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1) Anyone/he/I can ride a bike. (we are talking about any bike in general)


2) Person A: Can you solve this problem?

Person B: Well it looks tough to me, but I can. (the speaker thinks they can solve it)

Person A: Then please solve it.


3) Anyone/he/I can ride that bike/your bike/the new bike in the market. (we are talking about a specific bike)


4) Robbing a bank/banks can/could get anyone into trouble. (we are talking about any bank in general)


5) Robbing a bank/banks can/could get him into trouble. (we are talking about any bank in general)


6) Robbing the bank can/could get him into trouble. (we are talking about a specific bank)


7) Robbing the bank can/could get anyone into trouble. (we are talking about a specific bank)


Q1) Do all the examples above make sense?

Q2) What time frame does a sentence with "can" or "could" refer to? Do all of the above sentences refer to the present or to the future or are they just timeless statements?


Note: "could" is used here in the hypothetical/tentative/indirect sense, not the past of "can".

Comments  

OK. This is my own understanding:

By "timeless" statements, I mean a statement that started to be true at some point in the past or that has started to be true just now, and continues to be true in the future until the assumptions implicit in the statement are broken. For example:

1) I/he can ride a bike. (= I/he knows how to ride/I/he has the skill)

which, to me, means that the speaker acquired that skill in the past by riding a bike themselves. So whoever has seen them riding a bike has known that they can ride a bike. In other words, the statement, "I/he can ride a bike", started to be true at the time they acquired the skill, is true now, and will continue to be true in the future, assuming they do not get an injury or have an accident etc.

2) Well it looks tough to me, but I can solve this math problem. (= The speaker only thinks/is confident that they can solve it. They have never seen/solved the same problem in the past. It's completely new to them)

Here, the statement, "I can solve this math problem", starts to be true when the speaker is shown the problem, ie, now and will continue to be true in the future until it's proven that they can't solve it.

3) I can ride/solve that bike/that math problem.

Here, the speaker is talking about a specific bike/math problem.

If the speaker is familiar with the bike/math problem, ie, they acquired the ability to ride/solve that particular bike/math problem in the past, then the statement, "I can ride/solve that bike/that math problem", started to be true at some point in the past, it is true now, and it will continue to be true in the future.

If the speaker is NOT familiar with that bike/math problem, ie, they have no experience of riding the bike/solving the problem (as in explanation 2 above), then the statement, "I can ride/solve that bike/that math problem", starts to be true at present, and will continue to be true in the future.

5) Robbing a bank/banks can/could get him into trouble.

In the past, "he" has attempted to rob banks several times. He was successful on some occasions, and got into trouble on others. Observing these facts, the speaker concludes that robbing banks can/could get him into trouble. This is completely based on past observations. A similar sentence would be this motorway sign: Tiredness can kill. Take a break. The statement, "Robbing banks can/could get him into trouble", started to be true in the past when the observation was made, is true now, and will continue to be true in the future, if "he" continues to rob banks.

I'm not quite sure about the use of "could" in the above sentence though.

6) Robbing the bank can/could get him into trouble.

This is similar to (5) above, except that here we're talking about a specific bank. He has attempted several times to rob the same bank and the observation was made on those attempts.

Again, I'm not sure about the use of "could" in the above sentence.

Q: Is my understanding correct?

I consider all the sentences given in the OP to be timeless, because of the above reasons and because of the fact that there are no time indicators in those sentences