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Auteur: Alessandro ZUCCHI

Co-Auteur(s): Fabio DEL PRETE, CNRS Laboratory CLLE-ERSS, Toulouse, France

Monsters begat by quantifiers

Abstract/Résumé: It is standard practice in formal semantics to assume that context specifies, among other coordinates, an assignment of values to variables. Rabern (2012) argues that ordinary quantifiers are Kaplanian monsters, since, if variable assignments are coordinates of contexts, the clause for universally quantified formulae has form (1): (1) [every ν S]c,w,t = 1 iff [S]c',w,t = 1 for every c' that is like c except for the fact that c'g differs from cg at most for the value that c'g assigns to ν. For similar reasons, the lambda-operator would also qualify as a monster. If Rabern were right, monsters would be much more widespread in natural languages than one might think. However, although the evidence for having variable assignments as contextual coordinates is substantive, this does not show by itself that quantifiers are monsters. In Kaplan’s (1977) system, worlds and times are contextual coordinates, and modal operators and tenses require evaluating the sentence to which they apply relative to worlds and times different from those of the context. However, this does not qualify modal operators or tenses as monsters: worlds and times, besides being contextual coordinates, also belong to the circumstances of evaluation, and modal operators and tenses require us to evaluate sentences at different circumstances, not at different contexts. Suppose denotation is relative to a context (specifying a variable assignment cg) and to a circumstance of evaluation including an assignment g, a world, and a time. Then, quantifiers and lambdas require evaluating the formulae to which they apply with respect to assignments minimally differing from g, with no context shift (and no monster) involved. The question that needs to be settled to assess the monster status of quantifiers and lambdas is thus whether there is any reason to assume that variable assignments occur both as contextual coordinates and in the circumstances of evaluation. We argue that there are both conceptual and empirical reasons favoring the option of doubling variable assignments as contextual coordinates and as elements of the circumstances of evaluation.