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I have interest in ontology of numbers. I know that the two main schools of thought regarding the metaphysical status of numbers are mathematical Platonism and mathematical Nominalism. But I wonder - What other schools of thought address the question of the ontology of Numbers? And, where may I find concise but yet profound introduction to this subject?

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Here is a very good SEP entry that covers a lot of ground regarding the subject in a clear and informative manner: Platonism in the Philosophy of Mathematics. (It has 'Platonism' in the title but gives you a good idea about opposing views as well).

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    Thank you for this reference. It does indeed cover some ground of the subject. Nonetheless, am still looking for a philosophical review or introduction which focuses directly on ontology of numbers. Thank you again. – L.M. Student Apr 1 '16 at 8:37
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    @L.M.Student Try Frege's 'The Foundations of Arithmetic' – Eliran Apr 1 '16 at 8:59

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