Are lexicons finite in principle?

Question

As we all know, every language has open classes of morphemes. If we discovered a new mineral whose natural florescence captured the public's attention, there would be no difficulty coining a new name for it in either technical or popular vocabulary. Odds are, the new name would be derived from existing morphemes, yielding something like "glo-stone." But nothing theoretical could prevent the coinage of a new morpheme like "fraz."

I have often heard that the number of morphemes in a language is finite because there are only so many morphemes in a language at a given time.

However, only so many sentences are being spoken in a given language at a given time.
It simply isn't possible for there to be an actual infinity of sentences in a given language. But because of recursion, we can rightly characterize the number of sentences in a language as non-finite in principle.

Can't we say the same about the number of morphemes? There may be practical and cognitive limits on the lengths of morphemes, but not theoretical limits as far as I know.

If the numbers of both sentences and morphemes in a language are actually finite but non-finite in principle, then how could any language be characterized as having only a finite number of sentences in principle even if said language lacks recursion? True, new morphemes are uttered with far lower frequency than new sentences are, but what theoretical difference would that make?

Answer 1

This is a bit of a philosophical question, but I agree with your reasoning: in theory, or in principle, a language could contain an infinite number of different morphemes (one of which might have to have an infinite length, but that doesn't matter).

However, in practice, one observes that the number of new, intelligible sentences recorded on the Internet every day is very large, whereas the creation of new, intelligible morphemes is very small. For all practical purposes, it makes sense to treat the number of possible sentences as infinite, and the number of morphemes as nearly fixed.

The number of morphemes becomes larger already if you include more, such as every unknown letter combination recorded; but it makes more sense to only count as morphemes combinations that are to some degree understood by people. Of what we count as newly created sentences, most are to some degree understood by people.