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1.1. ability ( objective meaning )
The ability of "can" expresses the subject ability of a sentence. Therefore, as the subject, the person and the creature are often used. See the following examples.

a. I can speak English.
b. I can swim very well.
c. He can cook some Italian cuisine.

Even if the subject is not the creature, it can be used if it is considered as its ability. See the following example.

This hotel can accommodate 300 guests.

"Be able to" is similar to "can", but "can" is preferred to express the present. "Be able to" pays attention to the actual act. See the following examples.

a. She could speak French.
b. He could swim very well.

"Could" does not express the actual act in the definite point. The above expresses the only ability, that is, the past habitualness.

a. She couldn't play the violin.
b. He couldn't cook anything.

The acts can be expressed with the negative, because the acts were not occurred. To express the actual past act, "was able to" is used. See the following examples which are changed form (4).

a. *She could speak French then.
b. She was able to speak French then.

a. *He could swim then.
b. He was able to swim then.

"Then" means the definite past point, therefore, "was able to" is used. Each (a) is unacceptable. (Cf. 2.3.2 of The sense of time in English 2)
Now, the perception verb can use "could" as the act, since it means the duration. (*6)

*6 "Can" is the same. See the following example.

I can hear something.
(I'm listening to something.)

a. I could hear the door slamming.
(I'm listening to that.)

The above can not be changed into the next (9a), since the meaning is not parallel to "slam" which is the temporary act.

a.*I could hear the door slam.
b. I heard the door slam. (*7)

(Cf. of the sense of time in English2)

*7 The perception verb usually expresses the temporary act. When the modal auxiliary is co-occurred, it expresses the durative act.

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