Speaker: Lorenzo Pinton (MIT)
Title: Exclusive disjunction in bilateral logic: Hurford Disjunctions as evidence for split connectives in natural language
Time: Wednesday, March 20th, 1pm – 2pm
Location: 32-D461
Abstract: “Disjoint Hurford Disjunctions” (DHD; Amir Anvari, p.c.) are a novel class of examples of deviant disjunctions that resemble Standard Hurford Disjunctions (SHD; Hurford, 1974), but don’t present any classical entailment (or overlap) relation between the two disjuncts:
(1) SHD: # John lives in Paris, or he lives in France.
(after Hurford, 1974)
(2) DHD: # John lives in Paris and he’s married, or he lives in France and he’s single.
(Amir Anvari, p.c.))
In order to unify (1) and (2) under the ‘Hurford disjunction’ label, we have to make certain assumptions about how conjunction and disjunction work, and examples like (2) might therefore be particularly revealing of what type of logic is at play in language and reasoning. In this talk I will extend Bilateral State-based Modal Logic (BSML) from Aloni (2022) with an exclusive disjunction (ED). ED will be “classically” defined as supporting the disjunction of its disjuncts and rejecting their conjunction. Crucially, in BSML, supported disjuncts and rejected conjuncts are defined in a split way, and have therefore an ‘independent life’ from one another (for instance, to reject (A ⋀ B) you need to be able to reject A and B independently). I will claim that ED – implemented in a system that rules out zero models by default (i.e. BSML* from Aloni, 2022) – is a better predictor of assertability conditions of disjunction in natural language compared to both the classical logic and the standard BSML definitions of disjunction. First, equipping BSML* with ED provides a unified and direct semantic explanation to both standard Hurford Disjunctions and “Disjoint Hurford Disjunctions”. Second, ED yields the correct ‘uniqueness’ interpretation for sentences with multiple disjuncts, which has been a major challenge for past proposals of natural language disjunction as inherently exclusive. I will conclude the talk with possible challenges to the present system by showing that (i) conjunctions are not always split and we need a device to capture these cases (possibly along the lines of subject matter, from Truthmaker semantics (Fine, 2017)) and that (ii) assuming ED as the standard meaning for disjunction actually clashes with some results in Aloni (2022) (wide scope free choice) and Degano et al. (2023) (absence of exclusivity in production tasks). Time permitting, I will briefly sketch in-progress solutions to solve the conflicts.