'If', 'Unless', and Quantification

In R. Stainton & C. Viger (eds.), Compositionality, Context, and Semantic Values (2008)

Sarah-Jane Leslie
Princeton University
Higginbotham argues that conditionals embedded under quantifiers constitute a counterexample to the thesis that natural language is semantically compositional. More recently, Higginbotham and von Fintel and Iatridou have suggested that compositionality can be upheld, but only if we assume the validity of the principle of Conditional Excluded Middle. I argue that these authors’ proposals deliver unsatisfactory results for conditionals that, at least intuitively, do not appear to obey Conditional Excluded Middle. Further, there is no natural way to extend their accounts to conditionals containing ‘unless’. I propose instead an account that takes both ‘if’ and ‘unless’ statements to restrict the quantifiers in whose scope they occur, while also contributing a covert modal element to the semantics. In providing this account, I also offer a semantics for unquantified statements containing ‘unless’
Keywords Compositionality  Quantification  Conditionals  Unless
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References found in this work BETA

Generalized Quantifiers and Natural Language.John Barwise & Robin Cooper - 1981 - Linguistics and Philosophy 4 (2):159--219.
Restrictions on Quantifier Domains.Kai von Fintel - 1994 - Dissertation, University of Massachusetts at Amherst
E-Type Pronouns and Donkey Anaphora.Irene Heim - 1990 - Linguistics and Philosophy 13 (2):137--77.
An Investigation of the Lumps of Thought.Angelika Kratzer - 1989 - Linguistics and Philosophy 12 (5):607 - 653.
Adverbs of Quantification.David K. Lewis - 1975 - In Edward L. Keenan (ed.), Formal Semantics of Natural Language. Cambridge University Press. pp. 178--188.

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Citations of this work BETA

Talking About Worlds.Matthew Mandelkern - 2018 - Philosophical Perspectives 32 (1):298-325.
Evidence Sensitivity in Weak Necessity Deontic Modals.Alex Silk - 2014 - Journal of Philosophical Logic 43 (4):691-723.
Counterfactuals and Propositional Contingentism.Peter Fritz & Jeremy Goodman - 2017 - Review of Symbolic Logic 10 (3):509-529.

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