Can and May provoke some odd ideas in ‘popular’ grammar. When adults tell children Don’t say, ‘Can I leave the table?’; it should be ‘May I leave the table the table?’, the assumption often seems to be that can is restricted solely to ability – Am I able to leave the table? – and has nothing to do with either permission or compulsion.
In fact, the distinction between the two verbs is far more subtle. Can does have a meaning relating to permission – specifically when the permission is general or of unknown origin. You would hardly say ? May children under 12 see this film? or? I may do whatever I want. You would use can.
May is used when you are giving permission yourself (You may go now) or when you are asking permission of a specific person: May I go now? So Can I smoke here? is a question about general rules and customs; May I smoke here? is a specific request for permission from someone with the power to grant it.
In many contexts, either can or may will do. If you have to ask your manager for a day off work you could say Can I or May I have tomorrow off? There may be a theoretical difference: Can I . . . ? – Is there anything against it? May I . . . ? – Do you say I can? But in effect it comes down to the same thing.
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