First-Order Connexivity for Classical Logic: Quantifiers, Empty Domains, and Existential Commitments

Connexive logics are typically understood as contra-classical: in order to validate the Aristotelian and Boethian theses, one gives up core principles of classical logic. Fiore has challenged this picture by introducing a metalevel relation of antisoundness and arguing that, at the propositional level, classical logic already satisfies suitable reinterpretations of the connexive theses without any change to its language, proof theory, or model theory. In this paper we extend Fiore's approach to first-order classical logic and study how it interacts with quantifiers. Our main result, the Existence Theorem, shows that a natural family of quantifier-level connexive patterns holds if and only if all models have non-empty domains. Thus first-order connexivity, in Fiore's sense, comes with a substantive existential commitment. We further isolate several quantifier-level connexive schemes already implicit in classical first-order logic and use them to articulate a tension between modern, empty-domain-friendly semantics and an Aristotelian reading of quantification.