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  1. Otavio Bueno & Newton da Costa, Rationality, Inconsistency, and Partial Structures.
  2. Newton C. A. Da Costa & Federico Holik (2015). A Formal Framework for the Study of the Notion of Undefined Particle Number in Quantum Mechanics. Synthese 192 (2):505-523.
    It is usually stated that quantum mechanics presents problems with the identity of particles, the most radical position—supported by E. Schrödinger—asserting that elementary particles are not individuals. But the subject goes deeper, and it is even possible to obtain states with an undefined particle number. In this work we present a set theoretical framework for the description of undefined particle number states in quantum mechanics which provides a precise logical meaning for this notion. This construction goes in the line of (...)
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  3. Newton C. A. Da Costa & Roque Da C. Caiero (2014). K-Transforms in Classical and Paraconsistent Logics. Logic and Logical Philosophy 7:63.
    We study some metamathematical properties of various classicaland paraconsistent logical systems. In particular, we discuss the concept ofa k-transform of a formula and consider some of its applications.
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  4. Newton C. A. Da Costa & Décio Krause (2014). Physics, Inconsistency, and Quasi-Truth. 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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  5. Newton da Costa & Olimpia Lombardi (2014). Quantum Mechanics: Ontology Without Individuals. Foundations of Physics 44 (12):1246-1257.
    The purpose of the present paper is to consider the traditional interpretive problems of quantum mechanics from the viewpoint of a modal ontology of properties. In particular, we will try to delineate a quantum ontology that (i) is modal, because describes the structure of the realm of possibility, and (ii) lacks the ontological category of individual. The final goal is to supply an adequate account of quantum non-individuality on the basis of this ontology.
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  6. Newton da Costa, Olimpia Lombardi & Mariano Lastiri (2013). A Modal Ontology of Properties for Quantum Mechanics. Synthese 190 (17):3671-3693.
    Our purpose in this paper is to delineate an ontology for quantum mechanics that results adequate to the formalism of the theory. We will restrict our aim to the search of an ontology that expresses the conceptual content of the recently proposed modal-Hamiltonian interpretation, according to which the domain referred to by non-relativistic quantum mechanics is an ontology of properties. The usual strategy in the literature has been to focus on only one of the interpretive problems of the theory and (...)
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  7. Newton Ca da Costa (2010). Some Aspectos of Quantum Physics. Principia: An International Journal of Epistemology 11 (1):77-95.
     
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  8. Newton da Costa & Otávio Bueno (2010). Paraconsistent Logic. In Susana Nuccetelli, Ofelia Schutte & Otávio Bueno (eds.), A Companion to Latin American Philosophy. Wiley-Blackwell
  9. Newton Da Costa, DÉcio Krause & OtÁvio Bueno (2010). Issues in the Foundations of Science, I: Languages, Structures, and Models. Manuscrito 33 (1):123-141.
    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. (...)
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  10. Otavio Bueno & Newton da Costa (2007). Quasi-Truth, Paraconsistency, and the Foundations of Science. Synthese 154 (3):383 - 399.
    In order to develop an account of scientific rationality, two problems need to be addressed: (i) how to make sense of episodes of theory change in science where the lack of a cumulative development is found, and (ii) how to accommodate cases of scientific change where lack of consistency is involved. In this paper, we sketch a model of scientific rationality that accommodates both problems. We first provide a framework within which it is possible to make sense of scientific revolutions, (...)
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  11. Newton Da Costa (2007). Logical and Philosophical Remarks on Quasi-Set Theory. Logic Journal of the Igpl 15 (5-6):421-431.
    Quasi-set theory is a theory for dealing with collections of indistinguishable objects. In this paper we discuss some logical and philosophical questions involved with such a theory. The analysis of these questions enable us to provide the first grounds of a possible new view of physical reality, founded on an ontology of non-individuals, to which quasi-set theory may constitute the logical basis.
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  12. Newton da Costa, Otávio Bueno & Steven French (2007). A coherence theory of truth/Uma teoria coerentista da verdade. Manuscrito 30 (2):539-568.
