Srinivasan, Radhakrishnan (2023) Logical foundations of physics. Resolution of classical and quantum paradoxes in the finitistic paraconsistent logic NAFL. [Preprint]
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Abstract
NonAristotelian finitary logic (NAFL) is a paraconsistent logic that redefines finitism and correctly captures the notion of a potential infinity. 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. A decisive critique of classical / intuitionistic propositional logic and classical infinitary reasoning, which require preexisting truths, is given. This leads directly to the definition of NAFL truth as timedependent axiomatic declarations of the human mind via provability in NAFL theories, with the consequent negative resolution of Hilbert's program. 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 firstorder 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 waveparticle 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. Zeno's dichotomy paradox and its variants, which lead to metainconsistencies in classical infinitary reasoning, are shown to be resolvable in NAFL.
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Item Type:  Preprint  

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Additional Information:  A critique of classical / intuitionistic propositional logic and comparison of these logics with NAFL is given in Remark 2.  
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 

Depositing User:  Dr. Radhakrishnan Srinivasan  
Date Deposited:  14 Dec 2023 18:14  
Last Modified:  14 Dec 2023 18:14  
Item ID:  22860  
Subjects:  Specific Sciences > Mathematics > Foundations Specific Sciences > Mathematics > Logic Specific Sciences > Physics > Quantum Mechanics Specific Sciences > Physics > Relativity Theory 

Date:  13 December 2023  
URI:  https://philsciarchive.pitt.edu/id/eprint/22860 
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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)

Logical foundations of physics. Resolution of classical and quantum paradoxes in the finitistic paraconsistent logic NAFL. (deposited 27 Feb 2023 20:14)
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Logical foundations of physics. Resolution of classical and quantum paradoxes in the finitistic paraconsistent logic NAFL. (deposited 27 Feb 2023 20:14)
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