Leibniz on Reasoning about Impossible Concepts

Abstract

Leibniz wrote down a proof for the existence of God accompanied by a note on im- possible concepts. A possibly true contradiction is quite unusual and not compatible with mainstream logic or his “Theodicy”. His example of such a contradiction about an impossible concept, the “square circle”, is still popular in contemporary metaphysics. Similar examples make the proposition of contradiction and possible truth controversial. An alter- native formalization approach avoids contradictions by using a description logics extension to a different kind of concept composition.