Operators or restrictors? A reply to Gillies

Semantics and Pragmatics 4:1-25 (2011)
According to operator theories, "if" denotes a two-place operator. According to restrictor theories, "if" doesn't contribute an operator of its own but instead merely restricts the domain of some co-occurring quantifier. The standard arguments (Lewis 1975, Kratzer 1986) for restrictor theories have it that operator theories (but not restrictor theories) struggle to predict the truth conditions of quantified conditionals like (1) a. If John didn't work at home, he usually worked in his office. b. If John didn't work at home, he must have worked in his office. Gillies (2010) offers a context-shifty conditional operator theory that predicts the right truth conditions for epistemically modalized conditionals like (1b), thus undercutting one standard argument for restrictor theories. I explore how we might generalize Gillies' theory to adverbially quantified conditionals like (1a) and deontic conditionals, and argue that a natural generalization of Gillies' theory -- following his strategy for handling epistemically modalized conditionals -- won't work for these other conditionals because a crucial assumption that epistemic modal bases are closed (used to neutralize the epistemic quantification contributed by "if") doesn't have plausible analogs in these other domains.
Keywords philosophy of language  conditionals  modals  semantics  adverbs of quantification
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Daniel Rothschild (2015). Conditionals and Propositions in Semantics. Journal of Philosophical Logic 44 (6):781-791.

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