-
18Non-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
-
17This is a general philosophical paper where I overview some of my ideas concerning the non-reflexive foundations of quantum mechanics. By NRFQM I mean an interpretation of QM that considers an involved on- tology of non-individuals as explained in the text. Thus, I do not endorse a purely instrumentalist view of QM, but believe that it speaks of something, and then I try to show that one of the plausible views of this ‘something’ is as entities devoided of identity conditions.
-
38Quantum Logical Structures For Identical ParticlesCadernos de História E Filosofia da Ciéncia 2 (1): 13-58. 2016.In this work we discuss logical structures related to indistinguishable particles. Most of the framework used to develop these structures was presented in [17, 28] and in [20, 14, 15, 16]. We use these structures and constructions to discuss possible ontologies for identical particles. In other words, we use these structures in order to characterize the logical structure of quantum systems for the case of indistinguishable particles, and draw possible philosophical implications. We also review s…Read more
-
118In this paper, we examine the concept of particle as it appears in quantum field theories, focusing on a puzzling situation regarding this concept. Although quantum ‘particles’ arise from fields, which form the basic ontology of QFT, and thus a certain concept of ‘particle’ is al- ways available, the properties ascribed to such ‘particles’ are not completely in agreement with the mathematical and logical description of such fields, which should be taken as individuals.
-
1444Scientific Theories, Models and the Semantic ApproachPrincipia: 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
-
90In this first paper of a series of works on the foundations of science, we examine the significance of logical and mathematical frameworks used in foundational studies. In particular, we emphasize the distinction between the order of a language and the order of a structure to prevent confusing models of scientific theories with first-order structures, and which are studied in standard model theory. All of us are, of course, bound to make abuses of language even in putatively precise contexts. Th…Read more
-
1Quasiset theories for microobjects: A comparisonIn Elena Castellani (ed.), Interpreting Bodies, Princeton University Press. pp. 142--52. 1998.
-
94Quantum Sortal PredicatesSynthese 154 (3). 2007.Sortal predicates have been associated with a counting process, which acts as a criterion of identity for the individuals they correctly apply to. We discuss in what sense certain types of predicates suggested by quantum physics deserve the title of 'sortal' as well, although they do not characterize either a process of counting or a criterion of identity for the entities that fall under them. We call such predicates 'quantum-sortal predicates' and, instead of a process of counting, to them is a…Read more
-
86Scientific Theories, Models and the Semantic ApproachPrincipia: 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
-
39The Quasi-lattice of Indiscernible ElementsStudia Logica 97 (1): 101-126. 2011.The literature on quantum logic emphasizes that the algebraic structures involved with orthodox quantum mechanics are non distributive. In this paper we develop a particular algebraic structure, the quasi-lattice ( $${\mathfrak{I}}$$ -lattice), which can be modeled by an algebraic structure built in quasi-set theory $${\mathfrak{Q}}$$. This structure is non distributive and involve indiscernible elements. Thus we show that in taking into account indiscernibility as a primitive concept, the quasi…Read more
-
74A obra de Newton C.A. Da Costa em LogicaTheoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 7 (1-3): 347-386. 1992.In this paper we present an overview of Professor Newton C. A. da Costa’s work in logic, emphasizing the main results obtained by him in the several areas of his research activity. The text furnish a detailed bibliographic reference of his works, which are listed in the last section
-
Classical Logic or Non-Reflexive Logic?: A Case of Semantic UnderdeterminationRevista Portuguesa de Filosofia 68 (1-2): 73-86. 2012.
-
108In this paper we make some general remarks on the use of non-classical logics, in particular paraconsistent logic, in the foundational analysis of physical theories. As a case-study, we present a reconstruction of P.\ -D.\ F\'evrier's 'logic of complementarity' as a strict three-valued logic and also a paraconsistent version of it. At the end, we sketch our own approach to complementarity, which is based on a paraconsistent logic termed 'paraclassical logic'.
-
71This paper is the sequel of a previous one where we have introduced a paraconsistent logic termed paraclassical logic to deal with 'complementary propositions'. Here, we enlarge upon the discussion by considering certain 'meaning principles', which sanction either some restrictions of 'classical' procedures or the utilization of certain 'classical' incompatible schemes in the domain of the physical theories. Here, the term 'classical' refers to classical physics. Some general comments on the log…Read more
-
3616. On The Concept Of Identity In Zermelo-fraenkel-like Axioms And Its Relationships With Quantum StatisticsLogique Et Analyse 48. 2005.
