O objetivo deste artigo é tentarmos elucidar a extravagante tese de Wittgenstein de que todo e qualquer avanço matemático envolve alguma “mutação semântica”, ou seja, alguma alteração nos próprios significados dos termos envolvidos. Para isso, argumentaremos a favor da ideia de uma “incompatibilidade modal” entre os conceitos envolvidos, como eram antes do avanço, e o que se tornam após a obtenção do novo resultado. Também argumentaremos que a adoção dessa tese altera profundamente nossa maneira tradicional de construir a ideia de (...) “progresso” em matemática. (shrink)

This paper offers a new interpretation for Wittgenstein`s treatment of mathematical identities. As it is widely known, Wittgenstein`s mature philosophy of mathematics includes a general rejection of abstract objects. On the other hand, the traditional interpretation of mathematical identities involves precisely the idea of a single abstract object – usually a number –named by both sides of an equation.

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

This paper offers an overview of various alternative formulations for Analysis, the theory of Integral and Differential Calculus, and its diverging conceptions of the topological structure of the continuum. We pay particularly attention to Smooth Analysis, a proposal created by William Lawvere and Anders Kock based on Grothendieck’s work on a categorical algebraic geometry. The role of Heyting’s logic, common to all these alternatives is emphasized.

This article discusses some of Chateaubriand’s views on the connections between the ideas of formalization and infinity, as presented in chapters 19 and 20 of Logical Forms. We basically agree with his criticisms of the standard construal of these connections, a view we named “formal proofs as ultimate provings”, but we suggest an alternative way of picturing that connection based on some ideas of the late Wittgenstein.

This paper offers a reconstruction of Wittgenstein's discussion on inductive proofs. A "algebraic version" of these indirect proofs is offered and contrasted with the usual ones in which an infinite sequence of modus pones is projected.

Wittgenstein’s philosophy of mathematics involves two highly controversial theses: the idea that mathematical propositions are not about (abstract) objects and the idea that no mathematical conjecture is ever answered as such, because the advent of the proof always determines a semantical shift of the meanings of the terms involved in the conjecture. The present article offers a reconstruction of Wittgenstein’s arguments supporting these theses within a very restricted setting: Archimedes’ discovery of an algorithm for calculating the number Pi.

This paper deals with the mutations in Wittgenstein’s treatment of the notions of “generality” and of “singularity”, from his first philosophy, in the Tractatus Logico-Philosophicus, to his later mature philosophy represented by the Philosophical Investigations. As we shall see, Wittgenstein’s philosophical handling of the notion of “visual perception” plays a key role in those conceptual transformations.

Trata-se de capítulo de um livro sobre a noção de "substância" na história da filosofia e contém uma discussão sobre a noção ordinária de "corpo" do ponto de vista da filosofia analítica.

The objective of this article is to try to elucidate Wittgenstein’s ex-travagant thesis that each and every mathematical advancement involves some “semantical mutation”, i.e., some alteration of the very meanings of the terms involved. To do that we will argue in favor of the idea of a “modal incompati-bility” between the concepts involved, as they were prior to the advancement, and what they become after the new result was obtained. We will also argue that the adoption of this thesis profoundly (...) alters the traditional way of con-struing the idea of “progress” in mathematics. (shrink)

The objective of this paper will be to present a critical evaluation of the so-called “standard conception of a proof”. According to this conception, a text could only be called a “demonstration of a certain mathematical proposition” if we could find a completely formalized version of that demonstration, its “corresponding formal proof”. We will compare these ideas with the treatment of the same topic within two markedly different contexts, that of contemporary Swedish intuitionism and that of modern software engineering. Finally, (...) we will offer a quick discussion of some of Wittgenstein's proposals regarding the subject. /// -/- O objetivo deste texto será o de apresentar uma avaliação crítica da assim chamada “concepção estândar” do que seja uma prova. Segundo essa concepção, um texto só poderia ser chamado de uma “demonstração de uma certa proposição matemática” se pudéssemos encontrar uma versão completamente formalizada daquela demonstração, sua “prova formal correspondente”. Faremos comparações com o tratamento do mesmo tópico em dois contextos muito distintos, aquele do intuicionismo sueco contemporâneo e o da moderna engenharia de software. Por fim, faremos uma rápida apresentação de algumas propostas de Wittgenstein sobre o assunto. (shrink)

O presente artigo tem como tema as extensas discussões de Wittgenstein sobre uma das formas mais simples e elementares de infinitude em matemática: as dízimas periódicas. Tentamos organizar os vários argumentos do autor em uma única exposição continuada. No final do artigo, introduzimos, ainda que de forma breve, o famoso argumento sobre “execução de regras” de Wittgenstein, bem como a idéia de interpretações nãostandard de processos infinitos.

