The new discoveries of QM led to re-assessing, broadening the meanings of many physical concepts, and formulating a new logic that was no longer based on the classical principles of non-contradiction, identity, and causality. Heisenberg considered the classical logic and the conception of language expressed in the Tractatus Logico-Philosophicus inadequate for the understanding of the problems of language with which the physicists of the Copenhagen school had had to deal in order to define the foundations of Quantum Mechanics. On the contrary, he saw in Wittgenstein’s posthumous Philosophical Investigations the key to solving those problems. One may formulate a proportion and state that the use of language described in the Tractatus fits the use of language in Classical Mechanics, as the use of language described in PI fits the use of language in QM. I interpret the reflections of the physicists of the Copenhagen school on the limits of language relative to QM by highlighting how the epistemological revolution of quantum physics shares a conception of language similar to that expressed by late Wittgenstein in PI. I also aim to explain why Heisenberg considered it inappropriate to subsume the propositions and concepts of QM under the rules of the propositional logic of Tractatus. I explain why the philosophy of language expounded in PI, which is based on language games and resemblance families, sheds a light on how and why QM has contributed to renewing existing concepts (such as space, trajectory, observer, etc.) and to formulate a new logic (quantum logic).
The new discoveries of QM led to re-assessing, broadening the meanings of many physical concepts, and formulating a new logic that was no longer based on the classical principles of non-contradiction, identity, and causality. Heisenberg considered the classical logic and the conception of language expressed in the Tractatus Logico-Philosophicus inadequate for the understanding of the problems of language with which the physicists of the Copenhagen school had had to deal in order to define the foundations of Quantum Mechanics. On the contrary, he saw in Wittgenstein’s posthumous Philosophical Investigations the key to solving those problems. One may formulate a proportion and state that the use of language described in the Tractatus fits the use of language in Classical Mechanics, as the use of language described in PI fits the use of language in QM. I interpret the reflections of the physicists of the Copenhagen school on the limits of language relative to QM by highlighting how the epistemological revolution of quantum physics shares a conception of language similar to that expressed by late Wittgenstein in PI. I also aim to explain why Heisenberg considered it inappropriate to subsume the propositions and concepts of QM under the rules of the propositional logic of Tractatus. I explain why the philosophy of language expounded in PI, which is based on language games and resemblance families, sheds a light on how and why QM has contributed to renewing existing concepts (such as space, trajectory, observer, etc.) and to formulate a new logic (quantum logic).
This paper examines the philosophical implications of quantum mechanics through the lens of Ludwig Wittgenstein’s later philosophy, particularly the concept of “language games” and rule-following. The discourse surrounding quantum mechanics – characterized by terms like superposition, measurement, observer and entanglement – is deeply metaphoric and often stretches the bounds of classical language-use. This creates interpretative confusions not just in science, but in the metaphysical and epistemological debates that follow. Building on Philosophical Investigations, this paper argues that many foundational problems in quantum mechanics (e.g., the measurement problem, wave-function collapse, observer effect) are not exclusively ontological or physical but are entangled in language-use anomalies. The paper proposes that interpretative divergence among schools (Copenhagen, Many-Worlds, QBism, etc.) can be partly understood as conflicts between distinct language games with different rule-sets about what counts as a “measurement”, “reality”, or “causality”. By reading quantum discourse through Wittgensteinian criteria of meaning-as-use, the paper shows how the scientific community performs tacit normativity in deploying quantum terms – frequently without shared agreement on referents. Quantum mechanics, then, becomes a philosophical case study in the fragility and productivity of linguistic scaffolds in scientific theory. Finally, this paper makes a case for a deflationary yet clarifying approach: instead of seeking a “true” interpretation of quantum mechanics, we may better understand the philosophical stakes by analyzing the discursive rules, contextual boundaries, and pragmatic criteria that underlie quantum speech acts.
‘Sprache und Wirklichkeit in der modernen Physik’ is the title of a lecture Heisenberg gave in 1960 at the Bayerische Akademie der Schönen Künste. The polemics that had accompanied the establishment of quantum mechanics were over by then and the so-called problems of its foundations had lost much of their initial interest. Einstein had been dead for some years. Right up to the end he had expressed his profound dissatisfaction with a theory which, in his opinion, had something unreasonable about it. With the volume dedicated to him by the community of physicists and philosophers, the long debate between Bohr and Einstein had come to an end. It had been a disappointing conclusion, marked by the reaffirmation of the respective viewpoints of two scientists who by now found great difficulty even in defining a common code of communication. As though seeking to narrow the gap between them, Heisenberg took the opportunity to underline the existence of a common feature in their contributions to 20th century physics. Their discoveries had in fact made it possible to recognize that ‘even the fundamental and most elementary concepts of science, such as space, time, place, velocity, have become problematic and must be re-examined’. The conceptual and cognitive implications of relativity and of quantum mechanics were obviously different but Heisenberg maintained that both theories asked the same question: ‘Does the language we use when we speak of experiments correspond to the artificial language of mathematics which, as we know, describes real relationships correctly; or has it become separated from it so that we must be content with imprecise linguistic formulations and only return to the artificial language of mathematics when we are forced to express ourselves with precision?’.
