Works by Newton C. A. Da Costa
72 found
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- Science and Partial Truth: A Unitary Approach to Models and Scientific Reasoning.Newton C. A. Da Costa &Steven French -2003 - New York, US: Oup Usa.Da Costa and French explore the consequences of adopting a 'pragmatic' notion of truth in the philosophy of science. Their framework sheds new light on issues to do with belief, theory acceptance, and the realism-antirealism debate, as well as the nature of scientific models and their heuristic development.
- On the theory of inconsistent formal systems.Newton C. A. da Costa -1974 -Notre Dame Journal of Formal Logic 15 (4):497-510.
- The Model-Theoretic Approach in the Philosophy of Science.Newton C. A. Da Costa &Steven French -1990 -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.
- The Paraconsistent Logic of Quantum Superpositions.Newton C. A. da Costa &Christian de Ronde -2013 -Foundations of Physics 43 (7):845-858.Physical superpositions exist both in classical and in quantum physics. However, what is exactly meant by ‘superposition’ in each case is extremely different. In this paper we discuss some of the multiple interpretations which exist in the literature regarding superpositions in quantum mechanics. We argue that all these interpretations have something in common: they all attempt to avoid ‘contradiction’. We argue in this paper, in favor of the importance of developing a new interpretation of superpositions which takes into account contradiction, (...) as a key element of the formal structure of the theory, “right from the start”. In order to show the feasibility of our interpretational project we present an outline of a paraconsistent approach to quantum superpositions which attempts to account for the contradictory properties present in general within quantum superpositions. This approach must not be understood as a closed formal and conceptual scheme but rather as a first step towards a different type of understanding regarding quantum superpositions. (shrink)
- Pragmatic truth and approximation to truth.Irene Mikenberg,Newton C. A. da Costa &Rolando Chuaqui -1986 -Journal of Symbolic Logic 51 (1):201-221.
- (1 other version)A semantical analysis of the calculi Cn.Newton C. A. da Costa -1977 -Notre Dame Journal of Formal Logic 18:621.
- The Logic of Pragmatic Truth.Newton C. A. Da Costa,Otávio Bueno &Steven French -1998 -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 (...) accommodated. One of the main results of this paper is that the logic of pragmatic truth is paraconsistent. The philosophical import of this result, which justifies the application of pragmatic truth to inconsistent settings, is also discussed. (shrink)
- On Suppes' Set Theoretical Predicates.Newton C. A. da Costa &Rolando Chuaqui -1988 -Erkenntnis 29 (1):95-112.
- Pragmatic Probability.Newton C. A. Da Costa -1986 -Erkenntnis 25 (2):141 - 162.
- On Jaśkowski's Discussive Logics.Newton C. A. da Costa &Francisco A. Doria -1995 -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.
- On paraconsistent deontic logic.Newton C. A. Da Costa &Walter A. Carnielli -1986 -Philosophia 16 (3-4):293-305.No categories
- Quasi-truth, paraconsistency, and the foundations of science.Otávio Bueno &Newton C. A. da Costa -2007 -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, (...) but which still preserves some (partial) relations between old and new theories. The existence of these relations help to explain why the break between different theories is never too radical as to make it impossible for one to interpret the process in perfectly rational terms. We then defend the view that if scientific theories are taken to be quasi-true, and if the underlying logic is paraconsistent, it's perfectly rational for scientists and mathematicians to entertain inconsistent theories without triviality. As a result, as opposed to what is demanded by traditional approaches to rationality, it's not irrational to entertain inconsistent theories. Finally, we conclude the paper by arguing that the view advanced here provides a new way of thinking about the foundations of science. In particular, it extends in important respects both coherentist and foundationalist approaches to knowledge, without the troubles that plague traditional views of scientific rationality. (shrink)
- A model theoretic approach to 'natural' reasoning.Newton C. A. da Costa &Steven French -1993 -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.
