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They sound alike. Are they cognate historically?

Morphologically, is よ in both cases a particle or part of the morpheme in -ましょう?

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I think ましょ might be a sound change from the other surface form of the 未然形 of ます, which is ませ. So, ませう -> ましょう. –  snailboat Dec 27 '12 at 22:36
    
@snailplane, oh, the long vowel. Sounds feasible, since you can trace a diphthong becoming a long vowel even in the spelling. –  katspaugh Dec 27 '12 at 22:49
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Not merely feasible, but well-documented. The historical spelling of 〜ましょう was indeed 〜ませう. –  Zhen Lin Dec 28 '12 at 6:25
    
Zhen Lin, thank you! @snailplane, if you might post an answer, I would gladly accept it. –  katspaugh Dec 28 '12 at 10:22
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(Though someone might have already said this) goo dictionary says the「う」is an auxiliary verb... ましょ+う[ませう]:[連語]《丁寧の助動詞「ます」の未然形+推量の助動詞「う」》dictionary.goo.ne.jp/leaf/jn2/208020/m0u –  Choko Dec 29 '12 at 21:24

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up vote 9 down vote accepted

The short answer to your initial question is no. The historical/etymological spelling of 〜ましょう was 〜ませう, which is the expected form of the volitional, since the irrealis (未然形) stem of 〜ます is 〜ませ. Regular sound change explains the rest: せう becomes しょう.

The same story applies to the consonant-stem (五段活用) verbs: the old spelling for 行こう was 行かう (as seen here) etc. However, something strange happened to the vowel-stem (一段活用) verbs; instead of 見む → 見う → **みゅう or せむ → せう → **しょう, these were replaced by the forms with 〜よう we know today.

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Thanks for the detailed and informed answer! –  katspaugh Dec 28 '12 at 17:25
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@katspaugh, Zhen Lin -- I've lost the link at the moment, but apparently せ and し were at one point both pronounced with an initial sound of /sh/. So せう == /sheu/ changing to /shoː/. –  Eiríkr Útlendi Jun 7 at 0:03
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@katspaugh, Zhen Lin -- More data from Shogakukan about the change: 補注 一・二段活用の動詞に推量の助動詞「む」を伴ったもの、たとえば「見む」「上げむ」は、室町時代末までに「みう」「あげう」から「みょう」「あぎょう」のような‌​融合したオ列拗長音の形に変化していたが、そこから再び動詞未然形と助動詞とが分かれて、助動詞「よう」の形を生じた。これが、近世にはいって、一・二段活用の動詞一般のこ‌​ととなり、カ変・サ変にも及んだ。ただし、この変化は、東国で進んだものと思われ、現代の標準語のように、五(四)段活用の動詞には「う」が、その他の活用には「よう」が付‌​いて、接続を補い合う用法は、近世後期江戸語で勢力を得た。 –  Eiríkr Útlendi Jun 9 at 16:51
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Translation: Note: The forms of ichi- and ni-dan verbs accompanied by supposition auxiliary mu, such as 見む{mimu} and 上げむ{agemu}, changed by the end of the Muromachi period [circa 1573] to form a fused long /o/ sound as in /miu/ and /ageu/ becoming /myoː/ and /agyoː/, but this then again underwent a division between the irrealis form of the verb and the auxiliary, producing verbal auxiliary . This then became the general auxiliary used with ichi- and ni-dan verbs in modern Japanese, and was even applied to ka-hen and sa-hen verbs [such as 来る and する]. –  Eiríkr Útlendi Jun 9 at 16:59
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[cont.] However, this change is thought to have happened in eastern Japan, and as in modern standard Japanese, u attaches to go-dan (yo-dan) verbs, while attaches to other verbs, with this complementary usage gaining prevalence in late modern Edo speech. –  Eiríkr Útlendi Jun 9 at 17:03

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