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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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    check out husserl, just recently a book fell into my hand, that was mainly about the ontology of numbers. so, the difference between cardinal numbers, ordinal numbers. onfortunately I don't remember the title at the moment.
    – Anton Harald
    Commented Mar 28, 2016 at 10:03
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    @AntonHarald, thank you for this direction; if you (or anyone else) get to remember the precise name of the relevant text of Husserl or of any other philosopher, it would be helpful.
    – L.M. Student
    Commented Apr 1, 2016 at 7:28
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    I found the text now, however here it is in german: freidok.uni-freiburg.de/fedora/objects/freidok:6159/datastreams/… English wiki page about the book: en.wikipedia.org/wiki/Philosophy_of_Arithmetic
    – Anton Harald
    Commented Apr 1, 2016 at 12:49

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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
    Commented Apr 1, 2016 at 8:37
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    @L.M.Student Try Frege's 'The Foundations of Arithmetic'
    – E...
    Commented Apr 1, 2016 at 8:59

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