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25We show that using quasi-set theory, or the theory of collections of indistinguishable objects, we can define an algebra that has most of the standard properties of an orthocomplete orthomodular lattice, which is the lattice of all closed subspaces of a Hilbert space. We call the mathematical structure so obtained $\mathfrak{I}$-lattice. After discussing some aspects of such a structure, we indicate the next problem of axiomatizing the corresponding logic, that is, a logic which has $\mathfrak{I…Read more
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160Structures and Structural RealismLogic Journal of the IGPL 13 (1): 113-126. 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 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 as we know, there is not…Read more
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195Q-spaces and the Foundations of Quantum MechanicsFoundations of Physics 38 (11): 969-994. 2008.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, alt…Read more
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56Perspectivismo na filosofia da ciência: um estudo de caso na física quântica / Perspectivism in philosophy of science: a case-study in quantum physicsScientiae Studia 11 (1): 159-183. 2013.PORTUGUESE: Neste artigo, apresentaremos uma visão particular do desenvolvimento de teorias científicas que denominamos (inspirados em Ortega y Gasset) "perspectivismo". Discutiremos como, através desse enfoque, é possível compatibilizar diversas descrições aparentemente distintas e incompatíveis de uma suposta realidade que se investiga. Fazemos isso distinguindo entre a "realidade" (R) e a "descrição empírica da realidade" (Re). Aceitando que podemos ter diversas descrições empíricas de uma me…Read more
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56Schrödinger LogicsStudia Logica 53 (4): 533-550. 1994.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 that identity lacks sense for elementary particles of modern physics, and the way which physicists deal with this concept; normally, they understand identity as meaning indistinguishability . Observing that these concepts are equivalent in classical logic and mathematics, which underly the usual physical theories, we presen…Read more
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155Is Identity Really so Fundamental?Foundations of Science 24 (1): 51-71. 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
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321A inseparabilidade entre lógica E a éticaPhilósophos - Revista de Filosofia 18 (1): 245-259. 2013.
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82An Intensional Schrödinger LogicNotre Dame Journal of Formal Logic 38 (2): 179-194. 1997.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' hav…Read more
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150Vague Identity and Quantum Non-IndividualityAnalysis 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
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33Resenha de: DUTRA, L. H. de A. e MORTARI, C. A. (eds.) Princípios: seu papel na filosofia e nas ciênciasPrincipia: An International Journal of Epistemology 4 (2): 327-330. 2000.Resenha
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118Physics, inconsistency, and quasi-truthSynthese 191 (13): 3041-3055. 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 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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25Física e OntologiaDiscusiones Filosóficas 9 (12). 2008.objeto físicolas teorías físicas. En la medida en quela física se ocupa de los constitutivosesencial. A pesar de que la física actual node explicar por qué el mundo es comolas físicas
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78From primitive identity to the non-individuality of quantum objectsStudies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 46 (2): 273-282. 2014.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 princ…Read more
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52A discussion on quantum non-individualityJournal of Applied Non-Classical Logics 22 (1-2): 105-124. 2012.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 to ask for a…Read more
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106Some 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. At the en…Read more
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Quantum objects are vague objectsSorites 6 (1): 21--33. 1996.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 `veil'. Sec…Read more
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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
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30Sobre uma fundamentação não reflexiva da mecânica quânticaScientiae Studia 10 (1): 71-104. 2012.
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27Is Priscilla, the trapped positron, an individual? Quantum physics, the use of names, and individuationArbor 187 (747): 61-66. 2011.
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111Uma Lógica da IndistinguibilidadeDisputatio 4 (34): 555-573. 2012.Arenhart_Krause_Uma-logica-da-indistinguibilidade
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27Indiscernibilidade e identidade em química: aspectos filosóficos e formaisManuscrito 37 (1): 113-160. 2014.
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108In 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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3616. On The Concept Of Identity In Zermelo-fraenkel-like Axioms And Its Relationships With Quantum StatisticsLogique Et Analyse 48. 2005.
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74This 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
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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 |