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.

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.

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)

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.

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.

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

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)

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 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.

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)

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.

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)

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 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.

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.

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)

The works of the early Greek philosophers are not only a fundamental source for understanding archaic Greek culture and the whole of ancient philosophy, but also a perennially fresh resource that has stimulated Western thought until the present day. This nine-volume edition presents all the major fragments from the sixth to the fourth centuries BC.

During the past decade, a small but rapidly growing number of Law&Tech scholars have been applying algorithmic methods in their legal research. This Article does it too, for the sake of saving disclosure regulation failure: a normative strategy that has long been considered dead by legal scholars, but conspicuously abused by rule-makers. Existing proposals to revive disclosure duties, however, either focus on the industry policies (e.g. seeking to reduce consumers’ costs of reading) or on rulemaking (e.g. by simplifying linguistic intricacies). (...) But failure may well depend on both. Therefore, this Article develops a `comprehensive approach', suggesting to use computational tools to cope with linguistic and behavioral failures at both the enactment and implementation phases of disclosure duties, thus filling a void in the Law & Tech scholarship. Specifically, it outlines how algorithmic tools can be used in a holistic manner to address the many failures of disclosures from the rulemaking in parliament to consumer screens. It suggests a multi-layered design where lawmakers deploy three tools in order to produce optimal disclosure rules: machine learning, natural language processing, and behavioral experimentation through regulatory sandboxes. To clarify how and why these tasks should be performed, disclosures in the contexts of online contract terms and privacy online are taken as examples. Because algorithmic rulemaking is frequently met with well-justified skepticism, problems of its compatibility with legitimacy, efficacy and proportionality are also discussed. (shrink)

It is held by many philosophers that it is a consequence of epistemic contextualism that speakers are typically semantically blind, that is, typically unaware of the propositions semantically expressed by knowledge attributions. In his ?Contextualism, Invariantism and Semantic Blindness? (this journal, 2009), Martin Montminy argues that semantic blindness is widespread in language, and not restricted to knowledge attributions, so it should not be considered problematic. I will argue that Montminy might be right about this, but that contextualists still face a (...) serious and related problem: that it is a consequence of epistemic contextualism that subjects are typically unaware of contents conveyed by knowledge attributions, independently of whether these are semantic or non-semantic contents. Even if semantic blindness is widespread in language, it does not seem that content unawareness of this sort is. (shrink)

In a recent paper, Erasmus et al. (2021) defend the idea that the ambiguity of the term “explanation” in explainable AI (XAI) can be solved by adopting any of four different extant accounts of explanation in the philosophy of science: the Deductive Nomological, Inductive Statistical, Causal Mechanical, and New Mechanist models. In this chapter, I show that the authors’ claim that these accounts can be applied to deep neural networks as they would to any natural phenomenon is mistaken. I also (...) provide a more general argument as to why the notion of explainability as it is currently used in the XAI literature bears little resemblance to the traditional concept of scientific explanation. It would be more fruitful to use the label “understandable AI” to avoid the confusion that surrounds the goal and purposes of XAI. In the second half of the chapter, I argue for a pragmatic conception of understanding that is better suited to play the central role attributed to explanation in XAI. Following De Regt (2017) and Kuorikoski and Ylikoski (2015), the conditions of satisfaction for understanding an ML system are fleshed out in terms of an agent’s success in using the system. (shrink)

O artigo se propõe a uma investigação da potência filosófica presente na poesia japonesa clássica conhecida como waka. O aspecto formal mais proeminente do waka é a sua curta estrutura composta geralmente de 31 sílabas moraicas divididas, respectivamente, em 5 versos de 5, 7, 5, 7 e 7 sílabas cada. Para erguer-se como uma forma poética, o waka emprega o recurso rítmico da pausa e uma retórica que vinculam cada poema individual ao todo da tradição através de precedentes. Defendemos que (...) na tradição intelectual constituída pelo waka há uma filosofia do real – que denominamos intertextualidade do real – que entende a realidade como vazia e impermanente. Dessa forma, seria o waka a forma mais adequada através da qual exprimir o real uma vez que ele é mais profundo e excelente a medida em que cria um movimento de esvaziamento e tornar impermanente através de seus recursos formais e retóricos: seu cerne, sua disposição e significado e suas palavras. (shrink)

