An Empty Can

It seems that, as my mother uses it, 'can' is empty:

"She surely can do a lot of complex arithmetic calculations"

she'd say -- of some neighbour's child.

But _I_'ve never seen the child doing any complex arithmetic calculation. Or arithmetic calculation, simpliciter.

"She still can", my mother assumes.

People use "can" implicature-free.

"Pigs can fly". They won't, but the can.

Pigs have a right to fly, said the Duchess to Alice, "As much as you have a right to think".

Is this use of 'can' empty?

I hold it is. Sometimes, implicaturally, we narrow down the use of 'can' to mean 'know':

Do you can John Peele, with his coat so grey?

-- meaning ...?

"2 + 2" can it be, "5"?

Possibly -- if you change the syntax of arithmetic.

But can "2 + 2" become a butterfly?