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Décio Krause
University of São Paulo (PhD)
  1. Scientific Theories, Models and the Semantic Approach.Otávio Bueno & Décio Krause - 2007 - Principia: An International Journal of Epistemology 11 (2):187-201.
    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 parallel between van Fraassen’s (...)
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  2.  42
    Contradiction, Quantum Mechanics, and the Square of Opposition.Jonas R. B. Arenhart & Décio Krause - unknown
    We 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 exist.We analyze that (...)
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  3. Q-Spaces and the Foundations of Quantum Mechanics.Graciela Domenech, Federico Holik & Décio Krause - 2008 - Foundations of Physics 38 (11):969-994.
    Our aim in this paper is to take quite seriously Heinz Post’s claim that the non-individuality 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, quasi-set theory, we avoid working within a label-tensor-product-vector-space-formalism, to use Redhead and Teller’s words, and get a more intuitive way of dealing with the formalism of quantum mechanics, although the underlying logic should be modified. We build (...)
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  4.  68
    Remarks on the Theory of Quasi-Sets.Steven French & Décio Krause - 2010 - Studia Logica 95 (1-2):101 - 124.
    Quasi-set 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 non-classical logic (a non-reflexive logic). In this paper we revise and correct some aspects of quasi-set 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 also (...)
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  5.  28
    On a Quasi-Set Theory.Decio Krause - 1992 - Notre Dame Journal of Formal Logic 33 (3):402--11.
  6. Quantum Vagueness.Steven French & Décio Krause - 2003 - Erkenntnis 59 (1):97 - 124.
    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.
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  7.  35
    Potentiality and Contradiction in Quantum Mechanics.Jonas R. B. Arenhart & Decio Krause - unknown
    Following 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 issue once again into the center of the (...)
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  8.  86
    Logical Aspects of Quantum (Non-)Individuality.Décio Krause - 2010 - Foundations of Science 15 (1):79-94.
    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, based on (...)
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  9.  13
    Does Newtonian Space Provide Identity to Quantum Systems?Décio Krause - forthcoming - Foundations of Science:1-19.
    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 they are discernible —we say that the (...)
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  10.  44
    From Primitive Identity to the Non-Individuality of Quantum Objects.Jonas Becker Arenhart & Décio Krause - 2014 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 46 (2):273-282.
    We consider the claim by Dorato and Morganti 591–610) that primitive individuality should be attributed to the entities dealt with by non-relativistic quantum mechanics. There are two central ingredients in the proposal: in the case of non-relativistic quantum mechanics, individuality should be taken as a primitive notion and primitive individuality is naturalistically acceptable. We argue that, strictly understood, naturalism faces difficulties in helping to provide a theory with a unique principle of individuation. We also hold that even when taken in (...)
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  11.  5
    Is Priscilla, the Trapped Positron, an Individual? Quantum Physics, the Use of Names, and Individuation.Décio Krause - 2011 - Arbor 187 (747):61-66.
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  12. Identity, Indiscernibility, and Philosophical Claims.Décio Krause & Antonio Mariano Nogueira Coelho - 2005 - Axiomathes 15 (2):191-210.
    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.
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  13. A ética do uso E da seleção de embriões.Decio Krause & Pedro Merlussi - 2013 - Philósophos - Revista de Filosofia 18 (1):219-232.
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  14.  93
    Structures and Structural Realism.Décio Krause - 2003 - Logic Journal of the IGPL 13 (1):113-126.
    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 set-theoretical 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 (...)
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  15.  27
    Quantifiers and the Foundations of Quasi-Set Theory.Jonas R. Becker Arenhart & Décio Krause - 2009 - Principia: An International Journal of Epistemology 13 (3):251-268.
    In this paper we discuss some questions proposed by Prof. Newton da Costa on the foundations of quasi-set theory. His main doubts concern the possibility of a reasonable semantical understanding of the theory, mainly due to the fact that identity and difference do not apply to some entities of the theory’s intended domain of discourse. According to him, the quantifiers employed in the theory, when understood in the usual way, rely on the assumption that identity applies to all entities in (...)
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  16. A inseparabilidade entre lógica E a ética.Decio Krause - 2013 - Philósophos - Revista de Filosofia 18 (1):245-259.
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  17. Vague Identity and Quantum Non-Individuality.Steven French & Décio Krause - 1995 - Analysis 55 (1):20 - 26.
    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 (...)