    In this paper, we provide a new formulation of a coherence theory of truth using the resources of the partial structures approach − in particular the notions of partial structure and quasi-truth. After developing this new formulation, we apply the resulting theory to the philosophy of mathematics, and argue that it can be used to develop a new account of nominalism in mathematics. This application illustrates the strength and usefulness of the proposed formulation of a coherence theory of truth.Neste artigo, (...)
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  13. Newton da Costa, Otávio Bueno & Steven French (2005). A Coherence Theory of Truth. Manuscrito 28 (2):263-290.
    In this paper, we provide a new formulation of a coherence theory of truth using the resources of the partial structures approach − in particular the notions of partial structure and quasi-truth. After developing this new formulation, we apply the resulting theory to the philosophy of mathematics, and argue that it can be used to develop a new account of nominalism in mathematics. This application illustrates the strength and usefulness of the proposed formulation of a coherence theory of truth.
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  14. Newton C. A. Da Costa (2004). Opening Address: Paraconsistent Logic. Logic and Logical Philosophy 7:25-34.
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  15. Newton C. A. Da Costa & Roque da C. Caiero (2004). K-Transforms in Classical and Paraconsistent Logics. Logic and Logical Philosophy 7:63-80.
    We study some metamathematical properties of various classicaland paraconsistent logical systems. In particular, we discuss the concept ofa k-transform of a formula and consider some of its applications.
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  16. Newton C. A. da Costa & Steven French (2003). Science and Partial Truth a Unitary Approach to Models and Scientific Reasoning. Monograph Collection (Matt - Pseudo).
     
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  17. Newton C. A. da Costa & Décio Krause, Remarks on the Applications of Paraconsistent Logic to Physics.
    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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  18. Newton C. A. Da Costa & Adonai S. Sant'Anna (2002). Time in Thermodynamics. Foundations of Physics 32 (11):1785-1796.
    We use Padoa's principle of independence of primitive symbols in axiomatic systems in order to show that time is dispensable in continuum thermodynamics, according to the axiomatic formulation of Gurtin and Williams. We also show how to define time by means of the remaining primitive concepts of Gurtin and Williams system. Finally, we introduce thermodynamics without time as a primitive concept.
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  19. Newton C. A. da Costa (2001). Paraconsistency. Theoria 16 (1):119-145.
    In this expository paper, we examine some philosophical and technical issues brought by paraconsistency (such as, motivations for developing a paraconsistent logic, the nature of this logic, and its application to set theory). We also suggest a way of accommodating these issues by considering some problems in the philosophy of logic from a new perspective.
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  20. Newton C. A. Da Costa & Otávio Bueno (2001). Paraconsistency: Towards a Tentative Interpretation. Theoria 16 (40):119-145.
    In this expository paper, we examine some philosophical and technical issues brought by paraconsistency . We also suggest a way of accommodating these issues by considering some problems in the philosophy of logic from a new perspective.
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  21. Newton da Costa & Steven French (2000). Models, Theories, and Structures: Thirty Years On. Philosophy of Science 67 (3):127.
    Thirty years after the conference that gave rise to The Structure of Scientific Theories, there is renewed interest in the nature of theories and models. However, certain crucial issues from thirty years ago are reprised in current discussions; specifically: whether the diversity of models in the science can be captured by some unitary account; and whether the temporal dimension of scientific practice can be represented by such an account. After reviewing recent developments we suggest that these issues can be accommodated (...)
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  22. Newton C. A. Da Costa (1999). Opening Address: Paraconsistent Logic. Logic and Logical Philosophy 7:25.
    I am honoured with and touched by the invitation of delivering the opening address of this Congress. Firstly, to see paraconsistent logic flourishing and growing, as we can readily see by simply glacing over the programme of this conference, is among one of my greatest joys. Secondly, and equally important, because this congress takes place in the University of Toruń.I am honoured for having lectured here, a most congenial and stimulating place, and could not think of a better place for (...)
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  23. Newton C. A. da Costa, Jean-Yves Béziau & Otávio Bueno (1999). Professor Newton CA da Costa Awarded Nicholas Copernicus University Medal of Merit. Logic and Logical Philosophy 7:7-10.
