Gilles-Gaston Granger est l’une des figures majeures de l’épistémologie de la seconde moitié du xx e siècle. Son œuvre est cependant encore trop méconnue, et sans doute sous-évaluée, en particulier dans le contexte international dont les intérêts prioritaires et les méthodes suivies sont restés longtemps assez éloignés de ceux du penseur aixois. L’évolution récente laisse entrevoir un changement assez radical de perspective avec, d’une part, une redécouverte de la philosophie mathématique de tradition francophone : Brunschvicg, Cavaillès, Lautman, Vuillemin…, et, d’autre (...) part, le développement corrélatif d’un intérêt pour l’épistémologie historique, de Bachelard à Foucault en passant par leurs réappropriations chez des philosophes comme Ian Hacking [_Historical Ontology_, Harvard University Press, 2002]. Le structuralisme, très présent en France dans les mathématiques et les sciences humaines des années 1960-1970, fait par ailleurs l’objet d’une attention renouvelée, à la fois du fait... (shrink)

This article is an attempt to present Gödel's discussion on concepts, from 1944 to the late 1970s, in particular relation to the thought of Frege and Russell. The discussion takes its point of departure from Gödel's claim in notes on Bernay's review of ?Russell's mathematical logic?. It then retraces the historical background of the notion of intension which both Russell and Gödel use, and offers some grounds for claiming that Gödel consistently considered logic as a free-type theory of concepts, called (...) intensions, considered as the denotations of predicate names. (shrink)

Internationally recognized logicians present current thinking on the understanding of the role of deduction in human reasoning.

After a brief discussion of Kreisel’s notion of informal rigour and Myhill’s notion of absolute proof, Gödel’s analysis of the subject is presented. It is shown how Gödel avoids the notion of informal proof because such a use would contradict one of the senses of “formal” that Gödel wants to preserve. This Gödelian notion of “formal” is directly tied to his notion of absolute proof and to the question of the general applicability of concepts, in a way that overcomes both (...) Kreisel and Myhill’s conceptions. This paper aims to contribute to the present-day debate on informal and epistemic mathematics, focusing on what appears necessary for a better understanding of the issues at stake. (shrink)

The editors present the essays that are collected in the volume and which are the outcome of talks given at the international conference “Kurt Gödel Philosopher: From Logic to Cosmology” that was held in Aix en Provence (France) in summer 2013. Many of the authors belong to a group of scientists who have contributed to an ANR project with the same title under the direction of Gabriella Crocco.

Is it possible to characterize the notion of proof in terms of acts, without focusing on a specific domain of application and a specific linguistic formalization of it? This is the question that this paper addresses through a comparative analysis between two logicians who reflected on this issue: Kurt Gödel and Jean-Yves Girard. A comparative analysis of their respective theoretical frames, their respective results, the similarities and the differences between their methodological assumptions is proposed. More specifically, the aim of the (...) paper is to compare Gödel’s notion of absolute proof and Girard’s notion of Ludic from their common core: a conception of proof in terms of acts. (shrink)

L'application de la notion de structure à l'analyse des systèmes philosophiques est sans doute l'un des développements les plus fructueux de ce qu'on a appelé le structuralisme. La tradition inaugurée par Martial Gueroult et poursuivie par Victor Goldschmidt, Jules Vuillemin et d'autres a conduit à une fondation critique de la notion de système philosophique et a renouvelé profondément la méthode de l'histoire de la philosophie. En cherchant à reconstituer les orientations principales de cette tradition, nous essayons d'abord de distinguer le (...) structuralisme en philosophie du structuralisme en mathématique et en linguistique. Nous prenons comme base de discussion de cette question l'analyse de Gilles-Gaston Granger donnée en 1967, dans Pensée formelle et sciences de l'homme. Ensuite, nous abordons trois problèmes centraux de l'application de la notion de système en philosophie. La question de la clôture des concepts philosophiques ; la question de la vérité ; la question des rapports entre science et philosophie. (shrink)

