Version 1
: Received: 21 June 2023 / Approved: 21 June 2023 / Online: 21 June 2023 (16:52:36 CEST)
How to cite:
Krause, D. A Remark on Quasi-automorphisms and Deformable Structures in Quasi-set Theory and Its Account to the Logical Foundations of Quantum Theory. Preprints2023, 2023061583. https://doi.org/10.20944/preprints202306.1583.v1
Krause, D. A Remark on Quasi-automorphisms and Deformable Structures in Quasi-set Theory and Its Account to the Logical Foundations of Quantum Theory. Preprints 2023, 2023061583. https://doi.org/10.20944/preprints202306.1583.v1
Krause, D. A Remark on Quasi-automorphisms and Deformable Structures in Quasi-set Theory and Its Account to the Logical Foundations of Quantum Theory. Preprints2023, 2023061583. https://doi.org/10.20944/preprints202306.1583.v1
APA Style
Krause, D. (2023). A Remark on Quasi-automorphisms and Deformable Structures in Quasi-set Theory and Its Account to the Logical Foundations of Quantum Theory. Preprints. https://doi.org/10.20944/preprints202306.1583.v1
Chicago/Turabian Style
Krause, D. 2023 "A Remark on Quasi-automorphisms and Deformable Structures in Quasi-set Theory and Its Account to the Logical Foundations of Quantum Theory" Preprints. https://doi.org/10.20944/preprints202306.1583.v1
Abstract
Quantum theory is the land of indiscernible things, of things that in some situations cannot be put apart. This contrasts in much with standard mathematics and classical logic, which were elaborated to deal with \textit{individuals}, discernible things. Many thinkers, among them the mathematician Yuri Manin, have proposed that a more general theory of `sets' than standard set theories (where sets are collections of discernible elements) should be elaborated to cope with quantum physics. Quasi-set theory was proposed with such an aim. In this paper, we consider some aspects of this theory and discuss the way we can use such a theory as a framework for constructing deformable (not rigid) structures where indiscernible things can be considered but with one additional and fundamental detail: these structures cannot be extended to rigid structures as it happens in the standard frameworks. Really, the way of dealing with indiscernible (or indistinguishable) elements within a `standard' framework such as a `classical' set theory (like the ZFC system) requires the confinement of the discussion to deformable (non-rigid) structures. But in ZFC every structure can be extended to a rigid structure (encompassing only the trivial automorphism -- the identity function), so that in the extended structure (or in the whole universe) one can realize that the supposed indiscernible objects are not indiscernible at all. Quasi-set theory is such that the universe of quasi-sets is deformable and in such a theory one can construct deformable structures which cannot be extended to rigid ones. The aim of this paper is to put these things in a clear way.
Keywords
logical foundations of quantum theory; indistinguishability; indiscernibility; quantum objects; deformable structures; quasi automorphisms
Subject
Arts and Humanities, Philosophy
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