Rendre hommage à un auteur, ce n'est pas seulement célébrer ce qu'il fut mais c'est aussi alerter sur ce que son oeuvre apporte au présent et à l'avenir de la connaissance. C'est bien le sens donné à cet hommage à André-Jean Arnaud. Repenser le droit, c'était pou r cet auteur érudit : repenser les lieux, les conditions et les façons de l'étudier en dépassant les frontières géographiques en même temps que les frontières disciplinaires. En montrant en quoi André-Jean (...) Arnaud fut, hors des sentiers battus et des orthodoxies de la production et de la transmission des savoirs en la matière, un exceptionnel précurseur et l'infatigable artisan d'un nouveau régime de connaissance sur le droit, le présent ouvrage s'adresse à toutes celles et à tous ceux, enseignants, chercheurs, étudiants ou simples citoyens, pou r qui l'étude du droit permet de mieux comprendre ce que sont et ce que sont susceptibles de devenir nos sociétés. (shrink)

The philosophy problem of identity and the related problem of change go back to the ancient Greek philosophers and fascinated later figures including Leibniz, Locke and Hume. Heraclitus argued that one could not swim in the same river twice because new waters were ever flowing in. When is a river not the same river? If one removes one plank at a time when is a ship no longer a ship? What is the basic nature of identity and persistence? This book (...) introduces and asseses the philosophical puzzles posed by things persisting through time. Beginning with essential historical background to the problem it explores the following key topics and debates: mereology and identity, including 'Leibniz's Law' the constitution view of identity the 'relative identity' argument concerning identity temporary identity four-dimensionalism, counterpart and mulitiple counterpart theory supervenience the problem of temporary intrinsics the necessity of identity presentism ontological and epistemological criteria for persistence and the difference between them. Including chapter summaries, annotated further reading and a glossary this book is essential reading for anyone seeking a clear and informative introduction to and assessement of the metaphysics of identity. (shrink)

Recent attempts to develop and apply digital ethics principles to address the challenges of the digital transformation leave organisations with an operationalisation gap. To successfully implement such guidance, they must find ways to translate high-level ethics frameworks into practical methods and tools that match their specific workflows and needs. Here, we describe the development of a standardised risk assessment tool, the Principle-at-Risk Analysis (PaRA), as a means to close this operationalisation gap for a key level of the ethics infrastructure at (...) many organisations – the work of an interdisciplinary ethics panel. The PaRA tool serves to guide and harmonise the work of the Digital Ethics Advisory Panel at the multinational science and technology company Merck KGaA in alignment with the principles outlined in the company’s Code of Digital Ethics. We examine how such a tool can be used as part of a multifaceted approach to operationalise high-level principles at an organisational level and provide general requirements for its implementation. We showcase its application in an example case dealing with the comprehensibility of consent forms in a data-sharing context at Syntropy, a collaborative technology platform for clinical research. (shrink)

Mit seiner Theorie der vernünftigen Übereinkunft liefert André Olbrich die Grundlegung eines Kriteriums für moralische Urteile über richtig und falsch: Im Anschluss an klassische und moderne Vertragstheoretiker wird die Akzeptanz eines Urteils durch die Betroffenen zum obersten Rechtfertigungsmaßstab erhoben. Das vertragstheoretische Denken wird weiterentwickelt und konsequent als umfassende normative Theorie ausformuliert. Die Leserinnen und Leser erfahren, von welchem Standpunkt aus sich die Regeln unseres sozialen Miteinanders einer Kritik unterziehen lassen und auf welchen moralischen Grundlagen Recht und Politik aufbauen.

