 It is certainly important and worthy to pursue this direction, but a mild caution is entered here: the axiomatic project is a bit different from inconsistent mathematics. As noted earlier, Meyer in this phase was consistentist – he sought a consistent theory with an inconsistency-tolerant logic. With similar motivation, he was also concerned to try to settle what he called “the gamma problem”, which was essentially the question of whether the axiomatic theory R# could be shown to contain classical Peano arithmetic as a sub-theory. If this were so, then his proof of nontriviality for R# would immediately yield a new proof of the negation consistency of classical Peano arithmetic! Note that this would not be contrary to Godel’s Second Theorem, since presumably the proof of the gamma result would not be confined to finitary techniques. (In the case of Meyer’s theory, it turned out to be not so.)