On the Essence and Identity of Numbers



Published 12-11-2015
Mario Gómez-Torrente


Taking as premises some intuitions about the essences of natural numbers, pluralities and sets, the paper offers an argument that the natural numbers could not be the "Zermelo numbers", the "Von Neumann numbers", the "Kripke numbers", or the "positions in the ω-structure", among other things. The argument's conclusion is thus Benacerrafian in form, but it is emphasized that the argument is anti-Benacerrafian in substance, as it is perfectly compatible and in fact congenial with some views on which the numbers could be things of certain other kinds.

How to Cite

Gómez-Torrente, M. (2015). On the Essence and Identity of Numbers. THEORIA. An International Journal for Theory, History and Foundations of Science, 30(3), 317–329. https://doi.org/10.1387/theoria.14099
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Arithmetic, Ontology, Benacerraf