From logical and linguistic generics to Hilbert’s tau and epsilon quantifiers

International audienceWith our starting point being (universal) generics appearing in both nat- ural language and mathematical proofs, and were further conceptualised in philosophy of language, we introduce the tau subnector that maps a formula F to an individual term τx F such that F (τx F ) whenever ∀xF . We then in- troduce the dual subnector εxF which expresses the existential quantification since F(εxF) ≡ ∃xF, and describe its use for the semantics of indefinite and definite noun phrases. Some logical and linguistic properties of this intriguing way to express quantification are discussed — but the reader is referred to the article by Abrusci in this volume for the impact of epsilon on Hilbert’s work the logical foundations of mathematics