Print

Print


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.

--gary