The testing of inconsistent non-trivial theories

Popper restricted his definition of falsifiability to consistent theories through what we may call his requirement of consistency. His main argument was that an inconsistent theory does not distinguish the sentences that corroborate it from those that contradict it, for all sentences follow from it. This is due to the principle of explosion from classical logic, according to which ex contradictione sequitur quodlibet —i.e. from contradictions anything follows. Paraconsistent logicians have objected that logic can be revised in such a way that not all contradictions be false or, at least, that from some contradictions not every follows. This could, in principle, be exploited by science because some interesting theories, such as the infinitesimal calculus of Leibniz and Newton, or the first version of quantum theory, are inconsistent. In this project, I investigate whether or not falsificationism could be redefined so that some inconsistent theories can satisfy Popper’s principle of falsifiability.