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Jonas R. B. Arenhart [15]Jonas R. Becker Arenhart [13]
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Jonas R. B. Arenhart
Universidade Federal de Santa Catarina
  1.  44
    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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  2.  13
    Quasi-Truth and Defective Knowledge in Science: A Critical Examination.Jonas R. B. Arenhart & Décio Krause - unknown
    Quasi-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 given developments do not deliver all that is promised. We examine the most prominent account of quasi-truth available in the literature, advanced by da Costa and collaborators in many places, and argue that it cannot legitimately account for (...)
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  3. Structural Realism and the Nature of Structure.Jonas R. Becker Arenhart & Otávio Bueno - 2015 - 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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  4.  36
    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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  5.  16
    Liberating Paraconsistency From Contradiction.Jonas R. Becker Arenhart - 2015 - 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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  6.  29
    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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  7.  85
    Many Entities, No Identity.Jonas R. Becker Arenhart - 2012 - 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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  8.  5
    Dialetheists’ Lies About the Liar.Jonas R. B. Arenhart & Ederson S. Melo - 2018 - Principia: An International Journal of Epistemology 22 (1):59-85.
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  9.  8
    New Logics for Quantum Non-Individuals?Jonas R. Becker Arenhart - 2018 - Logica Universalis 12 (3-4):375-395.
    According to a very widespread interpretation of the metaphysical nature of quantum entities—the so-called Received View on quantum non-individuality—, quantum entities are non-individuals. Still according to this understanding, non-individuals are entities for which identity is restricted or else does not apply at all. As a consequence, it is said, such approach to quantum mechanics would require that classical logic be revised, given that it is somehow committed with the unrestricted validity of identity. In this paper we examine the arguments to (...)
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  10. Ontological Frameworks for Scientific Theories.Jonas R. B. Arenhart - 2012 - 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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  11.  26
    Finite Cardinals in Quasi-Set Theory.Jonas R. Becker Arenhart - 2012 - 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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  12.  23
    Classical Negation Strikes Back: Why Priest’s Attack on Classical Negation Can’T Succeed.Jonas R. Becker Arenhart & Ederson Safra Melo - 2017 - Logica Universalis 11 (4):465-487.
    Dialetheism is the view that some true sentences have a true negation as well. Defending dialetheism, Graham Priest argues that the correct account of negation should allow for true contradictions and \) without entailing triviality. A negation doing precisely that is said to have ‘surplus content’. Now, to defend that the correct account of negation does have surplus content, Priest advances arguments to hold that classical Boolean negation does not even make sense without begging the question against the dialetheist. We (...)
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  13.  20
    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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  14.  62
    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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  15.  77
    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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  16.  33
    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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  17.  20
    Full-Blooded Anti-Exceptionalism About Logic.Newton Da Costa & Jonas R. Becker Arenhart - 2018 - Australasian Journal of Logic 15 (2):362-380.
    Problems of logical theory choice are current being widely dis- cussed in the context of anti-exceptionalist views on logic. According to those views, logic is not a special science among others, so, in particular, the methodology for theory choice should be the same in logic as for other scientific disciplines. Richard Routley advanced one such methodology which meshes well with anti-exceptionalism, and argued that it leads one to choosing one single logic, which is a kind of ultralogic. We argue that (...)
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  18.  15
    Individuality, Quantum Physics, and a Metaphysics of Non-Individuals: The Role of the Formal.Décio Krause & Jonas R. B. Arenhart - unknown
    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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  19.  17
    Structures and Models of Scientific Theories: A Discussion on Quantum Non-Individuality.Décio Krause & Jonas R. B. Arenhart - unknown
    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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  20.  13
    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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  21.  74
    Separability and Non-Individuality: Is It Possible to Conciliate 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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  22.  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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  23.  30
    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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  24.  15
    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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  25.  20
    Ontology and the Mathematization of the Scientific Enterprise.Décio Krause, Jonas R. B. Arenhart & Newton C. A. da Costa - unknown
    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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  26.  17
    Estruturas, Modelos e os Fundamentos da Abordagem Sem'ntica DOI:10.5007/1808-1711.2010v14n1p15.Jonas R. Becker Arenhart & Fernando T. F. Moraes - 2010 - Principia: An International Journal of Epistemology 14 (1):15-30.
    In this paper, gathering several topics present in the work of Newton da Costa, we propose a rigorous foundation for a possible formulation of scientific theories according to the semantic approach. Following da Costa, as a first step we develop a general theory of structures; inside this theory we show how we can characterize formal languages as particular kinds of structures, more specifically, as free algebras. Next we discuss how we can link a language to a structure, with which we (...)
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  27.  22
    Estruturas, Modelos e os Fundamentos da Abordagem Semântica.Jonas R. Becker Arenhart & Fernando T. F. Moraes - 2010 - Principia: An International Journal of Epistemology 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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  28.  11
    Entangling and Disentangling Realism and Wave Function.Décio Krause & Jonas R. B. Arenhart - 2014 - Metascience 23 (3):467-473.