Date: Feb 12, 2013 2:19 PM Author: dan.ms.chaos@gmail.com Subject: Re: infinity can't exist On Feb 12, 5:19 pm, Craig Feinstein <cafei...@msn.com> wrote:

> Let's say I have a drawer of an infinite number of identical socks at time zero. I take out one of the socks at time one. Then the contents of the drawer at time zero is identical to the contents of the drawer at time one, since all of the socks are identical and there are still an infinite number of them in the drawer at both times. But the contents of the drawer at time zero is also identical to the contents of the drawer at time one plus the sock that was taken out, since they are exactly the same material. So we have the equations:

>

> Contents of drawer at time 0 = Contents of drawer at time 1

> Contents of drawer at time 0 = (Contents of drawer at time 1) plus (sock taken out of drawer).

>

> Subtracting the equations, we get

>

> Nothing = sock taken out of drawer.

>

> This is false, so infinity cannot exist.

>

> How does modern mathematics resolve this paradox?

Your 'reified' equation doesn't reflect the reality of the situation .

You can assume each sock has a different atomic structure . Then the

situation would be different .The socks can only be identical as far

as you can observe . From the moment you took a sock , the remaining

pile is a different pile from the one that was before , regardless of

what you would like to think.

Even if we take socks to be fully identical and you're equations to be

true , what they say is that taking 'nothing' out of the pile of socks

has the same effect as taking a 'one sock' of the pile of socks . If

you can get an infinite number of socks , one sock might as well be

worth nothing :) .

Let's attempt to look at this another way : since no sock is supposed

to be different from another sock , equations must be ,

ultimately ,referring to numbers , that is , quantity ,abstracting

individual existence . When I say 'two pears' , I abstract the fact

that they may be of different color .

Your equations reduce to , basically :

infinity = infinity

infinity = infinity + 1 =>

infinity - infinity = 1 - 0 = 1 =>

0 = 1

The problem is 'infinity' is not a proper quantity , not a number .

The reason it can't 'stand' as a quantity is it's defined as being

equal to a proper part of itself . (infinity = infinity + 1) .

Also , you can't make a choice from any number of 'absolutely-

identicals' . According to Leibniz's principle of 'identity of

indiscernibles' a number of 'absolutely-identicals' is a false

concept . Metaphysically , there's , ultimately , only 'one' of

anything . From the moment you choose a sock from the drawer of

socks , and even, extending in time , forever before and after that

moment, that sock is and was no longer identical to the other socks.

That sock is 'chosen' , all the others are 'not chosen' .

If all the socks were white , your choice of sock acts as a 'red

dye' , forever marking the chosen sock as 'red/chosen' . So what your

equations really say is :

socks = 'chosen sock' + 'unchosen socks' .

"socks = unchosen socks" is clearly false .

Interesting thought experiment , nonetheless .