The Annual European Meeting of the Association for Symbolic Logic, generally known as the Logic Colloquium, is the most prestigious annual meeting in the field. Many of the papers presented there are invited surveys of recent developments. Highlights of this volume from the 2005 meeting include three papers on different aspects of connections between model theory and algebra; a survey of recent major advances in combinatorial set theory; a tutorial on proof theory and modal logic; and a description of Bernay's (...) philosophy of mathematics. (shrink)
We study the strength (over bounded induction) of axioms expressing particular cases of the Chinese Remainder Theorem with respect to the axiom ∀ x, y∃ z (z = xy).
We present a comprehensive study of the axiom schemas IΣ - n , BΣ - n (induction and collection schemas for parameter free Σ n formulas) and some closely related schemas.
In this paper, we look at applying the techniques from analyzing superintuitionistic logics to extensions of the cointuitionistic Priest-da Costa logic daC (introduced by Graham Priest as “da Costa logic”). The relationship between the superintuitionistic axioms- definable in daC- and extensions of Priest-da Costa logic (sdc-logics) is analyzed and applied to exploring the gap between the maximal si-logic SmL and classical logic in the class of sdc-logics. A sequence of strengthenings of Priest-da Costa logic is examined and employed to pinpoint (...) the maximal non-classical extension of both daC and Heyting-Brouwer logic HB . Finally, the relationship between daC and Logics of Formal Inconsistency is examined. (shrink)
Este artigo pretende introduzir os três volumes de Principia que aparecerão em sequência homenageando os 80 anos do professor Newton da Costa. Ao invés de apresentar os artigos um a um, como se faz usualmente em uma introdução como esta, preferimos deixar os artigos falarem por si, e oforoecer aos leitores brasileiros, especialmente nossos estudantes, alguns aspectos da concepção de ciência e da atividade científica de Newton da Costa, fundamentadas no conceito de quase-verdade, que ele contribuiu para desenvolver de modo (...) rigoroso. Da Costa e conhecido como urn dos fundadores da lógica paraconsistente, mas suas contribuições alcançam também os fundamentos da física, da ciência da computação,a teoria dos modelos, a lógica algébrica, a teoria dos reticulados, as aplicações de lógicas não-clássicas à ciência do direito e à tecnologia, etc. No entanto, talvez sua maior contruição tenha sido proporcionar a base para a criação de uma escola de lógica em nosso país (Brasil), à qual serviu como professor e inspirador par gerações. É com satisfação que vimos uma imediata aceitaçãoo pelos editors de Principia para a organização desses volumes. Gostaria de agradecer a todos os que contribuiram com artigos e aos editors da revista, em especial ao professor Cezar Mortari pela ajuda na organização desta homenagem. (shrink)
This paper is a reply to D'Costa's article ("Religious Studies," 32, pp. 223-32) in which he argues that there is no such position as religious pluralism because in distinguishing between, e.g., Christianity or Buddhism, and Nazism or the Jim Jones cult, a criterion is involved and to use a criterion is a form of exclusivism. In reply I point out that this sense of 'exclusivism', as consisting in the use of criteria, is self-destructive; that the pluralistic hypothesis, as a meta-theory (...) about the religions, has a different logical status from the creeds of the historical religions; and I also show the origin of the ethnical criterion used by the religious pluralist who stands within one or other of the great world faiths. (shrink)
In 1999, da Silva, D'Ottaviano and Sette proposed a general definition for the term translation between logics and presented an initial segment of its theory. Logics are characterized, in the most general sense, as sets with consequence relations and translations between logics as consequence-relation preserving maps. In a previous paper the authors introduced the concept of conservative translation between logics and studied some general properties of the co-complete category constituted by logics and conservative translations between them. In this paper we (...) present some conservative translations involving classical logic, Lukasiewicz three-valued system L 3, the intuitionistic system I 1 and several paraconsistent logics, as for instance Sette's system P 1, the D'Ottaviano and da Costa system J 3 and da Costa's systems C n, 1 n. (shrink)
A dominant cultural narrative within Costa Rica describes Costa Ricans not only as different from their Central American neighbours, but it also exalts them as better: specifically, as more white, peaceful, egalitarian and democratic. This notion of Costa Rican exceptionalism played a key role in the creation of their health care system, which is based on the four core principles of equity, universality, solidarity and obligation. While the political justification and design of the current health care system does, in part, (...) realize this ideal, we argue that the narrative of Costa Rican exceptionalism prevents the full actualization of these principles by marginalizing and excluding disadvantaged groups, especially indigenous and black citizens and the substantial Nicaraguan minority. We offer three suggestions to mitigate the self-undermining effects of the dominant national narrative: 1) encouragement and development of counternarratives; 2) support of an emerging field of Costa Rican bioethics; and 3) decoupling health and national successes. (shrink)
In this paper we present an overview of Professor Newton C. A. da Costa’s work in logic, emphasizing the main results obtained by him in the several areas of his research activity. The text furnish a detailed bibliographic reference of his works, which are listed in the last section.
