Can and could

Can is used to express ability (as in "I can speak English", meaning "I am able to speak English" or "I know how to speak English"), permission (as in "Can I use your phone?", meaning "Do you permit me to use your phone?"), willingness (as in "Can you pass me the cheese?", meaning "Please pass me the cheese"), or possibility ("There can be a very strong rivalry between siblings", meaning "There is sometimes a very strong rivalry between siblings"). (Some of these senses may be perceived as incorrect in some dialects; in particular, formal American English often prefers to use may when the sense is permission and could when the sense is willingness.) The negative of can is the single word cannot or the contraction can't.

Could has at least three distinct functions. First, it can often replace can, although generally it gives the phrase a more conditional tone. For example, "I can help you with your work" suggests that the speaker is ready and willing to help, whereas "I could help you with your work" gives a more tentative sense of ability to help. In this sense, could is often used like a conditional: "I could help you if you helped yourself."

Second, could functions as a kind of past tense for can, though could doesn't function grammatically like any regular past simple verb.

Third, could carries the same meaning as might or may in the present. That is, could suggests that something is a possibility. For instance, John is not in the office today, he could be sick. In this phrase, might or may would carry the same meaning. Note that can in the negative carries the same idea as couldn't in this sense: "He can't have left already; why would he want to get there so early?" Also note that when regarding potential futures actions could is not equivalent to might or may. "I might go to the mall later," doesn't have the same connotations as "I could go to the mall later," which suggests ability more than possibility.