The main objective of the article is to understand the notion of power in Foucault as an action on action in a relationship of forces. In principle, the power of sovereignty and biopower in classical times are investigated. Where it is perceived that the former has negative and repressive connotations, while this one has positive and productive connotations of facts, happenings. Then, an analysis of Foucault's power is analyzed, where it is possible to verify that there is no construction of (...) a Theory of Power in Foucault, but only an ascending analysis of power, thus departing from specificity for general aspects. Finally, we will analyze the power relationship, seen as an action over action, in this action-reaction movement, there is its need, its becoming, its truth, which is the exercise of power, functioning. Thus, from the molecular to the complex composition, from the invisible to the visible, from the body to the population, power is understood, that is, power relations in the Foucaultian web. (shrink)

The title of the paper is an allusion to Philip K. Dick’s book Do Androids Dream of Electric Sheep? (which inspired the movie Blade Runner) and aims, at once, to highlight the (possible) relation between Criminal Law and Artificial Intelligence in its two dimensions of criminal protection (hence the reference to ‘electric crimes’) and criminal liability (hence the reference to the androids’ dreams), within the background problem of knowing whether Artificial Intelligence is truly mind. The purpose of this paper is, (...) precisely, to identify whether there is indeed such relation, in those two dimensions, and making use of a mediating concept, the concept of ‘mind (or ‘mentality’). I argue that Artificial Intelligence “specimens” do not have a mind and, therefore, its protection and regulation by Criminal Law is impaired. I conclude by presenting a choice between a total irrelevance model of Artificial Intelligence to Criminal Law and a model in which Artificial Intelligence emerges as object and subject of Criminal Law by analogy with persons. (shrink)

The clarification of the relation between norm and value was historically one of the main philosophical concerns of the phenomenological current of the movement known as Philosophy of Values. One of its major characters, Nicolai Hartrnann, in his bookEthik, argues in favor of almost identifying one with the other. For him, the “ideal ought-to-be” (the one indifferent to the way reality is) already belongs to the nature of values, since they have an inherent tendency towards reality. In this communication, I’ll (...) criticize this thesis based on the meaning of the concepts involved. (shrink)

Porventura, o principal problema a enfrentar em Filosofia Normativa é aquele que designarei de ‘problema da compatibilidade’: as normas têm duas características essenciais, a necessidade e a violabilidade, que parecem ser incompatíveis. De acordo com a primeira das características intrínsecas das normas, se p é obrigatório, então p tem de ser verdadeira. De acordo com a segunda das características intrínsecas das normas, mesmo sendo p obrigatório, p pode não ser verdadeira. A capacidade para acomodar esta aparente natureza paradoxal das normas (...) constitui o teste derradeiro de verdade de uma tese em Filosofia Normativa. Defendo que só uma tese passa este teste: a semântica condicional, fortemente inspirada no que Husserl diz nas Investigações Lógicas. Esta tese rivaliza directamente com a semântica dos mundos ideais, surgida a par do desenvolvimento da Lógica Deôntica no século XX. Para a semântica dos mundos ideais, ‘p é obrigatório’ significa ‘p é uma verdade em todos os mundos possíveis que são os ideais’. Como o mundo atual não é um mundo ideal, fica explicado o facto de p poder não ser verdadeira no mundo atual, mesmo havendo necessidade. E se o mundo atual for um mundo ideal? Continua a não haver violabilidade: a verdade de ‘p é obrigatório’ no mundo atual garante a verdade de ‘p’ no mundo atual. Seguindo a semântica dos mundos ideais, as normas são invioláveis em todos os mundos ideais. Nesta dissertação, defendo que o termo ‘necessário’ é ambíguo e que, no contexto normativo, é usado de um modo particular: não designa o conceito modal de necessidade mas o conceito de indispensabilidade. Dizer que p é normativamente necessário é o mesmo que dizer que p é indispensável (para alguma coisa). Ora, é possível que ‘p’ seja indispensável e falsa simultaneamente. (shrink)

