Most times, we have to slot it into p, then analyze its deep structure to see whether any of its presuppositions entail its falsity. I would be interested, however, in seeing how you would use MT to explicate a transcendental argument. I don't think a transcendental argument can be adequately formulated by MT or by transposition of the same. Too much is left implicit in the formulation.
Quine is probably good here too.
If not, the new axiom is rejected. That is, a system is saturated if the addition of another axiom results in inconsistency. Creeds can be seen as lists of theological axioms. Godel overturned the Hilbert formalist program by showing that there was at least one axiom that could be written but could not be proven without making the whole system inconsistent. I am unable to be helpful at this time.