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Platonism, Naturalism, and Mathematical Knowledge by James Robert Brown

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6    Semi-Naturalists and Reluctant Realists

Two characteristics of Platonism are paramount. The ontological ingredient is the claim that mathematical entities exist outside of space and time, independently from us, and mathematical statements are true (or false) in virtue of how things are. This is the realist part of Platonism. The epistemological ingredient is the claim that we can perceive or intuit these mathematical entities (at least some of them), and thereby come to know their properties. There are other sources of knowledge, as well, but intuition is the one that sets Platonism apart from other forms of realism. A semi-naturalist (as I shall use the term here) is someone who accepts Platonism's ontological ingredient, but rejects ...

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