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)

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 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.

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

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.

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.

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)

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)

This is an account of a reading project that began in February 2020. Australia was burning, a pandemic was simmering, the two of us were early in our PhD journeys at the Melbourne Law School. Already, we felt exhausted by critical theory which seemed to amplify the affects we felt all too intensely. Our reading project began as an attempt to find and inhabit texts that might move beyond critique, that might allow us to find wonder and vitality in legal (...) theory. Taking up the literary critic Rita Felski’s invitation to craft a post-critical reading practice, our reading list evolved iteratively to encompass themes and concerns that we identified as possibly correlating with said practice. It evolved too, in conversation with Melbourne, as the city journeyed through different stages of the pandemic. Constantly changing restrictions changed the ways in which we met and conversed, influencing in turn the texts we chose to read and the manner in which we read them. In this account, we pay attention to the time and place of our encounters with these interlocutors, and to the feelings these encounters generated. As such, this article takes the form of a series of (revised) diary entries: first written in 2020, then revisited in the corresponding months of 2021. What we hope emerges from these entries is a sense of how these theoretical texts train us to live in a world undergoing a compounding series of crises – and, perhaps, to imagine that world otherwise. In a more jurisprudential register, we hope that our experiment will identify the methods these texts might give us for (re-)engaging with law in a spirit of wonder and vitality. (shrink)

In this challenging study, André Gallois proposes and defends a thesis about the character of our knowledge of our own intentional states. Taking up issues at the centre of attention in contemporary analytic philosophy of mind and epistemology, he examines accounts of self-knowledge by such philosophers as Donald Davidson, Tyler Burge and Crispin Wright, and advances his own view that, without relying on observation, we are able justifiably to attribute to ourselves propositional attitudes, such as belief, that we consciously (...) hold. His study will be of wide interest to philosophers concerned with questions about self-knowledge. (shrink)

A bold and insightful departure from related texts, _Descartes_ goes beyond the categorical associations placed on the philosopher’s ideas, and explores the subtleties of his beliefs. An elegant, compelling and insightful introduction to Descartes' life and work. Discusses a broad range of his most scrutinized philosophical thought, including his contributions to logic, philosophy of the mind, epistemology, metaphysics, the philosophy of science, and the philosophy of religion. Explores the subtleties of Descartes' seemingly contradictory beliefs. Addresses themes left unexamined in other (...) works on Descartes. (shrink)

This paper advances the conception of social entrepreneurs as caring entrepreneurs. We argue that the care ethics of social entrepreneurs, implying the pursuit of caring goals through caring processes, can be challenged when they engage in the process of scaling up their ventures. We propose that social entrepreneurs can sustain their care ethics as the essential dimension of their venture only if they are able to build a caring enterprise. Organizational care designates the set of organizing principles that facilitate the (...) embedding of care ethics at an organizational level, beyond the imprinting induced by social entrepreneurs’ personal ethics. (shrink)

ArgumentLudwik Antoni Birkenmajer (1855-1929), following along the paths pioneered by Leopold Prowe, Maximilian Curtze, Franz Hipler, and J. L. E. Dreyer, joined them as trailblazers of Copernican scholarship in the nineteenth century. Educated in the classics and mathematics, Birkenmajer began by examining more closely the Cracow background to Copernicus's development and studying his works and annotations in books he owned or read. Birkenmajer contributed many discoveries that eventually became common knowledge, and his studies loomed over Polish research on Copernicus into (...) the 1970s. Focusing on historical context and his original insights, the essay reminds readers of his contributions (sections 1–2), relates them to discussions of Copernicus's precursors (section 3), to the debate about Maragha precedents (section 4), his reading of theUppsala Notebook(sections 2 and 5), and his account of the origin of Copernicus's heliocentrism (section 6). By means of a more critical assessment of his interpretation, the essay revises earlier accounts, rescuing the original insights that mark Birkenmajer's most important contributions to current debates and his efforts to reconstruct Copernicus's path to heliocentrism. (shrink)

O Tratado da Felicidade (ou Tratado da Bem-Aventurança), escrito por Tomás de Aquino como parte de sua Suma de Teologia, procura determinar qual é o fim último da vida humana, ou seja, o bem supremo da vida humana, e quais são os outros bens que não podem ser isso de nenhum modo. Tomás mostra conhecer uma divisão tríplice dos bens do homem, que inclui os bens exteriores, os bens do corpo e os bens da alma. A estes Tomás acrescenta um (...) tipo de bem que podemos chamar de “intermediário”, na medida em que se situa acima do homem e abaixo de Deus, e consiste no universo e nos anjos. Certamente, Tomás se refere também a Deus. No entanto, há mais um tipo de bem que Tomás menciona neste Tratado. É o bem em comum, ou bem em geral. Neste artigo, procurarei mostrar como Tomás de Aquino trata desses seis tipos de bens no Tratado da Felicidade, e indicarei se esse tratamento confirma ou não algumas teses de alguns estudiosos de Tomás de Aquino, como, por exemplo, a tese de que o homem não tem nenhum fim último natural. (shrink)

