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The Tale of Quantum Logic

Tim Maudlin

Published Jan 24, 2005• 33 citations

Abstract

Like all good tales, this is a story about temptation. It all begins with Kant. In the first Critique, Kant posed the fateful question: how is a priori synthetic knowledge possible? Among the items of undoubted knowledge to be accounted for: that the world as revealed by experience shall be in a Euclidean space; that it shall be governed by deterministic laws; that all substance is permanent, being neither created nor destroyed. The detailed argumentation brought forward in support of these claims is famously obscure, but the general outlines of the position are easy to sketch. We can know a priori that the world of experience will conform to these principles, not because they are conditions on things as they are in themselves, but rather because they are conditions on how things must be presented to us and conceived by us and judged by us in order to constitute experience. Items of experience must be given to us in perception, and so are subject to the forms of perceptive intuition (space and time). Further, in order to judge that our perceptions are of objective things, the appearances of things must conform to certain rules. In short, a priori synthetic knowledge is possible because it is not knowledge of how things are, but knowledge of how the world as revealed by experience must be, in order to be a world revealed by experience. The progress of science was not kind to Kant.

DOI: 10.1017/cbo9780511614187.006

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Abstract Quantum theory has presented scientists and philosophers of science with a series of perplexing questions. It seems to many that any attempt to comprehend a world described by quantum theory will require revision in our understanding of the nature of things far more radical than the revision in our understanding of the nature of space and time demanded by the theories of relativity. It has been claimed that to comprehend quantum theory we must revise our very understanding of such matters as the objective nature of reality and its independence from our perception of it, the nature of a complex system and its relation to its components, and the nature of causal and other kinds of determination in the world.

Though the truths of logic and pure mathematics are objective and independent of any contingent facts or laws of nature, our knowledge of these truths depends entirely on our knowledge of the laws of physics. Recent progress in the quantum theory of computation has provided practical instances of this, and forces us to abandon the classical view that computation, and hence mathematical proof, are purely logical notions independent of that of computation as a physical process. Henceforward, a proof must be regarded not as an abstract object or process but as a physical process, a species of computation, whose scope and reliability depend on our knowledge of the physics of the computer concerned.

In the Critique of Pure Reason Kant argues that the empirical knowledge of the world depends on a priori conditions of human sensibility and understanding, i. e., our capacities of sense experience and concept formation. The objective knowledge presupposes, on one hand, space and time as a priori conditions of sensibility and, on another hand, a priori judgments, like the principle of causality, as constitutive conditions of understanding. The problem is that in the XX century the physical science completely changed how we conceive our knowledge of the world. Face to this new situation, what was changed in our classical reason? However, if the transcendental point of view is adopted, in the specific case of quantum mechanics, we have to wonder about the general conditions of this theory that make possible such knowledge, which predictive value is much more accurate than the classical physics. The aim of this work is firstly to show the Kantian implications on Bohr’s interpretation of quantum phenomena and secondly to provide an overview of the key elements for understanding the transcendental locus of ordinary language in the quantum mechanics context, in order to give support to a transcendental pragmatic position in the analysis of science.

Abstract: In the Critique of Pure Reason Kant argues that the empirical knowledge of the world depends on a priori conditions of human sensibility and understanding, i. e., our capacities of sense experience and concept formation. The objective knowledge presupposes, on one hand, space and time as a priori conditions of sensibility and, on another hand, a priori judgments, like the principle of causality, as constitutive conditions of understanding. The problem is that in the XX century the physical science completely changed how we conceive our knowledge of the world. Face to this new situation, what was changed in our classical reason? However, if the transcendental point of view is adopted, in the specific case of quantum mechanics, we have to wonder about the general conditions of this theory that make possible such knowledge, which predictive value is much more accurate than the classical physics. The aim of this work is firstly to show the Kantian implications on Bohr’s interpretation of quantum phenomena and secondly to provide an overview of the key elements for understanding the transcendental locus of ordinary language in the quantum mechanics context, in order to give support to a transcendental pragmatic position in the analysis of science.

ENERAL philosophy claims to be the critical subject which lays down for all of us what we may be allowed to think, and yet it has played no part whatever in the great revolutions of human thought of the present century-those connected with relativity and the quantum theory. It might have been expected that the scientists would have been constantly consulting the philosophers as to the legitimacy of their various speculations, but nothing of the kind has happened. Since no one can dispense with some sort of metaphysic, each scientist has made one for himself, and no doubt they contain many crudities, but it would seem that a deep interest in metaphysic is a disadvantage rather than an advantage to the physicist-at least I have the impression that those of my friends who are most inclined to speculate on the ultimate things appear to be the ones whose scientific work is most hampered by doing so. Now I propose to risk a similar indiscretion. I want to embody in it the practical philosophy of a physicist, and I do not mean it as an attack on the pure philosophers, who are very reasonable people, only chargeable with the minor offence of not having made me want to read their books! I had better begin by stating shortly the ideas I intend to discuss. There is a notable contrast between the way we think about things and the way we think we ought to think about them.