Journal of Philosophical Logic:1-24 (forthcoming)

Authors
Zachary Goodsell
University of Southern California
Abstract
Orthodoxy holds that there is a determinate fact of the matter about every arithmetical claim. Little argument has been supplied in favour of orthodoxy, and work of Field, Warren and Waxman, and others suggests that the presumption in its favour is unjustified. This paper supports orthodoxy by establishing the determinacy of arithmetic in a well-motivated modal plural logic. Recasting this result in higher-order logic reveals that even the nominalist who thinks that there are only finitely many things should think that there is some sense in which arithmetic is true and determinate.
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DOI 10.1007/s10992-021-09613-9
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References found in this work BETA

Philosophy of Logic.W. V. O. Quine - 1970 - Harvard University Press.
On the Plurality of Worlds.David Lewis - 1986 - Revue Philosophique de la France Et de l'Etranger 178 (3):388-390.
Putnam’s Paradox.David Lewis - 1984 - Australasian Journal of Philosophy 62 (3):221 – 236.
Can There Be Vague Objects?Gareth Evans - 1978 - Analysis 38 (4):208.

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