Difference – Understanding ‘Might,’ ‘Might Have,’ and ‘Could Have’

The two words have overlapping meanings, so there are contexts where either one could be used. However, there are certain constructs where one would be regarded as much better than the other.

I'm not sure if I can provide an exhaustive list of contexts where you should use might instead of could, or vice versa. Let's start with the example you provided, which is when either word is followed by not.

The phrase might not indicates a possibility that the contrary could happen. The word cannot suggests that the contrary won't happen. And the phrase could not suggests that the contrary wasn't able to happen.

So:

He might not show up.

means that he might show up, but we're starting to think he may not, while:

He could not show up.

suggests that, because of some obstacle, he was not able to make it.

Let's say we're supposed to meet Mike at 8 o'clock, and it's now 8:20. We have no idea where Mike is. I might say:

Let's not wait any longer. He might not turn up.

However, just before I finish my sentence, my cell phone rings. It's Mike! Mike tells me that his flight is delayed; the airplane is having mechanical problems, they haven't even left the runway yet. Mike is 500 miles away. Now, I say:

Let's not wait any longer. He cannot be here; he's stuck in Memphis.

Next, my friend and I leave, and we go to Ted's house. Ted sees that Mike his missing, and asks, "Wasn't Mike coming with you guys?" I might reply:

We waited for him, but he could not be here. His flight got delayed.

This is because, while might infers a possibility, could can infer a possibility, or an ability. Let's say you set a bar a meter off the ground, and ask me if I'm able to jump over it without touching it. I could say:

I might be able to do that. (it's possible)

But now you raise the bar two meters off the ground, and ask me if I can jump over it. I might say:

There is no way I could do that. (it's impossible)

However, there are times when the words could be used interchangeably, as you have sensed. For example, let's say we're leaving the house for a few days, and we're trying to decide whether or not to leave the furnace on. I might say:

Let's make sure the furnace gets turned on before we leave. We might get some cold weather.

or:

Let's make sure the furnace gets turned on before we leave. We could get some cold weather.

In that context, the two phrases mean essentially the same thing.

Now, an interesting example for the advanced reader. Consider these two statements:

The repairman might come today, but he could come tomorrow.
The repairman could come today, but he might come tomorrow.

Is there a difference? I'd say that both of them mean that the repairman is supposed to come either today or tomorrow, although there's a little uncertainty as to which day he will arrive. But does one of them suggest a higher probability one way or the other? I don't think so, at least not reliably.

Lost opportunities

The meanings of these are indistinguishable, except for a subtlety that I'll explain later:

We may have been able to save the victims.

We might have been able to save the victims.

The words "would" and "could" suggest both the past tense and the consequence of some imagined hypothesis, with either or both meanings being activated when suitable to the context. To use "would" here, you need to establish an imagined hypothesis. Then "would" indicates the consequence:

If only we had the antidote yesterday! We would have been able to save the victims.

It's possible to say "could have been able to", but "could" is the past tense of "can", so it already indicates ability. So, "could have been able to save the victims" is awkward. However, you could say:

If only we had the antidote yesterday! We could have saved the victims.

"Would have" and "could have" imply that the opportunity is now lost.

"May have", "might have", and "could have" don't require context to set up an imaginary hypothesis, but they do suggest that you have such a hypothesis in mind:

"We might have been able to save the victims."

"How?"

"The most recent antidote has been sitting in the refrigerator since yesterday."

"What? And no one tested it?"

An important difference

A very big difference between the may/might and would/could sentences is that the would/could sentences claim a high level of certainty about the hypothetical situation: the antidote is assumed to work. The may/might sentences lack that certainty. They suggest only that in the hypothetical situation (which might not even be stated yet), the antidote might have worked. "Would" corresponds to "will", and says that the antidote will work (in the imagined situation, which occurred yesterday). "Could" corresponds to "can", and suggests that the antidote can work (in the imagined situation, which occurred yesterday).

A subtle difference

"May have" mainly indicates uncertainty about what we could have done. "Might have" suggests both uncertainty and that the opportunity, if it even existed, is now lost.

This is English, so don't take that as a rule. Instead, memorize this well-known couplet (by John Greenleaf Whittier, 1856):

For of all sad words of tongue or pen,

The saddest are these: "It might have been!"

One more power of might

There's one more possibility with "might", which illustrates the flexibility of these words. "Might" can suggest that the victims actually were saved, or are actually in the process of being saved:

We might have been able to save the victims. I just read an article in a medical journal, which says that the antidote we tried yesterday was proven to work on mice in a recent experiment.

In other words, the antidote we tried yesterday might be working, right now. Since the uncertainty of the word "might" applies to our ability to save the victims, if we had that ability yesterday, then our efforts yesterday were successful, or are on the way to succeeding. Currently, we don't know (that's the uncertainty of "might"). Obviously, your listener will hear this meaning only if the victims are still alive.

You can also do this with "may have" and "could have", but those don't make the pun in the title of this section. Since "may have" has the least connotation of lost opportunity, it provides the clearest way to express optimistic uncertainty about the effects of yesterday's action: "We may have saved the victims."