On Thursday, December 5, 2013 12:51:08 PM UTC-7, fom wrote: > On 12/5/2013 1:04 PM, Zeit Geist wrote: > > These sequences are not random. They are random in > relation to constructive methods. > > WM's ( and Herc's ) idea that the given sequence > can be "conditioned" in some manner that restricts > the sequence to constructive mathematics can only > apply to a set of measure zero. > > The arbitrariness of the given sequence precludes > one from being able to apply epistemic reasoning. > > Where WM is probably correct is that if the notion > of "given sequence" is epistemically bound in the > first place and if one does not admit a completed > infinity, then one is given a sequence in that > set of measure zero and one cannot implement the > Cantor diagonal. > > Unfortunately, I do not know enough about the > formalism to know if that can be made rigorous. > > The counter-argument is that the epistemically > bound sequence cannot be completed by virtue > of rejection of a completed infinity. Hence, > what is given is either plural or vague. > > But, that argument carries no weight for someone > who accepts the syntactic grounding of numbers > as strokes in an alphabet. All notions of identity > resolve to syntactic stipulations and, in the final > analysis, to inscriptional identity based upon > the shape of letters in the constructive alphabets.
You're point is well taken.
But I wish to reinforce my point.
The chosen sequence is arbitrary, and the only properties that it has are those that follow from the fact that it a sequence of real numbers.
We could look deeper and find that for "most" such sequences that its "lack of containing all" is rather trivial, and find that our sequence should be one of the "others" not included in the "most". For instance, a sequence contain Only all rationals is obviously lacks at least one real.