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  18.  60
    Why Non-Individuality? A Discussion on Individuality, Identity, and Cardinality in the Quantum Context.Jonas Rafael Becker Arenhart & Décio Krause - 2012 - Erkenntnis (1):1-18.
    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 situation comprising multiple particles there is a well-defined (...)
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  19.  69
    Is Identity Really so Fundamental?Décio Krause & Jonas R. Becker Arenhart - 2019 - Foundations of Science 24 (1):51-71.
    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 to hold that identity is fundamental; in fact, (...)
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  20.  18
    A Discussion on Quantum Non-Individuality.Décio Krause & Jonas R. Becker Arenhart - 2012 - Journal of Applied Non-Classical Logics 22 (1-2):105-124.
    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 (...)
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  21.  76
    A Formal Framework for Quantum Non-Individuality.Décio Krause & Steven French - 1995 - Synthese 102 (1):195 - 214.
    H. Post's conception of quantal particles as non-individuals is set in a formal logico-mathematical framework. By means of this approach certain metaphysical implications of quantum mechanics can be further explored.
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  22.  37
    An Intensional Schrödinger Logic.Newton C. A. da Costa & Décio Krause - 1997 - Notre Dame Journal of Formal Logic 38 (2):179-194.
    We investigate the higher-order modal logic , which is a variant of the system presented in our previous work. A semantics for that system, founded on the theory of quasi sets, is outlined. We show how such a semantics, motivated by the very intuitive base of Schrödinger logics, provides an alternative way to formalize some intensional concepts and features which have been used in recent discussions on the logical foundations of quantum mechanics; for example, that some terms like 'electron' have (...)
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  23.  15
    16. On The Concept Of Identity In Zermelo-Fraenkel-Like Axioms And Its Relationships With Quantum Statistics.Décio Krause - 2005 - Logique Et Analyse 48.
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  24. The Physics and Metaphysics of Identity and Individuality.Don Howard, Bas van Fraassen, Otávio Bueno, Elena Castellani, Laura Crosilla, Steven French & Décio Krause - 2011 - Metascience 20 (2):225-251.
    The 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 Castellani, Department of Philosophy, University of Florence, Via Bolognese 52, 50139 (...)
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  25.  56
    Axiomatization and Models of Scientific Theories.Décio Krause, Jonas R. B. Arenhart & Fernando T. F. Moraes - 2011 - Foundations of Science 16 (4):363-382.
    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 (...)
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  26.  31
    Oppositions and Quantum Mechanics.Jonas R. B. Arenhart & Décio Krause - unknown
    In 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 are entangled in discussions of this problem (...)
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  27.  11
    The Quasi-Lattice of Indiscernible Elements.Mauri Cunha do Nascimento, Décio Krause & Hércules Araújo Feitosa - 2011 - Studia Logica 97 (1):101-126.
    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 (J-lattice), which can be modeled by an algebraic structure built in quasi-set theory 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-lattice that 'naturally' arises is non distributive.
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  28.  91
    Physics, Inconsistency, and Quasi-Truth.Newton C. A. Da Costa & Décio Krause - 2014 - Synthese 191 (13):3041-3055.
    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 quasi-truth. We defend a pluralistic view of the philosophy of science, grounded on the existence of inconsistencies and on quasi-truth. Here, we treat only the ‘classical aspects’ of the subject, leaving for a forthcoming paper the ‘non-classical’ part.
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  29.  9
    Making Sense of Non-Individuals in Quantum Mechanics.Jonas R. B. Arenhart, Otávio Bueno & Décio Krause - forthcoming - In Olimpia Lombardi, Sebastian Fortin, Cristian López & Frederico Holik (eds.), Quantum Worlds. Different Perspectives about the ontology of quantum mechanics. Cambridge, U.K: Cambridge University Press.
    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 (...)
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  30.  54
    The Logic of Complementarity.Newton C. A. Da Costa & Décio Krause - unknown
    This 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 logical basis of a scientific theory are also put in (...)
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  31.  80
    Quantum Sortal Predicates.Décio Krause & Steven French - 2007 - Synthese 154 (3):417 - 430.
    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 (...)
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  32.  10
    Sobre uma fundamentação não reflexiva da mecânica quântica.Newton Carneiro Affonso da Costa, Décio Krause, Jonas Rafael Becker Arenhart & Jaison Schinaider - 2012 - Scientiae Studia 10 (1):71-104.
