```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 thesituation would be different .The socks can only be identical as faras you can observe . From the moment you took a sock , the remainingpile is a different pile from the one that was before , regardless ofwhat you would like to think.Even if we take socks to be fully identical and you're equations to betrue , what they say is that taking 'nothing' out of the pile of sockshas the same effect as taking a 'one sock'  of the pile of socks . Ifyou can get an infinite number of socks , one sock might as well beworth nothing :) .Let's attempt to look at this another way : since no sock is supposedto be different from another sock ,  equations  must be ,ultimately ,referring to numbers , that is , quantity ,abstractingindividual existence . When I say 'two pears' , I abstract the factthat they may be of different color .Your equations reduce to , basically :infinity = infinityinfinity = infinity + 1 =>infinity - infinity = 1 - 0 = 1 =>0 = 1The 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 beingequal 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 ofindiscernibles'  a number of 'absolutely-identicals' is a falseconcept . Metaphysically , there's , ultimately , only 'one' ofanything . From the moment you choose a sock from the drawer ofsocks , and even, extending in time , forever before and after thatmoment, 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 'reddye' , forever marking the chosen sock as 'red/chosen' . So what yourequations really say is :socks = 'chosen sock' + 'unchosen socks' ."socks = unchosen socks" is clearly false .Interesting thought experiment , nonetheless .
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