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Grounding and Auto-abstraction

Zanetti, Luca (2020) Grounding and Auto-abstraction. [Preprint]

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Abstract

Abstraction principles and grounding can be combined in a natural way (Rosen 2010, 117; Schwartzkopff 2011, 362]). However, some ground-theoretic abstraction principles entail that there are circles of partial ground (Donaldson 17, 793). I call this problem auto-abstraction. In this paper I sketch a solution. Sections 1 and 2 are introductory. In section 3 I start comparing different solutions to the problem. In section 4 I contend that the thesis that the right-hand side of an abstraction principle is (metaphysically) prior to its left-hand side motivates an independence constraint, and that this constraint leads to predicative restric- tions on the acceptable instances of ground-theoretic abstraction principles. In section 5 I argue that auto-abstraction is acceptable unless the left-hand side is essentially grounded by the right-hand side. In section 6 I highlight sev- eral parallelisms between auto-abstraction and the puzzles of ground. I finally compare my solution with the strategies listed in section 3.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Zanetti, Lucaluca.zanetti@iusspavia.it0000-0002-3733-9193
Additional Information: [forthcoming in Synthese]
Keywords: Abstraction Principles; Grounding; Auto-abstraction; Aristotelianism; Puzzles of Ground
Subjects: Specific Sciences > Mathematics > Foundations
Depositing User: Dr. Luca Zanetti
Date Deposited: 19 May 2020 20:49
Last Modified: 19 May 2020 20:49
Item ID: 17192
Subjects: Specific Sciences > Mathematics > Foundations
Date: 18 May 2020
URI: http://philsci-archive.pitt.edu/id/eprint/17192

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