But perhaps all languages have a countably infinite number of words, in which case that proof doesn't work. (In English we have: legless, leglessness, leglessnessless, leglessnesslessness, ... It's not a great example, but it's good enough.)
Even if the number of words in a language were finite we wouldn't have a reasonable way of counting them. There are too many kinds of fuzziness involved in deciding what counts as a "word" and you can't ignore the borderline cases because the borderline cases vastly outnumber the straightforward cases.
Even if the number of words in a language were finite we wouldn't have a reasonable way of counting them. There are too many kinds of fuzziness involved in deciding what counts as a "word" and you can't ignore the borderline cases because the borderline cases vastly outnumber the straightforward cases.