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.

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.

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.

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.

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)

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.

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.

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 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)

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)

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

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.

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)

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)

There is evidence of persistent inequalities in household financial protection of health and drugs spending in Latin America. Despite the expansion of coverage, strong inequalities persist in access to health and family spending on drugs in the region. Out-of-pocket spending in medicines is regressive in greater need for affordable medicines.

More and more organisations formulate a code of conduct in order to stimulate responsible behaviour among their members. Much time and energy is usually spent fixing the content of the code but many organisations get stuck in the challenge of implementing and maintaining the code. The code then turns into nothing else than the notorious "paper in the drawer", without achieving its aims. The challenge of implementation is to utilize the dynamics which have emerged from the formulation of the code. (...) This will support a continuous process of reflection on the central values and standards contained in the code. This paper presents an assessment method, based on the EFQM model, which intends to support this implementation process. (shrink)

IN the last decade deliberative democracy has developed rapidly from a “theoretical statement” into a “working theory.”1 Scholars and practitioners have launched numerous initiatives designed to put deliberative democracy into practice, ranging from deliberative polling to citizen summits.2 Some even advocate deliberation as a new “revolutionary now.”3 Deliberative democracy has also experienced the beginning of an empirical turn, making significant gains as an empirical (or positive) political science. This includes a small, but growing body of literature tackling the connection between (...) the normative standards of deliberation, how well they are met, and the empirical consequences of meeting them.4 This trend has, for instance, included the use of methods and frameworks borrowed from other fields, such as political and social psychology. Such studies suggest that cases approaching ideal deliberation are rare, but that group interaction sometimes works surprisingly well according to such ideals.5. (shrink)

Frühgeborene im Grenzbereich der Lebensfähigkeit befinden sich in einer prognostischen Grauzone. Das bedeutet, dass deren Prognose zwar schlecht, aber nicht hoffnungslos ist, woraus folgt, dass nach Geburt lebenserhaltende Behandlungen nicht obligatorisch sind. Die Entscheidung für oder gegen lebenserhaltende Maßnahmen ist wertbeladen und für alle Beteiligten enorm herausfordernd. Sie sollte eine zwischen Eltern und Ärzt*innen geteilte Entscheidung sein, wobei sie unbedingt mit den Präferenzen der Eltern abgestimmt sein sollte. Bei der pränatalen Beratung der Eltern legen die behandelnden Ärzt*innen üblicherweise numerische Schätzungen (...) der Prognose vor und nehmen in der Regel an, dass die Eltern ihre Behandlungspräferenzen davon ableiten. Inwieweit probabilistische Daten die Entscheidungen der Eltern in prognostischen Grauzonen tatsächlich beeinflussen, ist noch unzureichend untersucht. In der hier vorliegenden Arbeit wird eine Studie reflektiert, in welcher die Hypothese geprüft wurde, dass numerisch bessere oder schlechtere kindliche Prognosen die Präferenzen werdender Mütter für lebenserhaltende Maßnahmen nicht beeinflussen. In dieser Studie zeigte sich, dass die elterlichen Behandlungspräferenzen eher von individuellen Einstellungen und Werten als von Überlegungen zu numerischen Ergebnisschätzungen herzurühren scheinen. Unser Verständnis, welche Informationen werdende Eltern, die mit einer extremen Frühgeburt konfrontiert sind, wünschen und brauchen, ist noch immer unvollständig. Bedeutende medizinische Entscheidungen werden keineswegs nur rational und prognoseorientiert gefällt. In der vorliegenden Arbeit wird diskutiert, welchen Einfluss der Prozess der Entscheidungsfindung auf das Beratungsergebnis haben kann und welche Implikationen sich aus den bisher vorliegenden Studienergebnissen ergeben – klinisch-praktisch, ethisch und wissenschaftlich. (shrink)

Scientific realists have argued that the truth(likeness) of our theories provides the only explanation for the success of science. I consider alternative explanations proposed by antirealists. I endorse Leplin's contention that neither van Fraassen's Darwinist explanation nor Laudan's methodological explanation provides the sort of explanatory alternative which is called for in this debate. Fine's suggestion--that the empirical adequacy of our theories already explains their success--is more promising for antirealists. Leplin claims that this putative explanation collapses into realism on one reading (...) and into vacuity on another reading. But his analysis conflates three doctrines into two, and one of the three avoids both realism and vacuity. (shrink)

