modal verbs - Request a context for a hypothetical use of "could"

As Leech, Geoffrey N. suggests in Meaning and the English Verb §186, could can have the following usage:

#1. Hypothetical equivalent of can (= ‘possibility’)

The house is one of the most beautiful that could be imagined.

#2. Hypothetical equivalent of can (= ‘ability’)

Do you know anyone who could repair this clock for me?

I didn't understand how the hypothetical use was involved in these two examples until I found an explanation from here:

Part 1 If someone is messing around with your clock - but they haven't broken it yet - you can say:

• "Do you know anyone who could repair this clock for me?"

It means: "If you break my clock, who do you think is going to mend it?"

That's a hypothetical question and you have stated it correctly.

Part 2 Some sentences are definitely hypothetical - because that is their grammatical structure; others can be hypothetical because of the way they are used..

• 
  

  If you wanted to, you could go to a baseball game with me

  
  


• 
  

  You think I could mend your clock

  
  

The first is definitely hypothetical because it has "if" and "could"

The second does not seem to have a hypothetical structure but very often it will mean..

• If for one moment you were to think I could mend your clock then you'd be very much mistaken!

..in which case there is a hypothetical use

I think your textbook (Meaning and the English Verb) is saying that, on the one hand you need to see how the words: if, were, could, would and so on are used to form hypotheses; but on the other hand, you need to know that, in English, hypothesis is sometimes implied with only a hint of those words.

So what kind of context would be apt for #1 so that could could be regarded as a hypothetical equivalent of can (= ‘possibility’) rather than a mere representation of 'real' possibility?

Can you please contrive a hypothetical scenario for Leech's explanation of #1?

Answer

These are both hypothetical because they express uncertainty. The difference between "could fix my clock" and "can fix my clock" is that "could fix my clock" is less definite--it refers to someone who MIGHT be able to, vs "can fix my clock"--this person is definitely expected to be able to fix it. The only real difference is one of tone: "could" is more polite because it makes the speaker's request less demanding (I don't need you to guarantee the repair, just suggest someone I could ask).

In #1, I would say the difference is in what can be done, in some limited sense, vs. what hypothetically could be done, ever. Let me give you a different example that will be more clear:

(1) "This TV has the best display that can be produced."

vs.

(2) "This TV has the best display that could be produced."

In the first example, there is a definite implication of "at this time" or "with current technology," etc. Phrasing it that way suggests that under different circumstances, in the future, it will be possible to produce a better display. But in my second example, the speaker is saying people will never be capable of producing a better display. It's not just the best that can be done right now; it's the best that's theoretically possible, ever.*

Anyway, in your example, this house isn't one of the most beautiful that I personally can imagine, or that any of my friends can imagine, etc. It's one of the most beautiful that any human being at any point in history could possibly imagine. The sentence is referring to a broad hypothetical possibility rather than a more restricted or bounded possibility.

But please keep in mind I'm somewhat overstating the difference to clarify how the "hypotheticality" framework might apply. Practically speaking, the difference between "can" and "could" is mainly one of tone, which won't necessarily be obvious or easy to extrapolate from this framework.

[*] That difference goes away if I add some kind of limit to the second sentence: if I say "the best display that could be produced [under the circumstances / with available resources / with current technology / etc...]", that's a lot more like the "can" example. It's still talking about what's hypothetically possible, but it's stating boundaries for the hypothetical situations being discussed. But note! That changes the tone dramatically. If I say "The best TV that could be produced." I sound like a salesman talking about how awesome my product is. If I say "The best TV that can be produced." the tone sounds like I expect improvements to happen in the future. But if I say "The best TV that could be produced with available methods" I sound like I'm apologizing or making excuses for not doing better; if I say "The best TV that can be produced with available methods" it starts to sound like I'm bragging again, because I'm emphasizing that my company has made the best possible use of the methods available... When I add the qualifier, the tone flips, and "could" goes from making me sound more confident to making me sound less confident. So I would say that the theoretical difference is one thing, but to use it successfully, you'll need to look at a lot of examples.