When shop assistants have nothing else to do, they ask us, ‘Can I help you?’ (on those occasions when they don’t say, ‘You alright there?’). Would anyone reply on these lines?
Well, I have no knowledge of your physical or mental capacity, professional expertise, or training, so I can’t really comment on that. But if you’re asking me if I would like you to advise me on my prospective purchase, you should have asked my permission by saying, “May I help you”? And in any case, the answer is, “No”.
We wouldn’t, because we know that, ‘Can I ….’ in this context certainly does not indicate ability or its absence, but is used to make an offer, meaning, ‘Would you like me to …..?’ Can, like other modal verbs, is a versatile performer. Nobody seems to mind when a speaker uses must for deduction (‘People are putting up their umbrellas. It must be raining’) as well as for obligation (‘You must complete all fields marked with an asterisk.’) Why is there a problem with can?
On the two meanings of must, here’s a story (with apologies to those who may know it already). When Castro visited the Soviet Union, Kruschev showed him a new colleɡe buildinɡ. ‘This was donated by our friends, the Bulgarians,’ said Kruschev. They went on to inspect a new sports stadium. ‘This was donated by our friends, the Poles,’ said Kruschev. Finally they visited a new conference hall. ‘This was donated by our friends, the Hungarians,’ said Kruschev. Impressed, Castro said, ‘They must all be very good friends.’ ‘Yes, they must,’ said Kruschev.