This paper proposes a classification of economic models into three types: historical, axiomatic and conditional. Historical or empirical models utilize the historical-deductive method, and are generalizations from the economic regularities and tendencies that we find in the real world. Axiomatic models utilize the hypothetical-deductive method; they are syllogisms whose major premise is an axiom – a self-evident truth; they are appropriate for methodological sciences such as mathematics and econometrics. Conditional economic models are likewise syllogisms, but they are suitable for economics (...) because they make for clearer and more precise economic reasoning. The criterion of truth of the substantive sciences is the conformity with reality, of the methodological science, its internal consistency. When a school of economic thought adopts mainly axiomatic models, as is the case with neoclassical economics, it implicitly falls into contradiction because their best representatives believe in the conformity with reality criterion. (shrink)

In 2015 Dag Prawitz proposed an Ecumenical system where classical and intuitionistic logic could coexist in peace. The classical logician and the intuitionistic logician would share the universal quantifier, conjunction, negation and the constant for the absurd, but they would each have their own existential quantifier, disjunction and implication, with different meanings. Prawitz’ main idea is that these different meanings are given by a semantical framework that can be accepted by both parties. The aim of the present paper is [1] (...) to prove the normalization theorem for the propositional fragment NEp of Prawitz’ ecumenical system, and [2] to show that NEp is sound and complete with respect to a Kripke-style semantics for the language of NEp. (shrink)

The relation between ex falso and disjunctive syllogism, or even the justification of ex falso based on disjunctive syllogism, is an old topic in the history of logic. This old topic reappears in contemporary logic since the introduction of minimal logic by Johansson. The disjunctive syllogism seems to be part of our general non-problematic inferential practices and superficially it does not seem to be related to or to depend on our acceptance of the frequently disputable ex falso rule. We know (...) that the acceptance of the ex falso is a sufficient condition for the acceptance of the disjunctive syllogism, but the interesting question is: is the ex falso a necessary condition for the acceptance of the disjunctive syllogism? The aim of the present paper is to discuss some possible ways to define systems that combines the preservation of the disjunctive syllogism with the rejection of the ex falso. (shrink)

In 2015 Dag Prawitz proposed a natural deduction ecumenical system, where classical logic and intuitionistic logic are codified in the same system. In his ecumenical system, Prawitz recovers the harmony of rules, but the rules for the classical operators do not satisfy separability. In fact, the classical rules are not pure, in the sense that negation is used in the definition of the introduction and elimination rules for the classical operators. In this work we propose an ecumenical system adapting, to (...) the natural deduction framework, Girard’s mechanism of stoup. This allows for the definition of a pure harmonic natural deduction system for the propositional fragment of Prawitz’s ecumenical logic. We conclude by presenting an extension proposal to the first-order setting and a different approach to purity based on some ideas proposed by Julien Murzi. (shrink)

This collection of papers, celebrating the contributions of Swedish logician Dag Prawitz to Proof Theory, has been assembled from those presented at the Natural Deduction conference organized in Rio de Janeiro to honour his seminal research. Dag Prawitz’s work forms the basis of intuitionistic type theory and his inversion principle constitutes the foundation of most modern accounts of proof-theoretic semantics in Logic, Linguistics and Theoretical Computer Science.

This collection of papers, celebrating the contributions of Swedish logician Dag Prawitz to Proof Theory, has been assembled from those presented at the Natural Deduction conference organized in Rio de Janeiro to honour his seminal research. Dag Prawitz’s work forms the basis of intuitionistic type theory and his inversion principle constitutes the foundation of most modern accounts of proof-theoretic semantics in Logic, Linguistics and Theoretical Computer Science. The range of contributions includes material on the extension of natural deduction with higher-order (...) rules, as opposed to higher-order connectives, and a paper discussing the application of natural deduction rules to dealing with equality in predicate calculus. The volume continues with a key chapter summarizing work on the extension of the Curry-Howard isomorphism, via methods of category theory that have been successfully applied to linear logic, as well as many other contributions from highly regarded authorities. With an illustrious group of contributors addressing a wealth of topics and applications, this volume is a valuable addition to the libraries of academics in the multiple disciplines whose development has been given added scope by the methodologies supplied by natural deduction. The volume is representative of the rich and varied directions that Prawitz work has inspired in the area of natural deduction. (shrink)

Proceedings of the Tenth Brazilian Conference on Mathematical Logic. Coleção CLE, volume 14, 1995. Centro De Lógica, Epistemologia e História da Ciência, Unicamp, Campinas, SP, Brazil.