This volume represents the beginning of a new stage of research in interpreting Kurt Gödel’s philosophy in relation to his scientific work. It is more than a collection of essays on Gödel. It is in fact the product of a long enduring international collaboration on Kurt Gödel’s Philosophical Notebooks (Max Phil). New and significant material has been made accessible to a group of experts, on which they rely for their articles. In addition to this, Gödel’s Nachlass is presented anew by (...) the current state of research and the corpus of Gödel’s Philosophical Notebooks (Max Phil) is described in its entirety for the first time in its details. The volume is sub-divided into three parts. The fist part is dedicated to descriptions of the Gödel Nachlass that is to be found in The Shelby White and Leon Levy Archives Center des Institute for Advanced Study in Princeton. This part starts with an updated overview on Kurt Gödel’s Nachlass by the current state of research and is followed by a detailed description of Gödel’s Philosophical Notebooks (Max Phil). The second part is dedicated by several Gödel scholars to the close reading of single remarks in the Max Phil. And the third part of this volume unites a variety of papers by experts in Gödel studies, logic, and Leibniz as well as by some enthusiasts for Gödel. These papers are nearly all written for this volume. (shrink)

The authors describe the construction, development and content of Kurt Gödel’s Philosophical Remarks—the Max Phil notebooks—for the first time in detail and giving a thorough technical description of them. The Max Phil notebooks are part of the Nachlass that is handed down to us in the shorthand Gabelsberger. The notebooks start as an intellectual diary and then evolve to be philosophical notebooks that contain an outline of Gödel’s rational metaphysics as well as some of his reflections on logic, mathematics, physics, (...) biology, history, philology and theology. Crocco and Engelen make a first attempt to relate these reflections to Gödel’s published work and to his scientific oeuvre to make it clear why they enlarge our knowledge of Gödel’s thinking. They then go on to offer first insights into the content of the Philosophical Remarks. This article not only gives an insight into Gödel’s philosophical work that is not yet known to the academic world but it also constitutes the background to classify the publication of notebook Max Phil X within the context of the Max Phil notebooks in their entirety. (shrink)

Thorough a detailed analysis of version III of Gödel's Is mathematics syntax of language?, we propose a new interpretation of Gödel's criticism against the conventionalist point of view in mathematics. When one reads carefully Gödel's text, it brings out that, contrary to the opinion of some commentators, Gödel did not overlook the novelty of Carnap's solution, and did not criticise him from an old-fashioned conception of science. The general aim of our analysis is to restate the Carnap/Gödel debate in the (...) Fregean heritage. We stress the way both of them try to answer, from different Fregean perspectives, to the question of the nature of logic and mathematics in knowledge. (shrink)

La classification des systèmes philosophiques de Jules Vuillemin fonde les relations entre science et philosophie en éliminant la possibilité d’une philosophie scientifique. Elle éclaire la pratique de la philosophie, en explicitant les choix possibles tout en rejetant le relativisme. Elle se fonde sur ce que Vuillemin appelle une sémiologie générale, qui convoque toutefois l’analyse logique. L’article propose une ébauche d’analyse structurale de la déduction permettant de fonder la classification sur des moyens exclusivement logiques.

Après avoir indiqué ce qu’il entend par Mathématiques pures et par Théorie de la connaissance, Vuillemin annonce, dans l’Introduction au premier tome de La Philosophie de l’algèbre, que son but est double. En considérant le « rapport étroit » et l’« affinité d’inspiration » entre ces deux disciplines, il se propose d’examiner, d’une part, « comment une connaissance pure est possible » et, d’autre part, de « critiquer, reformer et définir, autant qu’il se pourra, la méthode propre à la philosophie (...) théorique » grâce aux « analogies » repérées dans la connaissance mathématique. Ce double but dérive du constat, reposant sur l’analyse de l’histoire des mathématiques et de la philosophie, qu’« un renouvellement des méthodes de celles-là a, à chaque fois, des répercussions sur celle-ci ». Les renouvellements des méthodes que les mathématiques modernes induisent portent essentiellement, selon Vuillemin, sur les notions de structure, d’infini et de logique. Le deuxième tome de La Philosophie de l’algèbre devait donc montrer comment définir la méthode propre à la philosophie théorique. On essaiera de montrer comment le dernier chapitre du premier tome de cet ouvrage contient en soi des difficultés qui commanderont l’abandon du projet et comment l’idée de pluralisme qui y est esquissée exige une refonte conceptuelle que Vuillemin ne fournira que plus de vingt ans après. (shrink)

