•  48
    Making Sense of Non-Individuals in Quantum Mechanics
    with Jonas R. B. Arenhart and Otávio Bueno
    In Olimpia Lombardi, Sebastian Fortin, Cristian López & Frederico Holik (eds.), Quantum Worlds. Different Perspectives about the ontology of quantum mechanics, Cambridge University Press. forthcoming.
    In this work, we focus on a very specific case study: assuming that quantum theories deal with “particles” of some kind, what kind of entity can such particles be? One possible answer, the one we shall examine here, is that they are not the usual kind of object found in daily life: individuals. Rather, we follow a suggestion by Erwin Schrödinger, according to which quantum mechanics poses a revolutionary kind of entity: non-individuals. While physics, as a scientific field, is not concerned with…Read more
  •  13
    An Approach to QST-based Nmatrices Semantics
    Principia: An International Journal of Epistemology 27 (3): 539-607. 2023.
    This paper introduces the theory QST of quasets as a formal basis for the Nmatrices. The main aim is to construct a system of Nmatrices by substituting standard sets by quasets. Since QST is a conservative extension of ZFA (the Zermelo-Fraenkel set theory with Atoms), it is possible to obtain generalized Nmatrices (Q-Nmatrices). Since the original formulation of QST is not completely adequate for the developments we advance here, some possible amendments to the theory are also considered. One of…Read more
  • Quasiset theories for microobjects: a comparison
    with Dalla Chiara and R. Giuntini
    In Elena Castellani (ed.), Interpreting Bodies, Princeton University Press. pp. 142--52. 1998.
  •  219
    This chapter argues that the general philosophy of science should learn metaphilosophical lessons from the case of metaphysical underdetermination, as it occurs in non-relativistic quantum mechanics. Section presents the traditional discussion of metaphysical underdetermination regarding the individuality and non-individuality of quantum particles. Section discusses three reactions to it found in the literature: eliminativism about individuality; conservatism about individuality; eliminativism a…Read more
  •  18
    In previous works, an ontology of properties for quantum mechanics has been proposed, according to which quantum systems are bundles of properties with no principle of individuality. The aim of the present article is to show that, since quasi-set theory is particularly suited for dealing with aggregates of items that do not belong to the traditional category of individual, it supplies an adequate meta-language to speak of the proposed ontology of properties and its structure.
  •  15
    It is supposed that any scientific theory (here we consider physical theories only) has an underlying logic, even if it is not made explicit. The role of the underlying logic of a theory T is mainly to guide the proofs and the accepted consequences of the theory’s principles, usually described by its axioms. In this sense, the theorems of the underlying logic are also theorems of the theory. In most cases, if pressed, the scientist will say that the underlying logic of most physical theories is …Read more
  •  1
    Einstein y la Indiscernibilidad
    Praxis Filosófica 22. 2011.
    El tema de esta contribución me fue sugerido por el Profesor Michel Paty. Sabiendo que estoy muy interesado en la cuestión de la indiscernibilidad (o indistinguibilidad, palabra que aquí usaré como sinónima) de las partículas elementales y de sus consecuencias lógicas y filosóficas, él me hizo la excelente sugerencia de que escribiera esta pequeña nota sobre el papel desempeñado por Einstein en la consolidación de ese concepto, y también para hablar un poco de sus consecuencias lógicas y filosóf…Read more
  •  3
    Defendemos el punto de vista de que la investigación de un amplio campo de la ciencia puede ser desarrollada desde diferentes puntos de vista (o perspectivas), las cuales pueden originar diferentes teorías informales y, entonces, teorías axiomáticas no equivalentes. Cada una de ellas aborda diferentes aspectos del dominio. Después de presentar ese punto de vista, de una forma general, intentamos aplicarla al dominio de la física cuántica. Entonces, siguiendo la indicación de Heinz Post de que lo…Read more
  •  126
    Indistinguishability and the origins of contextuality in physics
    Philosophical Transactions of the Royal Society A 377 (2157). 2019.
