Which word to use when we ask for help?
- We know that the person asked is able to do it.
- We don't know if the person asked is able to do it.
As waiwai993 answered, Can/May/Will have different meanings. However asking someone if they can help you usually implies that you would like their help, and it gives the person an opportunity to decline without being rude. Maybe they are able to help in theory, but can't right now because they are too busy. In that case they can say that they can't help. If they simply don't want to help they can just decline without a reason. So I would always use "Can you help me with this" or "Could you help me with this" unless I needed a more specific case (such as I KNOW that they CAN, but I am forcing to answer whether they WILL or not, or I know that they are ABLE, but maybe their mother won't let them*).
* Note: I think it's very unusual to use "May you help me" and would probably never say that under any circumstances, unless I was trying to be ironic.
I would actually offer a couple additional options:
Under condition 1 (that you know that the person is able to help, but you're unsure if they will):
Under condition 2 (you're unsure if that person is able to help):
These are similar in meaning to will and can respectively, but are a more polite way of asking. I would especially recommend these if you're in more formal setting, talking to strangers, etc.
Technically, this asks if it is physically possible for the other person to help. However, it is commonly used to mean "Will you help me with this?"
This is equivalent to "Are you permitted to help me with this?"
This is the one you probably want—it basically asks whether or not the other person is going to help.
As for me, I sometimes feel a bit shy talking to people, so I prefer polite variants like:
Or you can just say:
I don't have much experience in communication with English-speakers, but I think those variants can be used in different situations.
May implies that you are asking for permission. Can implies that you are questioning somebody's ability. Will implies that you are seeking an answer about the future.
Why not ask etymology for some help here?
"Can" and "could" come from Proto-Germanic *kunnan, “to be mentally able, to have learnt”, says the Online Etymology Dictionary.
"May" and "might" come from Proto-Germanic root *mag-, infinitivie *maganan, from Proto-Indo-European *magh-, “to be able, have power”.
So, "can/could" is about ability proper, the ability to do things for yourself, knowing how to do them,
"may/might"is more about power, the position a person is in which entitles them to grant or refuse you permission to do something; it is highly hierarchical.
So, "Can I go to the bathroom?", etymologically, is not really appropriate for asking permission as it means something like "Do you think I know how to go to the bathroom?" Rude, even!
On the other hand, "May I go to the bathroom?", etymologically again, means something like "Would your highness allow me to go to the bathroom?" and, in the classless world we live in (?) we are not really ready to your-highness anyone if we can avoid it! Well, little children cannot really avoid it for a question of stature, but when you have grown up, using "may" is felt as humbling, if not humiliating yourself, as if you were kneeling in front of someone.
A middle ground between rudeness and humiliation, which can satisfy both the speaker and the listener, is found in "Could I go to the bathroom?"
Using the modal "can" in the conditional, 'unrealising' the present, making it hypothetical, dampens the shock. I am asking about objective conditions (do you think I know how to) but using the conditional instead of the present puts more emphasis on the listener, on their ability to assess the situation, which is a tacit acknowledgement of their authority. It is give-and-take!
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