1. Who sent those flowers?- I'm not sure. It could have been your mother.
The above is correct written form. There's a lot of latitude with speaking, of course. Here are some alternatives:
- Who sent these flowers? Couda' been your mother.
- Who sent these flowers? Maybe your mother?
- Who sent these flowers? Could be your mother. <- not likely but understandable. This and other types of "incorrect and slightly odd" spoken responses happens often enough. It can make one think a second longer to fill in the gap or an opportunity to make a joke: "Oh! My mother turned into flowers? So who do you think sent my mother? (haha)"
2) He could have been Prime Minister now if he hadn't decided to leave politics.
The above is correct written form. You could find a place for your "could be" form in spoken language as a parallel, emphatic, emotional voice. The following illustrates this with a similar construction, but with some necessary context:
- Man #1: "It's not so bad...I'm doing well now... I've worked my way up to vice president of the Acme Corp!"
- Man's Tough Friend: "Don't give me that! You could be CEO now if you hadn't messed everything up in the first place."
3) We could have spent today at the beach, but we thought it was going to rain, so we decided not to.
The above third case is not correctly worded as you stated above. It doesn't make sense to say "I could have done X, but since Y I decided not to." That's because the decision was totally volitional. The format is "I would have done X, but since Y I decided not to." So the original sentence above would be more natural as:
- "We [were going to spend | would have spent] [the day | today] at the beach, but we thought it was going to rain, so we decided not to."
To use your original sentence wording ("could have spent"), it would need to be something less within the speaker's control, and perhaps an expression of disappointment like this:
- I could have spent the day at the beach, but Wendy got sick so I had to stay and babysit. Hrmph! (Note that this is also volitional in an absolute sense; yet has a sense of blame.)
To make it your alternative "could be spending" suggests a greater disappointment that is still ongoing and not fully accepted:
- On the phone: "I could be spending the day at the beach, right now, with all my friends, but Wendy just had to get sick and so I'm just stuck here baby sitting. Hrmph! (Note that this is also volitional in an absolute sense; but has a greater sense of disappointment and blame.)
The most mature way to handle the situation would be decisive and volitional:
- "Yes, I know... I was planning on spending the day at the beach with you guys. But Wendy got sick so I'm staying home to take care of her today. I'm certainly not going out if Wendy needs me. Have fun... I gotta go now. Bye."
As Geoffrey Leech (Leech 2004) puts it, “Past hypothetical meaning and the use of the modals is one of the most difficult areas of English not only for non-native speakers, but also for native speakers” (p. 127).
I have always thought that the oversimplified rules of conditional use, so common in old-style textbooks and no longer used in linguistics, should have been abandoned long ago. Your question is a case in point. Obviously, traditional rules cannot explain such sentences.
It is much better to think of (what is commonly referred to as) conditionals type 2 as unlikely (Huddleston’s remote) and conditionals type 3 as impossible (Huddleston’s doubly remote), without any reference to present, past, or future.
Trying to keep both analyses, Leech 2004 somewhat struggles and argues that “[t]here seems to be a growing tendency, in fact, to associate the Perfect after a secondary modal purely with ‘contrary to fact’ meaning, rather than past time” (p. 128).
He also observes that in such sentences, when modals are followed by perfect auxiliaries (in the main clause), “the past meaning of the Perfect seems to have been lost” and only the ‘contrary to fact’ meaning is applicable.
Mittwoch, Huddleston, and Collins 2002 - more linguistically oriented - offer a much better analysis (see Chapter 8 in The Cambridge Grammar of the English Language). They call such constructions doubly remote (conditional) constructions. They give the following examples:
[48] i. If you had told me you were busy I would have come tomorrow.
ii. If you had come tomorrow you would have seen the carnival.
iii. If your father had been alive today he would have been distraught to see his business disintegrating like this.
They argue that the perfect auxiliaries express modal rather than temporal meaning (p. 754). Huddleston 2002 (Chapter 3 in the same grammar) adds that the difference between remote and doubly remote constructions is "not very tangible," cf. his examples below
[6] i b. If they were alive now they would be horrified.
c. If they had been alive now they would have been horrified.
To conclude, Huddleston also argues that doubly remote constructions are "fairly rare" (p. 150).
Best 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.
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:
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.
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 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
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
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.
"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.
"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.
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
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".