Limited Symmetry in quantified sentences #
Kalomoiros states Limited Symmetry for the propositional fragment. Schlenker's comments on it apply the constraint to quantified sentences, and the case studies accompanying Chemla, Spector, Kalomoiros and Schlenker's Co-Linguistics paper derive the predictions by machine for more quantifiers. Neither result is published, so this file records them as theory under development.
A trigger in the restrictor of (Q _ . R) is followed by two parsing points: the end of the
restrictor, where every scope is a good final, and the end of the sentence, where the only good
final is the sentence itself. Limited Symmetry requires the presupposition to be stably
transparent at both (RestrictorLS). It is therefore implied by incremental Transparency, which
consults every scope at once, and it implies symmetric Transparency, which consults the sentence
alone. With the restrictor negated, (Q not _ . R), both Transparencies are unchanged, since
transparency is invariant under negating the gap (Presupposition.transparent_image_compl_iff).
In the restrictor's own position Limited Symmetry coincides with incremental Transparency for
every quantifier whose first row is not constant: both require every individual to satisfy the
presupposition (restrictorLS_iff). In a negated restrictor it coincides with symmetric
Transparency for every quantifier constant on no row above the first, since a nonempty negated
restriction is then never stable at the end of the restrictor (restrictorLS_neg_iff). For
some, no and every this is the summary table of Schlenker's comments
(some_table, no_table, every_table): local negation is where Limited Symmetry regains the
symmetric predictions, and where it departs from incremental Transparency.
The constraint extends to a trigger anywhere in a quantified clause as Kalomoiros's constraint on
the clause's occurrences (Kalomoiros2023.LimitedSymmetry, QuantifiedClause.occurrences). The
parsing points after the trigger are those of the string of the argument that holds it, each
followed by every good final of the clause, and then the end of the sentence
(QuantifiedClause.Env.continuations). For a trigger that is the restrictor, or its negation, these
are the two parsing points above (limitedSymmetry_trigger_iff, limitedSymmetry_not_trigger_iff).
With Kalomoiros's constraint on formulas, this makes a theory that Eval scores like a registered
account (limitedSymmetry). It is right on every tested cell of Chemla and Schlenker's inferential
experiments, and on Chemla's first experiment it shares Transparency's verdicts: wrong with every
presupposition accommodated in the context, right by Chemla's stipulations and by his one-step rule
(verdict_chemla2009a).
Main statements #
restrictorLS_iff,restrictorLS_neg_iff: in a restrictor Limited Symmetry is incremental Transparency, in a negated restrictor symmetric Transparency.some_table,no_table,every_table: the predictions for some, no and every.verdict_chemlaSchlenker2012,verdict_chemla2009a: the verdicts on the recorded experiments.
Implementation notes #
- Provenance. The table's predictions are Schlenker's, derived by hand. The case studies of the Co-Linguistics paper report them confirmed by machine for these and further quantifiers, and state the relations between the theories as theorems for the quantifiers they consider. Here the two coincidences are proved for every quantifier on van Benthem's tree whose rows satisfy the stated non-constancy conditions.
- The domain is a finite type, the same at every world, and the gap of a restrictor denotes a set
of world–individual pairs, as in
Presupposition.restrictorTruth. - The constraint on quantified clauses is this file's generalization of the two parsing points of Schlenker's comments, checked against them for the triggers those comments consider.
References #
The truth set of (Q not _ . R) as a function of the denotation of the negated restrictor.
Equations
Instances For
Limited Symmetry for a trigger in a restrictor, with r R the truth set of the sentence as a
function of the restrictor when the scope is R. The presupposition is stably transparent at the
end of the restrictor, where every scope is a good final, and at the end of the sentence, where
the only good final is the sentence itself.
Equations
- Lab.Colinguistics.RestrictorLS r R C π = (Presupposition.StablyTransparent C (Set.range r) π ∧ Presupposition.StablyTransparent C {r R} π)
Instances For
Between the two Transparencies #
Incremental Transparency implies Limited Symmetry, as Schlenker's comments observe.
Limited Symmetry implies symmetric Transparency.
Negating the restrictor leaves incremental Transparency unchanged.
Negating the restrictor leaves symmetric Transparency unchanged.
Stability of a restrictor #
In a restrictor, incremental Transparency requires every individual to satisfy the presupposition, for a quantifier whose first row is not constant.
In a restrictor, Limited Symmetry coincides with incremental Transparency, for a quantifier whose first row is not constant: both require every individual to satisfy the presupposition.
In a negated restrictor, Limited Symmetry coincides with symmetric Transparency, for a quantifier constant on no row above the first: a negated restriction with an individual is then stable at the end of the restrictor for no truth value, so that check is vacuous.
Some, no and every #
With the scope R, symmetric Transparency for a trigger in the restrictor of some requires
every individual in the scope to satisfy the presupposition.
With the scope R, symmetric Transparency for a trigger in the restrictor of no requires
every individual in the scope to satisfy the presupposition.
With the scope R, symmetric Transparency for a trigger in the restrictor of every requires
every individual outside the scope to satisfy the presupposition.
With the trigger in the restrictor of some, incremental Transparency and Limited Symmetry require everything to satisfy the presupposition and symmetric Transparency every individual in the scope; with the restrictor negated, Limited Symmetry falls with symmetric Transparency.
No makes the same predictions as some.
Every makes the predictions of some, except that symmetric Transparency, and with the restrictor negated Limited Symmetry, require every individual outside the scope to satisfy the presupposition.
In a negated restrictor of some, the theories make a crucial prediction. A context where every individual in the scope satisfies the presupposition but another individual does not is accepted by Limited Symmetry and rejected by incremental Transparency. No experiment recorded in the library tests a negated restrictor; Chemla's restrictor items are positive.
Quantified clauses #
A trigger that is the restrictor has the two parsing points of RestrictorLS.
A trigger that is the negated restrictor has the two parsing points of RestrictorLS for the
negated restrictor.
Scoring #
Limited Symmetry as a theory to score: Kalomoiros's constraint on formulas, and the constraint at the parsing points of each argument on quantified clauses.
Equations
- One or more equations did not get rendered due to their size.
Instances For
On Chemla and Schlenker's inferential experiments, Limited Symmetry is right on every tested cell, as the registered account is.
On Chemla's first experiment, Limited Symmetry is wrong with every presupposition accommodated in the context, and right by §4.1.2's stipulations and by the one-step rule.