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If a priori means "ahead of time" and a posteriori means "after the fact", is there a latin phrase to denote "during the course of the fact"?

A periori, perhaps? Or am I just making things up?

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    The question is based on wrong assumptions about the meaning of these terms. What the question roughly articulates is the origin of these terms. In the present-day English they have, however, acquired rather different meanings, which can be readily found in most dictionaries, including general-purpose ones. The epistemological concepts expressed by these terms are such that there cannot be a third one between them. – jsw29 Feb 10 '21 at 22:14

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In Latin, a priori means from the former and a posteriori means from what follows. In English, the former is often used to describe reasoning from cause to effect (OED), and the latter used to describe reasoning from effect to cause (OED). They're opposites; there isn't a third Latin-derived phrase that slots neatly in between the two.

Yet there is a Latin phrase, occasionally used in English, for the present time: hic et nunc, literally here and now (Merriam-Webster). It is usually used to refer to the present moment while looking erudite. Here are a few examples I found through COCA:

However farfetched the notion might appear at first, I realized in the end that, hic et nunc, Christ was not irrelevant to the problems that interest Professor Parker (Avery Dulles, "Ignatius Among Us," America, 2/4/2013.)

The yearning is for the hic et nunc of a close embrace of life, the celebration of some vast nuptials that might help him conjure away the time by which he has lived. (Victor Brombert, "Max Frisch: The Courage of Failure," Raritan, Fall 1993.)

A place shall be considered " artistic " whenever a critic has chosen to define it in a positive way, making of it a desired and desirable alternative to the French hic et nunc. (Stamos Metzidakis, "The Utopian Vision of French Criticism," Symposium, Fall 1990.)