Regarding the selection of the legislative representatives, the elective system is the system that most democratic organizations have adopted. It has become so present nowadays that we take for granted the identification between elective system and representative democracy. But is this identification a correct one? I argue that it is not, since the meaning of 'representative democracy' has no reference to specific mode of selection of the representatives. And, since democracy and other methods of selection are compatible, it should adopted (...) the best one. The criteria of competence for the exercise of the political power ought to be the adopted method of selection, for it is the best one. I too argue that, in the context of division of labor into public and private labor, this is precisely what public representation aims: to leave to the experts the exercise of public labor. (shrink)

I present and discuss in this paper Husserl’s investigation of the genesis of the modem conception of empirical reality as carried out in his last work The Crisis of European Sciences and Transcendental Phenomenology. The goal of Husserl’s genetic investigation was to uncover the rnany layers of constitution that frorn the life-world (the Lebenswelt) the modem scientific conception of Nature was originated and to point out the need to ground the scientific project of rnodemity in the life-world so as to (...) overcome the “alienation” that, for him, characterized the “crisis” of European science. I, however, approach his analyses from a different perspective. The problem that interests me here is the applicability of mathematics in the empirical science. My airn is to assess Husserl’s treatment of this question in order to see whether it can be sustained from a strictly scientific perspective. My conclusion is that it cannot. What Husserl takes for the “crisis” of science is inherent to the best scientific methodology. Nonetheless, Husserl’s analyses offer irnportant insights that I incorporate in what I believe to be a more satisfactory treatment of the problern concerning the role of mathematics in the ernpirical science. (shrink)

I here present and discuss Husserl’s clarification of the genesis of modern empirical science, particularly its mathematical methods, as presented in his last work, The Crisis of European Sciences and Transcendental Phenomenology. Although Husserl’s analyses have as their goal to redirect science to the lifeworld and to reposition man and his immediate experiences at the foundation of the scientific project so as to overcome the “crisis” of science, I approach them from a different perspective. The problem that interests me here (...) is the applicability of mathematics in empirical science, to assess Husserl’s treatment of this issue in order to see if it can be sustained from a strictly scientific point of view regardless of philosophical adequacy. My conclusion is that it cannot. What Husserl takes as the “crisis” of science is inherent to the best scientific methodology. (shrink)

It is a philosophical naiveté to believe that the object of science is some ready-made world out there that the scientist, free of any preconceptions, simply stumbles upon. Of course, there is a world out there, given to us through the senses, but that must be intentionally elaborated to become a world for us and a possible object of scientific inquiry. The intentional constitution of the world of science supports and “justifies” a priori conceptions about the empirical world, even those (...) of a logical nature, that are, then, properly transcendental rather than metaphysical. My goal here is to investigate what these presuppositions are and on what they are based. (shrink)

This article intends to explore the philosophical potency in the work of the black writer Carolina Maria de Jesus (1914-1977). Carolina de Jesus is best known for her work Quarto de Despejo, diary of a favelada (1960), our approach, however, focuses specifically on her short story “Socrates Africano”, in which she deals with her experience with her grandfather Benedito and the relationship between her wisdom and that of the Greek philosopher Sócrates (5th century BC). Her reflection starts from the attempt (...) to understand the reason why her grandfather was compared to Socrates and called “African Socrates”. In this sense, we intend to expand the idea of an African Socrates and the origins of one of the African philosophical matrices, the Yoruba tradition, dialoguing with the thought of the Nigerian philosopher Sophie Oluwole (1935-2018) and her approximation between Socrates and Orunmilá, as a motto to think about the philosophical potentialities of Carolina's work and the traits of an Afro-Brazilian philosophy. (shrink)

