Does the volitional form of a verb mean both "let's" and "I want to"?


I was taught ages ago that the volitional form of a verb means "let's" do
something. For example, if you take `行{い}く` and change it to `行{い}こう`, you get
"let's go".

However, I feel like I can use the same form to express "I want to". For
example:

> 行{い}こうかなと思{おも}っている ("[I'm] thinking maybe I'll go")

Am I wrong that it can be used this way?

If it's true that it can mean that, what is the difference between the
sentence I have above and this one:

> 行{い}くかなと思{おも}っている

My understandng of the plain form is that it can be used to imply future
tense, and if so, maybe it also implies intention. If so, then the two
sentences mean the same thing, don't they?

Perhaps I'm thinking too much in English, though, where "will go" can be both
intention and future tense?

So, my questions in summary are:

Does `行{い}こう` mean "will go" as well as "let's go"?

Can `行{い}こう` and `行{い}く` both be used to mean future tense and/or intention?




Japanese has a clearer distinction between volitional-future and simple-future
than English.

"I think I will go" can be parsed in two ways, one involving volition, and one
without.

> 私は行こうと思う (Volitional future)
>
> 私は行くと思う (Simple future)

* * *

"Will" being interpreted without volition when used in the first-person can be
a little counter-intuitive. So here's one way I look at it:

> "Tomorrow will be Saturday" \- Clearly no volition is involved. It is this
> sense of "will" that is used when talking about simple-future.

This is easy to see since there is nothing that can exert volition.

Now let's bring in something that can exert volition:

> "Because I did not study, I will fail the test".
>
> ｘ 勉強しなかったから、試験に落ちよう
>
> O 勉強しなかったから、試験に落ちる

Although there is something that can exert volition, it is however still not
volitional since the person is not intentionally exerting his will to fail the
test. This is simple-future.




Japanese has a clearer distinction between volitional-future and simple-future
than English.

"I think I will go" can be parsed in two ways, one involving volition, and one
without.

> 私は行こうと思う (Volitional future)
>
> 私は行くと思う (Simple future)

* * *

"Will" being interpreted without volition when used in the first-person can be
a little counter-intuitive. So here's one way I look at it:

> "Tomorrow will be Saturday" \- Clearly no volition is involved. It is this
> sense of "will" that is used when talking about simple-future.

This is easy to see since there is nothing that can exert volition.

Now let's bring in something that can exert volition:

> "Because I did not study, I will fail the test".
>
> ｘ 勉強しなかったから、試験に落ちよう
>
> O 勉強しなかったから、試験に落ちる

Although there is something that can exert volition, it is however still not
volitional since the person is not intentionally exerting his will to fail the
test. This is simple-future.

