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 characterize 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.
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We would like to thank the anonymous referees for their helpful comments and suggestions. Moreover, F. Poggiolesi would like to thank Nissim Francez for intense and useful discussions.
Open Access funding enabled and organized by Projekt DEAL. Funded by the IBS project (ANR-18-CE27-0012-01) hosted by IHPST, UMR 8590
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Genco, F.A., Poggiolesi, F. & Rossi, L. Grounding, Quantifiers, and Paradoxes. J Philos Logic 50, 1417–1448 (2021). https://doi.org/10.1007/s10992-021-09604-w
- Epsilon calculus
- Arbitrary objects
- Bernard Bolzano