The Grounds of Quantified Sentences: A Bolzanian Solution to the Paradoxes of Grounding

The Explanatory Inference Seminar is happy to announce its second session of the academic year, which will take place on 03/12/21, in Salle Ladrière, from 2 to 4 pm and on line (YouTube live).

The speaker will be Francesco Genco (IHPST, Paris) and his talk is entitled: The Grounds of Quantified Sentences: A Bolzanian Solution to the Paradoxes of Grounding (see the abstract below).

Abstract :

The notion of grounding is usually conceived as an objective and explanatory relation. It connects two relata if one—the ground—determines or explains the other—the consequence. In the contemporary literature on grounding, much effort has been devoted to logically characterise the formal aspects of grounding, but a major hard problem remains: defining suitable grounding principles for universal and existential formulae. Indeed, several grounding principles for quantified formulae have been proposed, but all of them are exposed to paradoxes in some very natural contexts of application. We introduce in this paper a first-order formal system that captures the notion of grounding and avoids the paradoxes in a novel and non-trivial way. The system we present formally develops Bolzano’s ideas on grounding by employing Hilbert’s ε-terms and an adapted version of Fine’s theory of arbitrary objects.