Where did I put those numbers?

The question is simple, do numbers exist independently of any human mind?  Put another way do we discover or invent mathematics? 

Also on a more important note it is written and spoken math.......s.  Afterall we british invented...er discovered...er conquered numbers!

without a mind to use numbers and use them in a productive way, numbers are just an abstrac idea.  in fact it still is, but with the laws and theories added to it there is some order to it

Yes, I think I have very good grounds for being a platonist here. 7 is a prime number, here on Earth, in our solar system, in our galaxy, in our whole universe in fact. 7 was not prime just when someone happened to understand it was so.

It should also make one suspicious of the "unreasonable effectiveness of mathematics". 1+1=2 not just 80% of the time, not just 95% of the time, but always, 100%. We may indeed have evolved an ability to use numbers, but why do we have to use something that works 100% of the time? We would have been quite as safe to calculate necessities for survival with something that works 90% of the time, or even 80% of the time. But 100% of the time?! I would say we came across something beyond us.

Just how much is one willing to accept in mathematics? To the Intuitionist, life is hard. There are no negative numbers floating around physically, neither is 0 probably existing in nature. Neither are there imaginary numbers, etc. Neither does pi or all other irrational numbers exist as a real physical entity either.

"without a mind to use numbers and use them in a productive way, numbers are just an abstrac idea."

How could they be an abstact idea if there wasn't a mind to use them, surely ideas only exist within a mind?  You are I assume not a realist regarding the existence of numbers, either am I.  However, many people are and indeed it seems the natural position of many people that numbers have an existence independent of our minds, this of course raises many philosophical questions.  I simply wish to have a debate and see what people think. 

See "What are You", I took a poll.

There is a philosophical school called realisme. Some of these realists believe that numbers, and all other mathematical abstractions, exist regardless of the human mind. They don't buy into the Copenhagen interpretation of QM either..

Hehe many people don't by into the Copenhagen Interpretation. I never claim to be for it or against it yet though. I don't believe I have your poll down yet?

I think it provides a nice first approximation for a description of the world at that level.. =)

I mean in terms of the philosophy of math, we're not doing quantum mechanics yet....

I think mathematics is just a way for humans to describe things. There may be a species out there that can understand quantity without assigning it to a number. For example, savants seems to be able to understand numbers to the point where computations are like knowing that mixing red and blue makes purple.

True, but that doesn't mean quantity doesn't exist just becuase some people use it. I don't think you were saying that, but I brought it up anyway. I do think mathematics is descriptive and like a language like you say.

Aren't those really two different questions?

Does the first question require the word "human"?  Isn't the real issue whether numbers exist independently of mind, period?  There is some evidence that certain other species possess an innate ability distinguish between different (small) quantities of objects.  And certainly we can imagine an intelligent alien race (who hasn't?) that would use numbers even if mankind were to go extinct.

The second question seems different to me in that even if we grant that without mind there is no such concept as "number" the universe continues to obey mathematical laws.  Ergo, such laws would await 'discovery' when and if a mind comes into being to discover them.  

What eternal said about certain animals.  Determining large from small doesn't mean that animals have the ability to understand numbers.  I think the same way that Val has described it, in that we use (discovered numbers in order to explain what we have though of as confusing.  Another example of that is religion.  Believe in it or not (I do) the point is that they are made to explain what we, as humans, cannot.  Numbers are what we have invented.

Hehe.. ok.. =) .. I will look at the poll..

Not definitive, I"ll grant you, but certainly suggestive...

http://news.google.com/newspapers?nid=1314&dat=20000106&id=fEESAAAAIBAJ&sjid=LPIDAAAAIBAJ&pg=5849,4312740

http://www.livescience.com/animals/080926-bees-count.html

http://answers.yahoo.com/question/index?qid=20081104030627AAs3kQw

http://www.neatorama.com/2009/09/25/animals-that-can-count/

Really, my first objection was merely (for me) a semantic quibble.  Replace "human mind" with simply "mind" and the argument is strengthened, not weakened.  

The crux if the matter is in the second question, which I believe is different from and more fundamental than the first.

If mathematical entities exist independently of human minds then mathematical entities exist independent of minds.  It does not matter about animals or aliens as if you can prove they exist indepently of human minds then you have proven they exist.  Afterall it is not like you can prove they exist independently of human minds but then find out they they depend on an aliens mind as that would make little sense (and lets not bring a certain dieties mind in here). 

I think the second question is definetely stongly linked to the first though perhaps I was too hasty in saying that the second was another way of putting the first.  If mathematical entities exist independent of minds then surely that solves the argument of whether maths is invented or discovered. 

To stangequark- yes there are fundemental laws to the universe which would go on regardless of our being here but we need not say they are mathematical.  Rather we could say that mathematics is the language we invented to describe these laws.  You say 7 is a prime number but seven objects are not a prime, rather the symbol 7 is a prime within the system of symbols we have invented to represent the fundemental laws of the universe.  Aslo you say that irrational numbers have no physical entities associated with them but I could say the same for the number 7, you can have seven objects but that is not the number 7.  I think there is an important distinction between mathematical entities and what they represent.  As to the unreasonable effectiveness of maths I think we didn't evolve the use of numbers, we evolved such that our cognitive faculties could understand the notion of quantities, then of adding, subtracting and so forth.  And so we invented a language to express this ability.  The effectiveness of it can I think be attributed to the simplicity of its basis.  maths can be very complicated but it is all derived from simple principles. 

Well as I've said elsewhere this is not my field so I may very well be wrong but I am just looking to instigate debate and see what problems with either answer to the question can be teased out.

Also I think the arguments for the platonist position are compelling but it the problems once you accept it that put me off.  Say I accept that mathematical entities exist independently of any mind then I think I have the right to ask what form these entities take?  How do they exist and where and how do we have knowledge of them?  Also occams razor can come in to play because if we can have mathematics without postulating new spurious entities, ie say mathematical entites are mind dependant and formulate that in to a coherent position, then surely we should.

I maintain that numbers are not just as good as their representations. I was trying to make a point of that, that life would be quite hard if we accepted this view.

Evolving perfect cognitive mechanisms, even for indirectly giving form to a language such as mathematics, is shaky ground to stand on. We have much "worse".

Does one really have the right to ask "what form would these objects take", etc., if one accepts platonism? One can argue that where, how, and form are also independent of the mind as well so I am not sure if such questions can be solved on such a simple level.

Concerning minds in general, I have read before about animal arithmetic, for example. I think Eternal Patzer has a great point here. I don't have any specific references on hand, but I've read these things from scientific journals so I am more likely to give credit to them, although of course that's not conclusive to merely say that.

So how about baby chicks, even? When one says that they can understand basic arithmetic, ought we to say that they, and probably many other animals, all just happen, at their various levels of development, to know the same exact perfect language that we use? Unlikely!

Just want to point something out...  Humans invented the symbols, but the quantities they represent are independent of our minds.  what is "one"?  it is something that is alone.  you may represent "one" as "1" or as something completely different, but that does not change it.  from this starting point, we can define all other integers, rational numbers, and approximate irrational numbers in terms of this starting concept of "one"... Just pointing out that logically, numbers exist without minds...