Contradiction, Quantum Mechanics, and the Square of Opposition

Jonas Becker Arenhart, Décio Krause


We discuss the idea that superpositions in quantum mechanics may involve contradictions or contradictory properties. A state of  superposition such as the one comprised in the famous Schrödinger’s cat, for instance, is sometimes said to attribute contradictory properties to the cat: being dead and alive at the same time. If that were the case, we would be facing a revolution in logic and science, since we would have one of our greatest scientific achievements showing that real contradictions exist. We analyze that claim by employing the traditional square of  opposition. We suggest that it is difficult to make sense of the  idea of contradiction in the case of quantum superpositions. From a metaphysical point of view the suggestion also faces obstacles, and we present some of them. We finish by arguing that superpositions are better understood as a violation of tertium non datur instead of as a violation of the law of contradiction.


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