
369The elimination of metaphysics through the epistemological analysis: lessons (un)learned from metaphysical underdeterminationIn Diederik Aerts, Jonas Arenhart, Christian De Ronde & Giuseppe Sergioli (eds.), Probing The Meaning Of Quantum Mechanics: Probability, Metaphysics, Explanation And Measurement, World Scientific. 2023.This chapter argues that the general philosophy of science should learn metaphilosophical lessons from the case of metaphysical underdetermination, as it occurs in nonrelativistic quantum mechanics. Section presents the traditional discussion of metaphysical underdetermination regarding the individuality and nonindividuality of quantum particles. Section discusses three reactions to it found in the literature: eliminativism about individuality; conservatism about individuality; eliminativism a…Read more

343A ética do uso E da seleção de embriõesPhilósophos  Revista de Filosofia 18 (1): 219232. 2013.

113Preface Special Issue Foundations of PhysicsFoundations of Physics 44 (12): 12451245. 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

113Axiomatization and Models of Scientific TheoriesFoundations of Science 16 (4): 363382. 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

106Separability and NonIndividuality: Is It Possible to Conciliate (At Least A Form Of) Einstein’s Realism with Quantum Mechanics?Foundations of Physics 44 (12): 12691288. 2005.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 logicomathematical 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 logicomathematical framework we use to de…Read more

104An Approach to QSTbased Nmatrices SemanticsPrincipia: An International Journal of Epistemology 27 (3): 539607. 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 ZermeloFraenkel set theory with Atoms), it is possible to obtain generalized Nmatrices (QNmatrices). 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

101Scientific Theories, Models and the Semantic ApproachPrincipia: An International Journal of Epistemology 11 (2): 187201. 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

90We discuss the idea that superpositions in quantum mechanics may involve contradictions or contradictory properties. A state of superposition such as the one comprised in the famous Schrödinger’s cat, for instance, is sometimes said to attribute contradictory properties to the cat: being dead and alive at the same time. If that were the case, we would be facing a revolution in logic and science, since we would have one of our greatest scientific achievements showing that real contradictions exis…Read more

78Quasiset theory: a formal approach to a quantum ontology of propertiesSynthese 200 (5): 126. 2022.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 quasiset theory is particularly suited for dealing with aggregates of items that do not belong to the traditional category of individual, it supplies an adequate metalanguage to speak of the proposed ontology of properties and its structure.

64Making Sense of NonIndividuals in Quantum MechanicsIn 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: nonindividuals. While physics, as a scientific field, is not concerned with…Read more

61In this paper we deal with two applications of the square of opposition to controversial issues in the philosophy of quantum mechanics. The first one concerns the kind of opposition represented by states in superposition. A superposition of “spin up” and “spin down” for a given spatial direction, for instance, is sometimes said to originate particular kinds of opposition such as contradictoriness. The second application concerns the problem of identical particles. Identity and indiscernibility a…Read more

56In this paper we consider the phenomenon of superpositions in quantum mechanics and suggest a way to deal with the idea in a logical setting from a syntactical point of view, that is, as subsumed in the language of the formalism, and not semantically. We restrict the discussion to the propositional level only. Then, after presenting the motivations and a possible world semantics, the formalism is outlined and we also consider within this schema the claim that superpositions may involve contradic…Read more

53Nonreflexive quantum mechanics is a formulation of quantum theory based on a non classical logic termed nonreflexive logic. In these logics, the standard notion of identity, as encapsulated in classical logic and set theories, does not hold in full. The basic aim of this kind of approach to quantum mechanics is to take seriously the claim made by some authors according to whom quantum particles are nonindividuals in some sense, and also to take into account the fact that they may be absolutely…Read more

51A discussion on quantum nonindividualityJournal of Applied NonClassical Logics 22 (12): 105124. 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 casestudy and argue that if a certain metaphysical view of quantum objects is adopted, one seeing them as nonindividuals, then there would be strong reasons to ask for a…Read more

48Schrödinger LogicsStudia Logica 53 (4): 533550. 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

43In 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 casestudy and argue that if a certain metaphysical view of quantum objects is adopted, namely, that which sees them as nonindividuals, then there would be strong reasons…Read more

40A Modal Logic of IndiscernibilityIn Aerts Diederik Et A. L. (ed.), Probing the Meaning of Quantum Mechanics: Superpositions, Dynamics, Semantics and Identity, World Scientific. pp. 259279. 2016.This paper is a continuation of the authors' attempts to deal with the notion of indistinguishability (or indiscernibility) from a logical point of view. Now we introduce a twosorted firstorder modal logic to enable us to deal with objects of two different species. The intended interpretation is that objects of one of the species obey the rules of standard S5, while the objects of the other species obey only the rules of a weaker notion of indiscernibility. Quantum mechanics motivates the deve…Read more

40In this paper, we introduce a quasiset theory without atoms. The quasisets (qsets) can have as elements completely indiscernible things which do not turn out to be the very same thing as it would be implied if its underlying logic was classical logic. A quasiset can have a cardinal, called its quasicardinal, but this is made so that, at least for the finite case, the quasicardinal is not an ordinal, and hence the indistinguishable elements of a quasiset cannot be ordered. In the last secti…Read more

38Ontology and the Mathematization of the Scientific EnterprisePhainomenon 25 (1): 109130. 2012.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

36The notion of an individual and the related issues on individuation are topics that appear in the philosophical discussion ever since the antiquity. The idea of an individual thing is intuitively clear: an individual is something of a specific kind that is a unity, having its own identity, and being so that it is possible at least in principle to discern it from any other individual, even of similar species. But when we try to leave the intuitive realm and push this idea to a logical analysis, w…Read more

34Book reviews (review)International Studies in the Philosophy of Science 21 (3). 2007.This Article does not have an abstract

31Brazilian Studies in Philosophy and History of Science: An Account of Recent Works (edited book)Springer. 2010.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

29It 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

19Models and Modeling in Science: the role of metamathematicsPrincipia: An International Journal of Epistemology 26 (1): 3954. 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 settheoretical structures, in discussing the issue we sha…Read more

18This 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 socalled semantic ap…Read more

16Quantifying Over IndiscerniblesAxiomathes 32 (3): 931946. 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

9Aspectos da indiscernibilidade qu'ntica e da teoria de quaseconjuntosPerspectivas 7 (2): 99119. 2023.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.

7Una Ojeada a Las Bases Ontológicas de la Física CuánticaPraxis Filosófica 21. 2011.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

6Einstein y la IndiscernibilidadPraxis 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

Federal University Of Santa CatarinaProfessor