The quantum logic of Zeno: Misconceptions and Restorations

• Autores: Constantin Antonopoulos
• Localización: Acta Philosophica: rivista internazionale di filosofia, ISSN 1121-2179, Vol. 16, Nº. 2, 2007, págs. 265-284
• Idioma: inglés
• Enlaces
  • Texto completo (pdf)
• Resumen

  • 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 violat-ion 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. When it is as-serted that neither A nor –A, the last thing which follows is that both A and –A. If these two are both false, contradicting LEM, they cannot also be both true. Unexpect-edly, a violation of LEM protects LNC. 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 transition, nothing self-contraditory can be said about it either. Discontinuous motion is nonbivalent but consistent.