The thesis that every truth is knowable is usually glossed by decomposing knowability into possibility and knowledge. Under elementary assumptions about possibility and knowledge, considered as modal operators, the thesis collapses the distinction between truth and knowledge (as shown by the so-called Fitch-argument). We show that there is a more plausible interpretation of knowability—one that does not decompose the notion in the usual way—to which the Fitch-argument does not apply. We call this the potential knowledge-interpretation of knowability. We compare our (...) interpretation with the rephrasal of knowability proposed by Edgington and Rabinowicz and Segerberg, inserting an actuality-operator. This proposal shares some key features with ours but suffers from requiring specific transworld-knowledge. We observe that potential knowledge involves no transworld-knowledge. We describe the logic of potential knowledge by providing models for interpreting the new operator. Finally we show that the knowability thesis can be added to elementary conditions on potential knowledge without collapsing modal distinctions. (shrink)

Research on implicit conflict detection suggests that people are sensitive to violations of logical principles. When they make reasoning errors, their epistemic radar presumably detects an anomaly....

A questão dos letramentos e da inovação demonstram-se fundamentais em períodos históricos como o atual, onde as práticas de ensino-aprendizagem tornam-se cada vez mais complexas, que requerem novas abordagens teóricas para compreendermos possibilidades alternativas de ensino. Tendo estas questões em mente, este artigo visa indicar relações possíveis entre o antifundacionismo, o pensamento de Paul Feyerabend e os letramentos científicos. Em um primeiro momento indicaremos questões relativas ao antifundacionismo, e em seguida verificaremos como tal questão se efetiva no pensamento de Feyerabend. (...) Finalizaremos avaliando como esta abordagem pode fundamentar novas práticas educacionais. (shrink)

Empirical research is largely supportive of the assertion of instrumental stakeholder theory that a positive relationship exists between “managing for stakeholders” and firm performance. However, despite considerable debate on the subject, the amount of variation across firm investments in stakeholders (stakeholder management performance) has not been adequately investigated. We address this gap using a sample of more than eighteen thousand firm-level observations over ten years. We find evidence to support an inverted U–shaped relationship between variation in stakeholder management performance and (...) Tobin’sq, suggesting that firms that have some imbalance in their stakeholder management, but not too much, perform best. We discuss the implications of our study for instrumental stakeholder theory and managerial practice. (shrink)

John Horty has proposed an approach to reasoning with ought-propositions which stands in contrast to the standard modal approach to deontic logic. Horty’s approach is based on default theories as known from the framework of Default Logic. It is argued that the approach cannot be extended beyond the most simple kinds of default theories and that it fails in particular to account for conditional obligations. The most plausible ways of straightening out the defects of the approach conform to a simple (...) theory of default reasoning in standard deontic language. (shrink)

My topic is extraterrestrial intelligence. Following current conventions, I use the abbreviation ‘ETI’ to stand for three related concepts: the abstract idea of extraterrestrial intelligence, individuals who are both extraterrestrial and intelligent, and the hypothesis that there are ETIs. SETI is the search for ETIs, and CETI is the attempt to communicate with ETIs. In this paper, I will try to answer the two most basic questions in extraterrestrial studies. First, what is the status of the ETI hypothesis? In the (...) light of what we know, how likely is it that there are ETIs? Secondly, what is the value of pursuing SETI? Are the expected epistemic and pragmatic payoffs sufficient to warrant an extensive search? The first, substantive question is discussed in Section 2, Section 3 and Section 4. The second, ‘program evaluation’ question is the subject of Section 5 and Section 6. But first we'll take a brief look at some of the early history of the topic. (shrink)

Les Lois de Platon constituent une œuvre majeure dans l'histoire de la pensée politique.

The aim of this book is not to impart a substantive knowledge of core psychological theories, or even to analyze critically selected theories. Instead, it is to prepare the reader to analyze and advance the theoretical literature in any tradition. Theoretical psychology stands in the same relation to psychology as theoretical physics does to physics. The traditional way to study theoretical psychology is to take up one approach after another--behavioral, psychoanalytic, cognitive, and so on. The aim of this book is (...) not to impart a substantive knowledge of core psychological theories, or even to analyze critically selected theories. Instead, it is to prepare the reader to analyze and advance the theoretical literature in any tradition. A good theoretician should be able to contribute to the study of psychoanalytic theory as readily as to behavioral theory. The skills required are the same. Instead of covering a sequence of theories, therefore, the book is organized around types of theoretical activities. It is not a work in theoretical psychology; it is a book about theoretical psychology. It also confronts psychologists' underestimation of the variety and the significance of theoretical work. Many theoretical issues do not call for empirical research--they require nothing but thinking. (shrink)

