ↔ ◇q with the asserted ◇(p ∨ q) gives free
choice.
(16): negation denies the prejacent and leaves the presupposition, so ¬pex[◇(p ∨ q)]
is double prohibition.
¬□T, read on the five-world model: the alternatives to ¬□(T ∧ B) — ¬□T, ¬□B,
¬□(T ∨ B) — have the same innocent-exclusion/inclusion structure as those to ◇(p ∨ q),
with ¬□T in the place of ◇q and ¬□B in the place of ◇p.
Instances For
¬□B on the five-world model.
Instances For
(19a): pex^{IE+II}[¬□(T ∧ B)] gives negative free choice.
(20): ¬pex^{IE+II}[□(T ∧ B)] gives double requirement.
Free choice under negative factives (§3) #
Under a negative factive the whole pex output is presupposed, so free choice is
presupposed, (21a).
The factive's assertion denies belief in the prejacent ◇(p ∨ q), hence belief in either
disjunct, (21b).
exh^{IE+II}[◇(p ∨ q)], fully assertive.
Equations
Instances For
With a flat exh complement the factive's assertion only denies belief in the
exhaustified conjunction, which an attitude holder who believes free choice but not
exclusivity satisfies (§3.1).
Filtering free choice (§4) #
In A or pex[◇(p ∨ q)] the homogeneity presupposition is satisfied in the second
disjunct's local context c ∧ ¬A, and free choice follows there.
A flat exh second disjunct has nothing to filter: its free-choice content is
assertive and stays inside the disjunct (§4.1).
Free choice under quantifiers (§5) #
(62): universal projection of homogeneity and the universal assertion give universal free choice.
(63): with a negated existential assertion, universal negative free choice.
(75): with an existential assertion, existential free choice.
(76a): under exactly one, the witness has free choice and every other student double prohibition.
(77a): under exactly one … can't, the witness has double prohibition and every other student free choice.