Aristotle says that a fallacy of accident takes place whenever something is held to belong in the same way to an object and to its accident (SE 5 166b28-30). The Received View among interpreters takes “accident” (συμβεβηκός) in that connection to stand for any predicate that is not identical to its subject, and makes the fallacy consist in mistaking predication for identity. Such an analysis, however, gives “accident” a meaning otherwise unattested in the corpus; makes all cases of the fallacy (...) inconclusive, whereas inferences of the same kind are warranted (with a qualification) at different places in the corpus; does not cover cases which in Aristotle’s view fall under the fallacy of accident, for which a different analysis and solution must be provided; and does not square with Aristotle’s own solution in terms of sameness or difference in substance and being. This chapter presents a new take on the subject, grounded on Aristotle’s expressed views in the Sophistical Refutations and other works, according to which the fallacy takes place whenever a substitution of co-extensives, or even of necessary equivalents, makes reciprocation fail to (necessarily) hold between relata. (shrink)

The present article argues that Chrysippus' reply to the objection that Fate does away with that which is up to us (and therefore with justice in honor and punishments) consists in shifting the notion of that which is up to us from one in terms of ultimate origination to one in terms of self-sufficient causation—and thus in shifting the very notion of justice in honor and punishments from one in retributive terms to one in rehabilitative terms.

The present paper draws a contrast between the notions of τὸ παρ’ ἡμᾶς and τὸ ἐφ’ ἡμῖν to the effect that, according to Chrysippus, each has a different role to play and different requirements to meet, the former being especially tailored to suit the exigencies of praise and blame taken as exhortations, the latter those of desert and justice in praising and blaming as well as honoring and punishing.

We present a new functional interpretation, based on a novel assignment of formulas. In contrast with Gödel’s functional “Dialectica” interpretation, the new interpretation does not care for precise witnesses of existential statements, but only for bounds for them. New principles are supported by our interpretation, including the FAN theorem, weak König’s lemma and the lesser limited principle of omniscience. Conspicuous among these principles are also refutations of some laws of classical logic. Notwithstanding, we end up discussing some applications of the (...) new interpretation to theories of classical arithmetic and analysis. (shrink)

In this article we study applications of the bounded functional interpretation to theories of feasible arithmetic and analysis. The main results show that the novel interpretation is sound for considerable generalizations of weak König’s Lemma, even in the presence of very weak induction. Moreover, when this is combined with Cook and Urquhart’s variant of the functional interpretation, one obtains effective versions of conservation results regarding weak König’s Lemma which have been so far only obtained non-constructively.

Nowadays, football goalkeepers play an important role in the team's organization, namely, considering the offensive and defensive processes. The purpose of our investigation focuses on the notational and T-pattern analysis of the offensive and defensive actions of elite young football GKs. The participating GKs presented 8 years of experience in the specific position, were internationally selected for the national team of Portugal, and competed in the national U-17 championship of Portugal. Thirty football matches were observed. The observational sample consisted of (...) defensive actions and offensive actions. Two observational instruments were used to codify the actions: the observation system of defensive technical-tactical actions of GKs and the observation system of offensive technical-tactical actions of GKs. Both instruments underwent a validation process, and inter- and intra-observer reliability was tested. The codification of the actions was performed with the LINCE program, and later the data were exported to Microsoft Excel and THEME 5.0. The notational data were analyzed in SPSS, and T-pattern detection analysis was performed in THEME 5.0. The predominant actions of young observed GKs were fundamentally goal defense and participation in the team's offensive process construction through actions performed with the foot and hand. The analysis of T-patterns allowed to identify T-pattern actions in the defensive actions of goal defense and exit of the goal, as well as related to the defensive set pieces. In the offensive process, the analysis of T-patterns reinforced the participation of the GK in the team's first phase of construction and in the execution of goal kicks and actions that start as a result of the actions of the opponent. The GK's defensive actions are mostly focused on the objective of goal defense and offensive actions with the hands and feet are important for their participation in positional attack construction. Our study contributes to a better knowledge of the GK's actions in the competition and is relevant to be considered by the specific position coaches in the training process organization. (shrink)

