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Análisis Revista de investigación filosófica

Suárez’s Paradox and Contemporary Debates in the Philosophy of Quantum Logics

José Alejandro Fernández Cuesta

Published Jul 21, 2025• 1 citation
Publisher

Abstract

In this paper my aim is to recover and use an argument outlined by Suárez concerning the philosophy of quantum logics, which I have termed “Suárez's Paradox”. Although originally written in 1992, this argument has only recently come to light through its publication. After briefly introducing the essentials of standard quantum logics formalism and the classical philosophical discussions associated in a nutshell, I will present an actualised version of the Suárez's Paradox inserting it in the philosophy of quantum logics discussion highlighting several non-trivial philosophical implications.

DOI
10.26754/ojs_arif/a.rif.2025111863

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In this paper my aim is to recover and use an argument outlined by Suárez concerning the philosophy of quantum logics, which I have termed “Suárez's Paradox”. Although originally written in 1992, this argument has only recently come to light through its publication. After briefly introducing the essentials of standard quantum logics formalism and the classical philosophical discussions associated in a nutshell, I will present an actualised version of the Suárez's Paradox inserting it in the philosophy of quantum logics discussion highlighting several non-trivial philosophical implications.
Quantum theory underpins much of modern physics and its implications draw the attention of industry, academia and public funding agencies. However there are many unsettled conceptual and philosophical problems in the interpretation of quantum mechanics which are a matter of extensive debate. These hotly debated topics include the meaning of the wave function, the nature of the quantum objects, the role of the observer, the non-locality of the quantum world, and the emergence of classicality from the quantum domain. Containing chapters written by eminent researchers from the fields of physics and philosophy, this book provides interdisciplinary, comprehensive and up-to-date perspectives of the problems related to the interpretation of quantum theory. It is ideal for academic researchers in physics and philosophy working on the ontology of quantum mechanics.
The title of this book brings to mind topics such as the Copenhagen Interpretation, Shrodinger's Cat, the EPR Paradox and Bell's Theorem. Certainly all of these are there, but there is much more. Starting with the Logic of Plato and Aristotle, the reader is guided through the Classical Philosophy of Knowledge. This is unfamiliar territory for most physicists; in fact I found the first four chapters (of a total of 16) quite difficult for someone untrained in philosophical discipline. Then comes a discussion of the formal logic of Mathematics - much more familiar ground this, to be enjoyed and savoured. Quite fascinating and original is the 'Orchard Analogy' in which the author invites us to imagine the Universe as a vast field sprinkled with countless trees representing all conceivable propositions. Some of these trees, the axioms, are the source of the water of Truth. The rules of logic determine a network of channels to carry water from tree to tree. This Truth will flow from the source (the axioms) to irrigate progressively the whole propositional field. Formal Physics enters at chapter 7, with a discussion of the concepts of Special and General Relativity and Quantum Theory. The Schrodinger Cat makes its appearance and is analysed in full in terms of Decoherence, which destroys quantum interference at macroscopic level. Again there are moments of light relief: I liked the classical example of non-commuting operators - the result is different when you boil potatoes and then crush, compared to crushing first and then boiling! Next comes our change of attitude towards `Physical Reality' in the context of Quantum Mechanics. The author argues that the counter-intuitive concepts of 'Quantum Reality' and the correlation of measurements of widely separated quantum systems are a fact of Nature, puzzling to 'common sense', but not at variance with logic. The final two chapters offer `some trails towards a Wide or Grand Realism' and a new Philosophy of Knowledge. Intelligibility and locality become `properties' valid at macroscopic level - the level of our senses. In summary I found that this book has broadened my awareness of some very deep philosophical concepts, and has given a new insight into topics such as Knowledge, Reality and Logic. I recommend it to all `natural philosophers' as a source of enjoyment and food for thought.
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.