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Revista de filosofía

On-line version ISSN 0718-4360

Abstract

QUEZADA, Wilfredo. Philosophy of mathematics and the cognitive basis of the large cardinals theory. Rev. filos. [online]. 2017, vol.73, pp.281-297. ISSN 0718-4360.  http://dx.doi.org/10.4067/S0718-43602017000100281.

In this paper we examine in first place some philosophical implications of P. Maddy’s mathematical naturalism as a philosophical account which allows us to overcome the drawbacks associated to both fictionalism and physicalistic realism in philosophy of mathematics. Besides that, the main virtue of that account seems to lie in the solution it provides to the applicability of mathematics problem when rejecting both the indispensability thesis and confirmative holism postulated by Quine. In second place, on the basis of difficulties intrinsic to Maddy’s philosophical program, we explore a better motivated naturalistic option -the embodied cognition approach- and suggest that it allows to adequately explain why most of set-theory specialists use to postulate the existence of some large cardinals, in particular, non-constructible sets.

Keywords : mathematical naturalism; set theory; large cardinals; constructible set; embodied cognition..

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