This monograph offers a fresh perspective on the applicability of mathematics in science. It explores what mathematics must be so that its applications to the empirical world do not constitute a mystery. In the process, readers are presented with a new version of mathematical structuralism. The author details a philosophy of mathematics in which the problem of its applicability, particularly in physics, in all its forms can be explained and justified. Chapters cover: mathematics as a formal science, mathematical ontology: what (...) does it mean to exist, mathematical structures: what are they and how do we know them, how different layers of mathematical structuring relate to each other and to perceptual structures, and how to use mathematics to find out how the world is. The book simultaneously develops along two lines, both inspired and enlightened by Edmund Husserl’s phenomenological philosophy. One line leads to the establishment of a particular version of mathematical structuralism, free of “naturalist” and empiricist bias. The other leads to a logical-epistemological explanation and justification of the applicability of mathematics carried out within a unique structuralist perspective. This second line points to the “unreasonable” effectiveness of mathematics in physics as a means of representation, a tool, and a source of not always logically justified but useful and effective heuristic strategies. (shrink)

In the first year of the twentieth century, in Gottingen, Husserl delivered two talks dealing with a problem that proved central in his philosophical development, that of imaginary elements in mathematics. In order to solve this problem Husserl introduced a logical notion, called “definiteness”, and variants of it, that are somehow related, he claimed, to Hilbert’s notions of completeness. Many different interpretations of what precisely Husserl meant by this notion, and its relations with Hilbert’s ones, have been proposed, but no (...) consensus has been reached. In this paper I approach this question afresh and thoroughly, taking into consideration not only the relevant texts and context, as others have also done before, but, more importantly, Husserl’s philosophy, his intuition-based epistemology in particular. Based on a system of clearly defined concepts that I here present, I reinforce an interpretation—definiteness as a form of syntactic completeness—that has, I believe, some advantages vis-à-vis alternative interpretations. It is in conformity with the available texts; it makes clear that Husserl’s notion of definiteness is indeed close to Hilbert’s notions of completeness; it solves the important problem of imaginaries for which it was created; and last, but not least, it fits naturally into Husserl’s system of concepts and ideas. (shrink)

In the first year of the twentieth century, in Gottingen, Husserl delivered two talks dealing with a problem that proved central in his philosophical development, that of imaginary elements in mathematics. In order to solve this problem Husserl introduced a logical notion, called “definiteness”, and variants of it, that are somehow related, he claimed, to Hilbert’s notions of completeness. Many different interpretations of what precisely Husserl meant by this notion, and its relations with Hilbert’s ones, have been proposed, but no (...) consensus has been reached. In this paper I approach this question afresh and thoroughly, taking into consideration not only the relevant texts and context, as others have also done before, but, more importantly, Husserl’s philosophy, his intuition-based epistemology in particular. Based on a system of clearly defined concepts that I here present, I reinforce an interpretation—definiteness as a form of syntactic completeness—that has, I believe, some advantages vis-à-vis alternative interpretations. It is in conformity with the available texts; it makes clear that Husserl’s notion of definiteness is indeed close to Hilbert’s notions of completeness; it solves the important problem of imaginaries for which it was created; and last, but not least, it fits naturally into Husserl’s system of concepts and ideas. (shrink)

In this paper I discuss Husserl's solution of the problem of imaginary elements in mathematics as presented in the drafts for two lectures hegave in Göttingen in 1901 and other related texts of the same period,a problem that had occupied Husserl since the beginning of 1890, whenhe was planning a never published sequel to Philosophie der Arithmetik(1891). In order to solve the problem of imaginary entities Husserl introduced,independently of Hilbert, two notions of completeness (definiteness in Husserl'sterminology) for a formal axiomatic (...) system. I present and discuss these notionshere, establishing also parallels between Husserl's and Hilbert's notions ofcompleteness. (shrink)

