The nature of mathematical objects

In Bonnie Gold & Roger Simons (eds.), Proof and Other Dilemmas: Mathematics and Philosophy. Mathematical Association of America. pp. 205--219 (2008)
Abstract
On the face of it, platonism seems very far removed from the scientific world view that dominates our age. Nevertheless many philosophers and mathematicians believe that modern mathematics requires some form of platonism. The defense of mathematical platonism that is both most direct and has been most influential in the analytic tradition in philosophy derives from the German logician-philosopher Gottlob Frege (1848-1925).2 I will therefore refer to it as Frege’s argument. This argument is part of the background of any contemporary discussion of mathematical platonism.
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Husserl and the Problem of Abstract Objects.George Duke & Peter Woelert - 2016 - Pacific Philosophical Quarterly 97 (1):27-47.
On What There is—Infinitesimals and the Nature of Numbers.Jens Erik Fenstad - 2015 - Inquiry : An Interdisciplinary Journal of Philosophy 58 (1):57-79.
The Syntactic Priority Thesis and Ontological Disputes.George Duke - 2012 - Canadian Journal of Philosophy 42 (2):149-164.

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