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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?

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2 Answers 2

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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.

  1. Epistemic meanings are abstract and refer to logical
    predictions and conclusions:
    This might/must/could/should/may/will/would be the place.

  2. 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.

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  • Shouldn't the second sentence in the original post be 'That must have been an uneasy task,' with the negation in the noun phrase rather than in the verb phrase? As in 'You must have felt tired after that long trip.' = 'You can't have felt fresh after that long trip.'
    – user58319
    Commented Apr 23, 2018 at 11:54
  • "An uneasy task" is a rather odd predicate noun phrase; I'd be unapt to use it, I think. In any event, the position of negation in a sentence is widely variable, even though the different negative morphemes may have different uses and idioms.
    – John Lawler
    Commented Apr 23, 2018 at 17:28
  • Got it! Pointing out other people's assumed mistakes while making real mistakes of my own should have made me uneasy!
    – user58319
    Commented Apr 24, 2018 at 7:26
  • unapt is new to me! We only have inapte in French!
    – user58319
    Commented Apr 24, 2018 at 7:33
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    Compare - there could not have been an easier task with there must not have been an easier task. These two are very different.
    – Phil Sweet
    Commented Jan 25, 2021 at 21:21
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More context would be useful here, but personally, I'd be more inclined to use "could" if talking to person B about something person C did, and to use the construction with "must", when talking about the same task to person C. But it's mostly a matter of style, and I"ll have to think about it to come up with a better answer.

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