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[5]
i  If she beats him he’ll claim she cheated. [non-deictic past]
ii If you eat any more you’ll say you don’t want any tea.[non-deictic present]

The preterite and present tense inflections on cheat and do indicate that Tr is respectively anterior to and simultaneous with To, but here To is clearly not Td. The time of the (possible) cheating is not anterior to the time of my uttering [5i], but to the time of his (possibly) making a claim of cheating.
                   — The Cambridge Grammar of the English Language, p126

I can understand To (time of orientation = utterance time), yet don’t get what the ‘deictic time (Td)’ is. Would you let me know the Td?

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Deictic (adjective form of deixis, 'pointing') is used in linguistics to designate expressions which explicitly refer to the spatial or temporal relationship between the speaker and what he is talking about. This and that are deictic adjectives or pronouns, and there, then, here, now, whence, whither, thither, hither are deictic adverbs, because they 'point' to objects or places or times from the standpoint of the speaker.

CGEL employs the term 'deictic time' (Td) to designate the speaker's standpoint in time, the time from which he 'points' to the events he is talking about. Deictic time thus seems to be equivalent to what the Reichenbach model calls 'Speech Time' (abbreviated 'ST') or 'Utterance Time'. CGEL's Tr (time referred to) is Reichenbach's 'Event Time' ('ET'), and To (time of orientation) is Reichenbach's 'Reference Time' ('RT').

And when CGEL speaks of 'non-deictive past', it means that the past tense on cheated in he will claim she cheated is not past with reference to Td—the speaker of the sentence is not 'pointing' to an event in the speaker's own past. The event lies in the past relative to To, the (future, hypothothetical) time when the claim of cheating is made.

There's a useful outline of the CGEL scheme here.

  • Having read your explanation about perfect tense, I tried and read the CGEL about it. And now your account is suppose to be jotted down on the book. Your words are very helpful to understand the book. And now, I want to ask a lexical meaning. When I hear ‘reference time’ it’s quite easier than the word ‘the time orientation.’ In this case, what does ‘ori-entation’ mean? – Listenever Jun 22 '13 at 1:06
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    @Listenever The word comes from orient, the East, the direction of the sunrise; because this is so easy to identify it is in many cultures the primary direction to which all other directions are related. To be oriented is to know which direction is East. In this case, the 'time of orientation' is the point in time which all the time relationships are 'lined up' with. – StoneyB Jun 22 '13 at 1:40

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