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  24. Newton C. A. da Costa & Otavio Bueno (1999). Quasi-Truth, Supervaluations and Free Logic. History and Philosophy of Logic 20 (3-4):215-226.
    The partial structures approach has two major components: a broad notion of structure (partial structure) and a weak notion of truth (quasi-truth). In this paper, we discuss the relationship between this approach and free logic. We also compare the model-theoretic analysis supplied by partial structures with the method of supervaluations, which was initially introduced as a technique to provide a semantic analysis of free logic. We then combine the three formal frameworks (partial structures, free logic and supervaluations), and apply the (...)
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  25. Newton C. A. da Costa & Otávio Bueno (1999). de Rouilhan Philippe. Russell et le cercle ties paradoxes. Épiméthée. Presses Universitaires de France, Paris 1996, 319 pp. [REVIEW] Journal of Symbolic Logic 64 (4):1845-1847.
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  26. Newton C. A. da Costa & Otavio Bueno (1999). Review: Philippe de Rouilhan, Russell et le cercle des paradoxes. [REVIEW] Journal of Symbolic Logic 64 (4):1845-1847.
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  27. Jair Minoro Abe, Curry Algebras Pt, Paraconsistent Logic, Newton Ca da Costa, Otavio Bueno, Jacek Pasniczek, Beyond Consistent, Complete Possible Worlds, Vm Popov & Inverse Negation (1998). Table Des Matieres Editorial Preface 3. Logique Et Analyse 41:1.
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  28. Newton C. A. da Costa & Jean-Yves Béziau (1998). Définition, Théorie des Objets et Paraconsistance (Definition, Objects' Theory and Paraconsistance). Theoria 13 (2):367-379.
    Trois sortes de définitions sont présentées et discutées: les définitions nominales, les définitions contextuelles et les définitions amplificatrices. On insiste sur le fait que I’elimination des definitions n’est pas forcement un procede automatique en particulier dans le cas de la logique paraconsistante. Finalement on s’int’resse à la théorie des objets de Meinong et l’on montre comment elle peut êrre considéréecomme une théorie des descripteurs.Three kinds of definitions are presented and discussed: nominal definitions, contextual definitions, amplifying definitions. It is emphasized that (...)
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  29. Newton C. A. da Costa, Otávio Bueno & Steven French (1998). Is There a Zande Logic? History and Philosophy of Logic 19 (1):41-54.
    The issue of what consequences to draw from the existence of non-classical logical systems has been the subject of an interesting debate across a diversity of fields. In this paper the matter of alternative logics is considered with reference to a specific belief system and its propositions :the Azande are said to maintain beliefs about witchcraft which, when expressed propositionally, appear to be inconsistent. When the Azande have been presented with such inconsistencies, they either fail to see them as such (...)
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  30. Newton C. A. Da Costa, Otávio Bueno & Steven French (1998). The Logic of Pragmatic Truth. Journal of Philosophical Logic 27 (6):603-620.
    The mathematical concept of pragmatic truth, first introduced in Mikenberg, da Costa and Chuaqui (1986), has received in the last few years several applications in logic and the philosophy of science. In this paper, we study the logic of pragmatic truth, and show that there are important connections between this logic, modal logic and, in particular, Jaskowski's discussive logic. In order to do so, two systems are put forward so that the notions of pragmatic validity and pragmatic truth can be (...)
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  31. Marcelo Tsuji, Newton C. A. Da Costa & Francisco A. Doria (1998). The Incompleteness of Theories of Games. Journal of Philosophical Logic 27 (6):553 - 568.
    We first state a few previously obtained results that lead to general undecidability and incompleteness theorems in axiomatized theories that range from the theory of finite sets to classical elementary analysis. Out of those results we prove several incompleteness theorems for axiomatic versions of the theory of noncooperative games with Nash equilibria; in particular, we show the existence of finite games whose equilibria cannot be proven to be computable.
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  32. Arthur Buchsbaum, Tarcisio Pequeno, A. General, Newton Ca da Costa & Jean-Yves Beziau (1997). Contemporary Brazilian Research in Logic Part II. Logique Et Analyse 40:3.