Sambin [6] proved the normalization theorem for GL, the modal logic of provability, in a sequent calculus version called by him GLS. His proof does not take into account the concept of reduction, commonly used in normalization proofs. Bellini [1], on the other hand, gave a normalization proof for GL using reductions. Indeed, Sambin's proof is a decision procedure which builds cut-free proofs. In this work we formalize this procedure as a recursive function and prove its recursiveness in an arithmetically (...) formalizable way, concluding that the normalization of GL can be formalized in PA. MSC: 03F05, 03B35, 03B45. (shrink)

Livro em homenagem ao filósofo brasileiro Luiz Henrique Lopes, um dos maiores expoentes da filosofia analítica. Neste livro grandes nomes da filosofia brasileira discorrem sobre a filosofia analítica e vários assuntos da filosofia contemporânea.

Recent works about ecumenical systems, where connectives from classical and intuitionistic logics can co-exist in peace, warmed the discussion on proof systems for combining logics. This discussion has been extended to alethic modalities using Simpson’s meta-logical characterization: necessity is independent of the viewer, while possibility can be either intuitionistic or classical. In this work, we propose a pure, label free calculus for ecumenical modalities, nEK\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf {nEK}$$\end{document}, where exactly one logical operator figures (...) in introduction rules and every basic object of the calculus can be read as a formula in the language of the ecumenical modal logic EK\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf {EK}$$\end{document}. We prove that nEK\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf {nEK}$$\end{document} is sound and complete w.r.t. the ecumenical birelational semantics and discuss fragments and extensions. (shrink)

Sambin [6] proved the normalization theorem for GL, the modal logic of provability, in a sequent calculus version called by him GLS. His proof does not take into account the concept of reduction, commonly used in normalization proofs. Bellini [1], on the other hand, gave a normalization proof for GL using reductions. Indeed, Sambin's proof is a decision procedure which builds cut-free proofs. In this work we formalize this procedure as a recursive function and prove its recursiveness in an arithmetically (...) formalizable way, concluding that the normalization of GL can be formalized in PA. MSC: 03F05, 03B35, 03B45. (shrink)

In 1930, Johann von Neumann, together with Rudolf Carnap and Arend Heyting, participated in a conference held in Königsberg, called “Second Seminar on the Epistemology of Exact Sciences”. The idea behind the reunion of these three researchers was to compose a fairly faithful picture of the three main foundational programs of mathematics at the time: formalism, logicism, and intuitionism. The main objective of this paper is to propose an analysis of the text “The Formalist Foundation of Mathematics” presented by von (...) Neumann in this conference. We show how, from von Neumann's perspective, the problem of the consistency of mathematical theories results from the transformation of a genuinely philosophical question into a genuinely logical-mathematical question and how a proof of consistency could be seen as the solution to the foundational problem. In the final part of the text, we present some considerations about Gerhard Gentzen’s consistency proofs and their importance to contemporary proof theory. (shrink)

Much has been said about intuitionistic and classical logical systems since Gentzen’s seminal work. Recently, Prawitz and others have been discussing how to put together Gentzen’s systems for classical and intuitionistic logic in a single unified system. We call Prawitz’ proposal the Ecumenical System, following the terminology introduced by Pereira and Rodriguez. In this work we present an Ecumenical sequent calculus, as opposed to the original natural deduction version, and state some proof theoretical properties of the system. We reason (...) that sequent calculi are more amenable to extensive investigation using the tools of proof theory, such as cut-elimination and rule invertibility, hence allowing a full analysis of the notion of Ecumenical entailment. We then present some extensions of the Ecumenical sequent system and show that interesting systems arise when restricting such calculi to specific fragments. This approach of a unified system enabling both classical and intuitionistic features sheds some light not only on the logics themselves, but also on their semantical interpretations as well as on the proof theoretical properties that can arise from combining logical systems. (shrink)

This paper deals with the recent Swedish proposals of a Intuitionistic notion of Truth, by Dag Prawitz and Per Martin-Löf.

