Type-free Predicational Theories of Ground

Abstract

The aim of this thesis is to extend predicational theories of metaphysical grounding. In the existing predicational theories of ground (Korbmacher 2018a, 2018b), the coding function is restricted such that the terms corresponding to sentences that contain the ground or the truth predicate cannot be arguments of the truth or ground predicates. In this thesis, I relax these restrictions. This makes the theories more expressive, but it also make possible to derive paradoxes of self referentiality for the ground predicate (Korbmacher 2015, 2018b), analogous to the Liar Paradox for the truth predicate, and predicational versions of Puzzles of Ground (Fine 2010, Kr¨amer 2013). In this thesis, I develop type-free theories of ground that avoid these paradoxes and puzzles. In section 1, I introduce the topic of metaphysical grounding, the operational and predicational approaches, the existing predicational theories, iterated ground and the paradoxes and puzzle previously mentioned. In section 2, I define the technical framework and notation I will use. In section 3, first, I develop a non-classical (K3) model for the ground and truth predicate in the style of Kripke fixed point semantics (Kripke 1975) that avoids the paradoxes of self-referentiality. Second, I develop an axiomatic theory for this model inspired by the Kripke-Feferman theory of truth. In section 4, first, I highlight the fact that, if some plausible principles about the interaction between the ground and truth predicate are added to the theories previously developed, they become inconsistent due to a version of Fine’s Puzzles of Ground (Fine 2010). Second, I develop a semantic model that avoids this inconsistency. In section 5, I draw some philosophical conclusions about the formal results of the previous two sections. I explain why a non-classical approach to the paradox of self-referentiality for the ground predicate is philosophically justified and interesting. I compare my solution to Fine’s puzzle with the solutions proposed by Fine ([2010, pp. 103-115]).