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The Foundations of Arithmetic?

Noûs 51 (4):775-801 (2017)

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  1. On the Schwartzkopff-Rosen Principle.Ciro De Florio & Luca Zanetti - forthcoming - Philosophia:1-15.
    Hume’s Principle states that the cardinal number of the concept F is identical with the cardinal number of G if and only if F and G can be put into one-to-one correspondence. The Schwartzkopff-Rosen Principle is a modification of HP in terms of metaphysical grounding: it states that if the number of F is identical with the number of G, then this identity is grounded by the fact that F and G can be paired one-to-one, 353–373, 2011, 362). HP is (...)
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  • Axiomatic Theories of Partial Ground II.Johannes Korbmacher - 2018 - Journal of Philosophical Logic 47 (2):193-226.
    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. In this part of the paper, we extend the base theory of 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 (...)
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  • Prioritizing Platonism.Kelly Trogdon & Sam Cowling - forthcoming - Philosophical Studies.
    Some see concrete foundationalism as providing the central task for sparse ontology, that of identifying which concreta ground other concreta but aren’t themselves grounded by concreta. There is, however, potentially much more to sparse ontology. The thesis of abstract foundationalism, if true, provides an additional task: identifying which abstracta ground other abstracta but aren’t themselves grounded by abstracta. We focus on two abstract foundationalist theses—abstract atomism and abstract monism—that correspond to the concrete foundationalist theses of priority atomism and priority monism. (...)
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  • Emptying a Paradox of Ground.Jack Woods - 2018 - Journal of Philosophical Logic 47 (4):631-648.
    Sometimes a fact can play a role in a grounding explanation, but the particular content of that fact make no difference to the explanation—any fact would do in its place. I call these facts vacuous grounds. I show that applying the distinction between-vacuous grounds allows us to give a principled solution to Kit Fine and Stephen Kramer’s paradox of ground. This paradox shows that on minimal assumptions about grounding and minimal assumptions about logic, we can show that grounding is reflexive, (...)
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  • Fundamentality And Modal Freedom.Jennifer Wang - 2016 - Philosophical Perspectives 30 (1):397-418.
    A fundamental entity is an entity that is ‘ontologically independent’; it does not depend on anything else for its existence or essence. It seems to follow that a fundamental entity is ‘modally free’ in some sense. This assumption, that fundamentality entails modal freedom (or ‘FEMF’ as I shall label the thesis), is used in the service of other arguments in metaphysics. But as I will argue, the road from fundamentality to modal freedom is not so straightforward. The defender of FEMF (...)
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