3
  • Let me know, should you come.

Like the one above, I've seen many sentences that had inverted conditionals which started with should, were, and had--but not with could, did, or have. So I wonder if sentences like, for example, the ones below can be idiomatic:

  • Like this video, did you find it fun.
  • Raise your hand, haven't you finished yet.
  • Let us know, would you consider joining.

If they are utterly unidiomatic, why did this happen? Why should, were, and had can be inverted and used as conditionals whereas other auxiliary verbs can't? I mean, as for questions, all auxiliary verbs can be inverted and work as questions, like "Did you?, Have you? Do you?" But why not in conditionals? Is there some special reason for that?

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    Just to let you know, the example Let me know, should you come is difficult to parse for a native speaker. Should you come, let me know is a more natural example of what you're trying to illustrate. The other three are utterly unidiomatic, but "why?" is an interesting question... I can find plenty of references to say that should, were and had are the only verbs that can be inverted like that, but nothing to explain how we've ended up that way. – Morton Jun 13 '15 at 16:25
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You used to be able to use could, would, and did in constructions like this. And in fact, the sentences I found below don't sound ungrammatical to me, although they do sound quite old-fashioned. Your proposed examples are all ungrammatical, because they don't belong in the subjunctive mood.

Searching 19th century texts, we find:

Could I find aught worth transmitting from so remote a region as this to which I have wandered, I should gladly send it;

and

Could I see him, I might on this side guard against his penetrating eye, or on the other side act something in secret, safe from his inspection.

and

Nothing is more common among men ... than to say, "could I but live to see such and such an event take place, I should die content."

and

Could I but find a substitute for matches, I might strike a light (he had left the candles with me in very derision), and then escape was certain.

You can also find did used this way, but it seems rarer than could.

For example

nay, torture itself could not be misery to me, did I but know that she was happy.

and

Surely no sinner would willingly incur eternal damnation, did he but really consider what it is

This is a past tense subjunctive mood construction, which rules out all of your suggested examples, as the condition must be counterfactual (or at least be likely to be counterfactual).

You can't use have, because it's present tense.

The remaining past tense auxiliary verbs are might and would. I believe the fact that this must be counterfactual means that might doesn't work, as it's hard to see how a counterfactual would work with might.

This type of construction is also hard to form with would, as in this case, would must mean if he were willing to. However, you can find it:

A palace to dwell in—coffers swelling with gold—honors unnumbered—office, dignity and favor—all that could gratify ambition, taste or desire, were within his grasp; would he but accomplish one end! And what was that? To plunge another in misery ...

and

He moved a few steps nearer, and those few steps were enough to prove in how gentlemanlike a manner, with what natural grace, he must have danced, would he but take the trouble.

Why has the list of grammatical inverted conditionals winnowed down to had, should, were today? The slow death of the English subjunctive means that these are now essentially frozen forms which are not perceived as subjunctive, but which are just idioms. So it's not surprising that the rarest modal verbs in this construction (definitely did and would; maybe could) are no longer used today.

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I don't know, but part of the answer is that this construction is used to express doubt about the content of the clause it occurs in. I suppose you could call it "subjunctive". It sounds old-fashioned, and I don't think it would ordinarily be used in modern American colloquial English. (Or, I could say "Were it to be used, I'd be surprised".)

But that doesn't tell us why we don't find "could" or "would" inverted, because they can express doubt in if-clauses, too: "If my sister could speak Sanskrit, I'd be shocked." but not *"Could my sister speak Sanskrit, I'd be shocked."

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    Just to confirm that, you wouldn't often use this construction in modern British colloquial English either, except perhaps in a few stock phrases like "Were I a betting man". Over here, I'd describe it as formal rather than old-fashioned - but the line between the two is often a fuzzy one. – Morton Jun 13 '15 at 17:49

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