This paper is an attempt to put forward a new kind of partial model for representing belief states. I first introduce some philosophical motivations for working with partial models. Then, I present the standard (total) model proposed by Hintikka, and the partial models studied by Humberstone and Holliday. I then show how to reduce Hintikka’s semantics in order to obtain a partial model which, however, differs from Humberstone’s and Holliday’s. The nature of such differences is assessed, and I provide motivations (...) for using the newly proposed semantics rather than the existing ones. Finally, I review some promising philosophical applications of the ideas developed throughout the discussion. (shrink)

Este ensaio examina quatro tradições sobre guerra e paz que se desenvolveram na história cristã. São elas: Pacifismo, Guerra Justa, Guerra Total, e Comunidade Mundial. O Pacifismo caracterizou os primeiros cristãos; a Guerra Justa apareceu no fim do quarto século e no quinto século; a Guerra Total, no século 11; e a Comunidade Mundial começou no século 16. Todas as quatro posições continuam hoje e são sustentadas por pessoas que sinceramente se chamam a si mesmas de cristãs.

European Journal of Political Theory, Volume 21, Issue 2, Page 368-389, April 2022. Epistemic impairment has been the decisive yardstick when excluding infants from political agency. One of the suggestions to bypass the epistemic requirement of political agency and to encourage the inclusion of infants in representative democracies is to resort to proxies or surrogates who share or advocate interests which may be coincidental with their interests. However, this solution is far from desirable, given that it privileges the political agency (...) of parents, guardians and trustees over other adult citizens. This article offers an alternative to this conceptual frame of reference by making a case for the political agency of infants. Firstly, it maintains that political agency can be understood in terms of the several facets involved in political representation. Secondly, it claims that the all-affected principle can be reformulated as an ‘infant-affected-interests principle’ in light of which infants are members of the class of the represented. Thirdly, it explores the ways through which this political agency can occur without having to resort to alternative conceptions of representation. The conclusion ascertains that infant enfranchisement is highly undesirable and that there are more viable forms to promote infant political agency, such as virtual representation, infant-beneficial principles of political action and ombudspersons for infants. (shrink)

Resumo: Reconstruiu-se a semiologia geral elaborada nos escritos inacabados e indiretos de Saussure, recolocando sua noção de sentido próxima à de Deleuze e explicando-a por meio deste. Defende-se que toda teoria baseada na noção de “diferença” precisa dar conta do processo de individuação e, junto disso, por meio da descrição de dois níveis de diferenciação. Demonstra-se que isto é realizado por ambos os autores, para além e mesmo junto de suas divergências. Assim, o artigo recoloca a teoria do valor de (...) Saussure na aurora de uma filosofia da diferença, mostrando que este inaugura e mesmo “repete” as teses que Deleuze explicitamente defende, nos anos 1960.: The paper reconstruct the general semiology elaborated in Saussure’s unfinished and indirect writings, replacing his notion of meaning next to that of Deleuze, and explaining it through the latter. We argue that any theory based on the notion of “difference” needs to account for the individuation process and, together, through the description of two levels of differentiation. We demonstrate that this is accomplished by both authors, beyond and even with their disagreements. Thus, the article puts Saussure’s theory of value on the dawn of a philosophy of difference, showing that it inaugurates and even repeats the theses that Deleuze explicitly defends in the 1960s. (shrink)

The prelims comprise: Half Title Title Copyright Contents preface.

Neste artigo, pretendo expor o texto de um capítulo do livro Scholasticism and Politics, do filósofo francês Jacques Maritain (1882-1973). Este livro está em inglês e nunca foi traduzido ao português. O capítulo visado se chama “Christianity and earthly civilizations” - “Cristianismo e civilizações terrenas”. Ele é dividido em quatro seções: 1) A Igreja e o mundo, 2) Civilizações de origem pré-medieval, 3) Civilização Ocidental, e 4) Tentativas de novas civilizações. Farei a tradução ou uma paráfrase do texto, indicando seus (...) principais pontos e as conexões implícitas com outros textos de Maritain. Assim, facilitarei a leitura e a compreensão do sentido imediato do texto por leitores de língua portuguesa, o que é pré-requisito para uma avaliação crítica dele. A filosofia de Maritain é chamada por ele mesmo de filosofia cristã, isto é, uma filosofia que amplia seu escopo para considerar conceitos que são mais próprios da teologia cristã, principalmente no campo da filosofia moral e política. No século XX, Maritain teve muitos adeptos e admiradores brasileiros. (shrink)

The prelims comprise: Half Title Title Copyright Contents preface.

The prelims comprise: Half Title Title Copyright Contents preface.

Visto em perspectiva histórica, o ensinamento de Santo Tomás sobre o desejo natural a Deus foi apenas um interlúdio na tradição agostiniana-escotista. Aqueles que continuam a falar da doutrina dele sobre um desejo natural pela visão "beatífica" dão testemunho da influência viva daquela tradição hoje. Embora ele não possa ser enquadrado na série que liga Santo Agostinho, São Boaventura, Duns Scotus e Domingo de Soto nessa questão, a posição dele não é menos cristã do que a da tradição com a (...) qual ele rompeu. A posição dele, entretanto, irá continuar a parecer incoerente e até mesmo contraditória, enquanto for colocada nos termos daquela tradição, em vez de nos seus próprios termos. (shrink)