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On Grounding Arithmetic

In Alessandro Giordani & Ciro de Florio (eds.), From Arithmetic to Metaphysics: A Path Through Philosophical Logic. De Gruyter. pp. 103-118 (2018)

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  1. On the Schwartzkopff-Rosen Principle.Ciro De Florio & Luca Zanetti - 2020 - Philosophia 48 (1):405-419.
    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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  • Identity criteria: an epistemic path to conceptual grounding.Massimiliano Carrara & Ciro De Florio - 2020 - Synthese 197 (7):3151-3169.
    Are identity criteria grounding principles? A prima facie answer to this question is positive. Specifically, two-level identity criteria can be taken as principles related to issues of identity among objects of a given kind compared with objects of a more basic kind. Moreover, they are grounding metaphysical principles of some objects with regard to others. In the first part of the paper we criticise this prima facie natural reading of identity criteria. This result does not mean that identity criteria could (...)
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