     
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  33. Arthur Buchsbaum, Tarcisio Pequeno, A. General, Newton Ca da Costa & Jean-Yves Beziau (1997). Table Des Matteres Contemporary Brazilian Research in Logic Parte. Logique Et Analyse 40:6.
     
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  34. Newton C. A. da Costa & Otavio Bueno (1997). [Omnibus Review]. Journal of Symbolic Logic 62 (2):683-685.
    Reviewed Works:Chris Mortensen, Inconsistent Mathematics.Chris Mortensen, Peter Lavers, Category Theory.William James, Closed Set Sheaves and Their Categories.Chris Mortensen, Joshua Cole, Foundations: Provability, Truth and Sets.
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  35. Newton C. A. Da Costa, Otávio Bueno & Steven French (1997). Suppes Predicates for Space-Time. Synthese 112 (2):271-279.
    We formulate Suppes predicates for various kinds of space-time: classical Euclidean, Minkowski's, and that of General Relativity. Starting with topological properties, these continua are mathematically constructed with the help of a basic algebra of events; this algebra constitutes a kind of mereology, in the sense of Lesniewski. There are several alternative, possible constructions, depending, for instance, on the use of the common field of reals or of a non-Archimedian field (with infinitesimals). Our approach was inspired by the work of Whitehead (...)
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  36. Newton C. A. Da Costa & Décio Krause (1997). An Intensional Schrödinger Logic. 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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  37. Newton Ca da Costa & Jean-Yves Béziau (1997). Overclassical logic. Logique Et Analyse 157:31-44.
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  38. Newton Ca da Costa & Jean-Yves Béziau (1996). Théories paraconsistantes des ensembles. Logique Et Analyse 39:51-67.
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  39. Newton [Y.] Otávio Bueno Da Costa (1996). Consistency, Paraconsistency and Truth: Logic, the Whole Logic and Nothing but the Logic. Ideas Y Valores 100:48-60.
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  40. Newton da Costa, Jean-Yves Béziau & Otávio Bueno (1996). Malinowski and Suszko on Many-Valued Logics: On the Reduction of Many-Valuedness to Two-Valuedness. Modern Logic 6 (1):272--299.
  41. Newton A. da Costa, Jean-Yves Beziau & Otavio S. Bueno (1995). Aspects of Paraconsistent Logic. Logic Journal of the Igpl 3 (4):597-614.
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  42. Newton C. A. da Costa & Francisco A. Doria (1995). On Jaśkowski's Discussive Logics. Studia Logica 54 (1):33 - 60.
    We expose the main ideas, concepts and results about Jaśkowski's discussive logic, and apply that logic to the concept of pragmatic truth and to the Dalla Chiara-di Francia view of the foundations of physics.
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  43. Newton C. A. da Costa & Francisco A. Doria (1995). Undecidability, Incompleteness and Arnol'D Problems. Studia Logica 55 (1):23 - 32.
    We present some recent technical results of us on the incompleteness of classical analysis and then discuss our work on the Arnol'd decision problems for the stability of fixed points of dynamical systems.
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  44. Newton Ca da Costa, Jean-Yves Beziau & Otavio Bueno (1995). Paraconsistent Logic in a Historical Perspective. Logique Et Analyse 38:111-125.
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  45. Newton Ca da Costa, Francisco A. Doria & Marcelo Tsuji (1995). The Undecidability of Formal Definitions in the Theory of Finite Groups. Bulletin of the Section of Logic 24:56-63.
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  46. Newton da Costa, Otávio Bueno & Jean-Yves Béziau (1995). What is Semantics? A Brief Note on a Huge Question. Sorites 3:43-47.
    After mentioning the cogent connection between pure semantics and the particular set theoretical framework in which it is formulated, some issues regarding the conceptual status of semantics itself, as well as its relationship to logic, are concisely raised.
     
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  47. Newton da Costa & Steven French (1995). Partial Structures and the Logic of Azande. American Philosophical Quarterly 32 (4):325 - 339.
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