O presente artigo toma em sua consideração o discreto apêndice do, então socialista, William English Walling – “Socialism and Pragmatism as seen in the Writings of Marx and Engels” – servindo de mote a um regresso à conceção materialista da história, com especial incidência nos escritos de Friedrich Engels. A escolha de Walling assinala-se pelo facto de uma alegada herança de tipo socialista-pragmatista ou marxista-pragmatista atravessar todo o século XX até aos nossos dias. Serão diversos os exemplos, mas parece residir (...) aqui o primeiro esboço de uma tal odisseia. (shrink)

No presente artigo procuramos recuperar a reflexão de Karl Marx e Friedrich Engels acerca do movimento dos trabalhadores estado-unidense do seu tempo, sobretudo no que ao papel dos socialistas dirá respeito. É nosso entendimento que esta reflexão contribui, apesar de pouco explorada, para a compreensão da conceção de ambos – a conceção materialista da história –, não porque tenha contribuído para a sua elaboração mais acabada, mas por via do exercício que os autores fizeram desta quando analisaram o que se (...) passava do outro lado do Atlântico. A reflexão destes dois autores pode ainda ser, além de questões meramente teóricas, bastante atual – daí o enfoque nas questões de estratégia político-partidária –, pois que os partidos que se reclamam da classe trabalhadora hoje são, apesar de tudo, bem mais do que na segunda metade do século XIX, mas, por outro lado, bem menos expressivos do que na segunda metade do século XX. Trata-se, em rigor, de um de vários contributos particulares da conceção dos dois autores alemães. (shrink)

O presente trabalho recupera a reflexão de Marx, acerca do desenvolvimento tecnológico, com base no seu famoso 13.º capítulo “Maquinaria e grande indústria”, pertencente ao Livro I de Das Kapital. Ao longo deste trabalho serão sucintamente analisadas questões fundamentais como a da acumulação de capital, a concorrência e a compulsão por mais-valia, o papel da luta de classes face a isto e a maneira como as relações sociais vigentes influenciam o desenvolvimento tecnológico. No final destrinçam-se as contradições da tecnologia dadas (...) as relações sociais de produção capitalistas. (shrink)

O móbil do presente artigo é dado a partir do subponto 52 da obra Justice as Fairness: A Restatement de John Rawls – “Addressing Marx’s Critique of Liberalism” –, mais precisamente quanto à objeção que o autor destaca de Karl Marx em relação à “divisão do trabalho” sob o capitalismo. Rawls considera que tal “divisão”, pelo menos da maneira como foi apontada por Marx, seria “superada” no âmbito dos princípios de justiça. Assim, através da Kritik des Gothaer Programms e de (...) uma famosa Lettre de Marx, procuramos uma confrontação com as considerações avançadas por Rawls. (shrink)

La conceptualización y el marco legal del odio en las democracias contemporáneas están en el centro de la atención por su proximidad al problema de la libertad de expresión. La reciente migración del discurso público de ambientes desconectados a escenarios en línea nos obliga a adoptar enfoques más penetrantes en esta cuestión, para entender cómo las dinámicas de género se reproducen entre los usuarios de internet. El artículo ofrece una aproximación legal, desde una perspectiva de género, al odio tal y (...) como aparece en la legislación internacional y europea, con el fin de comparar las legislaciones de Italia y España. El objetivo es mediar el conflicto entre libertad de expresión y los compromisos que los Estados asumen para dotar a específicos sujetos de protección contra formas de violencia de género que ocurren en internet. (shrink)

O desenvolvimento tecnológico promoveu o aumento de produção e compartilhamento de conteúdo em plataformas digitais, sendo difícil gerenciar o acesso adequado a informações. O presente artigo tem como objetivo discutir os efeitos do direito ao esquecimento no ambiente digital, considerando o processo de desindexação como estratégia para operacionalizar a efetividade desse direito. Tomando como referências arcabouços teóricos-conceituais acerca da complexidade compósita da informação e de antinomias entre a dignidade da pessoa humana e a liberdade de expressão e o direito à (...) informação, oriundos, respectivamente, da Ciência da Informação e do Direito, analisam-se e discutem-se algumas decisões jurisprudenciais e posicionamentos doutrinários no cenário brasileiro. O direito ao esquecimento está cercado de ambivalências e desafios de ordens normativa, tecnológica e cultural, num compartilhamento de informações em níveis sem precedentes que interferem negativamente na sua efetivação no ambiente digital. (shrink)

