Srinivasan, Radhakrishnan
(2019)
LOGICAL FOUNDATIONS OF PHYSICS. PART I. ZENO’S DICHOTOMY PARADOX,SUPERTASKS AND THE FAILURE OF CLASSICAL INFINITARY REASONING.
[Preprint]
Abstract
Several variants of Zeno’s dichotomy paradox are considered, with the objective of exploring the logical foundations of physics. It is shown that Zeno’s dichotomy paradox leads to contradictions at the metamathematical (as opposed to formal) level in the basic classical infinitary reasoning that is routinely used in theoretical physics. Both Newtonian mechanics and special relativity theory suffer from these metamathematical inconsistencies, which occur essentially because the classical refutation of the
dichotomy paradox requires supertasks to be completed. In previous papers, Non-Aristotelian Finitary Logic (NAFL) was proposed as a logical foundation for some of the basic principles of quantum mechanics, such as, quantum superposition and entanglement. We outline how the finitistic and paraconsistent reasoning used in NAFL helps in resolving the metamathematical inconsistencies that arise from the dichotomy paradox.
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