The Foundations of Arithmetic?

Noûs 51 (4):775-801 (2017)
Authors
Tom Donaldson
Rutgers University - New Brunswick (PhD)
Abstract
Gideon Rosen and Robert Schwartzkopff have independently suggested (variants of) the following claim, which is a varian of Hume's Principle: When the number of Fs is identical to the number of Gs, this fact is grounded by the fact that there is a one-to-one correspondence between the Fs and Gs. My paper is a detailed critique of the proposal. I don't find any decisive refutation of the proposal. At the same time, it has some consequences which many will find objectionable.
Keywords Hume's principle  grounding  Gideon Rosen  Robert Schwartzkopff  logic of ground
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Reprint years 2017
DOI 10.1111/nous.12147
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Citations of this work BETA

Prioritizing Platonism.Kelly Trogdon & Sam Cowling - forthcoming - Philosophical Studies.
Fundamentality And Modal Freedom.Jennifer Wang - 2016 - Philosophical Perspectives 30 (1):397-418.
Emptying a Paradox of Ground.Jack Woods - 2018 - Journal of Philosophical Logic 47 (4):631-648.
Axiomatic Theories of Partial Ground II.Johannes Korbmacher - 2018 - Journal of Philosophical Logic 47 (2):193-226.

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