On Monday, December 9, 2013 10:59:11 AM UTC-7, wpih...@gmail.com wrote: > To understand where WM is coming from one must note > > that for WM the statement > > for all n in N, p(n) is not true > > does not imply > > there is no n in N such that p(n) is true, > > but only that > > one cannot find an n in N such that p(n) is true. >
Yes, but he refuses to describe the meaning of "one cannot find". He uses the word "taken", which also has an unclear meaning.
His argument against the Infinite rests on Philosophicial grounds. However, he insists that assuming the Existence of an Infinite Set leads to a Logical Contradiction. But, when showing this purported Contradiction, he slips in an Implict Assumption of Anti-Infinity. Then, a Contradiction results. Wow! I imagine that.
> So for WM: > > If L is a constructable list of constructable 0/1 lists > then there is a constructable 0/1 list, y, such that one cannot > find a n in N with y the nth element of L. >
So, y could "really" be on L, but we can't "find" it's n? Let me know if I interpreted this right?
However, WM actually clims the we can't find All digits of y, and hence y can Not be shown Unequal to All members on the L.
> Most people would then argue, if n existed then we could find it, > so the fact that we cannot find it means that n does not exist. >
This would depend on the meaning of Find.
Can it Logically be stated in Mathematics?
Does it imply ~AoI? If so, its a Philosphical consideration.