RESUMO O presente ensaio aborda o período anterior às obras tidas como as diferentes reescrições da Doutrina da Ciência, de J. G. Fichte, e aí tenta não só perceber a origem da necessidade de um princípio da identidade, como ela surge aquando das primeiras ocorrências do mesmo, mas também discernir os primeiros passos de todo o problema da possibilidade de um princípio absoluto de toda a filosofia, que sempre animaria a empresa. O foco em questão é a «Aenesidemus-Rezension», onde Fichte (...) junta a sua voz ao aceso diálogo já anteriormente entabulado por K. L. Reinhold e G. E. Schulze, e, na necessidade de repensar o princípio da consciência do primeiro, e as críticas a este feitas pelo segundo, é trazido à convicção da necessidade de um novo princípio absoluto; mas onde, e é este o fulcro do presente ensaio, Fichte percebe a insuficiência filososófica do sistema reinholdiano como uma insuficiência de linguagem, e portanto todo o problema como um problema que depende intimamente de uma apoditicidade linguística, e daí parte para a proposta de uma nova terminologia nacional, uma linguagem filosófica sistematicamente certa e inequívoca, à altura de um sistema filosófico regido por um princípio absoluto – um problema que viria a ocupar as cogitações de toda a geração de jovens pensadores em torno do professor de Jena. ABSTRACT This essay approaches the period prior to the works considered as the different versions of the Doctrine of Science, by J. G. Fichte, and aims not only at discerning the origin of the need for a principle of identity, but also at retracing the first steps of the whole problem of the possibility of an absolute principle of all philosophy. The focus shall be the «Aenesidemus-Rezension», where Fichte joins his voice to the heated argument previously struck by K. L. Reinhold and G. E. Schulze, and, urged to rethink Reinhold's principle of consciousness and the criticism raised by Schulze, is brought to believe the necessity for a new absolute principle; but where, and this is the fundamental idea of this essay, Fichte realizes the philosophical insufficiency of Reinhold's system as a language-related insufficiency, and therefore the whole problem as one intimately dependent on a linguistic apodicticity, and moves on to propose a new national terminology, a systematically certain and unequivocal philosophical language, which might meet the demands of a philosophical system ruled by an absolute principle – a problem which would soon be in the agenda of a whole generation of young idealists around the Professor of Jena. (shrink)

«Die Art, wie er den Mechanismus der Natur mit ihrer Zweckmäßigkeit vereiniget, scheint mir eigentlich den ganzen Geist seines Systems zu enthalten»; This quotation, which originated the present essay, is solely extracted from a letter sent by Hölderlin to Hegel, and yet, it condensates three different approaches from the three Tübingen friends to the problem of Kant’s philosophy of religion and to its possible resolution between 1795 and 1796. From this epistolary dialogue emerges a simultaneous study of Kant, originated by (...) the growing dissension towards the orthodox thought of the Stift. The tuming point - or the maximum cumulative point - of this discordance happens precisely with the discovery of the «spirit of Kant’s System», as a combined explanation of the religious and philosophical phenomena [«Die Art, wie er den Mechanismus der Natur mit ihrer Zweckmässigkeit vereiniget»]. This, I think, is something which the three friends discover gradually and not independently from the concept of «providence», which Kant himself, according to Hölderlin, had used to «attenuate his antinomies», which Hegel uses in his first religious writings and the initial formation of his own philosophy and which Schelling will later explore in his System of Transcendental Idealism. In a word, providence is consensually the comprehension axis between man, God and nature and, thus, the explanatory link between the antinomical poles which regulate human existence. On the other hand, however - this being the aspect I would like to stress -, this decisive moment for a whole generation, for the history of philosophy itself, means the consummation of a new revolutionary perspective born in Kant, a new vision of the absolute and the divine and, therefore, a new way to write philosophy about philosophy, less philosophical than before, to the extent that the new situation of man and his reflection within the problem ultimately destined them - as is the case in the three young philosophers - to silence and death. The final aim of this essay is, therefore, to know what this «last step of philosophy» is and what dies along with it, what such a step may have meant and what it already foretold in terms of the development of philosophy. (shrink)

