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Logical and metaphysical approaches to quantum (non-)individuality: an introduction

Jonas R. Becker Arenhart, Raoni Wohnrath Arroyo

Published Jan 1, 2026• 0 citations
OpenAlex

Abstract

We provide a brief introduction to the special issue dedicated to logical and metaphysical aspects of contemporary issues concerning identity and individuality in quantum mechanics. After a discussion of the main theme, we present the contributed papers and the historical motivations for the special issue.

Related papers

A no-individuals account of quantum mechanics

Jonas R. Becker Arenhart

One of the most famous metaphysical problems in the philosophy of quantum mechanics concerns the individuality status of quantum entities: are they individuals, or non-individuals? The typical approach to the problem consists in defending one of the options by appealing directly to features of quantum mechanics with the addition, eventually, of theoretical virtues the favoured proposal may have. In this paper, we argue that this strategy is inappropriate, because the problem of individuality is ill formulated in the case of quantum mechanics. In a nutshell, our point is that considerations exclusively from quantum mechanics are too general and generic to grant the level of particularity required for providing for a principle of individuality. Problems of individuality appear only at the level of particular applications of the theory in specific contexts, and in these cases, we shall argue, search for a metaphysical notion of individuality may be substituted by an epistemic notion of individuation. The approach also has the benefits of dissolving the problems created by metaphysical underdetermination on this front. This article is part of the theme issue 'Identity, individuality and indistinguishability in physics and mathematics'.

Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences•Jul 30, 2023•2 citations

Individuality, quantum physics, and a metaphysics of non-individuals: the role of the formal

Décio Krause, Jonas R. Becker Arenhart

The notion of an individual and the related issues on individuation are topics that appear in the philosophical discussion ever since the antiquity. The idea of an individual thing is intuitively clear: an individual is something of a specific kind that is a unity, having its own identity, and being so that it is possible at least in principle to discern it from any other individual, even of similar species. But when we try to leave the intuitive realm and push this idea to a logical analysis, we find a cluster of problems that are difficult to overcome within standard logico-mathematical contexts. In this work, we shall be concerned with some aspects of this intuitive concept of an individual and on some related facts about individuation taken from recent discussions that arose ever since the inception of quantum theory, pushing the discussion to a “logical” view, which in our opinion is still lacking in the usual debates on such issues. In the final part of the paper, we propose a metaphysics where the notion of identity is substituted, for some objects, by a weaker notion of indiscernibility, and we try to justify such a move. In most of the uses of the expression “quantum theory”, we shall not make explicit the distinction between the non-relativistic and the relativistic approaches, although they of course are quite different, for we think that the problems as we shall present them appear in both versions. But, as the text goes, the context will distinguish between them and these questions will become clear to the reader.

•Jul 10, 2012•6 citations

A Prolegomenon to a Metaphysics of Non-Individuals for Quantum Mechanics

Raoni Wohnrath Arroyo, Jonas R. Becker Arenhart

This article critically examines the challenges of developing a metaphysics of non-individuals in the context of quantum mechanics. It investigates the Received View, which posits that quantum entities are non-individuals, and highlights several unresolved issues. Through these challenges, it is shown that a coherent metaphysics of non-individuals remains an ongoing project. Section 2 outlines the historical motivations behind a metaphysics of non-individuals in quantum mechanics, providing insight into how physics seems to necessitate such a framework. Section 3 discusses how these motivations have been articulated in the traditional approach (referred to here as the ‘non-reflexive proposal’), which characterizes non-individuality as a failure of the identity relation to apply. Section 4 situates the problem within a broader context, extracting methodological insights and clarifying the issue. Section 5 elaborates on the challenges that a metaphysics of non-individuals must still overcome, positioning this text as a prolegomenon to future formulations of such a metaphysics grounded in quantum mechanics, and section 6 wraps it all up.

Epistemology & Philosophy of Science•Jan 1, 2025•1 citation

Introduction*

Alyssa Ney

The purpose of this introduction is to provide the reader who is unfamiliar with contemporary debates in the metaphysics of quantum mechanics with some background in the central issues that arise in this volume. The goal is to sketch one clean, direct, accessible path from classical physics to quantum theory that will serve to clarify the main interpretive issues that arise in the volume. Key technical concepts of quantum mechanics are introduced as well as the main interpretive options.

Oxford University Press eBooks•Apr 8, 2013•26 citations

Foundations of quantum mechanics and their impact on contemporary society

Gerardo Adesso, Rosario Lo Franco, Valentina Parigi

Nearing a century since its inception, quantum mechanics is as lively as ever. Its signature manifestations, such as superposition, wave-particle duality, uncertainty principle, entanglement and nonlocality, were long confronted as weird predictions of an incomplete theory, paradoxes only suitable for philosophical discussions, or mere mathematical artifacts with no counterpart in the physical reality. Nevertheless, decades of progress in the experimental verification and control of quantum systems have routinely proven detractors wrong. While fundamental questions still remain wide open on the foundations and interpretations of quantum mechanics, its modern technological applications have captured the fascination of the general public and are having a transformative impact on society. This brief article acts as Introduction to a Special Issue in the Philosophical Transactions of Royal Society A, following from a dedicated Scientific Discussion Meeting where these fascinating topics were explored, giving rise to stimulating debates among speakers and audience. The present issue thus aims at conveying the spirit of those discussions.

arXiv:1806.00538•Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences•May 28, 2018•12 citations

The Non-Reflexive Formulation of Quantum Mechanics: the Whys and the Hows

Décio Krause

In the non-reflexive formulation of quantum physics, attention is given to a metaphysical view of quantum objects (q-objects) as non-individuals, characterised as entities to which the standard notion of identity lacks sense. The reference to the nature of q-objects is usually omitted in other interpretations and the most we can find is some vague reference to “to each [quantum] system we associate a Hilbert space”, and nothing more is said about them; we need to infer from the theory their characteristics, and it gives us several alternatives. One of them, to be justified here in broad aspects, is the non-individual view. It is important to enlighten that we are not trying to just find a way to deal with quantum entities but to defend a possible ontology of non-individuals, which can be applied also to ‘particles’ arising from quantum fields. Our account is based on two assumptions: (i) the ‘classical theory of identity’ does not apply to q-objects, and (ii) their non-individuality must be attributed from the start, that is, as a primitive notion and not ‘made a posteriori’ say by assuming symmetry principles. The underlying logic is called non-reflexive because the reflexive law of identity \(\forall{x{({x = x})}}\) is supposed not to hold for q-objects. Since all the details demand a lot of space, here we only sketch and justify our view. The references provide a more detailed account.

