On 12/05/2013 02:42 PM, fom wrote: > On 12/5/2013 2:28 PM, Michael F. Stemper wrote: >> On 12/05/2013 01:04 PM, Zeit Geist wrote: >>> On Thursday, December 5, 2013 12:49:37 AM UTC-7, fom wrote: >>> >>>> No. It also uses the fact that the listing may be >>>> >>>> arbitrarily given, >>>> >>>> http://en.wikipedia.org/wiki/Algorithmically_random_sequence#Interpretations_of_the_definitions >>>> >>>> >>> >>> Be careful here, the "arbitrarily chose" sequence does Not need to be >>> a "random" sequence. >>> It is just a sequence of Real Numbers who only properties is that it >>> IS a sequence of Real Numbers that "supposedly" contains all Real >>> Numbers. >> >> There is no need for the assumption that it contains all reals. We can >> prove that no sequence of reals contains all of them without having to >> first assume that it does.
> I had to think about that.
Now, you've caused me to think. Specifically, about the following paragraph:
> Cantor's proof had been directed to an audience > who thought of "infinity" as a monolithic concept. > Proving that any list asserting to put the set > of reals in correspondence with the naturals was, > in fact, not a complete list demonstrated that > "infinity" could be viewed as a plural notion subject > to logical analysis.
Unfortunately, even after sleeping on it and re-reading it, I still don't get it. Would you please expand on this? (For starters, did Cantor include the assumption that the list had all reals?)
> Your statement reflects Hilbert's formalism.
My inclinations are much more formalist than Platonist.
-- Michael F. Stemper I feel more like I do now than I did when I came in.