RESUMO A história do estatuto, bem como da posição da memória entre semelhantes forças, desde a formação do conceito moderno da antropologia, durante toda a tradição leibniz-wolffinana, e até Kant, é uma história de mudança ascendente, de cristalização de ambos os predicados desta faculdade, e também uma de grande influência sobre a história do próprio pensamento antropológico. O presente ensaio propõe-se analisar como Kant receberia essa evolução, e como ele sobre ela actuaria. Isto é, centrando-nos nas “Lições de Antropologia”, e (...) sobre a “Antropologia num Enfoque Pragmático”, queremos indagar até que ponto Kant daria continuidade à referida tradição, mas, sobretudo, a partir de onde este com ela rompe, talhando ele próprio um novo capítulo nessa história, e também na história da antropologia; mais concretamente, importa conhecer a posição de Kant em relação a Platner ou Hume e suas concepções de memória, sua cisão em relação a estes, e sua proposta de todo um reposicionamento, e também revalorização do estatuto da memória entre faculdades da alma; e, por fim, perceber como Kant traz estes propósitos a bom porto, a saber, por meio da memória judiciosa, a única que abre não só para as ciências, mas também para a faculdade de imaginação produtiva, e para a poesia, e portanto também a única capaz de unir inferiores e superiores faculdades da alma, e instaurar harmonia entre estas. ABSTRACT The history of the status, as well as the position of memory among similar forces, since the genesis of the modern concept of anthropology, during the Leibniz-Wolffian tradition, and until Kant, is a history of ascending transformation, a crystallization of both this faculty’s attributes, and also one of great influence on the history of anthropological thought itself. The present essay aims at analyzing how Kant would receive that evolution, and how he would act upon it. That is, by focusing on the “Lectures on Anthropology”, and on “Anthropology on a Pragmatic Point of View”, we wish to inquire to what extent Kant would resume the aforementioned tradition, but, above all, from which point he breaks with it, thus carving he himself a new chapter in that history, and also in the history of anthropology; namely, it is our objective to ascertain Kant’s position regarding Platner or Hume and their conceptions of memory, his scission from the latter two, and his proposition of a whole repositioning, and also revaluation of the status of memory among faculties of the soul; and finally, understanding how Kant succeeds in these purposes, namely, through the concept of judicious memory, the only one which enables not only sciences, but also the productive faculty of imagination, and hence poetry, and therefore the only one able to unite both inferior and superior faculties of the soul and to sow harmony between the latter. (shrink)

RESUMO: Fruto de longa maturação filosófica desde a sua estada em Jena, e instado a isso pelas influências de Karl L. Reinhold e Johann G. Fichte, o poeta Novalis produz, a partir do outono de 1795, um conjunto de anotações fragmentárias sobre a filosofia de Fichte, hoje conhecidas como Fichte-Studien. De entre os importantes temas aí abordados, um revela-se particularmente interessante: o tema do estatuto da Filosofia no seio do problema da autocompreensão do Eu -, e mais concretamente, o necessário (...) pensar da filosofia sobre si própria, as alterações que no processo têm de sobrevir à própria filosofia e a repercussão disto na compreensão de si próprio do Eu. Nesta senda, o seguinte ensaio propõe-se mostrar como, para Novalis, a filosofia é o natural pensar do homem, e como para além disto é a própria filosofia, com o decorrer do seu pensamento sobre si própria, que molda o curso da compreensão de si próprio do Eu: quer tendo com o Eu uma origem comum, nascendo com ele, lançando-o para o mundo e cindindo a união originária em que ele de outro modo sempre estaria, quer, por fim, afirmando-se como carência deste, ou como algo por que o Eu e a própria filosofia têm de passar no seu curso, para que possam experienciar a perda, e almejar à recuperação dessa origem. ABSTRACT: Fruit of a long philosophical maturation that began with his stay in Jena, and encouraged by the influence of Karl L. Reinhold and Johann G. Fichte, the poet Novalis produced, from autumn 1795 on, a set of fragmentary notes on the philosophy of Fichte. These are now known as Fichte-Studien. Among the important issues treated in the notes, one appears particularly interesting: the treatment of the theme of philosophy within the problem of the self-understanding of the "I" - and, more specifically, the need for philosophy to think about itself, about the changes that must come upon philosophy during this process, and about the impact of these on the self-understanding of the "I". The present article aims to show how, for Novalis, philosophy is the natural thought of man. Furthermore, it aims to show how philosophy, in the course of its thought on itself, shapes the course of the self-understanding of the "I", having with the "I" a common origin, being born with it, launching it into the world, cleaving the original union in which it otherwise would always be, and finally asserting itself as a lack of this union, something through which the "I" and philosophy itself must pass in their course so they can experience this loss and aim to recover its source. (shrink)

