```Date: Feb 24, 2013 9:56 AM
Author: William Hughes
Subject: Re: Matheology § 222 Back to the roots

So, when WM says that a natural number m does notexist, he may mean that you can prove it existsbut you cannot find it.Suppose that P is a predicate such thatfor every natural number m, P(m) is true.Let x be a natural number such thatP(x) is false. According to WM you cannotprove that x does not exist.  (WMrejects the obvious proof by contradiction:     Assume a natural number, x, such that P(x)     is false exists.     call it k     Then P(k) is both true and false.     Contradiction,  Thus the original assumption     is false and no natural number, x, such     that P(x) is false exists)We will say that x is an unfindable naturalnumber.It is interesting to note that WM agrees withthe usual results if you insert the term findable.E.g.There is no findable last element of the potentiallyinfinite set |N.There is no findable index to a line of L thatcontains d.There is no ball with a findable index in the vase.etc.It does not really matter if nonfindable naturalnumbers exist or not. They have no effect.I suggest we give WM a teddy bear marked unfindable.
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