a posteriori, a priori...?

Hello everybody!
One really short question about the expressions “a posteriori, a priori”. I am pretty sure that the ablative of “posterior” and “prior” ends in -e. Nevertheless, the expression is with the adjective in -i. How is that?
Thanks in advance!

Third declension ablatives in singular are quite notorious. They are a mess in classical Latin already, a motley group of (original) i-stems and consonantal stems in different cases and different words (the so-called parisyllabae and imparisyllabae), with analogical changes, of course. Yes, they should be a posteriore, a priore, but they are quite well established in -i in the general (non-Latinate) parlance and it has stuck. However, many Latinists will probably use the endings in -e, to some philosophers’ astonishment, no doubt.

Singular ablative and plural genitive are most commonly mentioned in this context, but also plural accusative -īs is an original i-stem. This plural accusative is not generally taught in elementary courses, but often first met when reading Vergil and others of that ilk. Original i-stem neuters tend to preserve the ending -ia in nom/acc plural. Then there are a few words with accusative singular in -im.

I’m not quite sure when a priori and a posteriori were coined or started to become prevalent as terms; my guess is the Renaissance, but I could well be wrong.