La conception des mathématiques chez Poincaré est une pièce maîtresse de sa théorie de la connaissance. Les mathématiques y jouent un rôle constitutif et médiateur, très proche de celui que Kant leur avait assigné dans sa Critique. Afin d’éclaircir les rapports complexes entre les notions d’intuition, de construction et de convention chez Poincaré, nous nous appuyons sur les analogies et les contrastes avec la source kantienne. La continuité et la cohérence de la théorie de la connaissance de Poincaré en sortent (...) renforcées.Poincaré’s philosophy of mathematics plays a key role in his general philosophy of knowledge. Mathematics is considered, by Poincaré, as a constitutive element of experience and it plays a “schematic” role between the conventional frameworks of geometry and theoretical physics on one hand and, on the other hand, sensations. We stress the Kantian roots of such a conception of mathematics, trying to explain the respective importance of the notions of intuition, construction and convention in Poincaré’s theory of knowledge. (shrink)

Difficulties and ambiguities of Carnap’s conception of logic and mathematics are the main target of Gödel’s analysis in his famous drafts of “Is mathematics Syntax of Language?”. In a recent article, Gregory Lavers discusses two main recent dismissive analyses of Gödel’s drafts, concluding at a defense of Gödel’s arguments against Carnap’s position in the 1930. Lavers partially integrates in his examination an argument that I presented in a paper published in 2003. Yet, there are three important differences between my understanding (...) of Gödel’s argument and Lavers’s interpretation of it. These differences concern the appreciation of (a) Gödel’s strategy of using, in any critical examination of his opponents, only arguments that can be accepted by them; (b) Gödel’s analysis of Carnap’s position in the 1950s; (c) Gödel’s understanding of Carnap’s philosophical project. The paper aims to argue that, contrary to Lavers’s opinion, Gödel takes seriously the details of Carnap’s original conception and does not overlook the novelty of its solutions in the 1930s and 1950s. In particular, the comparison between Gödel’s arguments in the Gibbs lecture of 1951 and in version III of his draft of ‘Is mathematics Syntax of Language?’ shows how Gödel had in 1953–55 a careful concern with Carnap’s philosophical project of LSL. (shrink)

This article is devoted to the analysis of the remarks of Gödel's Maxims and Philosophical remarks (Max Phil) that present a solution to the paradoxes of set theory, and to the analysis of the context. It is divided in two parts. The first part contains two remarks from the notebook IX, (pp. 48b, 51) on the question of the strategies for the solution of paradoxes. They clearly show Gödel’s preference for the strategy of limited ranges of significance. The reasons why (...) Gödel was also interested in the other strategies suggested by Russell is explained through two remarks of Max Phil IX (pp.69 and 72b) The second part presents a remark from Max Phil X (p. 28-29), and explains it from the perspective of Gödel analysis of concepts in the early 1943. (shrink)

This book looks at the ways in which conditionals, an integral part of philosophy and logic, can be of practical use in computer programming. It analyzes the different types of conditionals, including their applications and potential problems. Other topics include defeasible logics, the Ramsey test, and a unified view of consequence relation and belief revision. Its implications will be of interest to researchers in logic, philosophy, and computer science, particularly artificial intelligence.

The educational reform movement in social studies has focused on constructivist and inquiry-oriented approaches to the teaching of history. Since many social studies teacher education students have had little experience with such approaches in their own schooling, special attention needs to be given to these topics within teacher preparation programs if they are to be implemented in schools. One pathway for accomplishing this is through investigations of local history. This article presents an exploratory qualitative research study investigating pre-service teachers' understanding (...) of inquiry and the impact of a set of lessons in a methods class using local history in the service of inquiry-oriented learning. The results suggest that local history can be an effective tool for stimulating interest in and a deeper understanding of inquiry-oriented teaching. (shrink)

The article explores the complex experiences and positions of migrant women in the `nursing profession' in a southern European country, Greece. It looks at ways in which a rudimentary welfare state and a large informal economy have created the demand for les infirmières exclusives and for `quasi-nurses'. The supply and use of their services, on the one hand, helps perpetuate this informal welfare system and, on the other, has implications for migrant women themselves as, inter alia, it contributes to their (...) deskilling, exploitation, marginalization and exclusion. The multifarious degrees and forms that these processes take, to a large extent, depend on the cross-cutting of gender, ethnicity and class, as sexism intersects with different forms of `othering' and racialization processes in the destination country. The position of these women is also located in terms of ethnic and national boundaries. (shrink)

