Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

The effectiveness of mathematics in physics

Jane McDonnell

Published Jan 1, 2017• 0 citations
Publisher

Abstract

In this thesis I argue that many problems in the philosophy of science and mathematics (in particular, the unreasonable effectiveness of mathematics in physics) can only be addressed within a broader metaphysical framework which provides a coherent world view. I attempt to develop such a framework and draw out its consequences. The attempt is in two parts: first, I develop a speculative framework based on an analogy to set theory; then I combine elements of the framework with ideas from Leibnizian monadology and consistent histories quantum theory to introduce (what I call) quantum monadology. The two parts focus on different aspects of the problem and should be viewed as stages on the way to a final formulation. The inspiration for the thesis came from Plato’s Timaeus and Wigner’s comments on quantum mechanics. As it turned out, Leibniz’s Monadology became a third key source.

DOI
10.4225/03/58b61af65c266

Related papers

A Husserlian ontology of the science of physics

Jobst Landgrebe, Barry Smith

Since 1939, when Wigner published his proposal to define particles via symmetries expressed as algebraic groups, we have seen a long stream of attempts to formulate an ontology of matter based on mathematics. It has become apparent that such attempts must fail, and more particularly that we cannot derive an ontology of matter from the Standard Model on the basis of quantum field theory. We briefly recapitulate the reasons for this and demonstrate how the philosophy of physics has become scholasticised through a series of vain attempts to obtain a coherent ontology of matter. Here we propose an alternative approach in the form of an ontology of the science of physics. It draws on a framework developed by Husserl which admits not only real material entities but also the idealities which physicists make use of in their thinking. We specify the upper level of this ontology, which addresses the way in which physicists use mathematics when conducting their enquiries. This ontology provides a new perspective concerning the dilemmas of modern physics, including the measurement problem.

arXiv:2606.00805•May 30, 2026•0 citations

Phenomenological Aspects of the Quantum-Mechanical World-View

David Geoffrey Holdsworth

The contents of this paper consist of two independent but correlated topics. In Part I the history of nineteenth and twentieth century philosophy of science is traced in an effort to demonstrate the essential phenomenological aspects of the scientific methodology. Part II, on the other hand, is a technical exposition of some foundational aspects of quantum mechanics based on quantum logic. An effort is made to retain the theme that quantum mechanics is largely a phenomenological theory. As a summary, Part III constitutes an attempt to correlate the first two parts and to present tentatively some consequent reflections on the metaphysical significance of the quantum mechanical formalism.

•Sep 1, 1973•0 citations

Quantum Monadology: Glimmers of a Metaphysics of Universal Harmony

Rossella Lupacchini

Abstract Despite its extraordinary predictive power, quantum mechanics has been hailed as a paradoxical, self-contradictory theory of nature. How does it question the intelligibility of physical worldview? The wave-particle dualism, the incompatibility of physical quantities, the complementarity between the space-time description and the causal description of phenomena question key-notions of the traditional metaphysics, such as substance and cause, but they also call attention to the vital dialectical contrast between the continuous and the discrete, the infinite and the finite, consciousness and matter, and to the essential relational character of measuring, seeing, and knowing. Does quantum physics also question the Western way of thinking? The aim of this article is to show how quantum monadology not only breathes new life into Leibniz’s and Nicholas of Cusa’s monads, but also echoes Nishida’s ‘dialectical monadology’ and orients our gaze towards a metaphysics of universal harmony, i.e., a metaphysics of the dialectical universal or a metaphysics of indeterminacy.

Diogenes•Aug 1, 2024•0 citations

Bootstrap’s Monadology. Symmetry and Mirroring Connections between Chew’s Bootstrap Theory and Leibniz’s Monadology

Ramona Ardelean

The scientific paradigm which I rely upon in the framework of this article is quantum mechanics, whose “cognitive revolution” consisted of replacing the classical principle of separability with the principle of nonseparability or global intercorrelation. According to this intercorrelation, highlighted at the subatomic level, the part cannot be separated from the whole, because every part has a global and instantaneous connection with the whole universe. For this reason the foundation of the world cannot be the part (elementary particles), but the whole, which is therefore logically and ontologically prior to the part, i.e., self-consistent. Consequently, the principle of global intercorrelation elucidates and validates some of the oldest philosophical problems and intuitions about the unity or self-consistency of the world. An example in this sense is the bootstrap theory of American physicist Geoffrey Chew, which presents such striking similarities to the metaphysical system of Leibniz's Monadology that the two intertwine and mirror each other, like twin souls, to the extent that it could be stated that if Chew’s bootstrap theory represents the explanatory physical level of Leibniz’s metaphysics, then, analogously, Leibniz’s Monadology represents the explanatory metaphysical level of Chew’s physics.

Balkan Journal of Philosophy•Jan 1, 2022•1 citation

On the Present State of the Philosophy of Quantum Mathematics

Howard Stein

It was with some trepidation that I agreed to speak today, because of a strong doubt that I could say anything substantial not already to be found in the literature of the subject. I cannot say that this trepidation has been subsequently relieved: all I can claim to offer in this paper is a review of certain basic characteristics or themes in the quantum-mechanical situation (which by now should, I think, be thoroughly understood by everyone engaged with the matter), supplemented by some rather general reflections on our philosophical predicament. In aid of these more general reflections, I shall indulge a proclivity for calling on historical matters—some fairly recent, some older, some ancient—which I hope may serve to place current issues in a useful perspective; and I ask your forgiveness for allowing myself to quote certain previous, but hitherto unpublished, remarks of my own.

