@ACB,

ACB;85321 wrote:Isn't this just playing with words? Does the question of whether numbers 'exist' have any substance, or is it merely a matter of personal attitude? How could the question ever be satisfactorily resolved, and is it even meaningful? Does anything important depend on it? Ultimately, does it matter?

You ask me if something matters, and i don` t really know what answers would satisfy you. It seems that it does matter to you, because you take the time to reply.

The tradition of metaphysics has been trying to find a "logical" metaphysics that gives us a answer to "What does the symbols i am seeing mean on a 2-d surface ?". One solution is to take serious what "logic" say. That is, convert every statement to it` s logical form, and see what happens. In mathematics, the logical form suggest that the soluton to equations( say P(x)=0) is bounded to some sets. How does one make sense of solutions if they don` t mean anything, or that they are a product of the mind? What is at stack is the objectivity of mathematics.

If you want an objective mathematics, you are bounded to see the domain of quantification as real as the rocks on a sea shore.

---------- Post added 08-25-2009 at 11:19 PM ----------
Aedes;85365 wrote:The CONCEPT exists. That's different than saying the NUMBER exists.

The abstract notions of 1 and 2 denote concepts, and their properties are tautological:

2 is twice 1

1 is half 2

Then you have a different sense of what "exists" than I do.

philosophers try to make things more obvious, and saying that numbers are concepts are not more clear than to say numbers exist. What is a concept of? Is it a concept in your mind, or mine?

Now, to understand why so many philosophers, and mathematicians are glue to platonism. Take the following simple case.

For the equation f(x)=0. We ask what makes it true. The usually aswer is to say that there exist a set A such that each number in A is a solution to f(x)=0. A has to be objective for the purpose of math. Each element in A satisfy certain properties. It is easy to think that A exist, and each element in A exist. By "exist", i mean they exist as "abstract objects", technically specking.