Date: Feb 12, 2013 2:19 PM
Subject: Re: infinity can't exist

On Feb 12, 5:19 pm, Craig Feinstein <> 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 .