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  1. Newton C. A. Da Costa & Federico Holik (forthcoming). A Formal Framework for the Study of the Notion of Undefined Particle Number in Quantum Mechanics. Synthese:1-19.
    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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  2. Newton C. A. Da Costa (2014). Opening Address: Paraconsistent Logic. Logic and Logical Philosophy 7:25.
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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.
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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 C. A. da Costa, Décio Krause & Otávio Bueno, Issues in the Foundations of Science, I: Languages, Structures, and Models.
    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 (as set-theoretical structures) with first-order structures (called here order-1 structures), and which are studied in standard (first-order) model theory. All of us are, of course, bound to make abuses (...)
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  6. Newton C. A. da Costa & Décio Krause, Logical and Philosophical Remarks on Quasi-Set Theory.
    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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  7. 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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  8. 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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  9. 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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  10. Newton C. A. Da Costa & Otávio Bueno (2001). Paraconsistency: Towards a Tentative Interpretation. Theoria 16 (40):119-145.
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  11. 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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  12. 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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  13. 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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  14. 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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  15. 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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  16. 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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  17. 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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  18. 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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  19. Newton C. A. da Costa & Otavio Bueno (1997). [Omnibus Review]. Journal of Symbolic Logic 62 (2):683-685.
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  20. 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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  21. 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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  22. 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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  23. 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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  24. Newton C. A. da Costa & FranciscoAntonio Doria (1994). Gödel Incompleteness in Analysis, with an Application to the Forecasting Problem in the Social Sciences. Philosophia Naturalis 31 (1):1-24.
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  25. Newton C. A. da Costa & Décio Krause (1994). Schrödinger Logics. Studia Logica 53 (4):533 - 550.
    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 understand identity as meaning indistinguishability (agreemment with respect to attributes). Observing that these concepts are equivalent in classical logic and mathematics, which underly the usual physical (...)
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  26. Newton C. A. da Costa & Steven French (1993). A Model Theoretic Approach to 'Natural' Reasoning. International Studies in the Philosophy of Science 7 (2):177-190.
    Abstract A general framework is proposed for accommodating the recent results of studies into ?natural? decision making. A crucial element of this framework is the notion of a ?partial structure?, recently introduced into the semantic approach to scientific theories. It is through the introduction of this element that connections can be made with certain problems regarding inconsistency and rationality in general.
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  27. Newton C. A. da Costa & Francisco Antonio Doria (1992). On the Incompleteness of Axiomatized Models for the Empirical Sciences. Philosophica 50.
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  28. Newton C. A. da Costa & Steven French (1991). On Russell's Principle of Induction. Synthese 86 (2):285 - 295.
    An improvement on Horwich's so-called "pseudo-proof" of Russell's principle of induction is offered, which, we believe, avoids certain objections to the former. Although strictly independent of our other work in this area, a connection can be made and in the final section we comment on this and certain questions regarding rationality, etc.
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  29. Newton C. A. da Costa, V. S. Subrahmanian & Carlo Vago (1991). The Paraconsistent Logics PJ. Mathematical Logic Quarterly 37 (9‐12):139-148.
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  30. Leila Z. Puga, Newton C. A. da Costa & Roberto J. Vernengo (1991). Lógicas normativas, moral y derecho. Critica 23 (69):27 - 59.
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  31. Newton C. A. da Costa & Steven French (1990). Belief, Contradiction and the Logic of Self-Deception. American Philosophical Quarterly 27 (3):179 - 197.
    The apparently paradoxical nature of self-deception has attracted a great deal of controversy in recent years. Focussing on those aspects of the phenomenon which involve the holding of "contradictory" beliefs, it is our intention to argue that this presents no "paradox" if a non-classical, "paraconsistent", doxastic logic is adopted. (On such logics, see, for example, N. C. A. da Costa, 'On the theory of inconsistent formal systems', Notre Dame J Formal Logic 11(1974), 497-510, and A. I. Arruda, 'A survey of (...)
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  32. Newton C. A. da Costa & Steven French (1990). The Model-Theoretic Approach in the Philosophy of Science. Philosophy of Science 57 (2):248 - 265.
    An introduction to the model-theoretic approach in the philosophy of science is given and it is argued that this program is further enhanced by the introduction of partial structures. It is then shown that this leads to a natural and intuitive account of both "iconic" and mathematical models and of the role of the former in science itself.