Cet article poursuit un double but : d’une part, situer dans le parcours philosophique de Wittgenstein une partie de l’histoire du « problème du champ visuel », thème clé de sa période intermédiaire ; d’autre part, mettre en lumière sa critique de l’idée d’un champ visuel (et celle de l’idée d’un objet interne). Nous croyons que ses arguments sont nouveaux, pénétrants, et ainsi leur intérêt dépasse les limites d’un exposé purement exégétique.

Este artigo oferece uma nova reconstrução para os argumentos do famoso segundo capítulo de Word and Object de Quine e sua idéia da Tradução Radical . De acordo com essa abordagem, o maior alvo de Quine é a noção de composicionalidade como sendo o elemento fundamental para qualquer teoria do significado. Em poucas palavras, não poderia haver nenhuma “teoria do significado”, para Quine, simplesmente porque a noção de composicionalidade deveria ser rejeitada como a concepção central da semântica. Além disso, tomamos (...) o cuidado de diferenciar argumentos empíricos de argumentos a priori de natureza modal. Esses últimos constituem-se no que propomos chamar de Teorema do Automorfismo de Quine , a idéia de que há maneiras alternativas de se reconstruir a estrutura gramatical de qualquer língua incluindo predicação e que poderiam manter invariantes todas as nossas predisposições para comportamento verbal sob quaisquer estados de coisas, atuais ou meramente possíveis. Em nosso entender, é esse teorema que determina fundamentalmente a rejeição da composicionalidade por Quine e, assim, de todas as teorias do significado. (shrink)

Review of the translation of Ludwig Wittgenstein book: Observações Filosóficas. São Paulo: Edições Loyola, 2005. Tradução (do inglês) por Adail Sobral e Maria Stela Gonçalves.

This paper presents a new reconstruction of Wittgenstein’s famous (and controversial) rule-following arguments. Two are the novel features offered by our reconstruction. In the first place, we propose a shift of the central focus of the discussion, from the general semantics and the philosophy of mind to the philosophy of mathematics and the rejection of the notion of a function. The second new feature is positive: we argue that Wittgenstein offers us a new alternative notion of a rule (to replace (...) the rejected functions), a notion reminiscent of Category Theory’s notion of a morphism. (shrink)

We discuss some basic issues underlying the natural numbers: induction and recursion. We examine recursive formulations and their use in establishing universal and particular properties.

This article offers an explanation of perhaps Wittgenstein’s strangest and least intuitive thesis – the semantical mutation thesis – according to which one can never answer a mathematical conjecture because the new proof alters the very meanings of the terms involved in the original question. Instead of basing our justification on the distinction between mere calculation and proofs of isolated propositions, characteristic of Wittgenstein’s intermediary period, we generalize it to include conjectures involving effective procedures as well.

Esta resenha versa sobre a obra Cidadania e Democracia Deliberativa de Catherine Audard que se refere à uma articulação rawlsiana entre uma teoria da justiça e as teses centrais do seu liberalismo político sobre o pluralismo razoável, democracia deliberativa, cidadania participativa, razão pública, direito dos povos e multiculturalismo.

The main issue André Porto raises in his paper concerns the use of dot notation to indicate an infinite set of hypotheses. Whereas I agree that one cannot extract a unique infinite expansion from a finite initial segment, in my response I argue that this holds for finite expansions as well. I further explain how my remarks on infinite proof structures are neither motivated by the impact of Gödel’s incompleteness theorems on Hilbert’s program, nor by a negative view (...) of strict finitism.O problema central que André Porto discute em seu artigo diz respeito ao uso da notação de pontos para indicar um conjunto infinito de hipóteses. Mesmo estando de acordo não ser possível extrair uma expansão infinita a partir de um segmento inicial finito, em minha réplica argumento que isto vale igualmente para expansões finitas. Explico também que minhas observações sobre estruturas de prova infinitas não são motivadas pelo impacto dos teoremas de incompletude de Gödel no programa de Hilbert, e tampouco por uma visão negativa do finitismo estrito. (shrink)