For different reasons, Husserl's original, thought-provoking ideas on the philosophy of logic and mathematics have been ignored, misunderstood, even despised, by analytic philosophers and phenomenologists alike, who have been content to barricade themselves behind walls of ideological prejudices. Yet, for several decades, Husserl was almost continuously in close professional and personal contact with those who created, reshaped and revolutionized 20th century philosophy of mathematics, logic, science and language in both the analytic and phenomenological schools, people whom those other makers of (...) 20th century philosophy, Russell, Frege, Wittgenstein and their followers, rarely, if ever, met. Independently of them, Husserl offered alternatives to the well-trodden paths of logicism, nominalism, formalism and intuitionism. He presented a well-articulated, thoroughly argued case for logic as an objective science, but was not philosophically naive to the point of not seeing the role of subjectivity in shaping the sense of the reality facing objective science. Given the preeminent role that philosophy of logic and philosophy of mathematics have played in transforming the way philosophy has been done since Husserl's time, and given the depth of his insights and his obvious expertise in those fields, his ideas need to be integrated into present-day, mainstream philosophy. Here, philosopher Claire Ortiz Hill and mathematician-philosopher Jairo da Silva offer a wealth of interesting insights intended to subvert the many mistaken idees recues about the development of Husserl's thought and reestablish broken ties between it and philosophy now. (shrink)

En este artículo realizamos una reconstrucción del Programa original de Hilbert antes del surgimiento de los teoremas limitativos de la tercera década del siglo pasado. Para tal reconstrucción empezaremos por mostrar lo que Torretti llama los primeros titubeos formales de Hilbert, es decir, la defensa por el método axiomático como enfoque fundamentante. Seguidamente, mostraremos como estos titubeos formales se establecen como un verdadero programa de investigación lógico-matemático y como dentro de dicho programa la inquietud por la decidibilidad de los problemas (...) matemáticos y en específico la decidibilidad de la Lógica de primer orden cobra peso. Luego pasamos a analizar como la inquietud por la decibilidad toma lugar dentro del pensamiento filosófico-matemático de Hilbert presentándose como uno de los grandes problemas a los cuales la metamatemática debe encontrar una solución, esto lo hacemos mostrando un contraste con autores, como John von Neumann y Roberto Torretti, quienes de alguna u otra manera no interpretan el problema de la decidibilidad de la Lógica de primer orden como un problema de peso dentro del programa original de Hilbert. Finalmente argumentamos que el resultado meta-teórico de Church puede entenderse como una refutación del optimismo intelectual que permea a todo el programa original de Hilbert. (shrink)

This book addresses the European Court of Human Rights’ fairness standards in criminal appeal, filling a gap in this less researched area of studies. Based on a fair trial immediacy requirement, the Court has found several violations of Article 6 of the European Convention on Human Rights at the appellate level by at least eighteen States of the Council of Europe in a vast array of cases, particularly in contexts of first instance acquittals overturning and of sentences increasing on appeal. (...) -/- On the one hand, the book critically engages this case-law with the law revisions it has recently inspired in European countries, as well as with the critiques and difficulties that it continues to raise. On the other hand, it interweaves insight from criminal procedure theory with new discoveries in the field of cognitive sciences (neuroscience of memory, philosophy of knowledge, AI), shedding an interdisciplinary light on the (in)adequacy and limits of the Strasbourg Court’s jurisprudence. (shrink)

A partir dos problemas colocados ao pensamento na contemporaneidade pelas discussões acerca do Antropoceno, o ensaio propõe uma investigação sobre a possibilidade de uma nova relação da filosofia com a poesia. Para isso, a sugestão do líder indígena e pensador Ailton Krenak de manutenção de “nossas visões, nossas poéticas sobre a existência” é articulada com a filosofia da diferença de Gilles Deleuze, cujos esforços para realizar a gênese de um pensamento sem imagem pressuposta, e a sua concepção de uma natureza (...) poética da diferença, são mobilizados na tentativa de pensar e efetuar uma relação outra da filosofia com a poesia. O texto propõe o conceito de cosmopoética para definir a condição de efetuação dessa relação, e procura exemplificar sua manifestação nas obras de Antonin Artaud e de Roberto Piva, nas quais, de maneiras distintas, e em gérmen, são constatados rastros expressivos da natureza poética e selvagem da diferença. Por fim, conjectura-se que a cosmopoética pode ser pensada no campo de uma estética do devir e, quiçá, articulada a enunciações e ações cosmopolíticas coletivas de pensadores e pensadoras que se ocupam em pensar e resistir à catástrofe socioambiental em curso.Palavras-Chave: Antropoceno; Filosofia da Diferença; Poesia; Cosmopoética. (shrink)

