The nature of number

[jonb]

Is there an accepted standard definition of what a number is?
Do you think it could be defined within maths or does it have to be externally evaluated?

Here you go. Knock yourself out.

http://plato.stanford.edu/search/searche...ery=number

Yes you see this is my problem. I am not a mathematician, I am an artist and thus am trained to look. The idea that the number is a fixed point does not seem consistent with the results I am getting from my geometry. Also Russell's Paradox, it seems to me would naturally arise when both the observer and the observed are within the same system, in this case maths. As an artist I know to observe the nature of a thing I must be to some extent external. As such to understand the nature of number I would have to have an external tool which is not affected by the number.
In short I feel mathematical proofs of number cannot provide a definition of what number is.
Am I barking, or do you think there could be a scintilla of logic in my position?