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Proof that numbers exist

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Proof that numbers exist

Kwalish Kid
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Posted 07/18/09 - 05:28 AM:	#31
ughaibu wrote: It seems to me that you need a successor function for your inferences to order the formulae, and if you have a successor function, then you have, effectively, numbers. If you have a successor function, then you have a commitment to a certain sort of behaviour. If numbers exist, how do we know that they obey the successor function?
"Scientific truth is always paradox, if judged by everyday experience, which catches only the delusive nature of things." - KM, V, P and P Can you pass Religion 101?

former
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Posted 08/11/09 - 04:42 AM:	#32
Suppose numbers do not exist. And all we have is a universe with this proposition. Then how many concepts are in this proposition (without number)? existence supposition not 3 numbers exist. Edited by hyena in petticoat on 08/19/09 - 09:56 PM. Reason: Illiteracy.

Kwalish Kid
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Posted 08/11/09 - 05:18 AM:	#33
Well, you have shown that you know how to use numbers. Now, do you know how to describe a unicorn? Does this mean unicorns exist?
"Scientific truth is always paradox, if judged by everyday experience, which catches only the delusive nature of things." - KM, V, P and P Can you pass Religion 101?

former
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Posted 08/11/09 - 06:08 AM:	#34
As a construction of the mind, yes. What is the meaning of asking, "Does numbers exist in the word?" Of course they are concepts. They exist in the mind as a sort of distinguished property of the central nervous system. That's it. Edited by hyena in petticoat on 08/19/09 - 09:54 PM. Reason: Illiteracy.

Phaedruswax
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Posted 08/17/09 - 06:27 AM:	#35
ManiacJack wrote: Can someone please give me a proof that numbers exist? It is that in my journey through life and all the talk of numbers and whatnot, I realized the other day that I have never seen number. I have seen squiggles, and many attest to the squiggle being number, but it appears that many cultures have used many different squiggles throughout time; and so seeing that as such, are we sure that numbers are not something subjective- that is, a matter of opinion because there is no proof for their existence? Saying numbers don't exist is similar to saying happiness doesn't exist. Both depend upon observation.

xstoph
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Posted 08/20/09 - 06:53 PM:	#36
I don't mean to puport an answer to this puzzle. But I think its important to note that most mathematicians, when pushed, are Platonists...
A stupid man's report of what a clever man says can never be accurate, because he unconsciously translates what he hears into something he can understand.

Schlitz
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Posted 08/21/09 - 10:53 AM:	#37
Reasoning about numbers is possible. Things are true of numbers, and other things are false of numbers. Based on this, it doesn't make sense to doubt the existence of numbers. There just isn't a good argument that concludes "and, so, numbers don't exist," because it is impossible to frame that argument. That position is over before it begins. A person might be persuaded to still further ask, but what is a number, really? There isn't a more informative answer than "the object of number theory." This line of questioning does lead to the fascinating debate over which logic holds for the theory of numbers, and, possibly, for mathematical reasoning generally, but metaphysical investigation into the alleged reality or disreality of numbers is a non-starter for the same reasons as why a persuasive, but more importantly _true_, argument is impossible to give. The methods that mathematicians use to determine facts about numbers are themselves the wellspring of the concept of mathematical truth. Whether or not, for instance, the law of the excluded middle applies to mathematical reasoning is the central point of dispute in what is frequently framed as the Realist / Anti-Realist dispute in mathematics; and, this dispute, once resolved, will have foundational consequences to the theory of truth; however, this dispute is methodological and not metaphysical. It is tempting to call it metaphysical because of how much it would inform the theory of truth, but investigating truth itself is not metaphysical. The outcomes of investigating truth should be a list of what is true of truth, and what is false of it: a description of the concept of truth. Investigating truth is done by logicians and philosophers, using mathematical methods, which themselves embody whatever flighty "essence" of truth metaphysicians might chase. There is no better an answer to the question of the existence of numbers than to describe the methods used to investigate them.

rigelrover
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Posted 08/21/09 - 11:06 AM:	#38
former wrote: Suppose numbers do not exist. And all we have is a universe with this proposition. Then how many concepts are in this proposition (without number)? existence supposition not 3 numbers exist. [ everyone else: Ref. former's previous posting on this matter. ] follow-up... Numbers are not the abstraction. Everything else is abstracted from number-relations. They are perhaps the only 'thing in itself' that we can talk about as such. right, former?
I am more interested in questions than answers; dialog than dictation. If we can reasonably believe that there is not just a breach, but a fundamentally unclosable gap between the individual mind and the ultimate nature of the reality; the primordial thing in itself, then 'true' mystery does exist.

brainpharte
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Posted 08/21/09 - 11:26 AM:	#39
Schlitz wrote: Reasoning about numbers is possible. Things are true of numbers, and other things are false of numbers. Based on this, it doesn't make sense to doubt the existence of numbers. Is there any dispute about the existence of numbers in that sense of "exist"? There just isn't a good argument that concludes "and, so, numbers don't exist," because it is impossible to frame that argument. That position is over before it begins. Is it not possible, however, to dispute arguments that allege the independent existence of numbers apart from human beings? A person might be persuaded to still further ask, but what is a number, really? There isn't a more informative answer than "the object of number theory." But the dispute is about whether or not "the object of number theory" is an exhaustive explanation or description--about whether or not there is a more imnformative answer.
"I don't see much sense in that," said Rabbit. "No," said Pooh humbly, "there isn't. But there was going to be when I began it. It's just that something happened to it along the way."

Schlitz
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Posted 08/21/09 - 01:17 PM:	#40
brainpharte wrote: Is it not possible, however, to dispute arguments that allege the independent existence of numbers apart from human beings? I think it is possible to consider and evaluate this kind of question as far as the issue can be naturalized. There isn't a principled method of evaluating certain approaches to this question, such as ones that aim to discover facts about numbers using deductive methods exclusive to philosophy, and this is the reason such attempts, however entrancing and artfully done, will never produce results. brainpharte wrote: Schlitz wrote: A person might be persuaded to still further ask, but what is a number, really? There isn't a more informative answer than "the object of number theory." But the dispute is about whether or not "the object of number theory" is an exhaustive explanation or description--about whether or not there is a more informative answer. That's not quite right. It is because the methods of investigating numbers are the foundations of the concept of number, and so number theory, that "the object of number theory" necessarily does pick out everything there's to be said about numbers. This might seem like a triviality, and it is relative to concerns about what's true and false of numbers. The concept of number's being the object of number theory, from this perspective, seems like a triviality because it can be discovered by examining the meanings of sentences of mathematical language, and it surely can; however, count this as a successful result, because any successful approach to figuring out the the foundations of math that takes meaning as a central theoretical notion ought to milk some explanatory power from meanings. The allegedly metaphysical disputes in the philosophy of mathematics are really disputes about the meanings of mathematical claims. The correct answer to the dispute over which logic holds for number theory isn't justified by the ontological status of numbers, but rather by how the language of number theory is used.

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