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What does 'could' mean in the following sentences Or how is 'could' different from 'can' in these sentences?

I appreciate any help you can/could provide.

I will appreciate any help you can/could provide.

I would appreciate any help you can/could provide.

Does could mean 'might be able to'? That is, I doubt your ability to provide help.

Well, I know the difference between 'can' and 'could' as I've gone through many dictionaries and forums to understand all the modal verbs. I just wanted to know whether my understanding of 'could' in relation to the given sentences is correct or not.

Mr. X
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These are not just any sentences with can or could. These are requests, and as such they have special usages.

There is a grammatical construction for telling people what you want them to do:

  • Help me with this.

But instead of using the imperative, the speaker has asked a question. Using a question form is already indirect. The speaker is not asking for information. The speaker is asking for service, but indirectly, preserving the addressee's face by not imposing a demand.

Similarly, the use of modals is more softening. The speaker does not ask for a prediction or promise:

  • Are you going to help me?

but rather merely a question about possibility -- can you? could you? might you be able to? do you think it's conceivable that you would? -- these are all standard phrases by now, though the long ones are for more formal occasions.

So it's not a matter of the two modals having different senses -- and, incidentally, there's no issue of doubt involved; it's all just politeness formulas -- but rather that modals are very complex and have many social and idiomatic usages that don't follow normal kinds of rules. In fact, every modal I know anything about is terribly irregular in just about every conceivable way. That's just the way they are.

John Lawler
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I [will] appreciate any help you can (= are able) provide.

I [will] appreciate any help you could (= are possibly able to) provide.

The "could" form is a polite request as it does not assume that the amount of help that is required is capable of being given.

Compare: "Will you open that window?" This is almost a command.

"Would you open that window?" This is the polite version.

The "will" makes no difference.

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Greybeard
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