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Proof that numbers exist

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Proof that numbers exist
ManiacJack
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Posted 07/05/09 - 02:05 PM:
Subject: Proof that numbers exist
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#1
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?


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Posted 07/05/09 - 02:51 PM:
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I've met a professor of philosophy who has done some work in the philosophy of mathematics and he claims that numbers don't exist. I can't come up with the arguments for pros and cons because I don't know them, but one thing is for sure, you're in your full right to ask. It's reasonable to ask the question. I'll follow this. Is there anyone who has some knowledge on this? Cheers!

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Posted 07/05/09 - 03:23 PM:
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This is over my head. I don't understand what you mean by "numbers don't exist"! We invented numbers to help us count things!
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Posted 07/05/09 - 03:34 PM:
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Numbers are not things that can be said to exist or not in the first place, but denoting the quantity of a set of things.

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Posted 07/05/09 - 04:46 PM:
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"One is one and all alone and ever more shall be so."


how does one prove the existence of anything?


ManiacJack wrote:
I realized the other day that I have never seen number.


Seeing is proving?


ManiacJack wrote:
I have seen squiggles...


What, a number of squiggles? shocked


There is not in existence some other thing called 'five', but only the beans in a relationship of multiplicity. It's an adjective, not a noun.


It makes sense to say that there exists no largest prime number, or that there exists a number between 40 and 50 that is exactly divisible by nine. But again these are statements about relationships of properties, not 'things'.


 


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Posted 07/06/09 - 01:35 AM:
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Numbers are a formal man made system. Their existence is as real as street-names.
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Posted 07/06/09 - 07:48 PM:
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Well, first we must ask what does it mean to assert something exists.

W.V. Quine's view is that to be is to be the value of a bound variable. And we are committed to the existence of things that must take the place of the variables in our theories if they are assumed to be true.

One theory is that there is a thing x such that x is less than 5 and more than 3. Since we affirm this proposition, and its admissible values are numbers, we are committed to the existence of numbers.

Even more, numbers don't really exist, since talk of numbers can be reduced to statements that only refer to sets (or classes - the difference between sets and classes are immaterial). So, the question of the existence of numbers can be shifted to the question of the existence of classes.

So, the "real" question is: do classes exist?

Again, Quine's argument is that they are required for our accepted theories of science (in the widest sense) - therefore, they exist just as much as atoms do.
ManiacJack
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Posted 07/06/09 - 07:55 PM:
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My language is my ontology- the same applies to all of mankind.

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Posted 07/06/09 - 08:23 PM:
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Syntactically, numbers are adjectives. They are "signifiers" which describe properties of something else, (or a collection of something else -- do collections exist?). They don't exist any more than "red" or "blurry" exist. Unless you get into "qualia", of course.

Ethics is the measuring of morality. Morality is the measuring of good. Good is the measuring of benefit. Benefit is the measure of values.
ManiacJack
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Posted 07/06/09 - 10:08 PM:
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Well, do you exist?

I mean, "swstephe" is just a signifier.

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