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On the Schwartzkopff-Rosen Principle

  • Ciro De FlorioEmail author
  • Luca Zanetti


Hume’s Principle (HP) 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 (SR 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 (strictly, fully, and immediately) grounded by the fact that F and G can be paired one-to-one (Rosen 2010, 117; Schwartzkopff Grazer Philosophische Studien, 82(1), 353–373, 2011, 362). HP is central to the neo-logicist program in the philosophy of mathematics (Wright 1983; Hale and Wright 2001); in this paper we submit that, even if the neo-logicists wish to venture into the metaphysics of grounding, they can avoid the SR Principle. In Section 1 we introduce neo-logicism. In Sections 2 and 3 we examine the SR Principle. We then formulate an account of arithmetical facts which does not rest on the SR Principle; we finally argue that the neo-logicists should avoid the SR Principle in favour of this alternative proposal.


Hume’s Principle Neo-logicism Grounding Schwartzkopff-Rosen Principle Aristotelianism 



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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of PhilosophyCatholic University of the Sacred HeartMilanItaly
  2. 2.Department of Humanities and Life SciencesScuola Universitaria Superiore IUSS PaviaPaviaItaly

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