Does a metric exist that quantifies morphological richness in languages? Either a numerical score, or at least a ranking of languages would suffice.
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2What kind of morphology do you mean, general, derivational, inflectional, any other? Every word root is a morpheme, do you know that?– Yellow SkyFeb 8, 2017 at 1:05
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Generally if there is a lot of inflection, there is a lot of derivation to go with it. I would say the average number of frequent words (assuming "word" has a good definition in the language) that come from a particular root -- for derivation, combined with parameters about the number, size, and shape of relevant paradigms -- for inflection (those parameters could distinguish between fusional and agglutinative inflectoin) would do for both. We can consider root compounds to be syntax, if there's no bound forms necessarily involved.– jlawlerFeb 9, 2017 at 0:48
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What do you mean by "derivation"? In Bantu languages there is a vast amount of inflection, and not much derivation (depending on what your definitional criterion is for "derivation").– user6726Feb 9, 2017 at 0:57
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No, but as contrasted with the related notion of morphological complexity, it seems at least a bit more possible to define and count it. When people say a language has a "rich" morphological system, that usually means that there are very many non-lexical morphemes. It might also mean that there is the possibility of combining affixes, but I don't think that is inherent in the notion of richness. If a language has 200 affixes (a reasonably rich morphology), it would be unusual if e.g. there were 200 cases or mood suffixes, and no other morphemes. Simple counting would be a good measure of "richness".
Complexity is much harder to define, since it necessarily involves rules of combination. For example, instead of just saying "the past tense marker is -ile", you might have to say "the past tense marker is -ita after the causative -ʃ and -ile otherwise", which makes the system more complex. The problem is that there is no scientific utility to having a metric of "richness", that is, unlike water which boils when it reaches a specific temperature, languages don't have properties that depend on having a particular quantity of richness.
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1"Richness" involves multi-layered structures and lots of available construction techniques; "complexity", on the other hand, involves a significant degree of irregularity and asymmetry, with enough richness to be confusing.– jlawlerFeb 9, 2017 at 0:51