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Studies in History and Philosophy of Science Part A

Zygmunt Zawirski: The forgotten forefather of quantum logic

Elżbieta Drozdowska

Published Mar 23, 2026• 0 citations

Abstract

This paper reconstructs a forgotten episode in the early history of quantum logic by examining the work of Polish philosopher Zygmunt Zawirski. In the early 1930s, Zawirski developed an original system of many-valued logic explicitly designed to interpret quantum mechanics. Anticipating later views by Reichenbach and Putnam, Zawirski argued that the indeterminacy and probabilistic structure of quantum theory required a departure from classical two-valued logic. Drawing on Łukasiewicz's many-valued logic and Post's formal constructions, he built a system of truth-functional operators capable of representing probabilistic conjunction and disjunction. This article offers a technical and conceptual reconstruction of Zawirski's logic, based on his 1934 monograph and recent interpretations by Garbacz. While the system's practical limitations have been noted, its philosophical ambition and originality remain significant. Zawirski's logic not only constitutes the first formal system of quantum logic but also anticipates contemporary debates on the empirical foundations of logic and the relation between logic and probability. By recovering his overlooked contribution, this paper broadens our understanding of early responses to quantum theory and highlights the role of Polish logicians in shaping 20th-century philosophy of science.

DOI: 10.1016/j.shpsa.2026.102145

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This paper reconstructs a forgotten episode in the early history of quantum logic by examining the work of Polish philosopher Zygmunt Zawirski. In the early 1930s, Zawirski developed an original system of many-valued logic explicitly designed to interpret quantum mechanics. Anticipating later views by Reichenbach and Putnam, Zawirski argued that the indeterminacy and probabilistic structure of quantum theory required a departure from classical two-valued logic. Drawing on Łukasiewicz's many-valued logic and Post's formal constructions, he built a system of truth-functional operators capable of representing probabilistic conjunction and disjunction. This article offers a technical and conceptual reconstruction of Zawirski's logic, based on his 1934 monograph and recent interpretations by Garbacz. While the system's practical limitations have been noted, its philosophical ambition and originality remain significant. Zawirski's logic not only constitutes the first formal system of quantum logic but also anticipates contemporary debates on the empirical foundations of logic and the relation between logic and probability. By recovering his overlooked contribution, this paper broadens our understanding of early responses to quantum theory and highlights the role of Polish logicians in shaping 20th-century philosophy of science.

ABSTRACT The paper aims to bridge the history of quantum theory with its philosophical implications. The focus is not only on the scientific underpinnings of quantum mechanics (these theories emerged as ‘ad hoc’ responses to experimental anomalies) but also on the philosophical ramifications of its probabilistic nature and indeterminacy, which differ from classical realism. The paper examines Dirac's, Bell's, and modern views, focusing on how quantum mechanics (QM) challenges traditional notions of causality, objectivity, and truth while embracing epistemological and metaphysical perspectives. Debates over collapse theories and hidden variables are discussed, as well as Putnam's philosophical outlook, which includes his trenchant involvement with realism, logic, and the measurement problem. Finally, the paper proposes that QM represents a philosophical revolution that renews our understanding of reality, knowledge, and scientific explanation, rather than simply serving as a physical theory for assessing the prospects of quantum philosophy by connecting it to broader aspects such as relativity, causality, and scientific realism.

This paper treats some of the issues raised by Putnam's discussion of, and claims for, quantum logic, specifically: that its proposal is a response to experimental difficulties; that it is a reasonable replacement for classical logic because its connectives retain their classical meanings, and because it can be derived as a logic of tests. We argue that the first claim is wrong(1), and that while conjunction and disjunction can be considered to retain their classical meanings, negation cruciallydoes not.The argument is conductedviaa thorough analysis of how the meet, join and complementation operations are defined in the relevant logical structures, respectively Boolean- and ortholattices(3). Since Putnam wishes to reinstate a realist interpretation of quantum mechanics, we ask how quantum logic can be a logic of realism. We show that it certainly cannot be a logic ofbivalencerealism (i.e., of truth and falsity), although itisconsistent with some form ofontologicalrealism(4). Finally, we show that while a reasonable explication of the idealized notion of test yields interesting mathematical structure, it by no means yields the rich ortholattice structure which Putnam (following Finkelstein) seeks.

Quantum mechanics is a fundamentally probabilistic theory (at least so far as the empirical predictions are concerned). It follows that, if one wants to properly understand quantum mechanics, it is essential to clearly understand the meaning of probability statements. The interpretation of probability has excited nearly as much philosophical controversy as the interpretation of quantum mechanics. 20th century physicists have mostly adopted a frequentist conception. In this paper it is argued that we ought, instead, to adopt a logical or Bayesian conception. The paper includes a comparison of the orthodox and Bayesian theories of statistical inference. It concludes with a few remarks concerning the implications for the concept of physical reality.

In this paper we propose a unified conceptual framework in which quantum probability, quantum logic, and classical probability theory are understood as different structural levels of a single theoretical hierarchy. Starting from a statistical interpretation of quantum interference, previously developed by the authors, we argue that quantum probability is not an alternative to classical Kolmogorov probability, but a more general structure. Classical probability theory emerges as a limiting case corresponding to the disappearance of interference and the effective decomposition of the whole into independent elements. Within this framework, the Birkhoff–von Neumann quantum logic appears as a natural logical expression of quantum probability rather than as an abstract algebraic construction detached from physical meaning. The priority of the whole over its parts plays a central role in both quantum probability and quantum logic, while classical logic and probability arise when this priority becomes trivial. We emphasize that the proposed interpretation does not reject existing quantum formalism, but reinterprets its logical and probabilistic foundations. This approach may have implications for the conceptual understanding of quantum algorithms and quantum information processing.

Summary Foundational studies in quantum theory have consisted in large part of attempts to avoid paradoxical situations in describing properties of a physical system. Quantum logic addresses some of the perplexing problems that plague interpretations of quantum theory by invoking a non-classical propositional calculus for the set of propositions of a quantum system. Historically, quantum logic derives from von Neumann’s observation that the set of projection operators on a Hilbert space constitute a ‘logic’ of experimental propositions. More than two decades passed from the pioneering work of Birkho and von Neumann before interest in quantum logic was re-ignited by Mackey’s probabilistic analysis of quantum theory. Piron’s axiomatization provided a signicant