Srinivasan, Radhakrishnan (2022) Logical foundations of physics. Resolution of classical and quantum paradoxes in the finitistic paraconsistent logic NAFL. [Preprint]
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Abstract
Non-Aristotelian finitary logic (NAFL) is a finitistic paraconsistent logic that redefines finitism and correctly captures the notion of a potential infinity. Classical infinitary reasoning is refuted in NAFL, with the consequent negative resolution of Hilbert's program. It is argued that the existence of nonstandard models of arithmetic is an artifact of infinitary classical semantics, which must be rejected by the finitist, for whom the meaning of ``finite'' is not negotiable. The main postulate of NAFL semantics defines formal truth as time-dependent axiomatic declarations of the human mind, a consequence of which is the following metatheorem. If the axioms of an NAFL theory T are pairwise consistent, then T is consistent. This metatheorem, which is the more restrictive counterpart of the compactness theorem of classical first-order logic, leads to the conclusion that T supports only constructive existence, and consequently, nonstandard models of T do not exist, which in turn implies that infinite sets cannot exist in consistent NAFL theories. It is shown that arithmetization of syntax, Godel's incompleteness theorems and Turing's undecidability of the halting problem, which lead classically to nonstandard models, cannot be formalized in NAFL theories. The NAFL theories of arithmetic and real numbers are defined. Several paradoxical phenomena in quantum mechanics, such as, quantum superposition, Wigner's friend paradox, entanglement, the quantum Zeno effect and wave-particle duality, are shown to be justifiable in NAFL, which provides a logical basis for the incompatibility of quantum mechanics and infinitary (by the NAFL yardstick) relativity theory. Finally, Zeno's dichotomy paradox and its variants, which lead to meta-inconsistencies in classical infinitary reasoning, are shown to be resolvable in NAFL.
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| Item Type: | Preprint | ||||||
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| Additional Information: | Substantially revised and improved version. No major changes. | ||||||
| Keywords: | paraconsistent logic foundations finitism potential infinity quantum paradoxes | ||||||
| Subjects: | Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics > Logic Specific Sciences > Physics > Quantum Mechanics Specific Sciences > Physics > Relativity Theory |
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| Depositing User: | Dr. Radhakrishnan Srinivasan | ||||||
| Date Deposited: | 27 Feb 2023 20:14 | ||||||
| Last Modified: | 27 Feb 2023 20:14 | ||||||
| Item ID: | 21802 | ||||||
| Subjects: | Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics > Logic Specific Sciences > Physics > Quantum Mechanics Specific Sciences > Physics > Relativity Theory |
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| Date: | 1 June 2022 | ||||||
| URI: | https://philsci-archive.pitt.edu/id/eprint/21802 |
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Logical foundations of physics. Resolution of classical and quantum paradoxes in the finitistic paraconsistent logic NAFL. (deposited 01 Jun 2022 17:04)
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