About "so" in "I don't think so."

[Seiichi Myoga]

Hi,

Do you agree that "I don't think so" in (1) means (2a) but not (2b)?

(1) Speaker A: He can't be sane.
Speaker B: I don't think so.

(2) a. I don't think he is.
b. I don't think he can.

Thank you in advance
Seiichi MYOGA

[Mordant]

I think that it means both, but "can" would no longer refer to capability in the traditional sense. It would not mean "I don't think he has the ability to become sane."

Adam cannot be sane. - This indicates strong opinion about what already is, as "can" would in 2 (b). I am all but certain that Adam is not sane.

You cannot be serious. - This does not mean you are incapable of being serious. It means I strongly disbelieve you are right now.

In other words, 2 (a) and (b) can be read to mean the same thing. "I don't think so" matches both.