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Hereafter, TO = time of orientation (reference time).

[i] He said I could win if I really tried. [open conditional interpretation]

[ii] He knew he would be in trouble if they were to check his alibi. [remote interpretation]

(The Cambridge Grammar of the English Language, p198)

In [i], the preterite in could indicates that TO is in the past,
whereas in [ii] the preterite indicates modal remoteness and the location of TO is not expressed, says the book. Does [ii] say either Speech Time is not seen or there might be some Event Time in context apart from ST, for Reference Time?

CGEL,p.148) remote conditional; open conditional

remote) If he was here, he'd be upstairs. If you went tomorrow, you'd see Ed.

open) If he is here, he'll be upstairs. If you go tomorrow, you'll see Ed.

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    I don't know what you mean by “In [i],[...]To is in the past”. Does “To” mean something special when capitalized? I don't think Google can help me here.
    – Tyler James Young
    Nov 11, 2013 at 16:43
  • @TylerJamesYoung, snailboat once wrote the full name on this.
    – Listenever
    Nov 11, 2013 at 23:16
  • It's a bit late to be asking this, but: could you give more detail of what CGEL means by 'open conditional interpretation' and 'remote interpretation'? These could be backshifts of EITHER can/try//will/check OR could/tried//would/checked; but To is expressed by said/knew. Does CGEL perhaps mean that the embedded conditionals may be understood as EITHER tensed OR modal, but not both simultaneously?
    – StoneyB on hiatus
    Dec 22, 2013 at 3:09
  • @StoneyB Thank you very much. I’ve given up and forgot this, but by your stimulus I look up the page again. There’s no definition for open or remoteness but the examples as far as I’ve read. And so I added some of them below the OP. : As you say, identical form could be used both open conditional and remote conditional, is what the book says.
    – Listenever
    Dec 22, 2013 at 4:34
  • @StoneyB For example, ‘He said I could win if I really tried’ can be said from ‘I can win if I really try (open) (1)’ or ‘I could win if I really tried (remote) (2).’ (1)’s preterite indicates that To is in the past; “while (2)’s indicates modal remoteness and the location of To is not expressed.” The latter I understand, but it’s beyond the domain of my uttering.
    – Listenever
    Dec 22, 2013 at 4:35

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It appears that what CGEL is saying here is simply that past-form modals in a backshifted context such as past-tense reported speech may be understood as marked for either temporal or modal remoteness, but not both.

[i] He said I could win if I really tried ... may be understood as reflecting EITHER
  [a] You can win if you really try ... OR
  [b] You could win if you really tried.

[ii] He knew he would be in trouble if they were to check his alibi. ... may be understood as reflecting EITHER
  [a] I will be in trouble if they check my alibi ... OR
  [b] I would be in trouble if they checked my alibi.

The two [a] readings are what CGEL calls ‘open conditional’; they make a definite but contingent prediction about the outcome. If these readings are adopted, the past forms in both clauses of the embedded conditionals signify a past TO (Reference Time), without ‘modal remoteness’—could and tried match the past tense of said, would and were to match the past tense of knew.

The two [b] readings are what CGEL calls ‘remote l’; they signify that the prediction about the outcome is both contingent and, even if the contingency is met, uncertain. If these readings are adopted, the past forms in both clauses of the embedded conditionals signify ‘modal remoteness’ but say nothing about how TO in the conditionals aligns with the TO in the matrix clause.

CGEL is not saying that there is no Reference Time in the [b] readings of these sentences, merely that the embedded conditionals do not in these readings have independent RTs. They draw their RTs from the clauses in which they are embedded.

It's not clear to me what CGEL is driving at. These observations are true, but as they stand sort of trivial, which from what I know of Profs. Huddleston and Pullum is surprising. I suspect that CGEL employs these observations as a springboard from which to leap into contrasting sentences with embedded conditionals which do exhibit independent RT, either as true irrealis constructions or as inferentials with tense-sensitive conditions and consequences.

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