Classical logic mandates that any contradiction trivializes a theory by making every sentence of the theory provable.

In contrast to Zermelo’s, von Neumann’s and Quine’s strategies, which are in a sense purely set theoretic, there have also been attempts to avoid Russell’s paradox by altering the underlying logic. There have been many such attempts and we shall not review them all, but one stands out as being, at the moment, both radical and somewhat popular (although not with set theorists per se): this is the paraconsistent approach, which limits the overall effect of an isolated contradiction on an entire th