O presente artigo objetiva refletir sobre os impactos da globalização econômica na cultura contemporânea. O processo acelerado de transformação da cultura e das relações sociais distingue-se de outros processos de mudança estrutural porque as mudanças no campo da economia desde a década de 1980 provocaram uma grave crise cultural. O que mais caracteriza os novos tempos é a expansão do mercado que se torna omniabrangente e omnipresente, transformando as relações humanas em relações de mercado. Globalização neoliberal e a expansão do (...) mercado se articulam e isso gera profunda crise da cultura. A racionalização produzida pela modernidade reduziu o ser humano e a natureza aos interesses produtivos. A crise na primeira modernidade faz emergir outra redução: a razão substituida pela sensação. Daí caminha-se para um radical individualismo, até ao indiferentismo e a recusa de se buscar um sentido ou significado para a experiência e a vida humana. Essa realidade oferece riscos para o Cristianismo e as religiões. Elas podem ceder à tentação do mercado, à satisfação do desejo, do gozo superegóico, com dupla conseqüência: ou oferecendo uma religião de consumo e da prosperidade econômica, ou o fundamentalismo que leva os fiéis à renunciarem à sua autonomia e se submeterem às lideranças religiosas da “Ordem Simbólica”. Na conclusão o artigo apresenta as mais recentes críticas do cristianismo a essa realidade, retomando o pensamento de João XXIII, Paulo VI e João Paulo II. Palavras-chave : Cristianismo; Globalização; Economia; Cultura Contemporânea, Ensino Social da IgrejaThis article aims to reflect on the impacts of globalization economy in contemporary culture. The accelerated transformation of culture and of social relations differs from other processes of structural changes because change in the field of economy have caused serious cultural crisis since the 1980s. What best characterizes the new era is the expansion of market that has increasingly been “all embracing” and “omnipresent”, thus transforming human relations in market relations. Neoliberal globalization and the expansion of market articulate themselves thus producing a deep crisis of culture. Rationalization produced by modernity has reduced human being and nature to productive interests. Crisis in early modernity brings out another reduction: the one of reason replaced by sensation. In this way one can say that it has emerged a radical individualism and even a kind of indifferentism as well as the refusal to look for a sense or a meaning to the experience and human life. This reality presents some risks to Christianity and religions. They may succumb to the temptation of the market, satisfaction of desire and hiper egoic enjoyment, with double consequence: or by offering a religion based on consumerism and on economic prosperity, or by offering a fundamentalistic perspective that leads believers to renounce their autonomy and submit themselves to the religious leaders of the "Symbolic Order ". This articles ends up by presenting the most recent criticism of Christianity to this reality, returning to the thought of the popes John XXIII, Paul VI and John Paul II.] Key words : Christianity; Globalizing; Economics; Contemporary culture, Church’s Social Teaching. (shrink)

Este ensaio introdutório faz uma breve apresentação do tratado de óptica atribuído a Euclides de Alexandria, inserindo-o no contexto das teorias sobre a visão formuladas pelas doutrinas filosóficas antigas. Ressalta-se o antagonismo entre a análise geométrica da visão, empreendida por Euclides, e as considerações filosóficas acerca dos processos físicos subjacentes à sensação visual. Pretende-se mostrar que o objeto da óptica euclidiana é a percepção visual daquilo que Aristóteles denomina "sensível comum". This introductory essay provides an abridged presentation of the optical (...) treatise attributed to Euclid of Alexandria, placing it in the context of theories about vision formulated by the ancient philosophical doctrines. I emphasize the antagonism between the geometric analysis of vision, undertaken by Euclid, and the philosophical considerations about the physical processes underlying visual sensation. In addition, I aim to show that the object of Euclidean optics is the visual perception of what Aristotle calls "common sensible". (shrink)

Por meio de processos-crime, reflete-se sobre a organização racial/racista da sociedade no passado. O assassinato de Vicente Crioulo, no ano de 1848, funciona como o primeiro paradigma para que se entenda que o Estado representa apenas um dos canais para a subjugação de povos não-brancos aos brancos dominadores. Esta abordagem filia-se à micro-história, e procura ver a vida cotidiana de homens e mulheres negras, escolhendo três casos paradigmáticos, que caminham da tortura e morte de um homem negro à uma rebelião (...) de escravos contra o seu feitor. Trata-se de uma narrativa de dor, mas também de resistência à ordem escravocrata. (shrink)

