Axiomatic Theories of Partial Ground I: The Base Theory

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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 P T of positive truth. We construct models for the theory and draw some conclusions for the semantics of conceptualist ground.
Original languageEnglish
Pages (from-to)161-191
JournalJournal of Philosophical Logic
Volume47
Issue number2
DOIs
Publication statusPublished - Apr 2018

Keywords

  • metaphysical grounding
  • axiomatic theories of truth
  • predicational theories of ground
  • positive truth

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