The aim of this essay is to consider both Schmitt’s polemical and his analytical claims in dealing with a concept which is central to his theory and yet strangely overlooked by the secondary literature: the concept of friendship. The essay proceeds in three steps; first it makes some textual claims about the meaning and role of friendship in Schmitt’s writings; secondly its puts forward an interpretation of the significance of friendship in Schmitt’s political thought; finally, it tries to disentangle polemics (...) from diagnostics in Schmitt’s discourse and draws some tentative conclusions. (shrink)

The aggregation of individual judgments on logically interconnected propositions into a collective decision on the same propositions is called judgment aggregation. Literature in social choice and political theory has claimed that judgment aggregation raises serious concerns. For example, consider a set of premises and a conclusion where the latter is logically equivalent to the former. When majority voting is applied to some propositions (the premises) it may give a different outcome than majority voting applied to another set of propositions (the (...) conclusion). This problem is known as the discursive dilemma (or paradox). The discursive dilemma is a serious problem since it is not clear whether a collective outcome exists in these cases, and if it does, what it is like. Moreover, the two suggested escape-routes from the paradox—the so-called premise-based procedure and the conclusion-based procedure—are not, as I will show, satisfactory methods for group decision-making. In this paper I introduce a new aggregation procedure inspired by an operator defined in artificial intelligence in order to merge belief bases. The result is that we do not need to worry about paradoxical outcomes, since these arise only when inconsistent collective judgments are not ruled out from the set of possible solutions. (shrink)

Este artigo procura refletir sobre a reificação e as antinomias do pensamento burguês, que se edificam numa sociedade dominada pela produção e distribuição de mercadorias. Pautaremos nossa análise na obra História e Consciência de Classes (1923) de Georg Lukács e em sua relação com os estudos sobre a mercadoria realizados por Karl Marx. Assim, pretendemos realizar uma reflexão sobre a constituição da realidade social determinada pelos processos reificados da sociedade capitalista.

This book is a socio-historical analysis of rationalism as a worldview - that guides many of our actions in concrete everyday life - and as a philosophy - that guides our epistemological understanding of the reality around us. It explores the multifaceted manifestations of the idea in the Enlightenment philosophy, modern sociological theorising and in post-structural standpoints. The volume also critiques rationality from feminist, subaltern and post-colonial perspectives. Finally, it delves into the multilayered sociological significances of rationalisation of different domains (...) of life. Transdisciplinary in scope and with essays by foremost scholars in the field, this volume will be a major intervention across the humanities and the social sciences. It will be of interest to students and researchers in sociology, anthropology, history, philosophy, gender studies, political science, cultural anthropology, education, and religious studies. (shrink)

Although organizational and situational factors have been found to predict burnout, not everyone employed at the same workplace develops it, suggesting that becoming burnt out is a complex, multifaceted phenomenon. The aim of this study was to elucidate perceptions of conscience, stress of conscience, moral sensitivity, social support and resilience among two groups of health care personnel from the same workplaces, one group on sick leave owing to medically assessed burnout (n = 20) and one group who showed no indications (...) of burnout (n = 20). The results showed that higher levels of stress of conscience, a perception of conscience as a burden, having to deaden one’s conscience in order to keep working in health care and perceiving a lack of support characterized the burnout group. Lower levels of stress of conscience, looking on life with forbearance, a perception of conscience as an asset and perceiving support from organizations and those around them (social support) characterized the non-burnout group. (shrink)

