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Axiomatic Theories of Partial Ground II. Partial Ground and Typed Truth

Project: Predicational GroundPublished Article
Johannes Korbmacher
Journal of Philosophical Logic
Publication year: 2017

Abstract. This is part two of a two-part paper, in which we develop an axiomatic theory of the relation of partial ground. The main novelty of the paper is the of use of a binary ground predicate rather than an operator to formalize ground. This allows me to connect theories of partial ground with axiomatic theories of truth. In this part of the paper, we extend the base theory from the first part of the paper with hierarchically typed truth-predicates and principles about the interaction of partial ground and truth. We show that our theory is a proof-theoretically conservative extension of the ramified theory of positive truth up to epsilon-naught and thus is consistent. We argue that this theory provides a natural solution to Fine’s “puzzle of ground” about the interaction of truth and ground. Finally, we show that if we drop the typing of our truth-predicate, we run into similar paradoxes as in the case of truth: we get ground-theoretical paradoxes of self-reference.

Axiomatic Theories of Partial Ground I. The Base Theory

Project: Predicational GroundPublished Article
Johannes Korbmacher
Journal of Philosophical Logic
Publication year: 2017

Abstract. This is part one of a two-part paper, in which we develop an axiomatic theory of the relation of partial ground. The main novelty of the paper is the of use of a binary ground predicate rather than an operator to formalize ground. This allows us to connect theories of partial ground with axiomatic theories of truth. In this part of the paper, we develop an axiomatization of the relation of partial ground over the truths of arithmetic and show that the theory is a proof-theoretically conservative extension of the theory $PT$ of positive truth. We construct models for the theory and draw some conclusions for the semantics of conceptualist ground.

Yet Another Puzzle of Ground

Project: Predicational GroundPublished Article
Johannes Korbmacher
In: Kriterion. A Journal of Philosophy 29(2): 1–10.
Publication year: 2015

Abstract. We show that any predicational theory of partial ground that extends a standard theory of syntax and that proves some commonly accepted principles for partial ground is inconsistent. We suggest a way to obtain a consistent predicational theory of ground.