Agostinho ocupa um papel importante como ponte entre a filosofia antiga e a Idade Média. Sobre Aristóteles, mostrou conhecer as obras Categorias, Tópicos e Da interpretação, traduzidas por Mário Vitorino. Não obstante isso, Agostinho faz uso muito mais intenso da filosofia de Platão e de Plotino. Assim, este pensador cristão considerou possível conciliar preocupação cristã com reflexão filosófica a partir da tradição grega, bastando somente, neste processo, a realização de algumas correções. Deste modo, apresenta-se a forma como Agostinho incorporou a (...) reflexão grega e conciliou razão e fé. (shrink)

The following note has on purpose to introduce interested students to logicism. Our objective is not to show any new interpretation or thesis about logicism or its rebirth between the 60s and 80s of the last century. What we will do is systematically show the evolution of logicism from Frege to Russell-Whitehead, with greater emphasis on this latest development, and approach some problems that arise within that movement, for example: The logical paradoxes and the principle of intuitive comprehension, the impredicative (...) definitions and the semantic paradoxes, the Ramified Hierarchy and real numbers, the axiom of reducibility and the impossibility of reducing mathematics to logic, etc. (shrink)

Hacia finales del siglo XIX se llevó a cabo una gran revolución conceptual y metodológica en la matemática. En tal revolución se empezaron a emplear conceptos, métodos y técnicas que dejaban de lado la antigua forma de hacer matemática, propia del siglo XVIII y principios del siglo XIX, y a su vez proponían un Hacer abstracto, es decir, una forma abstracta de ocuparse del ente matemático. Pero no sólo se trataba de un cambio metodológico, sino que la pregunta por los (...) fundamentos se vuelve cada vez más importante y trae consigo interrogantes de carácter filosófico, como es el caso de la inquietud por la naturaleza del objeto matemático (la interrogante ontológica), y la posibilidad de conocimiento de dicho objeto (la interrogante epistemológica). Nuestro interés en este artículo es mostrar cómo la filosofía que respalda las investigaciones matemáticas de Cantor trata de dar respuestas a las interrogantes ontológicas y epistemológicas. Para ello hemos tratado de ofrecer un contexto histórico-conceptual que gira en torno a la pregunta por los fundamentos, y dentro de dicho contexto hemos señalado como se presenta el Platonismo absoluto de Cantor An approach to Cantor´s absolute PlatonismA great conceptual and methodological revolution in mathematics was carried out by the end of nineteen century. In that revolution people began to use concepts, methods and techniques which set aside the old way of doing mathematics, typical of the eighteenth and early nineteenth century, and in turn they proposed an Abstract Make, i.e., an abstract form of dealing with the mathematical entity. But it was not only a methodological change, but the question of the foundations is becoming increasingly important which arises more philosophical questions, such as the concern about the nature of the mathematical object -the ontological question- and the possibility of knowledge of this object -the epistemological question. Our interest in this article is to show how the philosophy behind Cantor's mathematical research is intended to answer the ontological and epistemological questions. For it, this paper tries to provide a conceptual and historical context, which is revolving around the question of the foundations, and within this context, it is noted as the Absolute Platonism of Cantor. (shrink)

The turbulent times we live in, product of the COVID-19 pandemic, creating an ideal breeding ground for the proliferation of myths and conspiracy theories. These myths and theories are often popular on social media, defended by irresponsible politicians and published by the media in search of ratings or likes. But none of these meet the theoretical virtues that a good scientific theory should enjoy, in particular, none of these conspiracy theories about the disease caused by the SARS CoV-2 virus has (...) the attribute of being simple. Our purpose in this article is to illuminate how it is possible that simplicity, within the framework of theoretical virtues, can function as an epistemic criterion to reveal the irrational and, consequently, unscientific nature of myths and conspiracy theories. (shrink)

