@Glennn,
Quote:I concede the point that both are used for the same purpose. Asking whether or not someone could do something is like asking them whether or not they can do something.
Glennn, you may well be following the admonitions of an old false "grammar rule" about the meaning 'can', ie. can means ability, which led to the old schoolmarm admonition regarding 'may/can'.
Student: Can I go to the bathroom?
Teacher: You can but you may not.
The student's 'can' is not referencing their physical ability to go to the bathroom, it's a meaning of permission and it flows from the epistemic/level of certainty meaning of 'can' described in c - "used to indicate possibility". And further described in M-W 2 : have permission to.
The student's request is not, "Do I have the ability to go to the bathroom?". That 'can' can be paraphrased by "Is it possible for me to go to the bathroom?"
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M-W:
can
1.
a : know how to She can read.
b : be physically or mentally able to He can lift 200 pounds.
c —used to indicate possibility Do you think he can still be alive?Those things can happen. —sometimes used interchangeably with may
d : be permitted by conscience or feeling to can hardly blame her
e : be made possible or probable by circumstances to he can hardly have meant that
f : be inherently able or designed to everything that money can buy
g : be logically or axiologically able to 2 + 2 can also be written 3 + 1.
h : be enabled by law, agreement, or custom to Congress can declare war.
2 : have permission to —used interchangeably with may You can go now if you like.
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Quote:My beef is that politeness should not determine definitions.
Politeness/softness is definitely determined by the meanings that English modal verbs have come to hold.
In English the modal/semi-modal verbs have two major uses, one, as epistemic/level of certainty auxiliary verbs,
Examples: He might go/She may be pregnant/They must have heard/You should have known/
and, two, as deontic/politeness/social auxiliary or modal verbs.
Examples: Might I have a drink?/You may use my computer/Can I borrow you bike?/...
The epistemic/level of certainty meanings are primary and from those meanings flow the deontic/politeness meanings.
'can' and 'could' share an identical epistemic range of the M-W meaning described in c, "used to indicate possibility" but 'could' gains more deference/politeness from its place as the historical past tense of 'can'.
Both of the 'can' and 'could' meanings can be made to illustrate less certainty or greater certainty by the use of intonation or the addition of adverbs.
He cooooould be there. XHe cannnnnn be there.X
He certainly could be there. He certainly can be there.
Glennn: The writer understands that there is no question as to the recipient's ability to send a catalog. That's why he needn't ask the recipient whether or not he can or could send the catalog.
We would be grateful if you could send us your latest catalogue and price list.
This 'could' above, in the original sentence, marked in red, does not ask about 'ability', it is solely a deontic/politeness/social meaning that asks "is it possible for you to ... ?"