Veloso-Pereira-Haeusler_On-what-there-must-be.

A lógica não contém teoremas puramente existenciais: as únicas sentenças existenciaisválidas são aquelas com análogas universais válidas. Aqui, mostramos que istorealmente é assim quando corretamente interpretado: toda validade ex- istencial possuiuma análoga universal simples, que também é válida. Também caracterizamos validadesuniversais e existenciais em termos de tautologias.

Coletânea de artigos em homenagem a Guido Antonio de Almeida e Raul Ferreira Landim Filho.

While there is much literature analyzing the politics of implementing economic reforms, very little has been written on the social and political consequences of such reforms after they have been implemented. The basic premise of this book is that the convergence of many social, economic, and political ills in the context of unprecedented levels of political democratization in Latin America presents a paradox that needs to be explained. _What Kind of Democracy? _demonstrates how the myriad social problems throughout the region (...) are intimately linked both to a new economic development model and the weaknesses of Latin American democracy. This volume brings together prominent scholars from Canada, the United States, and Latin America, representing several different disciplines to analyze ongoing processes of economic, social, and political change in the region. The contributors are Werner Baer, Manuel Barrera, Juan Alberto Fuentes, Yoshiaki Nakano, Claudio Paiva, Luiz Carlos Bresser Pereira, Jean-François Prud'homme, Jorge Schvarzer, Francisco Weffort, and Francisco Zapata. (shrink)

In §1 I explain that my rejection of possible states of affairs as a basis for an account of falsity is not part of a general rejection of modal notions but is a rejection of possible and impossible entities of any sort. I then show that my account of senses and of propositions is indeed a modal account. In §2 I examine some of Wittgenstein’s ideas about falsity, as presented by Luiz Carlos, in relation to my account of (...) falsity and negation. In §3 I discuss the modal aspects of identification for propositions. (shrink)

Resenha do livro "O mais natural dos regimes. Espinosa e a Democracia", de Diogo Pires Aurélio.

Minga-Mutirão de Revistas de Teologia Latino-americanas Teologia da Libertação: de onde viemos, para onde vamos? (Liberation Theology: where do we come from? Where are we going to?).

O tema da alteridade é caro a ambosos autores. Contudo, a tematização da especificidadedesta alteridade é dissimétrica em cadaautor. Em Levinas, o privilégio é concedido àpresença originária do outro, enquanto produtorde um trauma desorganizante original para aprodução do eu e da própria relação com o outro.Por seu lado, para a psicanálise de Lacan, arelação mais originária do sujeito é com o símbolo,na medida em que o autor reivindica a anterioridadeoriginária da ordem simbólica que operacomo conditio sine qua non da assunção (...) dasubjetividade. (shrink)

Tradicionalmente, filosofia e psicanálisemuito pouco dialogam. O trabalho procuraampliar esta área de contato através de umconfronto entre a fenomenologia hermenêutica deHeidegger, em relação à análise do Dasein; ahermenêutica gadameriana, e o seu apelo àlinguagem como ambiente do humano e, de outrolado, a psicanálise de Lacan. Não se trata depsicanalisara filosofia mas, sim, tentar aprofundaro debate entre estas duas áreas, para possibilitara determinação daquilo que é especifico a cadacampo.

O artigo pretende tratar de um tema presente nos Discursos sobre a primeira década de Tito Lívio, bem como em outros textos de Maquiavel: o dos homens bons plenos de virtù e seu papel na fundação do campo jurídico-político. A primeira questão a ser trabalhada é a do método em Maquiavel. Após, o conceito de virtù será analisado no que se refere a sua importância para a fundação e manutenção jurídico-política da cidade.

O tema de fundo do artigo é o dos regimes políticos em Espinosa. O objetivo é o de analisar, no interior deste tema mais amplo, o da distribuição da potência entre os membros do corpo político como critério comum aos regimes. A questão dos regimes, em Espinosa, não passa apenas pela definição do número dos que governam. Um rol de conceitos - homem como potência, afetos, multidão, imperium, entre outros - deve ser levado em conta para tratar da clássica questão.

