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Journal for General Philosophy of Science

Leibniz, Kant, and Referring in the Quantum Domain

Cord Friebe

Published Jul 11, 2020• 3 citations
Publisher

Abstract

Abstract The paper addresses the referring problem in quantum mechanics, by spelling out the alternatives with complete or individual concepts (Leibniz; in modern terms: definite descriptive proper names), with directly referential labels (standard formalism of quantum mechanics), and with intuition (Kant). The connection between the way of referring and some metaphysical theses about objects will be explained. Then, the paper intends to make plausible that the Kantian way is the best way for the quantum domain, including quantum field theories.

DOI
10.1007/s10838-020-09515-5

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Abstract The paper addresses the referring problem in quantum mechanics, by spelling out the alternatives with complete or individual concepts (Leibniz; in modern terms: definite descriptive proper names), with directly referential labels (standard formalism of quantum mechanics), and with intuition (Kant). The connection between the way of referring and some metaphysical theses about objects will be explained. Then, the paper intends to make plausible that the Kantian way is the best way for the quantum domain, including quantum field theories.
Instead of either formulating new metaphysical images (as realists would do) or rejecting any metaphysical attempt (as empiricists would do), the case of quantum mechanics might well require from us a complete redefinition of the nature and task of metaphysics.The sought redefinition can be performed in the spirit of Kant, according to whom metaphysics is the discipline of the boundaries of human knowledge.This can be called a "reflective" conception of metaphysics.In this paper, each one of the most popular "interpretations" of quantum mechanics is shown to be naturally associated with a variety of Kant-like reflective metaphysics.Then, the two major "paradoxes" of quantum mechanics (the measurement problem and the EPR correlations) are reformulated by way of this reflective attitude, and they are thereby "dissolved".Along with this perspective, quantum mechanics becomes one of the most elegant and understandable theories of the history of physics in addition of being one of the most efficient.The only point that must be clarified is why it looks culturally so difficult to accept a reflective and non-ontological standpoint on physical theories.
Abstract Drawing on philosophical accounts of identity and individuality, as well as the histories of both classical and quantum physics, this book explores two alternative metaphysical approaches to quantum particles. It asks if quantum particles can be regarded as individuals, just like books, tables, and people. Taking the first approach, the book argues that if quantum particles are regarded as individuals, then Leibniz’s famous Principle of the Identity of Indiscernibles is in fact violated. Recent discussions of this conclusion are analysed in detail and the costs involved in saving the Principle are carefully considered. For the second approach, the book considers recent work in non-standard logic and set theory to indicate how we can make sense of the idea that objects can be non-individuals. The concluding chapter suggests how these results might then be extended to quantum field theory.
Russell’s theory of descriptions depends essentially on the concept of identity, in particular to eliminate definite descriptions by contextual definitions. But quantum objects, according to a possible metaphysical interpretation I shall assume without discussion here, seem not to satisfy the standard theory of identity, and do not have individuality in a sense. Even so, physicists refer informally to both ‘a quantum so-and-so’ and, worst, to ‘the quantum so-and-so’, as if these expressions were something like descriptions. In this article, we sketch a possible theory of ‘quantum (definite) descriptions’ using a weaker concept of indiscernibility (or indistinguishability), and advance some consequences such a theory may have for the discussions on the logical foundations of quantum theory.
Abstract Metaphysicians should pay attention to quantum mechanics, but not because it provides definitive answers to many metaphysical questions. The theory itself is remarkably silent on the nature of the physical world, and the various interpretations of the theory on offer present conflicting ontological pictures. Rather, quantum mechanics is essential to the metaphysician because it reshapes standard metaphysical debates and opens up unforeseen new metaphysical possibilities. Even if quantum mechanics provides few clear answers, there are good reasons to think that any adequate understanding of the quantum world will result in a radical reshaping of our classical worldview in some way or other. Whatever the world is like at the atomic scale, it is almost certainly not the swarm of particles pushed around by forces that is often presupposed. This book guides readers through the theory of quantum mechanics and its implications for metaphysics in a clear and accessible way. The theory and its various interpretations are presented with a minimum of technicality. The consequences of these interpretations for metaphysical debates concerning realism, indeterminacy, causation, determinism, holism, and individuality (among other topics) are explored in detail, stressing the novel form that the debates take given the empirical facts in the quantum domain. While quantum mechanics may not deliver unconditional pronouncements on these issues, the range of possibilities consistent with our knowledge of the empirical world is relatively small—and each possibility is metaphysically revisionary in some way.
The two major options on which the current debate on the interpretation of quantum mechanics relies, namely realism and empiricism, are far from being exhaustive. There is at least one more position available, which is metaphysically as agnostic as empiricism, but which shares with realism a committment to considering the structure of theories as highly significant. The latter position has been named transcendentalism after Kant. In this paper, a generalized version of Kant's method is used. This yields a reasoning that one is entitled to call a transcendental deduction of some major formal features of quantum mechanics.
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.