•  32
    In this basically expository paper we discuss the role oflogic and mathematics in researches concerning the ontology of scientific theories, and we consider the particular case of quantum mechanics. We argue that systems of logic in general, and classical logic in particular, may contribute substantially with the ontology of any theory that has this logic in its base. In the case of quantum mechanics, however, from the point of view of philosophical discussions conceming identity and individuali…Read more
  • Probing the Meaning of Quantum Mechanics (edited book)
    with Christian de Ronde, Diederik Aerts, and M. L. Dalla Chiara
    World Scientific. 2019.
  •  59
    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
  •  61
    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
  •  303
    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
  •  43
    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.
  •  20
    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
  •  2
    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
  •  28
    Book reviews (review)
    International Studies in the Philosophy of Science 21 (3). 2007.
    This Article does not have an abstract
  •  340
    A ética do uso E da seleção de embriões
    with Pedro Merlussi
    Philósophos - Revista de Filosofia 18 (1): 219-232. 2013.
  •  97
    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
  •  107
    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
  •  102
    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
  •  4
    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
  •  7
    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
  •  13
    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
  •  30
    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
  •  16
    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.
  •  18
    Non-relativistic quantum mechanics is grounded on ‘classical’ space and time. The mathematical description of these con- cepts entails that any two spatially separated objects are necessarily dif- ferent, which implies that they are discernible — we say that the space is T2, or "Hausdorff". But quantum systems, in the most interesting cases, some- times need to be taken as indiscernible, so that there is no way to tell which system is which, and this holds even in the case of fermions. But in th…Read more
  •  56
    Schrödinger Logics
    Studia Logica 53 (4): 533-550. 1994.
    Schrödinger logics are logical systems in which the principle of identity is not true in general. The intuitive motivation for these logics is both Erwin Schrödinger's thesis that identity lacks sense for elementary particles of modern physics, and the way which physicists deal with this concept; normally, they understand identity as meaning indistinguishability . Observing that these concepts are equivalent in classical logic and mathematics, which underly the usual physical theories, we presen…Read more
  •  88
    Scientific Theories, Models and the Semantic Approach
    with Krause Décio and Bueno Otávio
    Principia: An International Journal of Epistemology 11 (2): 187-201. 2007.
    According to the semantic view, a theory is characterized by a class of models. In this paper, we examine critically some of the assumptions that underlie this approach. First, we recall that models are models of something. Thus we cannot leave completely aside the axiomatization of the theories under consideration, nor can we ignore the metamathematics used to elaborate these models, for changes in the metamathematics often impose restrictions on the resulting models. Second, based on a paralle…Read more
  •  78
    List of Contents: Volume 10, Number 5, October 1997
    with Adonai S. Sant’Anna, Croca Jr, M. Ferrero, A. Garuccio, and V. L. Lepore
    Foundations of Physics 28 (2). 1998.
  •  18
    Questões a uma teoria de quase-objetos
    Manuscrito 32 (2): 399-436. 2009.
    Discutimos algumas quest~oes relacionadas a uma possvel teoriade quase-objetos, isto e, objetos para os quais as condic~oes usuais de identidaden~ao se aplicariam. Desde que a principal motivac~ao para uma tal teoriae a mec^anica qu^antica, a discuss~ao e realizada tendo-se essa intepretac~ao pretendidaem mente.We discuss some questions related to a possible theory of quasiobjects,that is, objects for which the standard identity conditions should nothold. Since the main motivation for such a the…Read more
  •  159
    Inspired in Quine's well known slogans “To be is to be the value of a variable” and "No entity without identity", we provide a way of enabling that non-individual entities (as characterized in the text) can also be values of variables of an adequate "regimented" language, once we consider a possible meaning of the background theory Quine reports to ground his view. In doing that, we show that there may exist also entities without identity, and emphasize the importance of paying attention to the …Read more
  •  52
    A discussion on quantum non-individuality
    Journal of Applied Non-Classical Logics 22 (1-2): 105-124. 2012.
    In this paper we consider the notions of structure and models within the semantic approach to theories. To highlight the role of the mathematics used to build the structures which will be taken as the models of theories, we review the notion of mathematical structure and of the models of scientific theories. Then, we analyse a case-study and argue that if a certain metaphysical view of quantum objects is adopted, one seeing them as non-individuals, then there would be strong reasons to ask for a…Read more