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.
Highlights
Partial ground is the relation of one truth holding either wholly or partially in virtue of another [13, 15].1 To illustrate the concept, consider a couple of paradigmatic examples: J
Once we’ve formulated the usually accepted principles of partial ground using a ground predicate, we can bring out the truth-theoretic commitments of theories of partial ground, in the sense that we can show that the resulting theory of partial ground is a conservative extension of the well-known theory P T of positive truth [16, p. 116–22]
We will show in this paper that if we formulate the usually accepted principles for partial ground using a ground predicate, the resulting theory turns out to be a conservative extension of the well-known theory of positive truth [16, p. 116–22]
Summary
Partial ground is the relation of one truth holding either wholly or partially in virtue of another [13, 15].1 To illustrate the concept, consider a couple of paradigmatic examples: 1For (opinionated) introductions to the concept(s) of ground, see [7, 13]. Partial ground is the relation of one truth holding either wholly or partially in virtue of another [13, 15].1. Most research focuses on the notion of full ground: the relation of one thing holding wholly in virtue of a possibly plurality of other truths [13, p. The main novelty of the paper is that we will use a ground predicate rather than an operator to formalize partial ground. This approach to formalizing partial ground has several philosophical benefits, which we will outline in more detail . The predicate approach will allow us to connect theories of partial ground with axiomatic theories of truth. Once we’ve formulated the usually accepted principles of partial ground using a ground predicate, we can bring out the truth-theoretic commitments of theories of partial ground, in the sense that we can show that the resulting theory of partial ground is a conservative extension of the well-known theory P T of positive truth [16, p. 116–22]
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