It is well known that Frege's system in the Grundgesetze der Arithmetik is formally inconsistent. Frege's instantiation rule for the second-order universal quantifier makes his system, except for minor differences, full (i.e., with unrestricted comprehension) second-order logic, augmented by an abstraction operator that abides to Frege's basic law V. A few years ago, Richard Heck proved the consistency of the fragment of Frege's theory obtained by restricting the comprehension schema to predicative formulae. He further conjectured that the more encompassing Δ₁¹-comprehension (...) schema would already be inconsistent. In the present paper, we show that this is not the case. (shrink)

We construct a weak second-order theory of arithmetic which includes Weak König's Lemma (WKL) for trees defined by bounded formulae. The provably total functions (with Σ b 1 -graphs) of this theory are the polynomial time computable functions. It is shown that the first-order strength of this version of WKL is exactly that of the scheme of collection for bounded formulae.

In "'Yes" and "No'" (2000), Ian Rumfitt proposed bilateralism--a use-based account of the logical words, according to which the sense of a sentence is determined by the conditions under which it is asserted and denied. One of Rumfitt's key claims is that bilateralism can provide a justification of classical logic. This paper raises a techical problem for Rumfitt's proposal, one that seems to undermine the bilateralist programme.

We show how to interpret intuitionistic propositional logic into a predicative second-order intuitionistic propositional system having only the conditional and the universal second-order quantifier. We comment on this fact. We argue that it supports the legitimacy of using classical logic in a predicative setting, even though the philosophical cast of predicativism is nonrealistic. We also note that the absence of disjunction and existential quantifications allows one to have a process of normalization of proofs that avoids the use of "commuting conversions.".

RESUMO Em diversas obras do Círculo (Bakhtin, Volóchinov, Medviédev), a referência a Saussure e/ou às especificidades da Linguística, enquanto ciência da língua, pode ser encontrada em diálogo, mais ou menos polêmico, entre pensadores e tendências epistemológicas, teóricas e metodológicas que propõem diferentes abordagens para a complexidade representada pela linguagem humana e, consequentemente, para seu estudo. Neste artigo, o objetivo é circunscrever e discutir a presença da Linguística, enquanto ciência da língua instaurada por Saussure, nos escritos de Mikhail Bakhtin. Após uma (...) introdução, o texto se organiza em três seções, que tratam (1) de uma forte presença de Saussure nos escritos do Círculo; (2) do diálogo de Bakhtin com a ciência na unidade da cultura; (3) do diálogo com a ciência linguística da escola de Genebra em “O problema do conteúdo, do material e da forma”; e, finalmente, de considerações inconclusas, mas necessárias. Destacam-se importantes momentos-chave de reflexão em textos assinados por Bakhtin, em que Saussure (ainda que não nomeado, mas designado pela ciência por ele estabelecida) merece destaque, como contraponto científico-filosófico necessário para a constituição de outra possibilidade de compreensão e estudo da linguagem: a perspectiva dialógica. Como resultado, espera-se demonstrar que, desde os anos 1920, o diálogo Bakhtin/Saussure se estabelece, para distinguir e qualificar duas formas complementares de compreensão da linguagem e do lugar da ciência na unidade da cultura. (shrink)

ABSTRACT In several works by the Circle (Bakhtin, Vološinov, Medvedev), the reference to Saussure and/or the specificities of Linguistics, as a science of language, can be found in a dialogue, more or less controversial, between thinkers and epistemological, theoretical and methodological trends that propose different approaches to the complexity represented by human language and, consequently, to its study. In this article, the objective is to circumscribe and discuss the presence of Linguistics, as a science of language established by Saussure, in (...) the writings of Mikhail Bakhtin. After an introduction, the text is organized into three sections, which deal with (1) Saussure’s strong presence in the Circle’s writings; (2) Bakhtin’s dialogue with science in the unity of culture; (3) the dialogue with the linguistic science of the Geneva school in “PCMF”; and, finally, of inconclusive but necessary considerations. Important key moments of reflection stand out in texts signed by Bakhtin, in which Saussure (although not named, but designated by the science he established) deserves to be highlighted, as a necessary scientific-philosophical counterpoint for the constitution of another possibility of understanding and study of language: the dialogical perspective. As a result, it is expected to demonstrate that, since the 1920s, the Bakhtin/Saussure dialogue has been established to distinguish and qualify two complementary ways of understanding language and the place of science in the unity of culture. (shrink)