El uso de sistemas de machine learning en los procesos de selección laboral ha sido de gran utilidad para agilizarlos y volverlos más eficientes, pero al mismo tiempo ha generado problemas en términos de equidad, confiabilidad y transparencia. En este artículo comenzamos explicando los diferentes usos de la Inteligencia Artificial en los procesos de selección laboral en Estados Unidos. Presentamos los sesgos sexuales y raciales que han sido detectados en algunos de ellos y explicamos los obstáculos jurídicos y prácticos para (...) su detección y análisis. Un posible remedio jurídico a la discriminación algorítmica es el régimen de impacto diferencial sistémico utilizado en Estados Unidos. Usamos algunas características de este régimen para señalar los vacíos jurídicos frente a la discriminación en el acceso al empleo en el ámbito del derecho laboral colombiano, y ofrecemos algunas características generales que podría tener un régimen de esa naturaleza. (shrink)

Hegelians normally consider Hegel's philosophical system from two perspectives: metaphysics, interpreting this discipline as the central one to understand the work of the German philosopher, or non-metaphysics, being more relevant alternative interpretations that avoid it. This article presents a study on the senses of reflection. These senses can be extrinsic or absolute. These two senses are the backbones of the Hegelian system. Therefore, by means of a study of whether extrinsic and absolute reflection are notions that guide us towards metaphysical (...) or non-metaphysical readings, we try to give an answer to the debate between the possible interpretations of Hegel. (shrink)

Lo psíquico, que no la psicología como ciencia, es un tema poco tratado en la filosofía de Polo. En este escrito se busca dar explicación de qué es lo psíquico y cuál es su importancia. Se defiende que lo psíquico tiene dos condiciones reduccionistas implícitas que se constituyen a partir de la crisis de la filosofía de Hegel. La primera es creer que la realidad es reductible a la percepción individual. La segunda consiste en que el pensamiento ya esté determinado (...) preconceptualmente. (shrink)

André Tosel, décédé en mars 2017, était un philosophe engagé, attaché tout au long de son existence à faire vivre un marxisme critique puisant notamment dans le meilleur de la tradition italienne de ce courant de pensée ; il fut l'un des rares français à introduire et discuter les oeuvres majeures d'A. Labriola et surtout d'A. Gramsci, ainsi par ailleurs que celles de Vico dont il fut un fin connaisseur. Il consacra sa thèse de doctorat d'état aux rapports entre (...) religion, politique et philosophie chez Spinoza et contribua de façon décisive à de nouvelles lectures du philosophe en le mettant en miroir de Marx. Professeur de philosophie des universités de Besançon, Franche Comté, de Paris 1 Panthéon-Sorbonne et de Nice Sophia-Antipolis, dans lesquelles il occupa de nombreuses fonctions de directions administratives et scientifiques, il était un homme de collectif attaché à faire vivre le savoir, s'engageant dans la vie universitaire et politique, contribuant également de manière décisive au lancement et à l'animation de la revue Actuel Marx. Passionné par l'évolution des pensées contemporaines, il intervenait régulièrement dans des débats d'actualité, sous la forme de contributions dans L'Humanité ou dans des ouvrages destinés à un public large, tout particulièrement dans la dernière période sur les questions de sécularisation, de laïcité et de religion. Cet ouvrage entend lui rendre hommage en abordant les différentes facettes de son oeuvre, traversant un demi-siècle de vie intellectuelle. (shrink)

Diversität ist eines der zentralen Themen unserer Zeit. Sie durchdringt alle Lebensbereiche unserer Gesellschaften. Das Nachdenken über Diversität reicht von den Naturwissenschaften über die Geschichtswissenschaften, die Gesellschaftswissenschaften, die Philosophie bis zu den Künsten. Diversität ist zudem politisch und emotional beladen. Man denke an gesellschaftliche Minderheiten und ihre Rechte oder an das massive Artensterben unserer Tage. In diesem Buch wird nicht nur über Einzelaspekte von Diversität berichtet, es wird auch eine Synthese versucht. Drei einleitende Kapitel der HerausgeberInnen führen verständlich in komplexe (...) interdisziplinäre Problemzusammenhänge ein. Der Band versammelt 17 Beiträge namhafter Autorinnen und Autoren aus den Bereichen Kunst-, Kultur- und Wissenschaftsgeschichte, Medizin und Gesellschaftstheorie.00. (shrink)

