Cuesta, J.A.F. (2026). Lógica y Física: Ontologías, Teorías y Datos Empíricos [In Spanish: Logic and Physics: Ontologies, Theories and Empirical Data]. Culturas Científicas. Special Issue. Forthcoming.

Abstract — Standard quantum logics are the only non-classical logical formalism extracted from within a scientific theory formulated in classical logic. This feature motivates a three-level epistemological model: L1 fixes formal ontology, L2 contains theories and their event structures, and L3 comprises empirical data. The model shows that Putnam and Kripke share the same monist assumption, and it allows one to maintain that logic is empirical at L2 and a priori in a functional sense at L1.

Cuesta, J.A.F., Piazzai, M. and Rivieccio, U. (2025). Quantum logics in cognition: A proposal. Synthese, 206(1), 1–34.

Abstract — Quantum logics are non-classical logics defined from the mathematical formalism of quantum mechanics. While they are conventionally used to model inferential processes in physics, their scope of application is potentially much broader. We argue that quantum logics can serve as a framework to model human cognition, as their semantics seem able to capture not only how people make inferences about quantum mechanics, but also how they reason in general. We begin by defining quantum logics from an algebraic perspective in a classical first-order setting. Next, we present findings from cognitive science that suggest these logics are apt to characterize human reasoning. We then consider how such a connection between quantum logics and cognition contributes to longstanding philosophical debates about the epistemological status of logic and the problem of adoption. Finally, we discuss how cognitive applications of quantum logics could advance our understanding of human psychology and even quantum foundations.

Cuesta, J.A.F. (2025). Suárez’s Paradox and Contemporary Debates in the Philosophy of Quantum Logics. Análisis. Revista de Investigación Filosófica, 12(1), 93–105.

Abstract — In this commentary on Suárez’s recently published work (2025), I aim to retrieve an original argument hitherto unpublished –which I refer to as Suárez’s Paradox (Suárez, 1992)– together with the response he himself proposes. Drawing on both the paradox and the epistemological model proposed to resolve it, I argue that we are presented with a theoretical framework capable of enabling a philosophically significant approach to current debates on the interpretation of quantum logics. I conclude by assessing the value of this proposal not only in terms of its internal content but also considering its capacity to bridge two philosophical domains that, over recent decades, have largely evolved in isolation: the philosophy of logic and the philosophy of science.

Sánchez-Ovcharov, C., Gherab-Martín, K. and Cuesta, J.A.F. (2025). Quantum Counterfactuals: Interaction-Free Measurements and Classical Logic’s Constraints. Logos & Episteme, 16(4), 455–477.

Abstract — The aim of this paper is to carry out a critical analysis of the uses of the material conditionals employed to represent the counterfactual detections taking place inside Elitzur-Vaidman quantum bomb detectors in so-called quantum interaction free measurements (IFMs). We provide an exhaustive philosophical study of this classical approach focusing on its limitations. To do so, we formulate atomic propositions corresponding to the observable events of the experiments, to overcome the shortcomings of the conditional expression. Finally, we show that the standard definition ofcounterfactuality in quantum contexts based on classical logic is epistemologically too limited, presenting quantum logics as the most promising possible approach to address this type of quantum counterfactuality.

Philosophical Argumentation in the Foundations of Mathematics

PR17/24-31887 — AFIM

Funder: Comunidad de Madrid — PI: Víctor Aranda