In this paper I discuss the version of predicative analysis put forward by Hermann Weyl in Das Kontinuum. I try to establish how much of the underlying motivation for Weyl's position may be due to his acceptance of a phenomenological philosophical perspective. More specifically, I analyze Weyl's philosophical ideas in connexion with the work of Husserl, in particular Logische Untersuchungen} and Ideen.I believe that this interpretation of Weyl can clarify the views on mathematical existence and mathematical intuition which are implicit (...) in Das Kontinuum. (shrink)

Husserl left many unpublished drafts explaining (or trying to) his views on spatial representation and geometry, such as, particularly, those collected in the second part of Studien zur Arithmetik und Geometrie (Hua XXI), but no completely articulate work on the subject. In this paper, I put forward an interpretation of what those views might have been. Husserl, I claim, distinguished among different conceptions of space, the space of perception (constituted from sensorial data by intentionally motivated psychic functions), that of physical (...) geometry (or idealized perceptual space), the space of the mathematical science of physical nature (in which science, not only raw perception has a word) and the abstract spaces of mathematics (free creations of the mathematical mind), each of them with its peculiar geometrical structure. Perceptual space is proto-Euclidean and the space of physical geometry Euclidean, but mathematical physics, Husserl allowed, may find it convenient to represent physical space with a non-Euclidean structure. Mathematical spaces, on their turn, can be endowed, he thinks, with any geometry mathematicians may find interesting. Many other related questions are addressed here, in particular those concerning the a priori or a posteriori character of the many geometric features of perceptual space (bearing in mind that there are at least two different notions of a priori in Husserl, which we may call the conceptual and the transcendental a priori). I conclude with an overview of Weyl’s ideas on the matter, since his philosophical conceptions are often traceable back to his former master, Husserl. (shrink)

I discuss here the pragmatic problem in the philosophy of mathematics, that is, the applicability of mathematics, particularly in empirical science, in its many variants. My point of depart is that all sciences are formal, descriptions of formal-structural properties instantiated in their domain of interest regardless of their material specificity. It is, then, possible and methodologically justified as far as science is concerned to substitute scientific domains proper by whatever domains —mathematical domains in particular— whose formal structures bear relevant formal (...) similarities with them. I also discuss the consequences to the ontology of mathematics and empirical science of this structuralist approach. (shrink)

I discuss here the pragmatic problem in the philosophy of mathematics, that is, the applicability of mathematics, particularly in empirical science, in its many variants. My point of depart is that all sciences are formal, descriptions of formal-structural properties instantiated in their domain of interest regardless of their material specificity. It is, then, possible and methodologically justified as far as science is concerned to substitute scientific domains proper by whatever domains —mathematical domains in particular— whose formal structures bear relevant formal (...) similarities with them. I also discuss the consequences to the ontology of mathematics and empirical science of this structuralist approach. (shrink)

HIPERCONSUMO E COISIFICAÇÃO DA NATUREZA: A ÉTICA DO DECRESCIMENTO NO COMBATE AO DESPERDÍCIO DE ALIMENTOS.

Este ensaio discute porque o tema da metáfora, ao elucidar a compreensão davidsoniana de "significado literal", "interpretação", "convenção", "intencionalidade" e "competência semântica", pode servir com um breviário à filosofia pragmatista da linguagem e do conhecimento. -/- This article discusses why the theme of metaphor, understanding the davidsonian comprension of "literal meaning", "interpretation", "intentionality" and "semantic competence" can serves like and introduction to the pragmatic philosophy of language and knowledge.