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  33. Leila C. Puga, Newton C. A. Da Costa & Roberto José Vernengo (1990). Derecho, moral y preferencias valorativas. Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 5 (12):9-29.
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  34. Newton C. A. da Costa & Steven French (1989). On the Logic of Belief. Philosophy and Phenomenological Research 49 (3):431 - 446.
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  35. Newton C. A. Da Costa & Steven French (1989). Pragmatic Truth and the Logic of Induction. British Journal for the Philosophy of Science 40 (3):333-356.
    We apply the recently elaborated notions of 'pragmatic truth' and 'pragmatic probability' to the problem of the construction of a logic of inductive inference. It is argued that the system outlined here is able to overcome many of the objections usually levelled against such attempts. We claim, furthermore, that our view captures the essentially cumulative nature of science and allows us to explain why it is indeed reasonable to accept and believe in the conclusions reached by inductive inference.
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  36. Newton C. A. da Costa & Rolando Chuaqui (1988). On Suppes' Set Theoretical Predicates. Erkenntnis 29 (1):95 - 112.
  37. Newton C. A. da Costa & Steven French (1988). Belief and Contradiction. Critica 20 (60):3 - 11.
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  38. Leila Z. Puga & Newton C. A. Da Costa (1988). On The Imaginary Logic of N. A. VASILIEV. Mathematical Logic Quarterly 34 (3):205-211.
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  39. Leila Z. Puga & Newton C. A. da Costa (1987). Sobre a lógica deôntica não-clássica. Critica 19 (55):19 - 37.
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  40. Newton C. A. da Costa (1986). Pragmatic Probability. Erkenntnis 25 (2):141 - 162.
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  41. Irene Mikenberg, Newton C. A. Da Costa & Rolando Chuaqui (1986). Pragmatic Truth and Approximation to Truth. Journal of Symbolic Logic 51 (1):201 - 221.
    There are several conceptions of truth, such as the classical correspondence conception, the coherence conception and the pragmatic conception. The classical correspondence conception, or Aristotelian conception, received a mathematical treatment in the hands of Tarski (cf. Tarski [1935] and [1944]), which was the starting point of a great progress in logic and in mathematics. In effect, Tarski's semantic ideas, especially his semantic characterization of truth, have exerted a major influence on various disciplines, besides logic and mathematics; for instance, linguistics, the (...)
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  42. Ayda I. Arruda & Newton C. A. da Costa (1984). On the Relevant Systems P and P* and Some Related Systems. Studia Logica 43 (1/2):33 - 49.
    In this paper we study the systems P and $P^{\ast}$ (see Arruda and da Costa, O paradoxo de Curry-Moh Shaw-Kwei, Boletim da Sociedade Matemātica de São Paulo 18 (1966)) and some related systems. In the last section, we prove that certain set theories having P and $P^{\ast}$ as their underlying logics are non-trivial.
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  43. Ayda I. Arruda, Xavier Caicedo, Rolando Chuaqui & Newton C. A. da Costa (1983). Meeting of the Association for Symbolic Logic: Bogotá, Colombia, 1981. Journal of Symbolic Logic 48 (3):884 - 892.
  44. Newton C. A. da Costa & Chris Mortensen (1983). Notes on the Theory of Variable Binding Term Operators. History and Philosophy of Logic 4 (1-2):63-72.
    The general theory of variable binding term operators is an interesting recent development in logic. It opens up a rich class of semantic and model-theoretic problems. In this paper we survey the recent literature on the topic, and offer some remarks on its significances and on its connections with other branches of mathematical logic.
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  45. Ayda I. Arruda, Rolando Chuaqui, Newton C. A. da Costa & Irene Mikenberg (1981). Meeting of the Association for Symbolic Logic: Santiago, Chile, 1978. Journal of Symbolic Logic 46 (1):180 - 190.
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  46. Ayda I. Arruda, Francisco Miró Quesada, Newton C. A. Da Costa & Rolando Chuaqui (1978). Meeting of the Association for Symbolic Logic: Campinas, Brazil 1976. Journal of Symbolic Logic 43 (2):352 - 364.
  47. Newton C. A. Da Costa & E. H. Alves (1977). A Semantical Analysis of the Calculi ${\Bf C}_n$. Notre Dame Journal of Formal Logic 18 (4):621-630.
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