The concept of the morphome (i.e. a morphological unit at odds with syntax and semantics) is notoriously uncomfortable for many formal models of morphology. Many discussions have thus centred on whether morphomes exist and whether individual cases are morphomic or not. When one gets rid of theoretically-driven assumptions, however, there is little evidence for a dichotomic taxonomization of morphological minimal signs into morphemes and morphomes. Cross-linguistic variation suggests that morphological units can be arranged on a scale from those having the simplest morphosyntactic distributions to those whose distributions are most complex. The properties of the former vs the latter are, however, not substantially different. I argue, therefore, that we should avoid this arbitrary taxonomy and explore instead the diversity of form-meaning mappings objectively by developing adequate and cross-linguistically applicable quantitative measures.
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Borja Herce (2020) studied this question.
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