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Exact(8)
The epistemic reading of an unembedded non-root modal for the past is evaluated against the speaker's utterance time.
Keneng can be used as a metaphysical modal for the past, with a past temporal perspective and a future temporal orientation.
Though some of those other uses of reng can co-occur with a non-root modal for the past, they do not license, or facilitate, a metaphysical interpretation for the modal.
When an aspectual adverb reng or hai appears before, and thus modifies, keneng intended as a non-root modal for the past, it requires that the relevant possibility had continued up to a past reference time.
The necessity grounded in essentiality has to be distinguished from other kinds of necessities, like "empirical" necessity or causality (cf. Reinach 1911b, 85f, where he uses the term "modal" for the necessity grounded in essences and, somehow misleadingly, "material" for "empirical" necessity).
By contrast, when it comes to the metaphysical use of an unembedded non-root modal for the past, such aspectual adverbs as reng and hai can back-shift the temporal perspective of the modal from the speaker's utterance time to some time within the past-denoting topic time of the modal.
Similar(52)
We choose the modal filters as the state estimator to obtain the modal co-ordinates and modal velocities for the modal space control.
To start with, does the same epistemic/metaphysical ambiguity for non-root modals for the past exist in Mandarin Chinese?
I think this is why reng and hai can "license" a metaphysical reading of non-root modals for the past.
I think that the above discussion of non-root modals for the past in Mandarin Chinese has important theoretical implications.
Prior introduces the collective term 'quasi-modals' for the non-alethic modes (p.749) and remarks, accurately, that 'there is a hint of a large field here' (p.752).
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com