    In this work, we discuss a formal way of dealing with the properties of contextual systems. Our approach is to assume that properties describing the same physical quantity, but belonging to different measurement contexts, are indistinguishable in a strong sense. To construct the formal theoretical structure, we develop a description using quasi-set theory, which is a set-theoretical framework built to describe collections of elements that violate Leibnitz's principle of identity of indiscernible…Read more
  •  17
    Book reviews (review)
    International Studies in the Philosophy of Science 21 (3). 2007.
    This Article does not have an abstract
  •  333
    A ética do uso E da seleção de embriões
    with Pedro Merlussi
    Philósophos - Revista de Filosofia 18 (1): 219-232. 2013.
  •  84
    In this paper we argue that physical theories, including quantum mechanics, refer to some kind of ‘objects’, even if only implicitly. We raise questions about the logico-mathematical apparatuses commonly employed in such theories, bringing to light some metaphysical presuppositions underlying such apparatuses. We point out to some incongruities in the discourse holding that quantum objects would be entities of some ‘new kind’ while still adhering to the logico-mathematical framework we use to de…Read more
  •  100
    Axiomatization and Models of Scientific Theories
    with Jonas R. B. Arenhart and Fernando T. F. Moraes
    Foundations of Science 16 (4): 363-382. 2011.
    In this paper we discuss two approaches to the axiomatization of scientific theories in the context of the so called semantic approach, according to which (roughly) a theory can be seen as a class of models. The two approaches are associated respectively to Suppes’ and to da Costa and Chuaqui’s works. We argue that theories can be developed both in a way more akin to the usual mathematical practice (Suppes), in an informal set theoretical environment, writing the set theoretical predicate in the…Read more
  •  93
    Preface Special Issue Foundations of Physics
    Foundations of Physics 44 (12): 1245-1245. 2014.
    The foundations of quantum mechanics are attracting new and significant interest in the scientific community due to the recent striking experimental and technical progress in the fields of quantum computation, quantum teleportation and quantum information processing. However, at a more fundamental level the understanding and manipulation of these novel phenomena require not only new laboratory techniques but also new understanding, development and interpretation of the formalism of quantum mecha…Read more
  •  2
    A indiscernibilidade das entidades quânticas é considerada como uma das noções centrais das teorias quânticas. Neste artigo expositivo, são apontadas algumas das razões para essa alegada importância, bem como as ideias básicas de uma teoria matemática que permite tratar de coleções dessas entidades. O artigo inicia com uma posição geral do autor sobre a filosofia da ciência.
  • This book provides an interdisciplinary perspective on one of the most fascinating and important open questions in science: What is quantum mechanics talking about? Quantum theory is perhaps our best confirmed physical theory. However, despite its great empirical effectiveness and the subsequent technological developments that it gave rise to in the 20th century, from the interpretation of the periodic table of elements to CD players, holograms and quantum state teleportation, it stands even tod…Read more
  •  4
    Quantifying Over Indiscernibles
    Axiomathes 32 (3): 931-946. 2022.
    One of the main criticisms of the theory of collections of indiscernible objects is that once we quantify over one of them, we are quantifying over all of them since they cannot be discerned from one another. In this way, we would call the collapse of quantifiers: ‘There exists one x such as P’ would entail ‘All x are P’. In this paper we argue that there are situations (quantum theory is the sample case) where we do refer to a certain quantum entity, saying that it has a certain property, even …Read more
  •  10
    Models and Modeling in Science: the role of metamathematics
    Principia: An International Journal of Epistemology 26 (1): 39-54. 2022.