La musique comme chemin d'existence et pour la penser... En effet, les moments d'intervention de la musique, de toutes les musiques, au fil des jours et au long de la vie ne manquent pas d'être signifiants. Ils instruisent autant sur la musique elle-même que sur la pensée et sur l'existence. Il serait prétentieux d'en produire une théorie générale. Toutefois, la voie de la chronique, jour après jour, aura tissé des fils permettant de s'attarder sur le sens, nécessairement ponctuel et subjectif (...) (chacun pourra substituer son écoute et ses pratiques propres), de l'Adieu en musique, des affinités qu'elle manifeste et peut-être révèle, de ses rapports avec telle image ou peinture, plus étonnamment avec la photographie, avec le son en général, la vérité ou encore le style. On verra aussi comment la musique s'entend dans le rêve et comment elle nous porte à considérer les animaux. Des oeuvres, des musiciens, et quelques philosophes et écrivains s'imposeront (Le Voyage d'Hiver, Le Boléro, Le Sacre du Printemps, Pelléas ; Haydn, Schubert, Mahler, Chostakovitch ; Descartes, Nietzsche, Adorno ; Goethe, Gerhard Meier, Sandor Maraï...). C'est pourtant davantage une vie dans la musique et par elle que la théorisation sur la musique qui inspire chacun des textes présentés ici. En s'efforçant de relever et de piquer leur objet, donc en le séparant et le thématisant staccato, peut-être la chance sera-t-elle donnée d'entrevoir l'existence dans sa continuité, legato. (shrink)

El pluralismo religioso trata de presentar lugares comunes en los que establecer diálogos entre diferentes religiones sin intención de persuadir. En esta investigación se aborda el pluralismo religioso en los periodos de Tubinga y Berna de Hegel. Esto es, en la filosofía del joven Hegel, periodo en el que se dedicó especialmente a la reflexión sobre la política y la religión. En este periodo, menos estudiado por la academia que su madurez, encontramos que hay al menos tres lugares comunes que (...) pueden facilitar el diálogo interreligioso: el sentimiento, la universalidad ética y la libertad. En esta investigación se presenta estos tres tópicos que Hegel descubre para el diálogo entre diferentes religiones para, finalmente, conectarlos con la discusión cronológicamente posterior sobre el pluralismo religioso. (shrink)

Pourquoi Averroès? Pourquoi Averroès juriste? Parce que dans le cadre du débat avec ceux qui soutiennent le caractère indubitable du texte sacré, Averroès affirme la primauté de la raison. Il a ainsi mis en avant le questionnement, le doute dans la recherche de la vérité. Ce doute toléré dans le cercle restreint des philosophes était inacceptable en droit (la charia) qui s'applique à tous les membres de la communauté des musulmans. D'où sa condamnation et son exil. La redécouverte de la (...) pensée d'Averroès pourrait permettre au monde arabo-musulman de s'extraire du chaos. (shrink)

On présente trop souvent Spinoza comme le créateur de l'un des systèmes conceptuels les plus arides de l'histoire de la pensée. Loin d'être un système de plus, il s'agit en fait d'un itinéraire existentiel, de l'effort d'un homme pour se libérer du malheur, de l'ignorance, de la souffrance, lot de tout homme venant en ce monde. Pour sortir de ce bourbier où la vie s'enlise, il faut prendre la décision ferme d'y voir enfin clair sur la nature des biens que (...) nous aimons et auxquels nou nous attachons car il y va de notre bonheur et de notre malheux. Pour y parvenir, 'il convient d'abord de trouver un moyen de guérir l'entendement' et de se consacrer entièrement à la mise en œuvre de cette guérison de soi. Ces pages, nées d'une libre méditation, ont pour seul but d'attirer l'attention sur un aspect de l'œuvre et de la vie d'un homme qui fut un Sage, et don't la voix demeure aussi vivante qu'au jour où elle s'éleva pour la première fois"--Page 4 of cover. (shrink)

En este libro, el autor traza un retrato histórico-conceptual del republicanismo que desmiente por completo la imagen con que se lo suele asociar: la de un discurso anticuado, conservador, que moraliza lo político. A contrapelo de esa visión, el autor desarrolla su argumentación a partir del análisis de cinco aspectos republicanos claves: "la libertad como no dominación, la virtud como soporte motivador y epistémico de la participación cívica, el debate como el elemento constitutivo de la política, la ley como la (...) otra cara de la libertad y la patria como el espacio particularista aunque estrictamente institucional de la república". (shrink)