21 found
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  1.  13
    Décio Krause & Jonas R. B. Arenhart, Is Identity Really so Fundamental?
    We critically examine the claim by Otávio Bueno that identity is a fundamental concept. Bueno advances four related theses in order to ground such a claim: 1) identity is presupposed in every conceptual system; 2) identity is required to characterize an individual; 3) identity cannot be defined; 4) the intelligibility of quantification requires identity. We address each of these points and argue that there are no compelling reasons to hold that identity is fundamental in these cases. So, in the end, (...)
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  2.  31
    Jonas R. B. Arenhart & Decio Krause, Potentiality and Contradiction in Quantum Mechanics.
    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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  3.  24
    Décio Krause & Jonas R. B. Arenhart, Presenting Nonreflexive Quantum Mechanics: Formalism and Metaphysics.
    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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  4.  30
    Jonas R. B. Arenhart & Décio Krause, Contradiction, Quantum Mechanics, and the Square of Opposition.
    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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  5.  45
    Jonas R. Becker Arenhart (2012). Many Entities, No Identity. Synthese 187 (2):801-812.
    The aim of this paper is to argue that some objections raised by Jantzen (Synthese, 2010 ) against the separation of the concepts of ‘counting’ and ‘identity’ are misled. We present a definition of counting in the context of quasi-set theory requiring neither the labeling nor the identity and individuality of the counted entities. We argue that, contrary to what Jantzen poses, there are no problems with the technical development of this kind of definition. As a result of being able (...)
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  6.  11
    Jonas R. Becker Arenhart (2012). Finite Cardinals in Quasi-Set Theory. Studia Logica 100 (3):437-452.
    Quasi-set theory is a ZFU-like axiomatic set theory, which deals with two kinds of ur-elements: M-atoms, objects like the atoms of ZFU, and m-atoms, items for which the usual identity relation is not defined. One of the motivations to advance such a theory is to deal properly with collections of items like particles in non-relativistic quantum mechanics when these are understood as being non-individuals in the sense that they may be indistinguishable although identity does not apply to them. According to (...)
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  7.  14
    Jonas R. Becker Arenhart & Décio Krause (2009). Quantifiers and the Foundations of Quasi-Set Theory. Principia 13 (3):251-268.
    http://dx.doi.org/10.5007/1808-1711.2009v13n3p251 Neste artigo discutimos algumas questões propostas por Newton da Costa relacionadas aos fundamentos da teoria de quase-conjuntos. Seus questionamentos aqui considerados tratam da possibilidade de uma compreenão semântica da teoria, principalmente devido ao fato de que identidade e diferença podem não ser aplicáveis para algumas das entidades no domínio pretendido da teoria. De acordo com ele, o modo usual de se compreender os quantificadores utilizados na teoria depende da hipótese de que a identidade deve valer para todas as entidades (...)
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  8.  26
    Jonas R. B. Arenhart & Décio Krause, Oppositions and Quantum Mechanics.
    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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  9. Jonas R. B. Arenhart (2012). Ontological Frameworks for Scientific Theories. Foundations of Science 17 (4):339-356.
    A close examination of the literature on ontology may strike one with roughly two distinct senses of this word. According to the first of them, which we shall call traditional ontology , ontology is characterized as the a priori study of various “ontological categories”. In a second sense, which may be called naturalized ontology , ontology relies on our best scientific theories and from them it tries to derive the ultimate furniture of the world. From a methodological point of view (...)
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  10.  71
    Jonas R. Becker Arenhart & Otávio Bueno (2015). Structural Realism and the Nature of Structure. European Journal for Philosophy of Science 5 (1):111-139.
    Ontic Structural Realism is a version of realism about science according to which by positing the existence of structures, understood as basic components of reality, one can resolve central difficulties faced by standard versions of scientific realism. Structures are invoked to respond to two important challenges: one posed by the pessimist meta-induction and the other by the underdetermination of metaphysics by physics, which arises in non-relativistic quantum mechanics. We argue that difficulties in the proper understanding of what a structure is (...)
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  11.  18
    Decio Krause & Jonas R. B. Arenhart, A Logical Account of Superpositions.
    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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  12.  9
    Jonas R. Becker Arenhart (2015). Liberating Paraconsistency From Contradiction. Logica Universalis 9 (4):523-544.
    In this paper we propose to take seriously the claim that at least some kinds of paraconsistent negations are subcontrariety forming operators. We shall argue that from an intuitive point of view, by considering paraconsistent negations as formalizing that particular kind of opposition, one needs not worry with issues about the meaning of true contradictions and the like, given that “true contradictions” are not involved in these paraconsistent logics. Our strategy will consist in showing that, on the one hand, the (...)
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  13.  10
    Décio Krause, Jonas R. B. Arenhart & Newton C. A. da Costa, Ontology and the Mathematization of the Scientific Enterprise.
    In this basically expository paper we discuss the role of logic 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 concerning identity and individuality, those contributions may (...)
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  14.  8
    Décio Krause & Jonas R. B. Arenhart, Individuality, Quantum Physics, and a Metaphysics of Non-Individuals: The Role of the Formal.
    The 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 (...)
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  15.  8
    Décio Krause & Jonas R. B. Arenhart, Structures and Models of Scientific Theories: A Discussion on Quantum Non-Individuality.
    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, namely, that which sees them as non-individuals, then there would be (...)
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  16.  53
    Décio Krause & Jonas R. B. Arenhart (2014). Separability and Non-Individuality: Is It Possible to Conciliate (At Least A Form Of) Einstein's Realism with Quantum Mechanics? 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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  17.  5
    Jonas R. Becker Arenhart & Fernando T. F. Moraes (2011). Estruturas, Modelos e os Fundamentos da Abordagem Semântica. Principia 14 (1):15-30.
    Neste artigo, a partir de tópicos presentes na obra de Newton C. A. da Costa, propomos uma fundamentação rigorosa para de uma possível formulação de teorias científicas através da abordagem semântica. Seguindo da Costa, primeiramente desenvolveremos uma teoria geral das estruturas; no contexto desta teoria de estruturas mostraremos como caracterizar linguagens formais como um tipo particular de estrutura, mais especificamente, como uma álgebra livre. Em seguida, discutiremos como associar uma linguagem a uma estrutura, com a qual poderemos formular axiomas que (...)
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  18.  2
    Décio Krause & Jonas R. Becker Arenhart (2012). A Discussion on Quantum Non-Individuality. 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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  19. Jonas R. Becker Arenhart & Fernando T. F. Moraes (2011). Estruturas, Modelos e os Fundamentos da Abordagem Sem'ntica DOI:10.5007/1808-1711.2010v14n1p15. Principia: An International Journal of Epistemology 14 (1).
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  20. Jonas R. Becker Arenhart & Décio Krause (2009). Quantifiers and the Foundations of Quasi-Set Theory. Principia: An International Journal of Epistemology 13 (3).
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  21. Décio Krause & Jonas R. B. Arenhart (2014). Entangling and Disentangling Realism and Wave Function. Metascience 23 (3):467-473.
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