On Thu, Jan 17, 2013 at 6:21 PM, Gary Shannon <[log in to unmask]> wrote:

> Two things.
> The list of valid sentences must include finite sentences, not just
> infinite ones if it is to be alist of ALL English sentences,
> complicating the diagonalization rule.
> The sentences must be grammatically correct or they are not "sentences
> of the English language", they are just strings of words.
> The second item means that English sentences, finite or infinite, are
> NOT amenable to diagonalization. Here is the first page of "Alice in
> Wonderland" diagonalized (until the diagonal hit the first
> sentence-ending punctuation mark:
> "Alice she nothing down on deep and of fall time ?"
> For Cantor's purposes this is a valid string of words. For claiming
> that "sentences of the English language" are uncountable, it doesn't
> work.

Consider the following set of infinite sentences:

I know that U know that I know that U know ...
I know that I know that U know that I know...
U know that U know that U know that U know ...

and so on. These sentences are purely grammatical. Yet, if you replace "I
know that" with 1's and "U know that" with 0, you may already use Cantor's
diagonal to create a words that does not exsists in Your countable list. So
basically English supports a continuum of infinite sentences.

> --gary