Deixis and past tense

[philo2009]

I think I understand the general concept of deixis but I can't understand how it relates to the simple past and perfect tenses.
For example,
He arrived eventually is simple past and is deictic but
He has arrived at last is present perfect, and not deictic apparently.

I've consulted both A Comprehensive Grammar of the English Language and the Cambridge Grammar of the English language and I'm still none the wiser.
Can anyone please explain how the first sentence is deictic but the second one isn't?

The author of the examples you cite appears to be applying the term 'deixis' in a slightly extended sense.

Essentially, a deictic word or phrase is any whose reference (be it of time or place) is determined according to external/non-linguistic factors, such as the time or place of utterance, while a nondeictic word/phrase is one whose reference is determined by internal/linguistic factors.

Thus, to take a very simple example, the adverbial 'yesterday' is deictic, since the day to which it refers can typically be calculated only by knowing when the word was uttered, while the nondeictic counterpart would be e.g. 'the previous day', whose reference would be determined by its linguistic context.

One limitation in English on the use of the present perfect is that it may not be modified by deictic past time adverbials (such as 'yesterday, last week, ...ago', etc.) - often popularly, although somewhat inaccurately, referred to as 'definite' past time phrases** - with the result that this tense is often designated as inherently 'nondeictic', whereas the preterite (simple past) tense, being that typically required in combination with such past time adverbials, is conceived of as inherently deictic.

Thus the writer's designation of your sentences would seem to derive primarily from the nature of their respective VPs.

**A word or phrase can be definite without necessarily being deictic.

[Hukeli]

Philo2009:
Thank you. That is a good, general way of describing the concept of deictic/non-deictic tenses without involving quasi-mathematical equations as does CamGEL. In another similar view, Quirk's CGEL talks about the perfective as being about the "indefinite past".

[philo2009]

Philo2009:
Thank you. That is a good, general way of describing the concept of deictic/non-deictic tenses without involving quasi-mathematical equations as does CamGEL. In another similar view, Quirk's CGEL talks about the perfective as being about the "indefinite past".

I regret to say that, despite being a graduate of Cambridge University myself, I have little faith in the CamGEL and find Quirk et al. to be, on the whole, much more reliable - not to say comprehensible!

As general labels for tense, as opposed to adverbials, 'definite vs. indefinite' make rather better sense to my mind than 'deictic vs. nondeictic'.