Are the terms a fortiori, a priori, and a posteriori bad Latin? If so, how and when did they become established?
I understand that the dative case never takes a preposition in Latin—a most welcome clue in a language where the dative and ablative have opposite meanings but often identical form. But fortiori appears to be unambiguously dative, yet introduced by a preposition. And yet the meaning appears to be ablative: "with stronger reason" ("all the more so" more colloquially in English). The stronger reason is the source of the conclusion being justified. And how would you fill in the elided noun: a fortiori rationi or a fortiore ratione? I don't see how the dative could even make sense here. Nothing is being given to the stronger reason and there’s no suggestion that the stronger reason has anything at stake in the matter. Weight is coming from the stronger reason, as suggested by the preposition a (short for ab as in ablative!).