Após a publicação do Discurso do método e seus ensaios, Descartes inicia uma campanha de divulgação da obra com o objetivo de introduzir suas ideias no ambiente filosófico e acadêmico. Seu maior interesse era obter a aprovação e o reconhecimento das suposições e explicações presentes em Os meteoros e em A dióptrica. Esse interesse vincula-se ainda ao seu desejo de ver seus ensaios discutidos e ensinados nos colégios jesuítas. Neste artigo discuto a recepção de algumas ideias contidas nesses ensaios, particularmente (...) entre os estudiosos jesuítas, e analiso algumas críticas de Morin à hipótese da matéria sutil. (shrink)

A recepção de Os meteoros, publicado em 1637 como um dos ensaios do Discurso do método, foi marcada por uma forte reação contra o mecanicismo cartesiano. Alguns de seus contemporâneos, adeptos da filosofia tradicional escolástica, elaboraram uma série de críticas quanto à maneira como Descartes concebia a natureza dos corpos e explicava os fenômenos naturais. Libert Froidmont, um de seus primeiros críticos, elaborou um conjunto de objeções contra A dióptrica e, principalmente, contra Os meteoros. Este artigo visa analisar alguns aspectos (...) sobre o debate entre Descartes e Froidmont concernente às hipóteses mecanicistas sustentadas pelo primeiro. (shrink)

It has been known for six years that the restriction of Girard's polymorphic system $\text{\bfseries\upshape F}$ to atomic universal instantiations interprets the full fragment of the intuitionistic propositional calculus. We firstly observe that Tait's method of “convertibility” applies quite naturally to the proof of strong normalization of the restricted Girard system. We then show that each $\beta$-reduction step of the full intuitionistic propositional calculus translates into one or more $\beta\eta$-reduction steps in the restricted Girard system. As a consequence, we obtain (...) a novel and perspicuous proof of the strong normalization property for the full intuitionistic propositional calculus. It is noticed that this novel proof bestows a crucial role to $\eta$-conversions. (shrink)

In Frege’s logicism, numbers are logical objects in the sense that they are extensions of certain concepts. Frege’s logical system is inconsistent, but Richard Heck showed that its restriction to predicative quantification is consistent. This predicative fragment is, nevertheless, too weak to develop arithmetic. In this paper, I will consider an extension of Heck’s system with impredicative quantifiers. In this extended system, both predicative and impredicative quantifiers co-exist but it is only permissible to take extensions of concepts formulated in the (...) predicative fragment of the language. This system is consistent. Moreover, it proves the principle of reducibility applied to concepts true of only finitely many objects. With the aid of this form of reducibility, it is possible to develop arithmetic in a thoroughly Fregean way. (shrink)

We introduce a new typed combinatory calculus with a type constructor that, to each type σ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma$$\end{document}, associates the star type σ∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma ^*$$\end{document} of the nonempty finite subsets of elements of type σ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma$$\end{document}. We prove that this calculus enjoys the properties of strong normalization and confluence. With the aid of this star combinatory (...) calculus, we define a functional interpretation of first-order predicate logic and prove a corresponding soundness theorem. It is seen that each theorem of classical first-order logic is connected with certain formulas which are tautological in character. As a corollary, we reprove Herbrand’s theorem on the extraction of terms from classically provable existential statements. (shrink)

Commuting conversions were introduced in the natural deduction calculus as ad hoc devices for the purpose of guaranteeing the subformula property in normal proofs. In a well known book, Jean-Yves Girard commented harshly on these conversions, saying that ‘one tends to think that natural deduction should be modified to correct such atrocities.’ We present an embedding of the intuitionistic predicate calculus into a second-order predicative system for which there is no need for commuting conversions. Furthermore, we show that the redex (...) and the conversum of a commuting conversion of the original calculus translate into equivalent derivations by means of a series of bidirectional applications of standard conversions. (shrink)

It is known that there is a sound and faithful translation of the full intuitionistic propositional calculus into the atomic polymorphic system F at, a predicative calculus with only two connectives: the conditional and the second-order universal quantifier. The faithfulness of the embedding was established quite recently via a model-theoretic argument based in Kripke structures. In this paper we present a purely proof-theoretic proof of faithfulness. As an application, we give a purely proof-theoretic proof of the disjunction property of the (...) intuitionistic propositional logic in which commuting conversions are not needed. (shrink)