Experiences of absence are common in everyday life, but have received little philosophical attention until recently, when two positions regarding the nature of such experiences surfaced in the literature. According to the Perceptual View, experiences of absence are perceptual in nature. This is denied by the Surprise-Based View, according to which experiences of absence belong together with cases of surprise. In this paper, I show that there is a kind of experience of absence—which I call frustrating absences—that has been overlooked (...) by the Perceptual View and by the Surprise Based-View and that cannot be adequately explained by them. I offer an alternative account to deal with frustrating absences, one according to which experiencing frustrating absences is a matter of subjects having desires for something to be present frustrated by the world. Finally, I argue that there may well be different kinds of experiences of absence. (shrink)

This book presents a comprehensive and detailed exploration of the relationship between the thought of G.W.F. Hegel and that of John McDowell, the latter of whom is widely considered to be one of the most influential living analytic philosophers. It serves as a point of entry in McDowell’s and Hegel’s philosophy, and a substantial contribution to ongoing debates on perceptual experience and perceptual justification, naturalism, human freedom and action. The chapters gathered in this volume, as well as McDowell’s responses, make (...) it clear that McDowell’s work paves the way for an original reading of Hegel’s texts. His conceptual framework allows for new interpretive possibilities in Hegel’s philosophy which, until now, have remained largely unexplored. Moreover, these interpretations shed light on various aspects of continuity and discontinuity between the philosophies of these two authors, thus defining more clearly their positions on specific issues. In addition, they allow us to see Hegel’s thought as containing a number of conceptual tools that might be useful for advancing McDowell’s own philosophy and contemporary philosophy in general. (shrink)

The survival of some masterpieces of literature across the ages is still an unexplained mystery. Deeply rooted in their time, they reflect the preoccupations of a given historical period and have an impact, by means of their testimony, on future generations. They bring into play images, drives and phantoms which have remained unchanged from prehistoric time to our day. The perfection of their form has remained unequaled; their examples incite us to meditation and creativity.

Burge famously argued that one can have thoughts involving a concept C even if one’s understanding of C is incomplete. Even though this view has been extremely influential, it has also been taken by critics as less than clear. The aim of this paper is to show that the cases imagined by Burge as being ones in which incomplete understanding of concepts is involved can be made clearer given an account of direct concept ascriptions—such as “Peter has the concept of (...) arthritis”—according to which these ascriptions are to be analysed in terms of ascriptions of the knowledge of what something is. The upshot is that the cases imagined by Burge can be explained is terms of the idea of subjects knowing in part what something is. (shrink)

Burns proposes an intriguing hypothesis by suggesting that the “schizophrenia genes” might not be regulatory genes themselves, but rather closely associated with regulatory genes directly involved in the proper growth of the social brain. We point out that this account would benefit from incorporating the effects of localized lesions and aberrant hemispheric asymmetry on cortical connectivity underlying the social brain. In addition, we argue that the evolutionary framework is superfluous.

We argue that the pivotal role assigned by Northoff to the principle of top-down modulation in catatonia might successfully be applied to other symptoms of schizophrenia, for example, hallucinations. Second, we propose that Northoff's account would benefit from a more comprehensive analysis of the cognitive level of explanation. Finally, contrary to Northoff, we hypothesize that “top-down modulation” might play as important a role as “horizontal modulation” in affective-behavioral alterations.

This article reports results of an experiment designed to analyze the link between risky decisions made by couples and risky decisions made separately by each spouse. We estimate both the spouses and the couples’ degrees of risk aversion, we assess how the risk preferences of the two spouses aggregate when they make risky decisions, and we shed light on the dynamics of the decision process that takes place when couples make risky decisions. We find that, far from being fixed, the (...) balance of power within the household is malleable. In most couples, men have, initially, more decision-making power than women but women who ultimately implement the joint decisions gain more and more power over the course of decision making. (shrink)