Neste artigo, relato os aspectos mais salientes do affair Sokal-Bricmont - uma paródia que evoluiu para uma crítica articulada dos excessos de um certo pensamento pós-modernista - e analiso algumas das reações que suscitou em artigos publicados na Folha de S. Paulo. Termino com algumas reflexões sobre a nefasta negligência para com as ciências exatas na educação em geral e, em particular, na formação dos profissionais das áreas de filosofia e ciências humanas.In this paper I summarize some of the most (...) relevant aspects of the so-called Sokal and Bricmont affair - a parody that evolved to a full-fledged criticism of the excesses of post-modernism - and analyze the reactions it elicited in some articles published in Folha de São Paulo. I close with a reflection on the unfortunate neglect of the exact sciences in education in general and, in particular, the education of philosophers and social scientists. (shrink)

In this paper I show the possibility of an ontology of mathematics that keeps some points in common with platonism and constructivism while diverging from them in other essencial ones. I understand that mathematical objects are simply the referential focus of mathematical discourse, I also understand that their existence is merely intentional but none the less objective, in the sense of being shared by all those who are engaged in the mathematical activity. However, the objective existence of mathematical entities is (...) not secured once and for all but only in so far as the mathematical discourse is consistent. This is the core of the criterium of objective existence put forward and that I believe should sustain a mathematical ontology without the presupposition of the independent existence of a domain of mathematical objects, and without the restrictions imposed on it by constructivism and formalism in their various versions.Neste artigo quero apontar para a possibilidade de uma ontologia da matemática que, mesmo mantendo alguns pontos em comum com o platonismo e com o construtivismo, desliga-se destes em outros pontos essenciais. Por objeto matemático entendo o foco referencial do discurso matemático, ou seja, aquilo sobre o qual a matemática fala. Entendo que a existência destes objetos é meramente intencional, presuntiva, mas, simultaneamente, objetiva, no sentido de ser uma existência comunalizada, compartilhada por todos aqueles engajados no fazer matemático. A existência objetiva das entidades matemáticas não está, entretanto, garantida de uma vez por todas, mas apenas enquanto o discurso matemático for consistente. Este é o espírito do critério de existência objetiva enunciado que, acredito, deve sustentar uma ontologia matemática sem o pressuposto da existência independente de um domínio de objetos matemáticos, sem o empobrecimento que lhe impõem as diferentes versões construtivistas e sem a aniquilação que lhe infringe o formalismo sem objetos. (shrink)

Este artigo procura mostrar que as idéias filosóficas de Husserl não apenas influenciaram o trabalho de alguns dos maiores matemáticos do século XX, mas foram decisivas para aproximarem uma epistemologia das ciências formais de uma fenomenologia do significado.

In this paper I argue for the view that structuralism offers the best perspective for an acceptable account of the applicability of mathematics in the empirical sciences. Structuralism, as I understand it, is the view that mathematics is not the science of a particular type of objects, but of structural properties of arbitrary domains of entities, regardless of whether they are actually existing, merely presupposed or only intentionally intended.

In this paper I argue for the view that the axioms of ZF are analytic truths of a particular concept of set. By this I mean that these axioms are true by virtue only of the meaning attached to this concept, and, moreover, can be derived from it. Although I assume that the object of ZF is a concept of set, I refrain from asserting either its independent existence, or its dependence on subjectivity. All I presuppose is that this concept (...) is given to us with a certain sense as the objective focus of a phenomenologically reduced intentional experience. The concept of set that ZF describes, I claim, is that of a multiplicity of coexisting elements that can, as a consequence, be a member of another multiplicity. A set is conceived as a quantitatively determined collection of objects that is, by necessity, ontologically dependent on its elements, which, on the other hand, must exist independently of it. A close scrutiny of the essential characters of this conception seems to be sufficient to ground the set-theoretic hierarchy and the axioms of ZF. (shrink)

