Pure Logic of Many-Many Ground

Journal of Philosophical Logic 45 (5):531-577 (2016)
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Abstract

A logic of grounding where what is grounded can be a collection of truths is a “many-many” logic of ground. The idea that grounding might be irreducibly many-many has recently been suggested by Dasgupta. In this paper I present a range of novel philosophical and logical reasons for being interested in many-many logics of ground. I then show how Fine’s State-Space semantics for the Pure Logic of Ground can be extended to the many-many case, giving rise to the Pure Logic of Many-Many Ground. In the second, more technical, part of the paper, I do two things. First, I present an alternative formalization of plg; this allows us to simplify Fine’s completeness proof for plg. Second, I formalize plmmg using an infinitary sequent calculus and prove that this formalization is sound and complete.

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Jon Litland
University of Texas at Austin

Citations of this work

Grounding, Essence, And Identity.Fabrice Correia & Alexander Skiles - 2019 - Philosophy and Phenomenological Research 98 (3):642-670.
Fundamentality.Tuomas E. Tahko - 2023 - Stanford Encyclopedia of Philosophy.
Ground.Michael J. Raven - 2015 - Philosophy Compass 10 (5):322-333.
A Survey of Logical Realism.Tuomas E. Tahko - 2021 - Synthese 198 (5):4775-4790.

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References found in this work

Writing the Book of the World.Theodore Sider - 2011 - Oxford, England: Oxford University Press.
Guide to Ground.Kit Fine - 2012 - In Fabrice Correia & Benjamin Schnieder (eds.), Metaphysical Grounding. Cambridge University Press. pp. 37--80.
Grounding in the image of causation.Jonathan Schaffer - 2016 - Philosophical Studies 173 (1):49-100.
The question of realism.Kit Fine - 2001 - Philosophers' Imprint 1:1-30.
Is there a fundamental level?Jonathan Schaffer - 2003 - Noûs 37 (3):498–517.

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