- Pragmatic Truth and the Logic of Induction.Newton C. A. da Costa &Steven French -1989 -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.
- $\alpha$-models and the systems $T$ and $T^\ast$.Newton C. A. da Costa -1974 -Notre Dame Journal of Formal Logic 15 (3):443-454.
- An Intensional Schrödinger Logic.Newton C. A. da Costa &Décio Krause -1997 -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 (...) no precise reference and that 'identical' particles cannot be named unambiguously. In the last section, we sketch a classical semantics for quasi set theory. (shrink)
- Revisiting the Applicability of Metaphysical Identity in Quantum Mechanics.Newton C. A. da Costa &Christian de Ronde -unknownWe discuss the hypothesis that the debate about the interpretation of the orthodox formalism of quantum mechanics might have been misguided right from the start by a biased metaphysical interpretation of the formalism and its inner mathematical relations. In particular, we focus on the orthodox interpretation of the congruence relation, '=', which relates equivalent classes of different mathematical representations of a vector in Hilbert space, in terms of metaphysical identity. We will argue that this seemingly "common sense" interpretation, at the (...) semantic level, has severe difficulties when considering the syntactic level of the theory. (shrink)No categories
- Aspects of Paraconsistent Logic.Newton C. A. da Costa,Jean-Yves Béziau &Otávio A. S. Bueno -1995 -Logic Journal of the IGPL 3 (4):597-614.
- Studies in paraconsistent logic I: The dialectical principle of the unity of opposites.Newton C. A. Da Costa &Robert G. Wolf -1980 -Philosophia 9 (2):189-217.No categories
- Is there a zande logic?Newton C. A. Da Costa,Otávio Bueno &Steven French -1998 -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 (...) or else accept them as non-problematical. Is our knowledge of logical truths a relative and culturally determined phenomenon, or is there some (transcendent) criterion that allows us to adjudicate between alternative logical systems? The authors propose an approach for resolving disputes about the status of Azande reasoning which assumes a paraconsistent framework, thus providing a new perspective on this debate. (shrink)
- Time in Thermodynamics.Newton C. A. Da Costa &Adonai S. Sant'Anna -2002 -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.
- Non-reflexive Logical Foundation for Quantum Mechanics.Newton C. A. da Costa &Christian de Ronde -2014 -Foundations of Physics 44 (12):1369-1380.On the one hand, non-reflexive logics are logics in which the principle of identity does not hold in general. On the other hand, quantum mechanics has difficulties regarding the interpretation of ‘particles’ and their identity, also known in the literature as ‘the problem of indistinguishable particles’. In this article, we will argue that non-reflexive logics can be a useful tool to account for such quantum indistinguishability. In particular, we will provide a particular non-reflexive logic that can help us to analyze (...) and discuss this problem. From a more general physical perspective, we will also analyze the limits imposed by the orthodox quantum formalism to consider the existence of indistinguishable particles in the first place, and argue that non-reflexive logics can also help us to think beyond the limits of classical identity. (shrink)
- Belief, Contradiction and the Logic of Self-Deception.Newton C. A. da Costa &Steven French -1990 -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 (...) paraconsistent logic', in A. I. Arruda, N. C. A da Costa and R Chuaqui, _Mathematical Logic in Latin America
, North-Holland, 1984, pp. 1-41.). (shrink) - (1 other version)The Paraconsistent Logics PJ.Newton C. A. da Costa,V. S. Subrahmanian &Carlo Vago -1991 -Mathematical Logic Quarterly 37 (9‐12):139-148.
- A formal framework for the study of the notion of undefined particle number in quantum mechanics.Newton C. A. da Costa &Federico Holik -2015 -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 (...) solving a problem posed by Y. Manin, namely, to incorporate quantum mechanical notions at the foundations of mathematics. We also show that our system is capable of representing quantum superpositions. (shrink)
- On the Incompleteness of Axiomatized Models for the Empirical Sciences.Newton C. A. da Costa &Francisco Antonio Doria -1992 -Philosophica 50.