Labour and employment law no longer has a monopoly on regulating labour relations and is facing a crisis as its effectiveness is questioned. Codes of conduct adopted by companies to recognise their social responsibility for the global supply chain are instruments that can usefully complement labour and employment law. The aim of this paper is to analyse in depth the legal nature of codes of conduct and their impact on labour and employment law. Will the use of codes of conduct (...) reinforce the crisis of labour and employment law in the era of globalisation or will these codes be part of a solution to this crisis? Do we have to consider codes of conduct as competitors to labour and employment law or as an opportunity for rethinking the way that labour and employment law norms should be produced and applied? (shrink)

We consider motivations for acknowledging that people participate in multiple levels of economic agency. One of these levels is characterized in terms of subjective utility to the individual; another, frequently observed, level is characterized in terms of utility to social groups with which people identify. Following Bacharach, we describe such groups as ‘teams’. We review Bacharach’s theory of such identification in his account of ‘team reasoning’. While this conceptualization is useful, it applies only to processes supported by deliberation. As this (...) is only one of a range of causal mechanisms underlying behaviour by humans and other strategic agents, a more general account is desirable. We then argue that Stirling’s account of ‘conditional games’ achieves the desired generalization. (shrink)

For many years G. E. Moore asked himself what was wrong with sentences like ‘I went to the pictures last Tuesday, but I don't believe that I did’, or ‘I believe that he has gone out, but he has not’. He discussed the problem in 1912 in his Ethics , and was still discussing it in 1944 in a paper to the Moral Sciences Club at Cambridge—an event we know about from a letter of Wittgenstein that I shall quote in (...) a moment. Throughout these years of pondering, Moore retained a remarkably stable vocabulary for setting out his solution. Briefly, he held this: saying ‘I went to the pictures last Tuesday, but I don't believe that I did’ is absurd, but not self-contradictory. Not self-contradictory, because ‘it may quite well be true’; yet absurd, because the speaker expressly repudiates, in the second part of the sentence, a belief which he implies by uttering the first part. The panoply of distinctions which subtends this doctrine—sentence v. utterance of sentence, saying v. implying, contradiction v. absurdity—was subjected to keen scrutiny a generation or so ago, and much of it has now passed into philosophical lore as a discussion of ‘Moore's Paradox’. (shrink)

A theory of intergenerational justice consists in the study of the moral and political status of the relations between present and past or future people, more specifically, of the obligations and entitlements they can potentially generate. The challenges that justify talking about responsibilities between generations are myriad. And the disputes they prompt can focus on the past just as much as on the present, even though the fact that the human species has reached a state of technological progress that enables (...) it to have an irredeemable impact on the planet and perhaps even endanger future human existence tends to make concerns about the future more pressing. Debates on intergenerational justice are twofold. The first revolves around the issue of whether claims of justice across generations whose members' lifetimes do not necessarily overlap could be justified. And the second revolves around the specific conception of justice in play, that is, around the nature of the standard that must be applied as well as around the identification of the contents of the duties that present generations supposedly have vis-à-vis past or future generations. This survey article depicts the conceptual and argumentative framework in which these debates are set. It aims to outline certain of the main features shared by the most influential contemporary theories of intergenerational justice, and the problems inherent in them. It concludes by suggesting that, even though the idea of succeeding generations is merely an abstraction, there are specific empirical states of affairs that require different theoretical responses to intergenerational justice. (shrink)

L'espace économique s'est profondément modifié au cours des vingt dernières années en raison, bien sûr, de la mondialisation, niais aussi de la déréglementation de nombreuses économies parmi les plus influentes du monde. D'une économie empirique de travail, nous sommes ainsi passés à une économie virtuelle de spéculation avec, à la clé, un recul de l'éthique au profit de logiques financières. C'est pour contrer les effets néfastes de cette financiarisation de l'économie que le mouvement de la finance socialement responsable s'est développé, (...) ses tenants utilisant les leviers économiques, en l'occurrence de nombreux fonds de placement, pour faire pression sur les décideurs et les orienter vers des avenues plus responsables. Ce livre présente le regard d'un philosophe et d'une sociologue sur ce mouvement. Les auteurs définissent les origines de la finance socialement responsable, pour ensuite exposer ses pratiques et ses stratégies, dresser un portrait de ses principaux acteurs et proposer des pistes de réflexion sur la dimension éthique de la finance ainsi que des outils pertinents aux pratiques des financiers. Il s'agit d'une introduction indispensable à tous ceux qui souhaitent s'initier au mouvement de la finance socialement responsable et qui recherchent des avenues éthiques en matière de développement économique. (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)