-
23Indistinguibilidade, não reflexividade, ontologia e física quânticaScientiae Studia 10 (1): 41-69. 2012.
-
30Introdução aos fundamentos axiomáticos da ciênciaPrincipia: An International Journal of Epistemology 6 (2): 315-319. 2002.Review of the KRAUSE, Décio "Introdução aos Fundamentos Axiomáticos da Ciência" São Paulo EPU, 2002
-
157Quantum vaguenessErkenntnis 59 (1). 2003.It has been suggested that quantum particles are genuinelyvague objects (Lowe 1994a). The present work explores thissuggestion in terms of the various metaphysical packages that areavailable for describing such particles. The formal frameworksunderpinning such packages are outlined and issues of identityand reference are considered from this overall perspective. Indoing so we hope to illuminate the diverse ways in whichvagueness can arise in the quantum context.
-
90The problem of identity and a justification for a non-reflexive quantum mechanicsLogic Journal of the IGPL 22 (2): 186-205. 2014.In this paper we try to justify our way of looking for an alternative approach to quantum mechanics, which is based on a non-classical logic. We consider two specific questions related to quantum theory, namely, entanglement and the indiscernibility of quanta. We characterize individuals, and then explain in what sense entanglement is a concept which can be applied to individuals in a restricted sense only. Then, we turn to indiscernibility and, after realizing that this concept is of a fundamen…Read more
-
22Brigitte Falkenburg, Editor, Between rationalism and empiricism. Selected Papers in the Philosophy of Physics; Erhard Scheibe, Springer, Berlin (2001) ISBN 0-387-98520-4 (627pp. Euro 88.76) (review)Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 36 (1): 210-217. 2005.
-
18Questões a uma teoria de quase-objetosManuscrito 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
-
94Why Non-individuality? A Discussion on Individuality, Identity, and Cardinality in the Quantum ContextErkenntnis (1): 1-18. 2012.Recently, in the debate about the ontology of quantum mechanics some authors have defended the view that quantum particles are individuals in a primitive sense, so that individuality should be preferred over non-individuality (the alternative option). Primitive individuality involves two main claims: (1) every item is identical with itself and (2) it is distinct from every other item. Non-relativistic quantum mechanics is said to provide positive evidence for that position, since in every situat…Read more
-
118Logical aspects of quantum (non-)individualityFoundations of Science 15 (1): 79-94. 2010.In this paper I consider some logical and mathematical aspects of the discussion of the identity and individuality of quantum entities. I shall point out that for some aspects of the discussion, the logical basis cannot be put aside; on the contrary, it leads us to unavoidable conclusions which may have consequences in how we articulate certain concepts related to quantum theory. Behind the discussion, there is a general argument which suggests the possibility of a metaphysics of non-individuals…Read more
-
35We show that using quasi-set theory, or the theory of collections of indistinguishable objects, we can define an algebra that has most of the standard properties of an orthocomplete orthomodular lattice, which is the lattice of all closed subspaces of a Hilbert space. We call the mathematical structure so obtained $\mathfrak{I}$-lattice. After discussing (in a preliminary form) some aspects of such a structure, we indicate the next problem of axiomatizing the corresponding logic, that is, a logi…Read more
-
73Remarks on quantum ontologySynthese 125 (1-2): 155-167. 2000.Despite the discrepancies between quantum objects and `classical' ones, mainly with regard to the fact that the latter may be thought of as `individuals', contrary to the former, we still regard the quanta as `things' in our ordinary discourse as well as in the logico-mathematical basis of quantum theories. This paper considers some possibilities for accomodating the logico-mathematical framework of the theories which deal with such a strange ontology where the inhabitants are things devoid of i…Read more
-
Federal University of Santa CatarinaProfessor
University of São Paulo
Department of Philosophy, Languages and Literature, and Human Sciences
PhD, 1990
Florianópolis, Santa Catarina, Brazil
Areas of Specialization
Logic and Philosophy of Logic |
Philosophy of Physical Science |