The Quantum Logic of Zeno: Misconceptions and Restorations
G. H. von Wright validly remarks that Zeno’s arrow “is neither moving nor at rest”. Then he invalidly proceeds to turn this into “both moving and at rest ” eo ipso. Hegel does the exact same thing and so, it seems, does everybody else. A violation of the Law of the Excluded Middle (LEM), in the form of –A and – –A, is equated (eo ipso) with a violation of the Law of Non-Contradiction (LNC), as A and –A. The move is both, circular (it employs double negation) and contradictory. In accordane [a] I argue that a system violating LEM eo ipso satisfies LNC, contrary to what von Wright, Hegel, paraconsistent logicians and everybody else seems to think. [b] Zeno’s paradoxes produce an antinomy, iff motion is continuous. (Ancient Atomists only reacted to Zeno’s infinite divisibility of processes.) [c] A comparable quantum model for discontinuous transitions, including motion, displays properties identical to those specified in [a] and [b]. If a body moves discontinuously from A to B, it is nowhere at all in-between A and B. And therefore cannot be where it is not, offerring an alternative to Zeno’s antinomies. [d] Zeno’s paradoxes, if handled by quantum discontinuity, lead to a 3-valued but consistent system. Discontinuity eliminates all possible descriptions of a system’s state. Hence, if nothing can be truthfully said about the system during a discontinuous transtion, nothing self-contraditory can be said about it either. Discontinuous motion is nonbivalent but consistent.