The Mechanism of Paradox in the Structures of Logic, Mathematics, and Physics
- 1 Independent Researcher, Midland, Canada
Abstract
This paper presents a model for the structure of universal frameworks in logic, mathematics, and physics that are closed to logical conclusion by the mechanism of paradox across a dualism of elements. The prohibition takes different forms defined by the framework of observation inherent to the structure. Forms include either prohibition to conclusion on the logical relationship of internal elements or prohibition to conclusion based on the existence of an element not included in the framework of a first element. The model is applied to logical arguments in philosophy, mathematics, and physics and is initially a geometrical analysis of quantum theory and its application in experiment. Conclusion from the analysis is extended to give insight into the complexity of infinities above the two-dimensional boundary of the model.
- Aharonov, Y., Botero, A., Popescu, S., Reznik, B., & Tollaksen, J. (2002). Revisiting Hardy’s Paradox: Counterfactual Statements, Real Measurements, Entanglement and Weak Values. Physics Letters A, 301, 130-138. https://doi.org/10.1016/S0375-9601(02)00986-6
- Bell’s Theorem (Stanford Encyclopedia of Philosophy/Fall 2021 Edition) (2021). https://plato.stanford.edu/archives/fall2021/entries/bell-theorem/
- Cantor Diagonal Method (n.d.). Wolfram MathWorld. https://mathworld.wolfram.com/CantorDiagonalMethod.html.
- Dark Energy, Dark Matter (n.d.). Science Mission Directorate. https://science.nasa.gov/astrophysics/focus-areas/what-is-dark-energy
- Deutsch, D. (1999). Machines, Logic and Quantum Physics. ArXiv: Math/9911150. https://arxiv.org/abs/math/9911150
- Gleick, J. (1993). Genius: The Life and Science of Richard Feynman. Van Haren Publishing.
- Herbert, N. (1985). Quantum Reality: Beyond the New Physics. Anchor Books.
- Lundeen, J. S., & Steinberg, A. M. (2008). Experimental Joint Weak Measurement on a Photon Pair as a Probe of Hardy’s Paradox. ArXiv: 0810.4229. https://arxiv.org/abs/0810.4229
- Overbye, D. (2003). Universe as Doughnut: New Data, New Debate. The New York Times. https://www.nytimes.com/2003/03/11/science/universe-as-doughnut-new-data-new-debate.html
- Penrose, R. (1994). Shadows of the Mind: A Search for the Missing Science of Consciousness (pp. 261-262, 334). Oxford University Press.
- Rayne, E. (2021). What Is up with That Hexagon on Saturn? We Might Have Finally Found Out. SYFY Official Site. https://www.syfy.com/syfy-wire/what-is-up-with-that-hexagon-on-saturn
- Russell’s Paradox (Stanford Encyclopedia of Philosophy Archive: Spring 2021 Edition) (2021). https://plato.stanford.edu/archives/spr2021/entries/russell-paradox/
- Szyk, B., & Díez, á (2023). Hexagon Calculator. Sided Polygon. Omni. https://www.omnicalculator.com/math/hexagon
- The Feynman Lectures on Physics Vol. II Ch. 19: The Principle of Least Action (n.d.). https://www.feynmanlectures.caltech.edu/II_19.html
- Tributsch, H. (2016). On the Fundamental Meaning of the Principle of Least Action and Consequences for a “Dynamic” Quantum Physics. Journal of Modern Physics, 7, 365-374. https://doi.org/10.4236/jmp.2016.74037