
Re: Was Cantor an "antiCantorian" ?
Posted:
Apr 14, 2014 2:56 PM


On Monday, April 14, 2014 10:52:32 AM UTC7, Bart Goddard wrote: > david petry <david_lawrence_petry@yahoo.com> wrote: > > On Monday, April 14, 2014 9:05:28 AM UTC7, Bart Goddard wrote: > >> david petry <david_lawrence_petry@yahoo.com> wrote:
> >> > Language is countable.
> >> No it's not. The set of all finite sentences is countable. > >> The set of all strings of words is not. Arthur C. Clarke > >> wrote an infinitely long short story, "The Longest > >> ScienceFiction Story Ever Told." So it's possible > >> for infinitely long strings, not only to exist, but > >> to make sense in English.
> > I'd be surprised if a majority or even a significant minority of > > professional mathematicians agree with your reasoning here.
> ALL professional mathematicians will agree that the > set of all strings of words is uncountable.
Actually we're talking about language, not the set of all strings.
> The only > "reasoning" in my paragraph is that I conclude that > there are sensible infinite strings of words and I > conclude it from the simple device of giving a well > known example. I'm pretty sure all professional > mathematicians will agree that this reasoning is sound.
Language is the set of strings we use to communicate. I'm forced to believe that you are twisting the definition of the word "language" just so that you don't have to confront the "antiCantorian" argument.

