We interpret the philosophy of Niels Bohr as related to the so called linguistic turn and consider paraconsistency in the light of the Bohrian notion of complementarity. Following [16], Jean-Yves Béziau has discussed the seemingly contradictory perspectives found in the quantum mechanical double slit experiment in terms of paraconsistent viewpoints [7, 8]. This interpretation goes in line with the well-known Bohrian Neo–Kantian epistemological account of quantum mechanics. In this chapter, we put forward the idea that one can also consider, within quantum mechanics and departing from the philosophy of the danish physicist, a more radical paraconsistency found within one of the main formal elements of the theory, namely, quantum superpositions. We will argue that, rather than epistemological, the contradictions found within quantum superpositions could be interpreted as ontological contradictions.