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PURE LOGIC OF ITERATED FULL GROUND

Published online by Cambridge University Press:  13 July 2018

JON ERLING LITLAND
JON ERLING LITLAND*
Affiliation:
Department of Philosophy, University of Texas at Austin
*
*DEPARTMENT OF PHILOSOPHY UNIVERSITY OF TEXAS AT AUSTIN STOP C3500 TX 78712, AUSTIN E-mail: [email protected]
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Abstract

This article develops the Pure Logic of Iterated Full Ground (plifg), a logic of ground that can deal with claims of the form “ϕ grounds that (ψ grounds θ)”—what we call iterated grounding claims. The core idea is that some truths Γ ground a truth ϕ when there is an explanatory argument (of a certain sort) from premisses Γ to conclusion ϕ. By developing a deductive system that distinguishes between explanatory and nonexplanatory arguments we can give introduction rules for operators for factive and nonfactive full ground, as well as for a propositional “identity” connective. Elimination rules are then found by using a proof-theoretic inversion principle.

Keywords

03A0503F99grounditerated groundexplanationlogic of groundinversion principlenatural deduction
Type
Research Article
Information
The Review of Symbolic Logic , Volume 11 , Issue 3 , September 2018 , pp. 411 - 435
Copyright
Copyright © Association for Symbolic Logic 2018 

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