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Following the first Greek grammars or even older sources, there is a traditional and apparently arbitrary order used for cases in most if not all living European languages, e.g. in declension tables. It often starts like this (NGDA):

  1. Nominative
  2. Genitive
  3. Dative
  4. Accusative

Other cases usually follow if they’re used, e.g.

  • Ablative (abbreviated ‘B’ below)
  • Vocative
  • Locative
  • Instrumental
  • Prepositional

In modern language teaching, it seems to become more common to group the cases by morphologic similarity to aid memorization. This results in NADG instead of NGDA for German. I’ve seen NAGD for Old English, though. Latin should probably use NVABDG, Russian maybe NAGPDI because Acc forms agree with either Nom or Gen depending on animacy.

How much does similarity of case morphemes differ by language? Is there a logical canonical order of (nominal) cases across (Indo-)European languages?

3

“Is there a logical canonical order of (nominal) cases across (Indo-)European languages?” I would say that the answer to this part of your question is “no”. The Nom Gen Dat Acc Voc order is traditional in Greek and Latin grammar since antiquity and it is imitated in modern languages like German and Russian. It is traditional, if you like “canonical”, but not “logical”.

In Sanskrit, on the other hand, the traditional order of the cases is Nom Voc Acc Instr Dat Abl Gen Loc. This order does have a logic: in the singular at least the Nom has typically long-grade ablaut, Voc Acc and Instr have full-grade ablaut and the others have zero-grade ablaut. So the “fuller” forms are grouped together at the beginning of the paradigm.

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  • How traditional is "Nom Gen Dat Acc Voc" in Latin? I'm pretty sure that I learned [in the 1960s] Nom Voc Acc Gen Dat Abl. – David Garner Feb 24 '16 at 16:43
  • @DavidGarner. I think there was a reform in the way Latin is taught in the UK some 50 years ago. – fdb Feb 25 '16 at 11:51

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