Paraconsistent logics actually are useful, not just in philosophy, and the author has done a lot of great work with them. This article just makes his case badly. I think it's because he's trying to leave out anything that might be intimidating, but he made some really strange choices if so; Konig's paradox originally applied to the reals. It applies to the ordinals, because all you need is an uncountably infinite well-ordered set, but everyone is familiar with the reals and not so many are familiar with transfinite arithmetic. edit: but Venn diagrams are always equivalent to expressions in boolean logic, because of the duality of set theory and logic.
But Venn diagrams are used freely and readily by people who would rather drink bleach than study set theory without having to know they're a part of set theory. Forcing set theory down the throat of people who think in Venn diagrams will never be a wise debate move.