# Do numbers exist?

vectorcube

Tue 25 Aug, 2009 10:02 pm
@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.

aimee phil

Wed 26 Aug, 2009 03:20 am
@vectorcube,
how can numbers 'exist in my opinion they dont at all, numbers are a device we have created so as we can measure things

jeeprs

Wed 26 Aug, 2009 03:28 pm
@vectorcube,
yes but they are the same for everyone and are not dependent on an individual's understanding of them. So they are different to, say, words.

Aedes

Wed 26 Aug, 2009 06:51 pm
@vectorcube,
vectorcube;85703 wrote:
Is it a concept in your mind, or mine?
It's a concept shared with communicative sufficiency. Language is the common denominator of shared concepts.

vectorcube;85703 wrote:
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.
And I'd say it's true because we've defined its terms and relationships as such. The statement 1 + 1 = 2 also requires a concept of + and a concept of =, not just the "existence" of 1 and 2. Does that mean that + and = "exist" as well?

vectorcube

Thu 27 Aug, 2009 10:41 pm
@Aedes,
Aedes;85889 wrote:
It's a concept shared with communicative sufficiency. Language is the common denominator of shared concepts.

And I'd say it's true because we've defined its terms and relationships as such. The statement 1 + 1 = 2 also requires a concept of + and a concept of =, not just the "existence" of 1 and 2. Does that mean that + and = "exist" as well?

I really don ` t know if + is exist, or not. So, i leave it to some other experb.