On the Essence and Identity of Numbers

Gómez-Torrente, Mario ^[1]
1. [1] Universidad Nacional Autónoma de México
  
  Universidad Nacional Autónoma de México
  
  México
Localización: Theoria: an international journal for theory, history and foundations of science, ISSN 0495-4548, Vol. 30, Nº 3, 2015 (Ejemplar dedicado a: History and Philosophy of Logic and Mathematics), págs. 317-329
Idioma: inglés
Enlaces
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Resumen
- 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.