-
15Models and Modeling in Science: the role of metamathematicsPrincipia: 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
-
30Brazilian 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
-
16This 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
-
187Identity in physics: a historical, philosophical, and formal analysisOxford University Press. 2006.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
-
13Quantum Non-individuality: Background Concepts and PossibilitiesIn Wuppuluri Shyam & Francisco Antonio Dorio (eds.), The Map and the Territory: Exploring the Foundations of Science, Thought and Reality, Springer. pp. 281-305. 2018.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
-
271The 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
-
50Quasi-truth and defective knowledge in science: a critical examinationManuscrito 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
-
60Following 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
-
53Does 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
-
188Contextuality and IndistinguishabilityEntropy 19 ((9)): 435. 2017.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
-
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.
-
39Quantum 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.
-
127Scientific 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
-
92In 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: Classical and Quantum Objects in Modern Physics, 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
-
95Scientific 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
-
29The 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
-
25A 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.
-
28Paraconsistent logics are logics that can be used to base inconsistent but non-trivial systems. In paraconsistent set theories, we can quan- tify over sets that in standard set theories, if consistent, would lead to contradictions, such as the Russell set, R = fx : x =2 xg. Quasi-set theories are mathematical systems built for dealing with collections of indiscernible elements. The basic motivation for the development of quasi-set theories came from quantum physics, where indiscernible entities …Read more
-
31Sobre uma fundamentação não reflexiva da mecânica quânticaScientiae Studia 10 (1): 71-104. 2012.
-
27Is Priscilla, the trapped positron, an individual? Quantum physics, the use of names, and individuationArbor 187 (747): 61-66. 2011.
-
111Uma Lógica da IndistinguibilidadeDisputatio 4 (34): 555-573. 2012.Arenhart_Krause_Uma-logica-da-indistinguibilidade
-
27Indiscernibilidade e identidade em química: aspectos filosóficos e formaisManuscrito 37 (1): 113-160. 2014.
-
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 |