In order to solve the problem of which is the real logic of Quantum Mechanics (QM), we suggest to study the mutual relationships between the physical theory (as a whole, that is both its experimental part and its theoretical part), its mathematics and its logic. That results to be a more general problem than what is considered by traditional studies on Quantum Logic (QL). These studies focus attention on the problem of the relationship between the experimental part of the physical theory and only its mathematics, from which logic is then derived. The new approach, that we suggest, generalises the interpretation that one of us (A. D.) successfully tested on the foundations of classical physical theories. The foundations of a theory are interpreted in terms of two options on the kind of mathematics, either classical one or constructive one, and the kind of logic, either classical logic or intuitionistic logic. It is remarkable that each theory making use of intuitionistic logic – i. e. L. Carnot’s classical mechanics, S. Carnot’s thermodynamics, Lobacevskij’s non-Euclidean geometry is organised in order to solve an universal problem (expressed by a double negated sentence), rather than in an entirely deductive way; hence, a non-classical logic does not belong exclusively to QM. From an historical and foundational analysis about QM, we conclude that in QM it is the law of double negation and not modular law (introduced by Birkhoff and von Neumann without giving physical evidence to it) which fails, i. e. which represents the true difference between Classical Logic (CL) and QL. We have looked for previous works on QL supporting our suggestion; in the past Destouches-Fevrier (1948), Fine (1974), Bell-Hallett (1981), Gauthier (1983), Adelman-Corbett (1995) already defended this thesis on the relevance of double negation law for QL. Under this light, QL results to have the same logic of a classical theory organised in a problematic manner. Hence, QM has to be referred to intuitionistic logic, in the same way every theory which is developed around a fundamental problem, expressed by a double negated sentence, does. In particular, by following the founder of intuitionism, Brouwer, we reject the identification of intuitionistic logic with an entirely deductive system; rather, the logical system of QL, as a theory, is organised in such a way to put a crucial problem to be solved. In agreement with this kind of organisation, among the several QM formulations we choose Heisenberg’s formulation, which was ignored by previous authors on QL. This formulation is aimed to solve the problem of quantum measurement, that originates the uncertainty methodological principle. Moreover, it is remarkable that it makes use of an operational mathematics (discrete matrices only). We interpret its characteristic arguing about its principal problem through double negated sentences; it results to be a moving from arguments belonging to non-classical logic expressed by a double negated sentence to the recognition of a suitable mathematics for QM formulation. In sum, QL shows how it is possible to state the relationship between QM and mathematics. This point has been almost ignored by the most traditional approaches to QL, which rather drew it from an a priori mathematics of QM (commonly, Hilbert space). As a verification of our approach, we show that even both Lobachevskij’s geometry and S. Carnot’s thermodynamics argued in order to achieve mathematical formulas expressing the content of the basic double negated sentences of respective theory. In the same way the recent book on QM by T. F. Jordan formalised his matrix mechanics. 1. Logic in classical physics and in Quantum Mechanics An historical analysis of Quantum Mechanics (QM) shows that there were at the origin of the theory two distinct formulations: Matrix Mechanics (Heisenberg, 1925) and Wave Mechanics (Schroedinger, 1926). Although Dirac subsumed these two formulations in a comprehensive mathematical framework (Hilbert space), we think that the organisation of the principles is different in Matrix Mechanics from that in Wave Mechanics, and this difference implies different logics. So we think that in order to characterise the logic of QM it is necessary to distinguish between this two formulations. In Matrix Mechanics, Heisenberg’s basic idea was to explain atomic spectra not in terms of atomic orbits (as Old Quantum Theory tried to make), but only by means of the study of experimental data; i. e., frequencies and intensities of light both emitted and absorbed by matter. Through a
Of all the many rival interpretations of quantum mechanics, none is more important or influential than the Copenhagen interpretation. Unfortunately, there is no one Copenhagen interpretation of quantum mechanics. If one uses the expression, and everyone does, one should not think of the Copenhagen interpretation as a single consistent interpretation of the theory. Philosophers of physics tend to use the expression ‘the Copenhagen interpretation of quantum mechanics’ as a label covering a variety of different interpretations all of which either originate with Niels Bohr or were invented by him, his colleagues and guests at the Institute for Theoretical Physics in Copenhagen beginning in the middle 1920s. Perhaps one should say that the Copenhagen interpretation in this diffuse sense goes back farther than this, back even before the rise of the new quantum mechanics. Heisenberg tells the story of a boat trip he, Bohr, and some friends took from Copenhagen to the island of Fyn around the time when the then new quantum mechanics was being developed. Bohr, ‘full of the new interpretation of quantum theory’, talked of ‘the difficulties of language, of the limitations of all our means of expressing ourselves’ and of how these limitations had been expressed ‘in the foundation of atomic theory in a mathematically lucid way’. ‘Finally,’ Heisenberg ends the story, ‘one of the friends remarked drily, “But, Niels, this is not really new, you said exactly the same ten years ago”
