I couldn't have come OR I couldn't come

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انجمن: 

hi i got a question on my mind. would u please be kind enough to answer ?

Suppose that a friend asks your over. for some reason u can't make it to his place. when he later on asks u why u didn't come over.
how would u answer , a) i couldn't have come b ) i couldn't come
sorry if it was a bit long just wanted to make it thorough

Hi,

The answer is choice b. Because he was not able to come over due to any reason (- certain action in the past).

Choice a is the structure (could +have pp) that shows the possibility and probability of an action in the past.

Example:

Boy: after picking the cherry, I jumped down the tree.

Father: why did you do that? You could have broken your leg (but you did not) or you could have lost your life for nothing (but you did not).

hello,

with all the respect I don't see how this explanation makes B a better option .

as you pointed out it shows possibility , yet it makes a perfect sense to say i didn't have the possibility to come to your place for some reasons , to a sense it's more of a matter of possibility than ability . because you didn't lose your ability to walk to his place but the situation didn't let you use it .

let me clear it up with an example :

this is how the friend might answer back : you could've (or whoulda ) made it if you'd tried harder ( common structure of if sentences )

so if the friend can answer like this which unquestionably makes sense , the guy of our story could very well go for the same structure .

thank you , looking forward to hearing more of your opinions and others' .

Hi back,
Modal auxiliary + verb has several usages. One is the real sense of the modals, their dictionary meaning, like (can= be able to), (must=obligatory action)
However, there is another usage for the modal auxiliary when they do not mean the dictionary meaning but they show the inferences you make for an event. There are three tenses in this usage, e.g.,
Simple Present inference:
The man standing there is wearing a jacket and tie. He must be the teacher.
Must here means most probably he’s our teacher.
Or you may say, he can't be the waiter.
Can't here does not mean ability but the least possible probability for being the waiter.
Present continuous inference:
I had a date with John at 9. It is 8:50 now. I called him and he is not at home now.
He must be coming now.
Here must does not mean obligatory action but it shows the strongest possibility and inference that he is coming here now.
Past inference:
The street is wet. It must have rained last night.
Here must shows the strong probability and inference that the wet street is due to the last night raining.
The degree of probability and inference is shown by the use of the modals here. The order is that must is the most probable one and can't is the least probable inference about an action about present (no. 1) and about past (no 3).
For probabilities less than must you can use could, then may, and the less probable than all is might before can't. So you can translate them like this:

زمين خيسه. به احتمال زياد بايد ديشب بارون اومده باشه.

The use of the above modals has nothing to do with their dictionary meanings. But the order from must to can't only decreases the degree of one's certainty on the predicate.
I hope it is clear enough.