Da Costa's C systems are surveyed and motivated, and significant failings of the systems are indicated. Variations are then made on these systems in an attempt to surmount their defects and limitations. The main system to emerge from this effort, system $CC_{\omega}$ , is investigated in some detail, and "dual-intuitionistic" semantical analyses are developed for it and surrounding systems. These semantics are then adapted for the original C systems, first in a rather unilluminating relational fashion, subsequently in a more illuminating (...) way through the introduction of impossible situations where and and or change roles. Finally other attempts to break out of impasses for the original and expanded C systems, by going inside them, are looked at, and further research directions suggested. (shrink)
Da Costa's C systems are surveyed and motivated, and significant failings of the systems are indicated. Variations are then made on these systems in an attempt to surmount their defects and limitations. The main system to emerge from this effort, system CC , is investigated in some detail, and dual-intuitionistic semantical analyses are developed for it and surrounding systems. These semantics are then adapted for the original C systems, first in a rather unilluminating relational fashion, subsequently in a more illuminating (...) way through the introduction of impossible situations where and and or change roles. Finally other attempts to break out of impasses for the original and expanded C systems, by going inside them, are looked at, and further research directions suggested. (shrink)
Resenha do livro de Andrade, Abraháo Costa. O pote e a rodilha : tempo e imaginaçáo como história por fazer segundo o pensamento de Paul Ricoeur. Natal: EDUFRN, 2006. [Coleçáo Metafísica]. 134 páginas.
Das obras de Newton da Costa, muitas pessoas na França conhecem apenas o renascimento da paraconsistência. Apresentamos algumas razões em defesa de investigações nessa parte da lógica. Acima de tudo, porém, relembramos uma das maiores contribuições de Newton da Costa: sua demonstração, em 1991, em colaboração com Doria, da indecidibilidade gödeliana do movimento na física matemátcia, um resultado que foi de certa forma previsto, por outras razões, por Duhem em 1906. DOI: 10.5007/1808-1711.2011v15n1p7.
The concept of fitness, central to population genetics and to the synthetic theory of evolution, is discussed. After a historical introduction on the origin of this concept, the current meaning of it in population genetics is examined: a cause of the selective process and its quantification. Several difficulties arise for its exact definition. Three adequacy criteria for such a definition are formulated. It is shown that it is impossible to formulate an adequate definition of fitness respecting these criteria. The propensity (...) definition of fitness is presented and rejected. Finally it is argued that fitness is a conceptual device, a useful tool, only for descriptive purposes of selective processes, changing from case to case, and thus devoid of any substantial physical counterpart. Any attempt to its reification is an apport to the metaphysical load evolutionary theory has inherited from Natural Theology. (shrink)
Laws of Postmodernity is the first work of legal scholarship to apply postmodern jurisprudence to an analysis of a number of substantive areas of law. In analyzing the cultural significance of law, the contributors show how critical jurisprudential analysis undermines positivistic attempts to support a normative viewpoint of the legal order. In addition, they criticize contextual, sociological accounts of legal phenomena. The contributors explore blasphemy laws in the wake of the Salman Rushdie affair, and French critical legal theory-- particularly the (...) work of Pierre Legendre--to highlight the repression of psychoanalysis within jurisprudence. Through detailed accounts, Laws of Postmodernity clearly illustrates the practical application and theoretical significance of postmodern jurisprudence. (shrink)
In this paper we examine whether the sense of agency represents an obstacle to the project of naturalizing the mental. On the basis of a thought experiment we suggest that the sense of agency is not an epiphenomenon. We also examine Frith's attempt to explain in functionalist terms the sense of agency through the comparator and metarepresentational mechanisms. Through a variety of arguments we try to show that explanation by recourse to these mechanisms is inadequate. We conclude by suggesting that (...) one possible reason for the failure of the functionalist approaches is that they begin from the assumption that thought is a form a of willed action. (shrink)
