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MENDEZ PINTO, Emilio. Detractors of Descartes, as well as of Frege? Critical Notes to “The Nature of Mathematical Entities. Descartes and His Detractors: Gassendi and Mersenne”. Diánoia [online]. 2021, vol.66, n.86, pp.129-144.  Epub Oct 11, 2021. ISSN 0185-2450.

In this discussion I present objections to the following theses in Velázquez 2020: 1) that both Descartes and Frege maintain that arithmetic entities are irreducible to empirical processes; 2) that, in the case of Descartes, these entities are “perennial, inherent to the very constitution and functioning of the mind”, and 3) that Frege contested Mill’s mathematical (arithmetic) philosophy for being psychologistic. I argue that the second thesis is not, per se, controversial, but that it is controversial in the context of Velázquez’s article.

Keywords : psychologism; logicism; Mill; philosophy of mathematics; philosophy of logic.

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