That 12-word
description doesn't
define a number, though its
grammatical form suggests it does. An expression "the X" intended to
refer to one single thing is called a
definite description (the term is
Russell's). It is
logically composed of several
assertions.
For example, "the tallest dog in Samoa" requires someting like (i) there are dogs in Samoa, (ii) dogs can be compared for tallness, (iii) among any set of dogs the tallness comparison results in a unique tallest one.
The expression "the largest... that can be..." will have different conditions. Probably the easiest way for it to fail is to attack the "can".
If English were frozen we could say there were (say) 500 000 words in the language, therefore 500 000 one-word expressions, 250 thousand million two-word expressions, and so on up to fourteen-word, and then inspect them all to see which define numbers; and of these we could determine the largest.
But in rejecting all the vast number that do not define numbers, we would reject such things as "the right cross swivel expansion of forty-seven factorial", which in the year 2270 could well be meaningful and define some newly-invented huge number.
This is known as Berry's Paradox. (Thanks to JerboaKolinowski for pointing this out.) Or the Richard Paradox, I see, that's French ree-shar.