This article argues that an application of Marxism to itself can help us transcend Gouldner's (1980) dichotomy between scientific and critical Marxism. After demonstrating that the paradigmatic document of scientific marxism, Marx's Preface to A Contribution to the Critique of Political Economy, turns the structural logic of capitalist economy into the basis for a transhistorical theory of social-economic development, this article explores the limitations of critical Marxism's response to scientific Marxism and concludes that a viable, not class-centered, reformulation of the (...) emancipatory project is possible through an analysis of capitalism's "dialectic of scarcity." The task of the emancipatory project, it is argued, is to turn humanity, and not the working class, from a political subject in itself to a political subject in and for itself. (shrink)
Since the fundamental challenge that I laid at the doorstep of the pluralists was to defend, with nonderivative models, a strong notion of genic cause, it is fatal that Waters has failed to meet that challenge. Waters agrees with me that there is only a single cause operating in these models, but he argues for a notion of causal `parsing' to sustain the viability of some form of pluralism. Waters and his colleagues have some very interesting and important ideas about (...) the sciences, involving pluralism and parsing or partitioning causes, but they are ideas in search of an example. He thinks he has found an example in the case of hierarchical and genic selection. I think he has not. (shrink)
No Órganon Aristóteles descreve alguns esquemas dedutivos nos quais a presença de inconsistências não acarreta a trivialização da teoria lógica envolvida. Esta tese é corroborada por três diferentes situações teóricas estudadas por ele, as quais são apresentadas neste trabalho. Analizamos o esquema de inferência utilizado por Aristóteles no Protrepticus e o método de demonstração indireta para os silogismos categóricos. Ambos os métodos exemplificam como Aristóteles emprega estratégias de redução ao absurdo logicamente clássicas. Na sequência, discutimos os silogismos válidos a partir (...) de premissas opostas (contrárias e contraditórias) estudadas pelo Estagirita no Analytica Priora (B15). De acordo com o autor, os seguintes silogismos são válidos a partir de premissas opostas, nos quais letras latinas minúsculas denotam termos como sujeito e predicado, enquanto que letras latinas maiúsculas denotam proposições categóricas tal como na notação tradicional: (i) na segunda figura, Eba,Aba ` Eaa (Cesare), Aba, Eba ` Eaa (Camestres), Eba, I ba ` Oaa (Festino), e Aba,Oba ` Oaa (Baroco); (ii) na terceira, Eab,Aab ` Oaa (Felapton), Oab,Aab ` Oaa (Bocardo) e Eab, Iab ` Oaa (Ferison). Por fim, discutimos a passagem do Analytica Posteriora (A11) no qual Aristóteles enuncia que o Princípio de Não-Contradição não é, em geral, pressuposto de toda demonstração (silogismo científico), mas apenas daquelas nas quais a conclusão deve ser provada a partir do Princípio; o Estagirita enuncia que se um silogismo da primeira figura tiver o termo maior consistente, os outros termos da demonstração podem ser separadamente inconsistentes. Estes resultados permitem-nos propor uma interpretação de sua teoria dedutiva como uma teoria paraconsistente lato sensu. Primeiramente, efetuamos uma análise hermenêutica, avaliando seu significado lógico e a correlação desses resultados com outros aspectos da filosofia de Aristóteles. Em segundo lugar, consignamos uma interpretação dos silogismos aristotélicos a partir de premissas opostas à luz dos antilogismos propostos por Christine Ladd-Franklin em 1883, e da demonstração aristotélica com termos inconsistentes nas lógicas paraconsistentes Cn, 1 n !, introduzidas por da Costa em 1963. Esses dois aspectos não parecem ter sido ainda detalhadamente analisados na literatura. DOI:10.5007/1808-1711.2010v14n1p71. (shrink)
One of Da Costa's motives when he constructed the paraconsistent logic Cw was to dualise the negation of intuitionistic logic. In this paper I explore a different way of going about this task. A logic is defined by taking the Kripke semantics for intuitionistic logic, and dualising the truth conditions for negation. Various properties of the logic are established, including its relation to CWo Tableau and natural deduction systems for the logic are produced, as are appropriate algebraic structures. The paper (...) then investigates dualising the intuitionistic conditional in the same way. This establishes various connections between the logic, and a logic called in the literature 'Brouwerian logic' or 'closed-set logic'. (shrink)
A new methodology for developing theories of action has recently emerged which provides means for formally evaluating the correctness of such theories. Yet, for a theory of action to qualify as a solution to the frame problem, not only does it need to produce correct inferences, but moreover, it needs to derive these inferences from a concise representation of the domain at hand. The new methodology however offers no means for assessing conciseness. Such a formal account of conciseness is developed (...) in this paper. Combined with the existing criterion for correctness, our account of conciseness offers a framework where proposed solutions to the frame problem can be formally evaluated. (shrink)