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  33.  68
    Preface Special Issue Foundations of Physics.Dennis Dieks, Décio Krause & Christian de Ronde - 2014 - Foundations of Physics 44 (12):1245-1245.
    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 mechanics itself, a mathematical structure whose connection to what happens in physical reality (...)
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  34.  76
    List of Contents: Volume 10, Number 5, October 1997.Adonai S. Sant’Anna, Decio Krause, Croca Jr, M. Ferrero, A. Garuccio & V. L. Lepore - 1998 - Foundations of Physics 28 (2).
  35.  82
    Remarks on the Applications of Paraconsistent Logic to Physics.Newton C. A. da Costa & Décio Krause - unknown
    In 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'.
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  36.  4
    The Quasi-Lattice of Indiscernible Elements.Mauri Cunha do Nascimento, Décio Krause & Hércules Araújo Feitosa - 2011 - Studia Logica 97 (1):101-126.
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  37. Classical Logic or Non-Reflexive Logic?: A Case of Semantic Underdetermination.Jonas Becker Arenhart & Décio Krause - 2012 - Revista Portuguesa de Filosofia 68 (1-2):73-86.
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  38. Entity, but No Identity.Decio Krause - unknown
    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 (...)
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  39.  93
    Ontological Issues in Quantum Theory.Decio Krause & Otavio Bueno - unknown
    In 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.
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  40.  62
    Relativizations of the Principle of Identity.Décio Krause & Jean-Yves Béziau - 1997 - Logic Journal of the IGPL 5 (3):17-29.
    We discuss some logico-mathematical 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 (...)
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  41.  5
    Contextuality and Indistinguishability.Acacio de Barros, Federico Holik & Décio Krause - unknown
    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 assume the ontological thesis that quantum particles or properties (...)
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  42.  42
    Remarks on Quantum Ontology.Décio Krause - 2000 - Synthese 125 (1-2):155-167.
    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 identity and both having and (...)
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  43.  86
    The Mathematics of Non-Individuality.Décio Krause - unknown
    Some of the forerunners of quantum theory regarded the basic entities of such theories as 'non-individuals'. 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 'quasi-sets'. The motivation for such a theory, linked to what we call 'the Manin problem', is presented, so as its specific axioms. (...)
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  44.  30
    Presenting Nonreflexive Quantum Mechanics: Formalism and Metaphysics.Décio Krause & Jonas R. B. Arenhart - unknown
    Nonreflexive 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 non-individuals in some sense, and also to take into account the fact that they may (...)
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  45. Quantum Objects Are Vague Objects.Steven French & Décio Krause - 1996 - Sorites 6 (1):21--33.
    Is there vagueness in the world? This is the central question that we are concerned with. Focusing on identity statements around which much of the recent debate has centred, we argue that `vague identity' arises in quantum mechanics in one of two ways. First, quantum particles may be described as individuals, with `entangled' states understood in terms of non-supervenient relations. In this case, the vagueness is ontic but exists at the level of these relations which act as a kind of (...)
     
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  46.  29
    A Logical Account of Superpositions.Decio Krause & Jonas R. B. Arenhart - unknown
    In 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 contradictions, (...)
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  47.  14
    A Modal Logic of Indiscernibility.Décio Krause, Pedro Merlussi & Jonas R. Becker Arenhart - 2016 - In A. L. Aerts Diederik Et (ed.), Probing the Meaning of Quantum Mechanics: Superpositions, Dynamics, Semantics and Identity. World Scientific. pp. 259-279.
    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 two-sorted first-order 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 (...)
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  48.  66
    Issues in the Foundations of Science, I: Languages, Structures, and Models.Newton C. A. da Costa, Décio Krause & Otávio Bueno - unknown
    In 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. This (...)
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  49.  71
    Separability and Non-Individuality: Is It Possible to Conciliate (At Least A Form Of) Einstein's Realism with Quantum Mechanics?Décio Krause & Jonas R. B. Arenhart - 2005 - Foundations of Physics 44 (12):1269-1288.
    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 deal with classical objects. The use of such apparatus (...)
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  50.  31
    Schrödinger Logics.Newton C. A. Costa & Décio Krause - 1994 - Studia Logica 53 (4).
    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 (which has been advanced by other authors) that identity lacks sense for elementary particles of modern physics, and the way which physicists deal with this concept; normally, they understandidentity as meaningindistinguishability (agreemment with respect to attributes). Observing that these concepts are equivalent in classical logic and mathematics, which underly the usual physical theories, we (...)
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