
1401Scientific 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

315A inseparabilidade entre lógica E a éticaPhilósophos  Revista de Filosofia 18 (1): 245259. 2013.

235The physics and metaphysics of identity and individuality Content Type Journal Article DOI 10.1007/s1101601094637 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

151Identity, indiscernibility, and philosophical claimsAxiomathes 15 (2): 191210. 2005.The concept of indiscernibility in a structure is analysed with the aim of emphasizing that in asserting that two objects are indiscernible, it is useful to consider these objects as members of (the domain of) a structure. A case for this usefulness is presented by examining the consequences of this view to the philosophical discussion on identity and indiscernibility in quantum theory.

145Qspaces and the Foundations of Quantum MechanicsFoundations of Physics 38 (11): 969994. 2008.Our aim in this paper is to take quite seriously Heinz Post’s claim that the nonindividuality and the indiscernibility of quantum objects should be introduced right at the start, and not made a posteriori by introducing symmetry conditions. Using a different mathematical framework, namely, quasiset theory, we avoid working within a labeltensorproductvectorspaceformalism, to use Redhead and Teller’s words, and get a more intuitive way of dealing with the formalism of quantum mechanics, alt…Read more

134Identity 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

133Inspired 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 nonindividual 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

133Structures and Structural RealismLogic Journal of the IGPL 13 (1): 113126. 2003.The ‘ontic’ form of structural realism , roughly speaking, admits a complete elimination of the objects in the discourse of scientific theories, leaving us with structures only. As put by the defenders of such a claim, the idea is that all there is are structures and, if the relevant structures are to be settheoretical constructs , as it has also been claimed, then the relations which appear in such structures should be taken to be ‘relations without the relata’. As far as we know, there is not…Read more

131Vague Identity and Quantum NonIndividualityAnalysis 55 (1). 1995.Lowe has recently argued that quantum particles offer examples of vague objects. While accepting the premise of the argument that such particles can be regarded as individuals, we point out that there is a lacuna here, to be filled by a detailed analysis of the nature of the entangled states which they enter into. We then elaborate the alternative view, according to which such particles should be regarded as non individuals' and situate it in the context of recent developments of a logic of non…Read more

127Quantum 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 ‘quantumsortal predicates’ and, instead of a process of counting, to them is a…Read more

119Quantum 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.

104Physics, inconsistency, and quasitruthSynthese 191 (13): 30413055. 2014.In this work, the first of a series, we study the nature of informal inconsistency in physics, focusing mainly on the foundations of quantum theory, and appealing to the concept of quasitruth. We defend a pluralistic view of the philosophy of science, grounded on the existence of inconsistencies and on quasitruth. Here, we treat only the ‘classical aspects’ of the subject, leaving for a forthcoming paper the ‘nonclassical’ part

103In 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.

98Logical aspects of quantum (non)individualityFoundations of Science 15 (1): 7994. 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 nonindividuals…Read more

96Uma Lógica da IndistinguibilidadeDisputatio 4 (34): 555573. 2012.Arenhart_Krause_Umalogicadaindistinguibilidade

95Is Identity Really so Fundamental?Foundations of Science 24 (1): 5171. 2019.We critically examine the claim that identity is a fundamental concept. According to those putting forward this thesis, there are four related reasons that can be called upon to ground the fundamental character of identity: identity is presupposed in every conceptual system; identity is required to characterize individuality; identity cannot be defined; the intelligibility of quantification requires identity. We address each of these points and argue that none of them advances compelling reasons…Read more

92Some of the forerunners of quantum theory regarded the basic entities of such theories as 'nonindividuals'. One of the problems is to treat collections of such 'things', for they do not obey the axioms of standard set theories like Zermelo Fraenkel. In this paper, collections of objects to which the standard concept of identity does not apply are termed 'quasisets'. The motivation for such a theory, linked to what we call 'the Manin problem', is presented, so as its specific axioms. At the en…Read more

92In this paper we make some general remarks on the use of nonclassical logics, in particular paraconsistent logic, in the foundational analysis of physical theories. As a casestudy, we present a reconstruction of P.\ D.\ F\'evrier's 'logic of complementarity' as a strict threevalued 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'.

91A formal framework for quantum nonindividualitySynthese 102 (1). 1995.H. Post's conception of quantal particles as nonindividuals is set in a formal logicomathematical framework. By means of this approach certain metaphysical implications of quantum mechanics can be further explored.

89Relativizations of the Principle of IdentityLogic Journal of the IGPL 5 (3): 1729. 1997.We discuss some logicomathematical systems which deviate from classical logic and mathematics with respect to the concept of identity. In the first part of the paper we present very general formulations of the principle of identity and show how they can be ‘relativized’ to objects and to properties. Then, as an application, we study the particular cases of physics and logic . In the last part of the paper, we discuss the alphabar logics, that is, those logical systems which violate a formulatio…Read more

82Quantum 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 'quantumsortal predicates' and, instead of a process of counting, to them is a…Read more

81Remarks on the Theory of QuasisetsStudia Logica 95 (12). 2010.Quasiset theory has been proposed as a means of handling collections of indiscernible objects. Although the most direct application of the theory is quantum physics, it can be seen per se as a nonclassical logic (a nonreflexive logic). In this paper we revise and correct some aspects of quasiset theory as presented in [12], so as to avoid some misunderstandings and possible misinterpretations about the results achieved by the theory. Some further ideas with regard to quantum field theory are…Read more

80The problem of identity and a justification for a nonreflexive quantum mechanicsLogic Journal of the IGPL 22 (2): 186205. 2014.In this paper we try to justify our way of looking for an alternative approach to quantum mechanics, which is based on a nonclassical 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

77Scientific 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

69In 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 firstorder 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

65Remarks on quantum ontologySynthese 125 (12): 155167. 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 logicomathematical basis of quantum theories. This paper considers some possibilities for accomodating the logicomathematical framework of the theories which deal with such a strange ontology where the inhabitants are things devoid of i…Read more

64A obra de Newton C.A. Da Costa em LogicaTheoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 7 (13): 347386. 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

63Why Nonindividuality? A Discussion on Individuality, Identity, and Cardinality in the Quantum ContextErkenntnis (1): 118. 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 nonindividuality (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. Nonrelativistic quantum mechanics is said to provide positive evidence for that position, since in every situat…Read more

62This 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

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 