In PHYSICS AND PHILOSOPHY: The Revolution Modern Science, (1) Werner Heisenberg aims, in not too technical language, to clarify change concept of reality manifesting itself quantum theory. He means to contribute to an articulation of the (not only epistemology) that underlies quantum theory's modified logical patterns. (2) To highly unusual degree, Heisenberg is gripped by sense of responsibility of modern quantum physicist to convey, language immediately intelligible to thinking public, his most serious and far-reaching reflections on metaphysical implications of his scientific work. One may go so far as to say that there is substantial evidence, partly within Physics and Philosophy, that Heisenberg regards such reflections and their public communication as his most important task. Heisenberg is especially apt for this intensely self-conscious contribution to humanity's historical-cultural development because his stature as principal originating architect of quantum at its most fundamental level is complemented by his deployment of an unusually broad and deep erudition and lifelong preoccupation with philosophic and artistic ontology from Anaximander through Kant and Goethe to Heidegger. No thinker has yet appeared who possesses such an authoritative combination of decisively necessary learning quantum physics and historical development of philosophic ontology. Despite flurry of renewed scholarly interest development of Heisenberg's scientific work, (3) and his complex relation to dramatic unfolding of German cultural his time, (4) there has yet to be executed sustained and philosophically critical interpretative commentary on this book that is his crucial philosophical-ontological legacy. Given profound ontological puzzles that continue to attend quantum physics and its implications for humanity's past as well as present and future conception of reality, such critical exegesis of this text is overdue. In what follows I try to extricate central nerve of Heisenberg's sinuously unfolding, dialectical exposition, and process to elucidate its strengths but also its deep ambiguities and perplexities--which express, I believe, fundamental dilemmas that pervade contemporary ontology. I Heisenberg makes inviolability of principle of noncontradiction cornerstone of his discussion. Unlike Aristotle (5) Heisenberg does not wrestle with challenge posed by possible denial of principle. He understands nonmathematical articulation of quantum to escape what would otherwise be devastating contradictions--most obviously contradiction wave/particle character of basic entities described by theory--through Bohr's famous principle of complementarity (which Heisenberg closely associates with von Weizsacker's notion of coexistent states), combined with Heisenberg's own principle of potentia, potentiality, potentialities. (6) II After brief introduction, Heisenberg his second chapter sketches history of quantum theory and process begins to explain what he means by potentia. In 1924 Bohr and his colleagues tried to solve apparent contradiction between picture and particle picture by concept of wave. The electromagnetic were treated not as 'real' waves but as mathematical descriptions of probabilities, every point relevant space, for the absorption (or induced emission) of light quantum by an atom at this point. Later this idea of was applied more effectively to much more abstract mathematical in many-dimensional configuration space that was discovered through researches of Schrodinger. Heisenberg reinterprets this mathematical probability wave ontological tenus, as signaling tendency [Tendenz] for a definite happening [einem bestimmten Geschehen], thus introducing remarkable kind of physical reality, standing middle between possibility and actuality: a quantitative version of old concept of 'dunamis' or 'potentia' philosophy of Aristotle. …
This book concerns the metasemantics of quantum mechanics (QM). Roughly, it pursues an investigation at the intersection of philosophy of physics and philosophy of language, and it offers a critical analysis of rival explanations of the semantic facts of standard QM. Two problems for such explanations are discussed: categoricity and permanence. New results include 1) a reconstruction of Einstein's incompleteness argument, which concludes that a local, separable, and categorical QM cannot exist, 2) a reinterpretation of Bohr's principle of correspondence, grounded in the principle of permanence, 3) a meaning-variance argument for quantum logic, which follows a line of critical reflections initiated by Weyl, and 4) an argument for semantic indeterminacy leveled against inferentialism about QM, inspired by Carnap's work in the philosophy of classical logic.