People talking about morphological analyses can often speak across each other because they have different purposes in mind. Here’s an initial attempt to outline five possibly distinct notions one might be referring to.
I’m tentatively labelling them:
although the labels matter less than being clear about the distinction.
Algorithmic means I can go from an inflected form to a lemma + morphosyntactic properties (or vice versa) efficiently on a computer. The way this is achieved might not be psychologically plausible or historically accurate but it can be implemented in software to get the job done.
Diachronic means I can explain (or at least speculate) how the inflected form came about: what the roots are, what grammaticalisation took place, what sound changes explain seeming irregularities, etc.
Synchronic means I can describe the inflected forms without recourse to historical data or reconstruction. This might focus on perspicuity rather than computational efficiency or psychological plausibility.
Psychological means the analysis is consistent with what I think is (or was) going on in the minds of native speakers. Some people may equate this with syncronic analyses but I think you can have a psychologically implausible yet still descriptively adequate synchronic analysis.
Pedagogical means a useful way of explaining it to students. This may be diachronic, but might be more synchronic (whether psychologically plausible or not).
Analyses can obviously be compatible with more than one of these. But I think it’s helpful to be clear what the goals of any morphological description are. If the goal is to lemmatise and tag a new text, then psychological or historical plausibility, or analytical or pedagogical clarity might not matter. If one’s goal is a diachronically-informed analysis to help students, it should be clear why an otherwise perfectly adequate morphological parser might not be producing useful information.
Those who have been following my Tour of Greek Morphology know I’ve tried to be careful distinguishing, for example, historical explanations from how I think native speakers internalise(d) word forms, or how students should learn them.
I still come across a lot of people who think the “modern” way of understanding morphology is learning the “morphemes” and rules, not memorising paradigms. Besides getting the history somewhat wrong, this is also making the mistake of conflating these different types of analyses and not recognising that one type of analysis might be perfectly valid for one purpose but not another.
Here’s a fun game to play: how would you analyse/explain the form λαμβάνω? Or ἔλαβον (especially when 3rd plural) or λήμψομαι? Or μαθητής vs μαθητοῦ? Or ἔδωκεν vs δέδωκα vs δός?
Maybe I haven’t quite nailed the labels yet. Maybe there are further distinctions to draw. I welcome people’s input.