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In greek, the indicative mediopassive in the 3rd person singular and plural are -εται and -ονται, however in PIE, the alpha was originally an o. Additionally, in the imperfect, the endings also have o in them. Why did this shift to alpha, since it seems like an omicron and iota seems phonologically legal in greek, such as in the masculine plural article οἱ.

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    I'll consult Willi's Origins of the Greek Verb later when I get a chance. If you can get your hands on it it's an excellent read on the PIE verbal system through the lens of Greek
    – Tristan
    Nov 29, 2023 at 13:24
  • Thanks for the suggestion, I'll try to look at it.
    – Blubber
    Nov 29, 2023 at 13:40
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    Greek takes a capital g, We should make an effort...
    – Lambie
    Nov 29, 2023 at 16:42

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Willi's Origins of the Greek Verb argues that it's by analogy from the 1sg, 2sg (from PIE *(m)h₂ei̯ & *soi̯/-sai̯), noting Arcado-Cypriot and Myceanaen forms in -τοι:

In Greek *-toi̯ > -τοι is attested in Arcado-Cyprian and Mycenaean; -ται is analogical after the 1sg./2sg.

Note that Willi does not assume the 1sg & 2sg directly continue the PIE middles, but instead consist of the h₂e-conjugation (stative) endings appended to the active athematic ones (-mi conjugation), and then followed by the primary -i in the present tense.

These are badsed on a combination of endings from both series/conjugations. ... the ending *-o acquired a mediopassive value and could be added to the 3sg. ending *-t of the m-conjugation form new 'oppositional' middles...

... Since Vedic 'primary' 2sg. med. -se can continue either *-sai or *-soi, a late-PIE 'primary' *-s-t(h₂)a-i̯ may have been 'regularised' after active *-si into *-sai̯ (> Ved. -se), while the vocalism of only 'secondary' *-s-th2e > *-s-t(h₂)a > 'regularised' *-sa was aligned with that of 3sg. *-to. This would imply that Proto-Grreek possessed a 'primary' middle series 1sg. *-mai̯ (cf below), 2sg. *-sai̯, 3sg. *-toi̯ vs 'secondary' *-mā(m) (cf.below), *-so, *-to, and it would thus account for the general a-vocalism of the 'primary', but not 'secondary', middle endings of most historical dialects (Att. -μαι, -σαι, -ται vs. -μην, -σο, -το).

[footnotes ommitted]

This does require two analogies (one for 2sg. *-st- > *-s-, and another for 3sg. *-oi̯ > *-ai̯).

The ablaut of the PIE middle is not consistently reconstructed (Sihler & Beekes reconstruct o-grade, whilst Fortson & Ringe reconstruct e-grade). An o-grade explains the lack of a-vocalism in the secondary middle (i.e. imperfect & aorist middles) but makes the a-grade in the primary middle (i.e. present middle) problematic, whilst the e-grade is exactly reversed (explaining the a-vocalism of the primary, but not the lack of it in the secondary middle). Willi's explanation using concatenation of the stative and active (athematic) endings explains both.

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