This dissertation is a study of some recent theories of truth. The theories fall into three groups: The Revision Theories, the context-sensitive theories, and the "Chrysippian theories". ;The "Chrysippian theories" are based on the intuition that pathologicalities arising from the concept of truth can be recognized and acknowledged with the concept of truth itself. Thus, from the pathologicality of the Liar, for example, we can conclude that the Liar is not true. This leads to immediate difficulties since the Liar claims (...) just that--that it is not true--and it would thus seem to be true. The Chrysippian theories are designed to avoid these difficulties while preserving the motivating intuition. Haim Gaifman's Pointer Semantics, and Brian Skyrms' Intensional Fixed-Point Theory of Truth are examples of such theories. They are exposited and criticized. ;The context-sensitive theories dealt with are Tyler Burge's Indexical Theory of Truth and the theory of Jon Barwise and John Etchemendy. These theories claim that an ambiguity due to a contextual parameter is the reason for the difficulties we encounter. Burge offers a theory of Tarskian levels coupled with a pragmatic theory that explains the assignment of levels to occurrences of 'true'. Barwise and Etchemendy make explicit a situational parameter in their account of propositions. They consider the ambiguity with respect to the situation a propositions is about a main source of the paradoxes. ;Finally, the Revision Theories of Truth of Anil Gupta and Nuel Belnap and two variations of this theory are considered. One is due to Aladdin Yaqub, the other, the "fully-varied theory", is due to Gupta and Belnap but remains largely unexplored. Revision theories are put forward as the most promising account of the difficulties. They are based on a definitional reading of all Tarski biconditionals. The circularity implied by such a reading is handled by Gupta's and Belnap's general theory of definitions. ;Yaqub's objections raised against the standard theory are examined, and his proposed solution is shown to be inadequate. The fully-varied Revision Theory is shown to provide a better solution. (shrink)

On peut distinguer, dans l'histoire du marxisme contemporain, deux tendances qui n'ont cessé de se confronter sous des formes plus ou moins radicales et qui tiennent à deux lectures apparemment inconciliables de l'oeuvre de Marx. La première, selon laquelle le marxisme se résorbe essentiellement en une théorie scientifique , en une sociologie . Cette tendance trouve son expression culminante dans l'althussérisme, dans le primat des relations constitutives de la structure sociale sur les individus-sujets. La seconde, qui veut que le marxisme (...) soit d'abord et avant tout un humanisme et/ou une philosophie de la praxis, tout travail théorique se trouvant subordonné à sa visée historico-pratique : celle de l'instauration de rapports sociaux dans lesquels seraient abolis les rapports d'exploitation de l'homme par l'homme. Poser la question de l'existence d'une éthique marxiste, c'est tenter de résoudre théoriquement cette épineuse dichotomie entre l'objectivisme des « déterminations » sociales des représentations de conscience morales et la capacité des individus-sujets de produire un ordre social, d'orienter le développement historique conformément à ces représentations . Pour un matérialiste, n'y a-t-il pas là une contradiction interne au marxisme? L'auteur de l'article a tenté de faire voir, à travers quelques propositions sommaires, comment une telle contradiction peut être dépassée.In the history of contemporary Marxism one can distinguish two conflicting tendencies which continue to confront each other in a more or less radical manner, and which give rise to two apparently irreconcilable readings of Marx's work. The first is that by which Marxism is essentially absorbed into a scientific theory , into a sociology. This tendency finds its ultimate expression in 'althussérisme', in the primacy of the constituent relations of the social structure involving individual subjects. In the second, which sees Marxism as essentially humanist and/or a philosophy of praxis, all theoretical work is subordinated to the practical-historical aim, that of establishing social relations in which the exploitation of persons by persons will be done away with. To ask whether a Marxist ethic exists is an attempt to resolve theoretically this thorny dichotomy between the objectivism of the social determinants of the prescriptions of moral conscience, and the capacity of individual subjects to produce a social order to orient historical development in accordance with these prescriptions. For a materialist, is there not here an apparent contradiction within Marxism? The author has attempted to clarify, by means of a few succinct propositions, how such a contradiction may be resolved. (shrink)