Qeios•Mar 19, 2025•0 citations
One of the most famous metaphysical problems in the philosophy of quantum mechanics concerns the individuality status of quantum entities: are they individuals, or non-individuals? The typical approach to the problem consists in defending one of the options by appealing directly to features of quantum mechanics with the addition, eventually, of theoretical virtues the favoured proposal may have. In this paper, we argue that this strategy is inappropriate, because the problem of individuality is ill formulated in the case of quantum mechanics. In a nutshell, our point is that considerations exclusively from quantum mechanics are too general and generic to grant the level of particularity required for providing for a principle of individuality. Problems of individuality appear only at the level of particular applications of the theory in specific contexts, and in these cases, we shall argue, search for a metaphysical notion of individuality may be substituted by an epistemic notion of individuation. The approach also has the benefits of dissolving the problems created by metaphysical underdetermination on this front. This article is part of the theme issue 'Identity, individuality and indistinguishability in physics and mathematics'.
The notion of an individual and the related issues on individuation are topics that appear in the philosophical discussion ever since the antiquity. The idea of an individual thing is intuitively clear: an individual is something of a specific kind that is a unity, having its own identity, and being so that it is possible at least in principle to discern it from any other individual, even of similar species. But when we try to leave the intuitive realm and push this idea to a logical analysis, we find a cluster of problems that are difficult to overcome within standard logico-mathematical contexts. In this work, we shall be concerned with some aspects of this intuitive concept of an individual and on some related facts about individuation taken from recent discussions that arose ever since the inception of quantum theory, pushing the discussion to a “logical” view, which in our opinion is still lacking in the usual debates on such issues. In the final part of the paper, we propose a metaphysics where the notion of identity is substituted, for some objects, by a weaker notion of indiscernibility, and we try to justify such a move. In most of the uses of the expression “quantum theory”, we shall not make explicit the distinction between the non-relativistic and the relativistic approaches, although they of course are quite different, for we think that the problems as we shall present them appear in both versions. But, as the text goes, the context will distinguish between them and these questions will become clear to the reader.
This article critically examines the challenges of developing a metaphysics of non-individuals in the context of quantum mechanics. It investigates the Received View, which posits that quantum entities are non-individuals, and highlights several unresolved issues. Through these challenges, it is shown that a coherent metaphysics of non-individuals remains an ongoing project. Section 2 outlines the historical motivations behind a metaphysics of non-individuals in quantum mechanics, providing insight into how physics seems to necessitate such a framework. Section 3 discusses how these motivations have been articulated in the traditional approach (referred to here as the ‘non-reflexive proposal’), which characterizes non-individuality as a failure of the identity relation to apply. Section 4 situates the problem within a broader context, extracting methodological insights and clarifying the issue. Section 5 elaborates on the challenges that a metaphysics of non-individuals must still overcome, positioning this text as a prolegomenon to future formulations of such a metaphysics grounded in quantum mechanics, and section 6 wraps it all up.
Nearing a century since its inception, quantum mechanics is as lively as ever. Its signature manifestations, such as superposition, wave-particle duality, uncertainty principle, entanglement and nonlocality, were long confronted as weird predictions of an incomplete theory, paradoxes only suitable for philosophical discussions, or mere mathematical artifacts with no counterpart in the physical reality. Nevertheless, decades of progress in the experimental verification and control of quantum systems have routinely proven detractors wrong. While fundamental questions still remain wide open on the foundations and interpretations of quantum mechanics, its modern technological applications have captured the fascination of the general public and are having a transformative impact on society. This brief article acts as Introduction to a Special Issue in the Philosophical Transactions of Royal Society A, following from a dedicated Scientific Discussion Meeting where these fascinating topics were explored, giving rise to stimulating debates among speakers and audience. The present issue thus aims at conveying the spirit of those discussions.
In the non-reflexive formulation of quantum physics, attention is given to a metaphysical view of quantum objects (q-objects) as non-individuals, characterised as entities to which the standard notion of identity lacks sense. The reference to the nature of q-objects is usually omitted in other interpretations and the most we can find is some vague reference to “to each [quantum] system we associate a Hilbert space”, and nothing more is said about them; we need to infer from the theory their characteristics, and it gives us several alternatives. One of them, to be justified here in broad aspects, is the non-individual view. It is important to enlighten that we are not trying to just find a way to deal with quantum entities but to defend a possible ontology of non-individuals, which can be applied also to ‘particles’ arising from quantum fields. Our account is based on two assumptions: (i) the ‘classical theory of identity’ does not apply to q-objects, and (ii) their non-individuality must be attributed from the start, that is, as a primitive notion and not ‘made a posteriori’ say by assuming symmetry principles. The underlying logic is called non-reflexive because the reflexive law of identity ∀x(x=x)\forall{x{({x = x})}}∀x(x=x) is supposed not to hold for q-objects. Since all the details demand a lot of space, here we only sketch and justify our view. The references provide a more detailed account.