Where do numbers come from?

[K-mac]

A while ago i was studying for The GRE and i had a tutor. I asked him a question and i am not so sure i am satisfied with the answer.
Where do numbers come from? Not the symbols that are used to represent them, but the concept that math exists.
The answer i was given was that people are just hardwired to see that numbers are there. He tried to explain that some people believed that the reason we see them as well as equations and math/physics as true is because numbers fit nicely and help to explain things.

I call B.S. on his statements.
How is it that math came about?
Are we really just hardwired to believe those things?

Numbers are a numeric expression of our inherent logical minds. It is my belief that this is because we were created with rational and logical minds by a rational and logical creator.

[Piz0wn0reD!!!!!!]

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Numbers are a numeric expression of our inherent logical minds. It is my belief that this is because we were created with rational and logical minds by a rational and logical creator.

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how irational...

[Piers]

Numbers only exist as part of a model.

Models that include the natural numbers have a tendency to be more useful for practical applications than models that don’t.

Numbers are macroscopic concepts that we find helpful to use; their existence does not extend beyond their usefulness.

References:

http://en.wikipedia.org/wiki/Natural_number
http://en.wikipedia.org/wiki/Numeral
http://en.wikipedia.org/wiki/Number

[K-mac]

So could concepts in the physical world be explained without numbers?

[mosquito]

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So could concepts in the physical world be explained without numbers?

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Anything can be explained in anumber of ways. Whether description without numbers would have the accuracy you desire is the question. Words, motions, pictures all describe without numbers.

[K-mac]

I mean things along the lines of the theory of relativity, or things in the world of quantum mechanics. There is something i a trying to get at but i cant.
Part of the question deals with the idea that physics would not exist, or be proven/unproven without math, or some type of functional mathematics. Is it possible for the branch of science known as physics to exist.
Now i know that all of the concepts would still be there, but would one be able to prove them without things like math.
Was math 'invented' as a way to prove some things, or is it just there?

[David Sklansky]

It is my understanding that the question you are asking is deep and unsolved to this day. Mathmeticians who believe numbers exist outside of our minds are, I believe, called Platonists. Otherwise, I believe they are called formalists.

Along the same lines:

There are indigenous tribes in the rain forest who have no discernment between the colors yellow and green. Everything is in a stage of becoming the other, and they don't see it as a true difference in color, only difference in the stage of its life.

Numbers were necessary to make a logical order of things. Without numbers, could we have a functional society? I completely doubt it, because we would cease to be functional as a group. Even if there aren't named numbers, there is still a concept of them. When a tribe divides its kill, it separates it into what the group feels fair. There is a quantifiable fraction that everyone is entitled to. Whether it's a concept of this or is explicit, it exists.

[malorum]

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It is my understanding that the question you are asking is deep and unsolved to this day.

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Not sure what you mean by 'deep' or 'unsolved', but yes there exists a debate.
For origins of the debate see Plato's Meno and the dialogue between Socrates and the slave boy.
In terms of the current definitions, I'm a formalist, I don't think we have any real evidence to the contrary.

[K-mac]

I now have some information regarding the origins of the debate, but where can i find info on the current debate?
Or more importantly what is a better guide for the current debate?

Thanks

[Good Friar]

Perhaps the best treatise on the subject is Frege's Grundlagen, which is a truly impressive work that addresses many different philosophies of mathematics. His basic approach, and one that is still fairly basic to our current use of number, etc, tries to reduce the idea of natural number to that of logic, that is, we know the difference between existence and non-existence, and hence the difference between 0 and 1. Likewise, we can differentiate two concepts/objects/ideas, by notice the existence of two non-equal things and so on. There are problems involving the Russell paradox in his formal approach, but you'd still probably find it at least a satisfying approach.

[Trantor]

[ QUOTE ]
Along the same lines:

There are indigenous tribes in the rain forest who have no discernment between the colors yellow and green. Everything is in a stage of becoming the other, and they don't see it as a true difference in color, only difference in the stage of its life.

Numbers were necessary to make a logical order of things. Without numbers, could we have a functional society? I completely doubt it, because we would cease to be functional as a group. Even if there aren't named numbers, there is still a concept of them. When a tribe divides its kill, it separates it into what the group feels fair. There is a quantifiable fraction that everyone is entitled to. Whether it's a concept of this or is explicit, it exists.

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There is a tribe with a pefectly functional society in which the only number they have is "one". No two or any other so no "numbers" (plural)

[alimomoney]

Some cognitive development dudes say that humans have an inate mathematical sense that develops around ages 2-3. For example, small children quickly pick up on the concept of "more" and "less". As for the ideas of specific numbers, they had to develop when the concepts of some and many were not accurate enough for some task at hand.