The following parts are taken from Michael Swan's, Practical English Usage (hereafter PEU):
259.2 could have ... and might have ...
We can use could have + past participle to mean 'would have been able to .. .', and might have + past participle to mean 'would perhaps have ... ' or 'would possibly have .. .'.
Example A: If he'd run a bit faster, he could have won.
Example B: If I hadn't been so tired, I might have realised what was happening.
But in 122.7 could have ...
We use this structure to talk about unrealised past ability or opportunities - to say that somebody was able to do something, but did not try to do it; or that something was possible, but did not happen.
Example C: I could have married anybody I wanted to.
Example D: I was so angry I could have killed her!
Example E: Why did you jump out of the window? You could have hurt yourself.
Example F: I could have won the race if I hadn't fallen.
Sometimes I feel it a little difficult to decide, for a given context, which of the following meanings of "could have" is being used:
- 'would perhaps have ...'
- 'would have been able to...'
- 'would have been allowed to... '
- 'would have the opportunity to ...'
I'm also not sure if could have can also mean "would possibly have". No grammar books explictly confirm this. Maybe the bold section in 122.7 suggests this (but I am not quite sure). So can I make the following substitutions (SUB) -- taken from the PEU text referenced above -- or would they change the original meaning or create an ambiguity?
- EXAMPLE B ORIG: If I hadn't been so tired, I might have realised what was happening.
- EXAMPLE B SUB: If I hadn't been so tired, I could have realized what was happening.
- EXAMPLE E ORIG: Why did you jump out of the window? You could have hurt yourself.
- EXAMPLE E SUB1: Why did you jump out of the window? You would possibly have hurt yourself.
- EXAMPLE E SUB2: Why did you jump out of the window? You might have hurt yourself.
- EXAMPLE F ORIG: I could have won the race if I hadn't fallen.
- EXAMPLE F SUB: I would possibly have won the race if I hadn't fallen.
Answer
Could have is saying that something was definitely possible in given circumstances.
Could have indicates that the option was available: that the possibility existed, not limited by circumstances, situation or personal ability. It tends to be used when you are talking about an entire hypothetical scenario.
When I was training for the marathon, I could easily have beaten you in a race!
The focus is on the capability: in this case the speaker knows that they definitely could have won the hypothetical race if such a race had occurred.
Note that saying they are definitely capable of doing so doesn't necessarily mean that it would definitely have happened, just that it had a probability of more than zero. A negative example might help to illustrate this:
Even if I had trained for a year, I could not have beaten Jesse Owens in a race.
It also doesn't give any indication of how likely the speaker thinks the possibility was, just that they believe it was definitely a possible outcome.
Would have defines a definite outcome given different circumstances.
Would have indicates that something intervened to stop the predicted outcome from arising. It tends to be used when you are talking about a change to the real sequence of events: if something had happened differently.
I would have beaten you in that race if I hadn't tripped up!
This is expressing certainty: if the situation was different (in this case, not tripping up), the predicted outcome (beating you) would definitely have occurred.
Might have defines a possible outcome given different circumstances.
Might have is the same as would have, but the speaker is less certain of the outcome.
I might have won that race if I had done more training.
I didn't win the race, I think I might have won if I'd done more training, but I also think that I still might not have won even if I had done more training.
Your specific examples
As you might have guessed, many of these sentences are correct but with subtle differences in nuance.
Example B
- If I hadn't been so tired, I might have realised what was happening.
- If I hadn't been so tired, I could have realised what was happening.
Because this is talking about a change from the actual situation, not an entire hypothetical scenario, "might" sounds more natural here than "could". That doesn't mean that "could" is wrong, just that it would be more common to say "might".
If you were sure that you would have realised what was happening if you'd been less tired, you could say "would" instead of "might".
Example E
- Why did you jump out of the window? You could have hurt yourself.
This is indicating that hurting yourself was definitely an option (and hence it was stupid to jump out of the window). For this reason, it expresses the sentiment most strongly out of all your "window" sentences. It's implied that you were lucky not to hurt yourself - in other words, luck was all that prevented you from hurting yourself.
- Why did you jump out of the window? You might have hurt yourself.
"I suppose you might have hurt yourself, but I'm not a window-jumping expert, so I don't know..." There's less certainty here, so it's less forceful. However, it's still entirely acceptable.
- Why did you jump out of the window? You would possibly have hurt yourself.
"Would possibly have" has the same meaning as "might have". To me, it sounds slightly less natural here, but I think that's because the question itself sounds a little accusatory, so adding the "possibly" in is a little awkward.
Example D
You didn't suggest a substitution for D but I'm including it to show the difference from E.
- I was so angry I could have killed her!
- I was so angry I might have killed her!
In this instance, it's actually the "might" example that is stronger. That's because the "could have" suggests that the speaker was angry enough to kill her, but chose not to. Because it's "could", we know it's a hypothetical scenario and that there was no chance of him actually killing her: just that his anger gave him the capability of doing so.
However, "might have" admits the possibility that this outcome might actually have occurred. It sounds like it's something external to the speaker that prevented it, like someone walking in, or maybe he went so far as to beat or shake her and it was only luck she didn't die.
Needless to say, "would have" is therefore the strongest of the three, indicating that she definitely would have died if something had been different (like they didn't get interrupted).
Example F
- I could have won the race if I hadn't fallen.
- I would possibly have won the race if I hadn't fallen.
These both sound equally natural, but the nuance is different. In the first one, the speaker is certain of their ability to win races, but acknowledges that that doesn't mean they'll win every race they ever run. Falling stopped them being able to win the race - an ability they had before they fell.
In the second sentence, on the other hand, the speaker is still acknowledging that the outcome of the race (even without falling) was uncertain, but they are doing it in a way that includes the possibility they might not have won the race because they simply weren't good enough. It's a broader statement: that they might have gone on to win if they hadn't fallen, but they don't know if they would have gone on to win.
Some other things you mentioned in comments
I think your would possibly/perhaps have example is the same as might have, and would have been able to is the same as could have, with would have been allowed to being a subset of that where permission is the limiting factor of the "could".
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