    The use of models of scientific theories should not be done without qualifications about the mathematics being used to build the models. This looks obvious, at least for logicians, but generally, it is not to the philosopher of science. Thus, some details about this point seem useful for both. Since any quick revision in the literature shows that in most cases, mainly after the raising of the semantic approach, the models are taken to be set-theoretical structures, in discussing the issue we sha…Read more
  •  7
    This volume, The Brazilian Studies in the Philosophy and History of Science, is the first attempt to present to a general audience, works from Brazil on this subject. The included papers are original, covering a remarkable number of relevant topics of philosophy of science, logic and on the history of science. The Brazilian community has increased in the last years in quantity and in quality of the works, most of them being published in respectable international journals on the subject. The chap…Read more
  •  10
    This book addresses the logical aspects of the foundations of scientific theories. Even though the relevance of formal methods in the study of scientific theories is now widely recognized and regaining prominence, the issues covered here are still not generally discussed in philosophy of science. The authors focus mainly on the role played by the underlying formal apparatuses employed in the construction of the models of scientific theories, relating the discussion with the so-called semantic ap…Read more
  • A True Polymath: A Tribute to Francisco Antonio Doria. (edited book)
    College Publications. 2020.
  •  171
    Steven French and Decio Krause examine the metaphysical foundations of quantum physics. They draw together historical, logical, and philosophical perspectives on the fundamental nature of quantum particles and offer new insights on a range of important issues. Focusing on the concepts of identity and individuality, the authors explore two alternative metaphysical views; according to one, quantum particles are no different from books, tables, and people in this respect; according to the other, th…Read more
  •  11
    It is not an exaggeration to say that quantum mechanics is at odds with most of our received metaphysical notions. In particular, an alleged revision is brought about by the theory on the metaphysical notion of ‘individuality’. Certainly, this should figure as being of great interest for metaphysicians and philosophers of science alike. What makes issues even more interesting is that some of the founding fathers of the theory, with their typical philosophical inclinations, suggested that the ent…Read more
  •  258
    The physics and metaphysics of identity and individuality Content Type Journal Article DOI 10.1007/s11016-010-9463-7 Authors Don Howard, Department of Philosophy and Graduate Program in History and Philosophy of Science, University of Notre Dame, Notre Dame, IN 46556, USA Bas C. van Fraassen, Philosophy Department, San Francisco State University, 1600 Holloway Avenue, San Francisco, CA 94132, USA Otávio Bueno, Department of Philosophy, University of Miami, Coral Gables, FL 33124, USA Elena Caste…Read more
  •  40
    Quasi-truth and defective knowledge in science: a critical examination
    with Jonas R. Becker Arenhart
    Manuscrito 46 (2): 122-155. 2023.
    Quasi-truth (a.k.a. pragmatic truth or partial truth) is typically advanced as a framework accounting for incompleteness and uncertainty in the actual practices of science. Also, it is said to be useful for accommodating cases of inconsistency in science without leading to triviality. In this paper, we argue that the formalism available does not deliver all that is promised. We examine the standard account of quasi-truth in the literature, advanced by da Costa and collaborators in many places, a…Read more
  •  53
    Following J.-Y.Béziau in his pioneer work on non-standard interpretations of the traditional square of opposition, we have applied the abstract structure of the square to study the relation of opposition between states in superposition in orthodox quantum mechanics in [1]. Our conclusion was that such states are contraries, contradicting previous analyzes that have led to different results, such as those claiming that those states represent contradictory properties. In this chapter we bring the …Read more
  •  42
    Does Newtonian Space Provide Identity to Quantum Systems?
    Foundations of Science 24 (2): 197-215. 2019.
    Physics is not just mathematics. This seems trivial, but poses difficult and interesting questions. In this paper we analyse a particular discrepancy between non-relativistic quantum mechanics and ‘classical’ space and time. We also suggest, but not discuss, the case of the relativistic QM. In this work, we are more concerned with the notion of space and its mathematical representation. The mathematics entails that any two spatially separated objects are necessarily different, which implies that…Read more
  •  142
    It is well known that in quantum mechanics we cannot always define consistently properties that are context independent. Many approaches exist to describe contextual properties, such as Contextuality by Default, sheaf theory, topos theory, and non-standard or signed probabilities. In this paper we propose a treatment of contextual properties that is specific to quantum mechanics, as it relies on the relationship between contextuality and indistinguishability. In particular, we propose that if we…Read more