Is the ’’おう’’' in the Volitional ending of verbs related to ''こう、そう、どう'' in any way?


Is there any knowledge on where the volitional ''おう'' Ending originated? As
far as my interpretations go having seen a lot of sentences with them, Both
the ''おう'' of the volitional and the ''おう'' of ’’こう、そう、どう'' seem to indicate
some kind of..estimate? Something uncertain/imprecise. Instead of being 100%
precise it's just a kind of general direction, a kind of estimate or
expectation that is probably that way but not 100%.

それ is certain, it is that, そう is more vague, it is ''that way''. And it is
used for ''seems like'' hearsay. 行く is just going. 行こう is more of an estimate,
in that you'll ''probably'' go, or you say it when you say ''let's'' go, which
isn't completely certain.

Another thing is how the other rows all start with the distance, and then some
kind of thing that modifies it. like, その Is それ but possessive instead, so you
use it in front of words.

Thing is, the こうrow has one that's ''ああ’’ which doesn't fall in line with this
at all, but it may also be a sound change for all I know.

For all I know this could be a complete coincidence or my interpretation is
completely false, soo, are they related in any way?




Nope, they're unrelated.

Although they look similar today, the う in こう comes from the く of
[斯{か}く](https://kobun.weblio.jp/content/%E6%96%AF%E3%81%8F), and the う of 食べよう
comes from the conjectural auxiliary
[む](https://kobun.weblio.jp/content/%E3%82%80), so they were originally quite
different.

  * こう **koʜ** 'this way' comes from **koʜ < kau < kaku**. When **kaku** became **kau** , it caused a regular sound change from **au** to **oʜ**. With this change the word better fit the modern こそあど pattern phonologically, which allowed Japanese speakers to fill out the rest of the the こう・そう・ああ・どう **koʜ soʜ aʜ doʜ** paradigm by analogy, taking **ʜ** as a new morpheme meaning 'manner; way'.

Note that the words ああ **aʜ** and どう **doʜ** are quite recent; these two words
did not appear until Modern Japanese and were clearly formed by analogy. そう
**soʜ** is slightly older, and Frellesvig gives **soʜ < sau** as a derivation,
which goes back to Old Japanese **sa(te)**.

In terms of meaning, these four adverbs express 'manner; way'. I don't think
the core idea of 'uncertain' or 'imprecise' is really included in the **ʜ**
morpheme in these words.

  * The suffix **(y)oʜ** , written with an オ段 kana ＋ う in Japanese orthography, comes from the Old Japanese conjectural inflecting auxiliary **-(a)m**. By Late Middle Japanese its conclusive form **-(a)mu** , written む in Japanese, had become **-(a)u** , and this caused the same regular sound change from **au** to **oʜ**. 

To avoid hiatus, the semivowel **y** is inserted between vowel-stem verbs and
**oʜ** :

[code]       行く　 **ik-** + う **(y)oʜ** = 行こう　 **ik-oʜ**  
      食べる **tabe-** + う **(y)oʜ** = 食べよう **tabe-yoʜ**
[/code]

Although the range of meanings expressed by **-(a)mu** and now **(y)oʜ** has
varied quite a bit, I think the core idea behind this auxiliary/suffix is
expressing some kind of modality, ranging from epistemic to boulomaic. The
former fits what you're expressing with 'uncertain' or 'imprecise', although
it's been used to express a somewhat wider range of meanings than just
epistemic modality.

Note that in this answer the symbol **ʜ** is used to indicate the long vowel
phoneme. In each word there is a long vowel sound today and not an う **u**
sound, but the words are nonetheless written with the kana う in Japanese
orthography, even for words like どう **doʜ** which were never pronounced with
**u** historically.




Nope, they're unrelated.

Although they look similar today, the う in こう comes from the く of
[斯{か}く](https://kobun.weblio.jp/content/%E6%96%AF%E3%81%8F), and the う of 食べよう
comes from the conjectural auxiliary
[む](https://kobun.weblio.jp/content/%E3%82%80), so they were originally quite
different.

  * こう **koʜ** 'this way' comes from **koʜ < kau < kaku**. When **kaku** became **kau** , it caused a regular sound change from **au** to **oʜ**. With this change the word better fit the modern こそあど pattern phonologically, which allowed Japanese speakers to fill out the rest of the the こう・そう・ああ・どう **koʜ soʜ aʜ doʜ** paradigm by analogy, taking **ʜ** as a new morpheme meaning 'manner; way'.

Note that the words ああ **aʜ** and どう **doʜ** are quite recent; these two words
did not appear until Modern Japanese and were clearly formed by analogy. そう
**soʜ** is slightly older, and Frellesvig gives **soʜ < sau** as a derivation,
which goes back to Old Japanese **sa(te)**.

In terms of meaning, these four adverbs express 'manner; way'. I don't think
the core idea of 'uncertain' or 'imprecise' is really included in the **ʜ**
morpheme in these words.

  * The suffix **(y)oʜ** , written with an オ段 kana ＋ う in Japanese orthography, comes from the Old Japanese conjectural inflecting auxiliary **-(a)m**. By Late Middle Japanese its conclusive form **-(a)mu** , written む in Japanese, had become **-(a)u** , and this caused the same regular sound change from **au** to **oʜ**. 

To avoid hiatus, the semivowel **y** is inserted between vowel-stem verbs and
**oʜ** :

[code]       行く　 **ik-** + う **(y)oʜ** = 行こう　 **ik-oʜ**  
      食べる **tabe-** + う **(y)oʜ** = 食べよう **tabe-yoʜ**
[/code]

Although the range of meanings expressed by **-(a)mu** and now **(y)oʜ** has
varied quite a bit, I think the core idea behind this auxiliary/suffix is
expressing some kind of modality, ranging from epistemic to boulomaic. The
former fits what you're expressing with 'uncertain' or 'imprecise', although
it's been used to express a somewhat wider range of meanings than just
epistemic modality.

Note that in this answer the symbol **ʜ** is used to indicate the long vowel
phoneme. In each word there is a long vowel sound today and not an う **u**
sound, but the words are nonetheless written with the kana う in Japanese
orthography, even for words like どう **doʜ** which were never pronounced with
**u** historically.