Diálogo intercultural é a relação ética capaz de dar conta do desafio posto pela globalização que acelerou o contato e a interferência entre as culturas. Para um diálogo autêntico, há pressupostos sine qua non: a desideologização do universalismo cultural, o desocultamento da pluralidade. Além disso, há necessidade de um aclaramento conceitual que ajude a fazer opções pelos conceitos operacionais que realmente possam ajudar a ter uma postura de diálogo. Entre estes conceitos, aqui se privilegia o conceito “sistêmico” e de cultura (...) como expressão de transcendência humana, de tal forma que, em sua transparência simbólica, a cultura permite que haja um "face a face” dos interlocutores desde suas respectivas culturas. (shrink)

De Auxiliis designa uma famosa controvérsia filosófico-teológica do final do século XVI e início do século XVII, que envolveu teólogos espanhóis dominicanos e jesuítas em torno do tema/problema do livre arbítrio humano sob a influxo da graça divina. Considerado filosoficamente, o problema central gira em torno à determinação semântica de enunciados condicionais contrafactuais, problema este já presente em todos os enunciados teóricos composicionais. A partir do contexto histórico e teológico da controvérsia, juntamente com o surgimento do Molinismo, apresentaremos, com alguns (...) aportes da Filosofia Estrutural-Sistemática proposta por Lorenz Puntel, o problema filosófico da determinação semântica de sentenças teóricas em geral e a nova forma de determiná-las semanticamente. Isso possibilitará a elaboração filosófica de uma nova Teoria do Ser, na qual a grande questão de “Deus” e seus atributos encontrará seu mais adequado lugar teórico no discurso filosófico sistemático. Palavras-chave: Tomismo. Molinismo. Filosofia Sistemático-Estrutural. Semântica Sentencial. Metafísica Primordial. (shrink)

Trata-se de mostrar as teses e argumentos de Holbach sobre a liberdade, a necessidade, bem como sobre seu "sistema do fatalismo". Objetiva-se sustentar a hipótese de que as teses de Holbach sobre a liberdade, a necessidade e o fatalismo não implicam a aceitação da imutabilidade ou cristalização do real.

Machado de Assis, no conto _A Sereníssima República_, aponta, por meio da alegoria, problemas de fundo do sistema político brasileiro. Uma espécie de cultura da fraude estaria presente nos comportamentos das aranhas, o que impossibilitaria a implantação reta e precisa da lei, bem como a instituição da paz e da _securitas_. Sérgio Buarque de Holanda, ao analisar, a partir de fontes primárias, o período em que se passa o conto, constata os mesmos problemas que Machado de Assis apontara. Os conceitos (...) políticos espinosanos são movimentados, ao final, para mostrar que em um _imperium_ no qual as leis são constantemente violadas, não se está distante do estado de natureza, com grande perigo de vida para os súditos-cidadãos. Seria este o caso da república do conto e do Brasil atual? (shrink)

It follows from Bell’s theorem and quantum mechanics that the detection of a particle of an entangled pair can (somehow) “force” the other distant particle of the pair into a well-defined state (which is equivalent to a reduction of the state vector): no property previously shared by the particles can explain the predicted quantum correlations. This result has been corroborated by experiment, although some loopholes still remain. However, it has not been experimentally proved—and it is far from obvious—that the absence (...) of detection, as in null-result (NR) experiments could have the very same effect. In this paper a way to try to bridge this gap is suggested. (shrink)

Na tarefa de reconstruir compreensivamente o saber trazido pela psicanálise de Jacques Lacan, é utilizado o framework da postura transcendental herdeira de Kant. O termo “amálgama” permite compreender a incorporação, no gesto lacaniano, de saberes oriundos de distintas áreas do conhecimento humano e que, submetidos ao cadinho da torção lacaniana, possibilitam a Lacan a produção de uma ontogênese originalíssima sobre o humano-ser. A metamorfose lacaniana é uma operação que implica numa revisão dos conceitos em seu campo originário e uma Aufhebung (...) da psicanálise freudiana. (shrink)