"Could not have been" vs. "must not have been"
What's the difference between "could not have been" and "must not have been"?
For example,
- That could not have been an easy task.
- That must not have been an easy task.
I've seen both used. What's the difference?
Solution 1:
The two sentences display the epistemic senses of two modal auxiliary verbs:
must and could.
Modal auxiliary verbs ("modals") are very irregular and have
extremely complex grammar. Every modal has two kinds of meaning:
its Epistemic sense and its Deontic sense.
-
Epistemic meanings are abstract and refer to logical
predictions and conclusions:
This might/must/could/should/may/will/would be the place. -
Deontic meanings are social and have to do with obligations,
permissions, and prohibitions:
She may/can/should/must go to the ball.
Negation works differently with modals in their epistemic and deontic senses.
- This may not be the place ≠ This can't be the place. (epistemic)
- You may not leave yet. = You can't leave yet. (deontic)
As for the particular pair of modals in the OQ, they interact with negation identically; epistemic could not/must not turns out to work the same way as deontic may not/can't above.
There's no difference in meaning between the two; there's just a difference in form and sound that some speakers may exploit for their own purposes. Some speakers, in fact, might come to believe that the way they use them is the correct way. But there are many ways, and lots of them work.
Like I said, modals are complex.