Torg was a game that gave stats for axioms, and some gamers have suggested that it influenced Mage.
The thing about Torg was that it didn’t just assume that the referee would be able to hand-wave a judgement about what a character believed – beliefs were determined according to numerical values in a certain vector. Belief can be calculated.
If I ever run Mage again, I suppose I will have to hand-wave Paradox again. However, if I homebrew an entirely new system, axiom violations could be done on the Torg system rather than the Mage system. The “spheres” would be more fundamental than the “paradigms,” but in any event, it would be necessary to have some automatic logic calculator to determine the propositions in play.
If the new game also has three spheres instead of nine, or an Ars-Magica-style verb-noun system, it will be quite different from Mage. (It would be straightforward to use the three “spheres” to classify the verbs and nouns in a GURPS Thaumatology style, and then the characters could be built with GURPS rather than with White Wolf rules.)