- (1 other version)On The Imaginary Logic of N. A. VASILIEV.Leila Z. Puga &Newton C. A. Da Costa -1988 -Mathematical Logic Quarterly 34 (3):205-211.
- On the Logic of Belief.Newton C. A. da Costa &Steven French -1989 -Philosophy and Phenomenological Research 49 (3):431 - 446.
- Suppes Predicates for Space-Time.Newton C. A. Da Costa,Otávio Bueno &Steven French -1997 -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 (...) (1919), though our philosophical stance is completely different from his. The structures obtained are idealized constructs underlying extant, physical space-time. (shrink)
- Logic and Ontology.Newton C. A. da Costa -2002 -Principia: An International Journal of Epistemology 6 (2):179–298.In view of the present state of development of non classical logic, especially of paraconsistent logic, a new stand regarding the relations between logic and ontology is defended In a parody of a dictum of Quine, my stand May be summarized as follows. To be is to be the value of a variable a specific language with a given underlying logic Yet my stand differs from Quine’s, because, among other reasons, I accept some first order heterodox logics as genuine alternatives (...) to classical logic I also discuss some questions of non classical logic to substantiate my argument, and suggest that may position complements and extends some ideas advanced by L Apostel. (shrink)No categories
- The Paraconsistent Approach to Quantum Superpositions Reloaded: Formalizing Contradictiory Powers in the Potential Realm.Newton C. A. da Costa &Christian de Ronde -unknownIn [7] the authors of this paper argued in favor of the possibility to consider a Paraconsistent Approach to Quantum Superpositions. We claimed that, even though most interpretations of quantum mechanics attempt to escape contradictions, there are many hints -coming from present technical and experimental developments in QM- that indicate it could be worth while to engage in a research of this kind. Recently, Arenhart and Krause have raised several arguments against the PAQS [1, 2, 3]. In [11, 12] it (...) was argued that their reasoning presupposes a metaphysical stance according to which the physical representation of reality must be exclusively considered in terms of the equation: Actuality = Reality. However, from a different metaphysical standpoint their problems disappear. It was also argued that, if we accept the idea that quantum superpositions exist in a potential realm, it makes perfect sense to develop QM in terms of a paraconsistent approach and claim that quantum superpositions are contradictory, contextual existents. Following these ideas, and taking as a standpoint an interpretation in terms of the physical notions of power and potentia put forward in [10, 12, 15], we present a paraconsistent formalization of quantum superpositions that attempts to capture the main features of QM. (shrink)
- Physics, inconsistency, and quasi-truth.Newton C. A. Da Costa &Décio Krause -2014 -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.
- α Logic and Infinitary Languages.Newton C. A. da Costa &Charles C. Pinter -1976 -Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 22 (1):105-112.
- Remarks on abstract Galois theory.Newton C. A. da Costa &Otávio Bueno -2011 -Manuscrito 34 (1):151-183.This paper is a historical companion to a previous one, in which it was studied the so-called abstract Galois theory as formulated by the Portuguese mathematician José Sebastião e Silva ). Our purpose is to present some applications of abstract Galois theory to higher-order model theory, to discuss Silva's notion of expressibility and to outline a classical Galois theory that can be obtained inside the two versions of the abstract theory, those of Mark Krasner and of Silva. Some comments are (...) made on the universal theory of structures. (shrink)
- Gödel’s Incompleteness Theorems and Physics.Newton C. A. da Costa -2011 -Principia: An International Journal of Epistemology 15 (3):453-459.This paper is a summary of a lecture in which I presented some remarks on Gödel’s incompleteness theorems and their meaning for the foundations of physics. The entire lecture will appear elsewhere.
