Totality=Every; Dependence=Some; Choice=Any; Chance=A (Elia Zardini)

The Logic and Metaphysics Workshop will meet on May 2nd from 4:15-6:15 (NY time) in-person at the Graduate Center (Room 5382) for a talk by Elia Zardini (Madrid).

Title: Totality=Every; Dependence=Some; Choice=Any; Chance=A

Abstract: I’ll first propose an interpretation of the multiplicative/additive distinction among operators arising in a logical framework lacking the structural property of contraction (focusing mostly on the quantifiers): multiplicative operators represent interaction among their operands (with universal quantification representing totality and particular quantification representing dependence) whereas additive operators represent selection (with universal quantification representing choice and particular quantification representing chance). I’ll then argue that reflection on the behaviour of natural-language determiners points towards a very natural working hypothesis that associates: multiplicative universal affirmative with ‘every’; multiplicative particular affirmative with ‘some’; additive universal affirmative with ‘any’; additive particular affirmative with ‘a’. I’ll illustrate the fruitfulness of this hypothesis with four examples, from the epistemic, normative, attitudinal and stative domains respectively.

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