PSA Proceedings of the Biennial Meeting of the Philosophy of Science Association•Jan 1, 1982•3 citations

Some aspectos of quantum physics

Newton C. A. da Costa

I discuss some questions of quantum physics, for instance the validity and limitations of the basic language of set theory to deal with problems related to elementary particles. I also present a sketch of a formalization of a “metaphysics of structures”, which might be useful for a kind of “ontic structural realism”, and briefly review the concept of quasi-truth, which underlies my way of understanding scientific theories and the scientific activity.

•Jan 1, 2007•0 citations
In this thesis I argue that many problems in the philosophy of science and mathematics (in particular, the unreasonable effectiveness of mathematics in physics) can only be addressed within a broader metaphysical framework which provides a coherent world view. I attempt to develop such a framework and draw out its consequences. The attempt is in two parts: first, I develop a speculative framework based on an analogy to set theory; then I combine elements of the framework with ideas from Leibnizian monadology and consistent histories quantum theory to introduce (what I call) quantum monadology. The two parts focus on different aspects of the problem and should be viewed as stages on the way to a final formulation. The inspiration for the thesis came from Plato’s Timaeus and Wigner’s comments on quantum mechanics. As it turned out, Leibniz’s Monadology became a third key source.
Since 1939, when Wigner published his proposal to define particles via symmetries expressed as algebraic groups, we have seen a long stream of attempts to formulate an ontology of matter based on mathematics. It has become apparent that such attempts must fail, and more particularly that we cannot derive an ontology of matter from the Standard Model on the basis of quantum field theory. We briefly recapitulate the reasons for this and demonstrate how the philosophy of physics has become scholasticised through a series of vain attempts to obtain a coherent ontology of matter. Here we propose an alternative approach in the form of an ontology of the science of physics. It draws on a framework developed by Husserl which admits not only real material entities but also the idealities which physicists make use of in their thinking. We specify the upper level of this ontology, which addresses the way in which physicists use mathematics when conducting their enquiries. This ontology provides a new perspective concerning the dilemmas of modern physics, including the measurement problem.
The contents of this paper consist of two independent but correlated topics. In Part I the history of nineteenth and twentieth century philosophy of science is traced in an effort to demonstrate the essential phenomenological aspects of the scientific methodology. Part II, on the other hand, is a technical exposition of some foundational aspects of quantum mechanics based on quantum logic. An effort is made to retain the theme that quantum mechanics is largely a phenomenological theory. As a summary, Part III constitutes an attempt to correlate the first two parts and to present tentatively some consequent reflections on the metaphysical significance of the quantum mechanical formalism.
Abstract Despite its extraordinary predictive power, quantum mechanics has been hailed as a paradoxical, self-contradictory theory of nature. How does it question the intelligibility of physical worldview? The wave-particle dualism, the incompatibility of physical quantities, the complementarity between the space-time description and the causal description of phenomena question key-notions of the traditional metaphysics, such as substance and cause, but they also call attention to the vital dialectical contrast between the continuous and the discrete, the infinite and the finite, consciousness and matter, and to the essential relational character of measuring, seeing, and knowing. Does quantum physics also question the Western way of thinking? The aim of this article is to show how quantum monadology not only breathes new life into Leibniz’s and Nicholas of Cusa’s monads, but also echoes Nishida’s ‘dialectical monadology’ and orients our gaze towards a metaphysics of universal harmony, i.e., a metaphysics of the dialectical universal or a metaphysics of indeterminacy.
The scientific paradigm which I rely upon in the framework of this article is quantum mechanics, whose “cognitive revolution” consisted of replacing the classical principle of separability with the principle of nonseparability or global intercorrelation. According to this intercorrelation, highlighted at the subatomic level, the part cannot be separated from the whole, because every part has a global and instantaneous connection with the whole universe. For this reason the foundation of the world cannot be the part (elementary particles), but the whole, which is therefore logically and ontologically prior to the part, i.e., self-consistent. Consequently, the principle of global intercorrelation elucidates and validates some of the oldest philosophical problems and intuitions about the unity or self-consistency of the world. An example in this sense is the bootstrap theory of American physicist Geoffrey Chew, which presents such striking similarities to the metaphysical system of Leibniz's Monadology that the two intertwine and mirror each other, like twin souls, to the extent that it could be stated that if Chew’s bootstrap theory represents the explanatory physical level of Leibniz’s metaphysics, then, analogously, Leibniz’s Monadology represents the explanatory metaphysical level of Chew’s physics.
It was with some trepidation that I agreed to speak today, because of a strong doubt that I could say anything substantial not already to be found in the literature of the subject. I cannot say that this trepidation has been subsequently relieved: all I can claim to offer in this paper is a review of certain basic characteristics or themes in the quantum-mechanical situation (which by now should, I think, be thoroughly understood by everyone engaged with the matter), supplemented by some rather general reflections on our philosophical predicament. In aid of these more general reflections, I shall indulge a proclivity for calling on historical matters—some fairly recent, some older, some ancient—which I hope may serve to place current issues in a useful perspective; and I ask your forgiveness for allowing myself to quote certain previous, but hitherto unpublished, remarks of my own.