- An Overview of Paraconsistent Logic in the 80s.Newton C. A. da Costa &Diego Marconi -1987 - Curitiba, Brazil: Sociedade Paranaense de Matemática.No categories
- Elementos de teoria paraconsistente de conjuntos.Newton C. A. da Costa -1998 - Campinas, SP: Centro de Lógica, Epistemologia e História da Ciência, UNICAMP. Edited by Jean-Yves Béziau & Otávio Bueno.
- Professor Newton CA da Costa awarded Nicholas Copernicus University medal of merit.Newton C. A. da Costa,Jean-Yves Béziau &Otávio Bueno -1999 -Logic and Logical Philosophy 7:7-10.
- (1 other version)Définition, Théorie des Objets et Paraconsistance (Definition, Objects' Theory and Paraconsistance).Newton C. A. da Costa &Jean-Yves Béziau -1998 -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 (...) the elimination of definitions is not necessarily straightforward in particular in the case of paraconsistent logic. Finally we have a look at Meinong’s theory objects and we show how it can be considered as a theory of descriptors. (shrink)
- Mathematical Logic in Latin America Proceedings of the Iv Latin American Symposium on Mathematical Logic Held in Santiago, December 1978.Ayda I. Arruda,R. Chuaqui &Newton C. A. da Costa (eds.) -1980 - New York: sole distributors for the U.S.A. and Canada, Elsevier North-Holland.Provability, Computability and Reflection.
- Mathematical Logic: Proceedings of the First Brazilian Conference.Ayda I. Arruda,Newton C. A. Da Costa &R. Chuaqui -1978
- Meeting of the Association for Symbolic Logic: Bogotá, Colombia, 1981.Ayda I. Arruda,Xavier Caicedo,Rolando Chuaqui &Newton C. A. da Costa -1983 -Journal of Symbolic Logic 48 (3):884 - 892.
- Meeting of the Association for Symbolic Logic: Santiago, Chile, 1978.Ayda I. Arruda,Rolando Chuaqui,Newton C. A. da Costa &Irene Mikenberg -1981 -Journal of Symbolic Logic 46 (1):180 - 190.
- Meeting of the Association for Symbolic Logic: Campinas, Brazil 1976.Ayda I. Arruda,Francisco Miró Quesada,Newton C. A. Da Costa &Rolando Chuaqui -1978 -Journal of Symbolic Logic 43 (2):352 - 364.
- Meeting of the Association for Symbolic Logic, Campinas, Brazil, 1976.Ayda I. Arruda,Francisco Miró,Newton C. A. da Costa &Rolando Chuaqui -1978 -Journal of Symbolic Logic 43 (2):352-364.
- On the Relevant Systems P and P* and Some Related Systems.Ayda I. Arruda &Newton C. A. da Costa -1984 -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.
- Meeting of the Association for Symbolic Logic.Xavier Caicedo,Rolando Chuaqui,Newton C. A. Da Costa &Carlos A. Di Prisco -1984 -Journal of Symbolic Logic 49 (4):1430-1440.
- Introdução à lógica elementar: com o símbolo de Hilbert.Rejane Carrion &Newton C. A. Da Costa -1988No categories
- Notes on the theory of variable binding term operators.Newton C. A. da Costa &Chris Mortensen -1983 -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.
- Belief and Contradiction.Newton C. A. da Costa &Steven French -1988 -Critica 20 (60):3-11.
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David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Area Editors:
David Bourget
Gwen Bradford
Berit Brogaard
Margaret Cameron
David Chalmers
James Chase
Rafael De Clercq
Ezio Di Nucci
Esa Diaz-Leon
Barry Hallen
Hans Halvorson
Jonathan Ichikawa
Monte Johnson
Michelle Kosch
Øystein Linnebo
Paul Livingston
Brandon Look
Manolo Martínez
Matthew McGrath
Michiru Nagatsu
Susana Nuccetelli
Giuseppe Primiero
Jack Alan Reynolds
Darrell P. Rowbottom
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