Sorry, that was poorly phrased. What I was interested in, is do you accept the reality of objects such as numbers that exist outside of space and time, or do you believe that any such apparent objects are really nominal constructions from actual, concrete occurences?
Personally, I feel driven to accept their existence, largely from considerations relating to the objectivity and necessity of mathematics, yet I can't help but feel they cause a bigger problem for materialism that is usually acknowledged - especially considering the comparative energy that is devoted to issues like the mind-body problem which I feel have more obvious solutions.
Numbers exist, but not as objects. I don't think numbers exist outside of mind; numbers of things exist, but the number itself is an abstraction created only through conceptualization, which is a mind-dependent process. Numbers are only as real as any other idea.
Thanks. That is kind of the view that I've always wanted to embrace, but - you don't worry that it risks making mathematics seem subjective? A lot of people historically have, like Frege for example.
I do think mathematics is all in our heads and is in that way subjective, but the truths therein are universal and are in no way subject to whims or personal fancies. If we agree on the terms, we will all independently come to the same conclusions (if we're doing it right!) even though the abstract objects we're dealing with exist only in our subjective consciousnesses. Subjective doesn't always have to mean arbitrary.
The numbers themselves, yes. They do not exist objectively, even though our understanding of them is gained through observation of discrete entities. So, mathematics -- knowledge concerning relationships between numbers -- is a subjective experience even if the laws therein are universal and absolute.