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If I had that book, I would give it to you.

I don't have the book, but if I did have it, I would give it to you.

If I had had that book, I would have given it to you.

I didn't have the book, but if I had the book, I would've given it to you.

Are both the interpretations correct?

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    Both are correct. – P. E. Dant Jul 3 '16 at 18:43
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    The first may also refer to a past habitual action: "On many occasions when we were students together you asked me for a book, and on each occasion, if I had that book I would give it to you." Ambiguities of this sort are generally ignored in teaching the 'n-conditionals', which is one reason many of us deplore this pedagogic categorization. – StoneyB Jul 3 '16 at 20:06
  • @StoneyB If there is one thing in the English language that I would eliminate if I were granted magical powers, it is the necessity, in certain narrowly defined circumstances, of using the construction "had had." – P. E. Dant Jul 4 '16 at 3:57
  • @P.E.Dant 1) I don't think had had is necessary in OP's second example. 2) Had had is eroding. What folks actually say is 'd had, and they're drifting toward 'da had. – StoneyB Jul 4 '16 at 10:16
  • Possible duplicate of Doubts with second and third conditional – Alan Carmack Aug 13 '16 at 4:32
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What seems confusing to me about the 3d Conditional sentence is that the "interpretation" is the same sentence without the double use of "had":

If I had had that book, I would have given it to you.

If I had the book, I would have given it to you.

Whether the use of the double "had" with a non-action verb, which "have" is here, in a 3d Conditional sentence correct, is another question.

Nevertheless, here is an example of the use of the double "had" when "have" is an action verb:

He has already had a drink, so he can't drive her home. (That's why she's going to order a taxi.)

If he hadn't had a drink, he could have driven her home. (That's why she got home by taxi.)

Also, see here.

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