O objetivo do trabalho é apresentar a compreensão de docentes do ensino superior sobre a importância da pedagogia problematizadora. O estudo apresenta uma abordagem quali-quantitativa realizada com 27 docentes de uma instituição privada de ensino superior na província de Maputo, em Moçambique. Esse é o número de docentes que aceitou participar da pesquisa e preencheu o instrumento de avaliação autoaplicado. O estudo usou uma amostragem intencional e não probabilística, dada a impossibilidade de inquirir a todos os docentes da instituição; buscou-se, (...) assim, selecionar um subgrupo da população que, com base nas informações disponíveis, pudesse ser considerado representativo de toda a população. Os dados da pesquisa foram coletados por meio de um questionário autoaplicável e os resultados dispostos em tabela de frequências e inferência a partir do teste de correlação de Spearman (r). Constitui uma inovação considerar os parâmetros de correlação de Spearman para investigar a força de relacionamento entre as variáveis de princípios pedagógicos. O ensino superior é um local por excelência de transmissão de conhecimentos e valores sociais geradores de mudanças no estudante, em que o professor supera a visão de simples transmissor de conteúdos e executor de tarefas, adotando um sistema de educação progressista. Do correlacionamento feito entre a “importância do ensino problematizador” vs “ter ouvido falar do ensino problematizador” vs “o estudante ter direito de trazer seus conhecimentos”, pode-se constatar dificuldades oriundas da vigência do sistema bancário, um sistema que considera o aluno apenas como recipiente vazio a ser preenchido. Pode-se observar que a Metodologia Problematizadora exige imbricar a realidade e a prática, o que desperta um conjunto de implicações no momento da sua implementação dentro da sala de aula. Feito o correlacionamento entre a “importância do ensino problematizador” vs “ter ouvido falar do ensino problematizador” vs “o estudante ter direito de trazer seus conhecimentos”, pode-se constatar que a maior parte dos docentes inquiridos já ouviu falar sobre o sistema problematizador o que representa um nível satisfatório, apesar de não completo por existir uma minoria que ainda não ouviu, apontando a prevalência do ensino bancário na instituição, um sistema de ensino e aprendizagem que vê o aluno como uma caixa vazia, apenas um receptáculo Freire (2001a). A recomendação, porém, é que apesar de todos os desafios, a problematização deve ser exigida às instituições do ensino superior, criando condições de interação aluno-professor, e a comunidade donde ambos brotam, como o pilar da construção do conhecimento científico de qualidade em conformidade com as metas da Agenda 2030. (shrink)

I consider backtracking reasoning: that is, reasoning from backtracking counterfactuals such as if Hitler had won the war, he would have invaded Russia six weeks earlier. Backtracking counterfactuals often strike us as true. Despite that, reasoning from them just as often strikes us as illegitimate. A number of diagnoses have been offered of the illegitimacy of such backtracking reasoning which invoke the fixity of the past, or the direction of causation. I argue against such diagnoses, and in favor of one (...) that invokes a principle I call the fixity of reasons. Backtracking reasoning violates the fixity of reasons. But, the fixity of reasons is a principle that must be observed in order to engage in practical reasoning at all. (shrink)

RESENHA: MENEZES, Sezinando Luiz. Antônio Vieira : o império do outro mundo e o império deste mundo. Maringá: Eduem, 2015, 131p.

The role of this article is to present a historical analysis of how the expropriation occurred and concentration of land in Brazil it has been since the arrival of the colonists to the present day. Evaluate how this event influenced, as a rule, expulsion and enslavement of indigenous peoples in their own lands, the enslavement of black Africans, in the Brazilian rural exodus, the swelling of the cities in recent decades; hunger in the field, the shortage of food commodities in (...) the cities and in the present family farming underdevelopment of the country as a whole and its consequent and continuous concentration in a few hands "the Brazilian agrarian oligarchy" preventing the implementation of agrarian reform and land distribution for families and landless farmers. (shrink)

O objetivo do trabalho consiste em apresentar o modelo libertário de educação como um encontro entre a liberdade e a responsabilidade. Para tanto, usou-se o método hermenêutico, que permitiu uma análise das interfaces entre a Pedagogia do Oprimido de Paulo Freire e o Princípio da Responsabilidade de Hans Jonas. O método dialético permitiu um diálogo entre os dois modelos, investigando as relações entre a liberdade e a responsabilidade. Essas relações entre os dois modelos surge do fato de que não se (...) pode pensar numa liberdade sem responsabilidade. Assim, a partir da responsabilidade, é possível pensar numa liberdade consciente que permite ao professor alcançar os objetivos pedagógicos estabelecidos na Agenda 2030 da ONU para o Desenvolvimento Sustentável. (shrink)