Philosophical Studies 159 (1):69-87 (2012)

Authors
Luca Incurvati
University of Amsterdam
Abstract
According to the iterative conception of set, sets can be arranged in a cumulative hierarchy divided into levels. But why should we think this to be the case? The standard answer in the philosophical literature is that sets are somehow constituted by their members. In the first part of the paper, I present a number of problems for this answer, paying special attention to the view that sets are metaphysically dependent upon their members. In the second part of the paper, I outline a different approach, which circumvents these problems by dispensing with the priority or dependence relation altogether. Along the way, I show how this approach enables the mathematical structuralist to defuse an objection recently raised against her view.
Keywords Iterative conception  Minimalism  Metaphysical dependence
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DOI 10.1007/s11098-010-9690-1
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References found in this work BETA

On What Grounds What.Jonathan Schaffer - 2009 - In David Manley, David J. Chalmers & Ryan Wasserman (eds.), Metametaphysics: New Essays on the Foundations of Ontology. Oxford University Press. pp. 347-383.
Essence and Modality.Kit Fine - 1994 - Philosophical Perspectives 8 (Logic and Language):1-16.
Truth.Paul Horwich - 1998 - Clarendon Press.
Mathematics as a Science of Patterns.Michael D. Resnik - 1997 - New York ;Oxford University Press.
Ontological Dependence.Tuomas E. Tahko & E. J. Lowe - 2020 - Stanford Encyclopedia of Philosophy.

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Citations of this work BETA

On How (Not) to Define Modality in Terms of Essence.Robert Michels - 2019 - Philosophical Studies 176 (4):1015-1033.
Truthmakers.Fraser MacBride - 2013 - Stanford Encyclopedia of Philosophy.
Prioritizing Platonism.Kelly Trogdon & Sam Cowling - 2019 - Philosophical Studies 176 (8):2029-2042.
The Deflationary Theory of Ontological Dependence.David Mark Kovacs - 2018 - Philosophical Quarterly 68 (272):481-502.
When Do Some Things Form a Set?Simon Hewitt - 2015 - Philosophia Mathematica 23 (3):311-337.

View all 12 citations / Add more citations

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