We introduce a herbrandized functional interpretation of a first-order semi-intuitionistic extension of Heyting Arithmetic and study its main properties. We then extend the interpretation to a certain system of second-order arithmetic which includes a (classically false) formulation of the FAN principle and weak König's lemma. It is shown that any first-order formula provable in this system is classically true. It is perhaps worthy of note that, in our interpretation, second-order variables are interpreted by finite sets of natural numbers.

We present a functional interpretation of Peano arithmetic that uses Gödel’s computable functionals and which systematically injects uniformities into the statements of finite-type arithmetic. As a consequence, some uniform boundedness principles are interpreted while maintaining unmoved the -sentences of arithmetic. We explain why this interpretation is tailored to yield conservation results.

We define a notion of realizability, based on a new assignment of formulas, which does not care for precise witnesses of existential statements, but only for bounds for them. The novel form of realizability supports a very general form of the FAN theorem, refutes Markov's principle but meshes well with some classical principles, including the lesser limited principle of omniscience and weak König's lemma. We discuss some applications, as well as some previous results in the literature.

Aristotle’s Eudemian Ethics has always proved to be fertile ground for at times needless textual emendation. I provide a translation and running commentary on Eudemian Ethics II 2 1220a39–b6 in accordance with the MSS text.

In the course of ten short sections, we comment on Gödel's seminal dialectica paper of fifty years ago and its aftermath. We start by suggesting that Gödel's use of functionals of finite type is yet another instance of the realistic attitude of Gödel towards mathematics, in tune with his defense of the postulation of ever increasing higher types in foundational studies. We also make some observations concerning Gödel's recasting of intuitionistic arithmetic via the dialectica interpretation, discuss the extra principles that (...) the interpretation validates and comment on extensionality and higher order equality. The latter sections focus on the role of majorizability considerations within the dialectica and related interpretations for extracting computational information from ordinary proofs in mathematics. (shrink)

Edward Nelson published in 1986 a book defending an extreme formalist view of mathematics according to which there is an impassable barrier in the totality of exponentiation. On the positive side, Nelson embarks on a program of investigating how much mathematics can be interpreted in Raphael Robinson's theory of arithmetic Q. In the shadow of this program, some very nice logical investigations and results were produced by a number of people, not only regarding what can be interpreted in Q but (...) also what cannot be so interpreted. We explain some of these results and rely on them to discuss Nelson's position. (shrink)

We present a refinement ofthe bounded modified realizability which provides both upper and lower bounds for witnesses. Our interpretation is based on a generalisation of Howard/Bezem's notion of strong majorizability. We show how the bounded modified realizability coincides with our interpretation in the case when least elements exist . The new interpretation, however, permits the extraction of more accurate bounds, and provides an ideal setting for dealing directly with data types whose natural ordering is not well-founded.

We give an elementary proof of the strong normalization of the atomic polymorphic calculus Fat.

Realizability notions in mathematical logic have a long history, which can be traced back to the work of Stephen Kleene in the 1940s, aimed at exploring the foundations of intuitionistic logic. Kleene’s initial realizability laid the ground for more sophisticated notions such as Kreisel’s modified realizability and various modern approaches. In this context, our work aligns with the lineage of realizability strategies that emphasize the accumulation, rather than the propagation of precise witnesses. In this paper, we introduce a new notion (...) of realizability, namely herbrandized modified realizability. This novel form of (cumulative) realizability, presented within the framework of semi-intuitionistic logic is based on a recently developed star combinatory calculus, which enables the gathering of witnesses into nonempty finite sets. We also show that the previous analysis can be extended from logic to (Heyting) arithmetic. (shrink)

Frege’s Grundgesetze der Arithmetik is formally inconsistent. This system is, except for minor differences, second-order logic together with an abstraction operator governed by Frege’s Axiom V. A few years ago, Richard Heck showed that the ramified predicative second-order fragment of the Grundgesetze is consistent. In this paper, we show that the above fragment augmented with the axiom of reducibility for concepts true of only finitely many individuals is still consistent, and that elementary Peano arithmetic (and more) is interpretable in this (...) extended system. (shrink)