In this paper I argue for the view that the axioms of ZF are analytic truths of a particular concept of set. By this I mean that these axioms are true by virtue only of the meaning attached to this concept, and, moreover, can be derived from it. Although I assume that the object of ZF is a concept of set, I refrain from asserting either its independent existence, or its dependence on subjectivity. All I presuppose is that this concept (...) is given to us with a certain sense as the objective focus of a ”phenomenologically reduced“ intentional experience.The concept of set that ZF describes, I claim, is that of a multiplicity of coexisting elements that can, as a consequence, be a member of another multiplicity. A set is conceived as a quantitatively determined collection of objects that is, by necessity, ontologically dependent on its elements, which, on the other hand, must exist independently of it. A close scrutiny of the essential characters of this conception seems to be sufficient to ground the set-theoretic hierarchy and the axioms of ZF. (shrink)

O estudo dos fatos e episódios científicos é importante no sentido de possibilitar a compreensão do desenvolvimento das Ciências em contextos tanto do ensino, em diversos níveis, quanto da pesquisa. No entanto, a leitura dessa construção histórica precisa considerar visões de Ciência que superem as perspectivas lineares e neutras sobre a construção do processo de produção científica. Sob tal perspectiva, propõe-se nesse artigo uma releitura do movimento de elaboração do modelo da dupla hélice do DNA a partir do aporte epistemológico (...) de Thomas Kuhn. Entendemos ser este um contexto importante que permeia a formação científica, tanto na educação básica quanto no ensino superior, no campo das Ciências Biológicas e que os conceitos desenvolvidos a partir da elaboração do modelo da dupla hélice são basilares para a compreensão de conhecimentos relacionados à genética, citologia, evolução, dentre outros. No processo de revisitar esse recorte histórico, identificamos os embates teóricos entre pesquisadores de diversos campos, a competição e o consenso como elementos que mobilizam a busca de respostas na concretização de um novo paradigma. Dessa forma, a dinamicidade da Ciência se mostra presente rejeitando a ideia do dado pronto e valorizando o processo no qual o conhecimento se constrói. Propomos que este seja um exercício de reflexão considerando-se que revisitar a história da Ciência a partir de diferentes perspectivas epistemológicas pode propiciar aos sujeitos novos olhares em um devir que descortine conceitos construídos de maneira dinâmica por homens e mulheres que, entre ires e vires, dão significado aos fenômenos que nos rodeiam. Palavras-chave: DNA, Thomas Kuhn, ciência normal, revolução científica. (shrink)

The fascination with the process inherent to understanding has always been something that has disturbed Philosophy with its question: what makes understanding possible? On the contrary, little attention has been paid to the use we make of this term. This took it out of its context and investigated it as related to a mental process, situated in the subject. This approach generated some questions, among them: if understanding and the processes involved in it take place in the mind, how can (...) one have access to them? How do you know what’s on the other’s mind? This text intends to present the role played, both by the verb meinen (to mean), in its disconnection with mental processes, in terms of its grammar, and by the expression lebensform (form of life), in Philosophical Investigations, as a condition in which, both the meinen has its most authentic use, as well as the background that makes it possible to understand the Investigations as a whole. (shrink)

Este artigo tem o objetivo de identificar em primeiro lugar o desdobramento da racionalidade nos mitos ao tempo em que surgem as cidades como novas formas de agrupamento social. Em seguida, analisar a formulação do conceito de justiça como estrutura ideal para a consolidação da República, considerando, em decorrência disto, a demanda por uma reforma educacional que se daria a partir da crítica filosófica à figura do poeta como representante onisciente do saber cuja linguagem ambivalente a distanciava do referencial de (...) verdade segundo Platão. Nesse entendimento, recorreremos aos estudos em autores como Vernant, Havelock, Matos e outros autores que poderão contribuir para a compreensão sobre os conceitos de política e estética em Platão. O presente artigo poderá servir de auxílio nas pesquisas cujo campo de análise se identifique especificamente com a educação, política, ética e estética, sem, contudo, pretender encerrar o debate concernente ao tema proposto. Palavras-chave: Poetas; República; Justiça; Linguagem; Verdade. (shrink)