Quantum Mereology and Quasi-Sets
DOI:
https://doi.org/10.35588/cc.v7d8354Keywords:
Mereology, Qsets, Quasets, ZF, IndiscernibilityAbstract
Mereology deals with the study of the relationships between the whole and the parts. In
this work, we discuss different developments and open problems related to the formulation of
a quantum mereology. In particular, we will discuss different advances in the development of
formal systems aimed at describing the whole-parts relationship in the context of quantum
theory. Since macroscopic physical systems are assumed to be composed of many quantum
systems, understanding the challenges associated with the development of a quantum mereology
is relevant to the problem of explaining the emergence of a macroscopic classical reality from a
microscopic quantum realm. This question is addressed from the perspective of two set theories
inspired by quantum ontology: the theories of quasi-sets without atoms (Q−) and the quaset
theory (QST), and also from a mereological formalism motivated by entities in the microworld
(ZF∗). All these systems are characterized, unlike ZF, by a certain degree of non-extensionality.
For us, non-extensionality is an indispensable characteristic of formalisms that aim to account
for the peculiarities of quantum entities. These formalisms are related, and some questions
remain open, which may point to new directions in the development of future mereologies for
quantum mechanics
Downloads
References
Cunha do Nascimento, M., Krause, D., and de Araújo Feitosa, H. (2011). The quasi-lattice of indiscernible elements. Studia Logica, 97(1):101–126.
da Costa, N. C. A. and Holik, F. (2015). A formal framework for the study of the notion of undefined particle number in quantum mechanics. Synthese, 192(2):505–523.
Dalla Chiara, M. L., Giuntini, R., Krause, D., et al. (1998). Quasiset theories for microobjects: a comparision. Interpreting bodies: Classical and quantum objects in modern physics, Princeton University Press, Princeton, pages 142–152.
Dalla Chiara, M. L. and Toraldo di Francia, G. (1993). Individuals, kinds and names in physics. Bridging the gap: philosophy, mathematics, physics, pages 261–283.
Domenech, G. and Holik, F. (2007). A discussion on particle number and quantum indistinguishability. Foundations of Physics, 37(6):855–878.
Domenech, G., Holik, F., and Krause, D. (2008). Q-spaces and the foundations of quantum mechanics. Foundations of Physics, 38(11):969–994.
Field, H. (2008). Saving Truth From Paradox. Oxford University Press.
French, S. and Krause, D. (2006). Identity in physics: A historical, philosophical, and formal analysis. OUP Oxford.
Holik, F. and Jorge, J. P. (2023). Open problems in the development of a quantum mereology: And their ontological implications. In Non-reflexive logics, non-individuals, and the philosophy of quantum mechanics: essays in honour of the philosophy of Décio Krause, pages 157–176.
Springer.
Holik, F., Jorge, J. P., Krause, D., and Lombardi, O. (2022). Quasi-set theory: A formal approach to a quantum ontology of properties. Synthese, 200(5):401.
Holik, F., Jorge, J. P., and Massri, C. (2025). Indistinguishability right from the start in standard quantum mechanics. In Individuals and non-individuals in quantum theory, pages 45–69. Springer.
Holik, F., Krause, D., and Gómez, I. (2013). Quantum logical structures for identical particles. arXiv preprint arXiv:1305.5242.
Holik, F., Massri, C., and Ciancaglini, N. (2012). Convex quantum logic. International Journal of Theoretical Physics, 51(5):1600–1620.
Jech, T. (2003). Set theory: The third millennium edition, revised and expanded. Springer.
Jorge, J. P. and Holik, F. (2023). Lógica cuántica, Nmatrices y adecuación: II. Teorema: Revista internacional de filosofía, 42(1):149–169.
Jorge, J. P., Holik, F., and Krause, D. (2023). Un acercamiento a las semánticas Nmatriciales basadas en QST. Principia: an international journal of epistemology, 27(3):8.
Jorge, J. P., Holik, F., and Krause, D. (2025). Relating quasi-sets and rough sets: from quantum entities to AI. International Journal of Theoretical Physics, 64(10):289.
Krause, D. (1992). On a quasi-set theory. Notre Dame Journal of Formal Logic, 33(3):402–411.
Krause, D. (1996). Axioms for collections of indistinguishable objects. Logique et analyse, pages 69–93.
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.
Krause, D. and Costa, N. C. A. d. (1990). Não-reflexividade, indistinguibilidade e agregados de weyl.
Krause, D. and Jorge, J. P. (2024). Sobre una teoría ‘pura’de casi-conjuntos y su aplicación a una ontología cuántica de propiedades. Forthcoming in Principia.
Krause, D., Jorge, J. P., and Lombardi, O. (2025). A quasi-set theory without atoms and its application to a quantum ontology of properties. Forthcoming Synthese.
Maia, N. and Nizzardo, M. (2024). Identity and extensionality in boffa set theory. Philosophia Mathematica, 32(1):115–123.
Marton, J., Bartalucci, S., Bertolucci, S., Berucci, C., Bragadireanu, M., Cargnelli, M., Curceanu, C., Di Matteo, S., Egger, J., Guaraldo, C., et al. (2013). Testing the pauli exclusion principle for electrons. In Journal of Physics: Conference Series, volume 447, page 012070. IOP Publishing.
Walls, D. F. (1983). Squeezed states of light. nature, 306(5939):141–146.
Wilczek, F. and Devine, B. (1989). Longing for the Harmonies Themes and Variations From Modern Physi. WW Norton & Company.
Downloads
Submitted
2026-08-12Published
Issue
Section
License
Copyright (c) 2026 Juan Pablo Jorge
This work is licensed under a Creative Commons Attribution 4.0 International License.