Au Moyen Âge, la théorie médicale de la complexio n’est pas confinée dans le domaine restreint de la théorie ou de la pratique de la médecine. Elle implique une anthropologie déterminée, qui ne concerne pas seulement la santé et le bien-être de l’homme, mais, dans certaines limites, la nature même de celui-ci ou, pour mieux dire, la manière dont la nature spécifique de l’homme s’articule avec la variété et la différence des tempéraments et des dispositions individuelles : ce qu’est chaque (...) individu dépend de la complexion qui lui est propre. Cette anthropologie médicale dépasse les limites de sa discipline et pénètre aussi la théologie, par une série d’implications, pas toujours prévisibles, qui concernent la place de l’homme dans l’univers, l’eschatologie, la démonologie et aussi la christologie. Le but de cette étude est de rendre compte de certaines de ces implications en regard de la pensée de Thomas d’Aquin. Les différents lieux où Thomas étudie la complexion corporelle – il en considère les implications dans les domaines intellectuel et moral – montrent une sorte d’assimilation de l’anthropologie médicale (indirectement galénique, mais surtout avicennienne) à l’intérieur de son horizon de pensée, constitué par la philosophie naturelle aristotélicienne et par les exigences propres à sa théologie. (shrink)

Hobbes's philosophical discourse is deconstructed as the interplay of the drama of individual behavior as perceived by rational agents and the detached analysis of conflict a by a political geometer . The author solves some long-standing problems in Hobbesian political philosophy (e.g., the role of glory, Hobbes' pessimism) and shows the consistency of Hobbes's attempt to derive absolutism as the only stable political association.

Ethical dilemmas in critical care may cause healthcare practitioners to experience moral distress: incoherence between what one believes to be best and what occurs. Given that paediatric decision-making typically involves parents, we propose that parents can also experience moral distress when faced with making value-laden decisions in the neonatal intensive care unit. We propose a new concept—that parents may experience “moral schism”—a genuine uncertainty regarding a value-based decision that is accompanied by emotional distress. Schism, unlike moral distress, is not caused (...) by barriers to making and executing a decision that is deemed to be best by the decision-makers but rather an encounter of significant internal struggle. We explore factors that appear to contribute to both moral distress and “moral schism” for parents: the degree of available support, a sense of coherence of the situation, and a sense of responsibility. We propose that moral schism is an underappreciated concept that needs to be explicated and may be more prevalent than moral distress when exploring decision-making experiences for parents. We also suggest actions of healthcare providers that may help minimize parental “moral schism” and moral distress. (shrink)

The report gives a survey of the Hungarian philosophy of science after 1973. The report throws some light on the history of Hungarian philosophy in the context of the political circumstances of the late sixties and seventies. It starts with the not so well-known history of 'persecution of philosophers' in 1973. Then it treats the emergence of the philosophy of science focussing on the most significant representatives of this branch of philosophy, which was up to that time almost unknown in (...) Hungary. Due to the fact that the important results in Hungarian philosophy of science run parallel with the reception and translation of the significant products of Western philosophy, such as Wittgenstein's, Popper's, Kuhn's, or Polanyi's works, the report gives relatively significant room to treat these achievements. The last part of the report presents a survey of the younger generation of the philosophers of science, concentrating on the most important insights. (shrink)

Research in ethical AI has made strides in quantitative expression of ethical values such as fairness, transparency, and privacy. Here we contribute to this effort by proposing a new family of metrics called “decisional value scores” (DVS). DVSs are scores assigned to a system based on whether the decisions it makes meet or fail to meet a particular standard (either individually, in total, or as a ratio or average over decisions made). Advantages of DVS include greater discrimination capacity between types (...) of ethically relevant decisions and facilitation of ethical comparisons between decisions and decision-making systems, including across different modalities (for instance: human, machine, or coupled human–machine systems). After clarifying ambiguities in the concept of “decision” itself, including the question of how to individuate the decisions made by a system, we discuss the role and meaning of “decision” in common AI and machine learning approaches such as decision trees, neural networks, SVMs, and unsupervised classifiers. We then show how DVSs may be defined for several ethical values of interest, with an extended discussion of transparency. Finally, we explore how such metrics can be applied to real decision-making systems through two case studies: evaluations of LLMs for transparency; and evaluations of criminal risk assessment tools for utility, rights violations, fairness, and transparency. (shrink)

Various methods have been employed to investigate different aspects of the brain activity modulation related to the performance of a cycling task. In our study we examined how functional connectivity and brain network efficiency varied during an endurance cycling task. To this purpose, we reconstructed EEG signals at source level: we computed current densities in 28 anatomical regions of interest (ROIs) through the eLORETA algorithm, then we calculated the Lagged Coherence of the 28 current density signals to define the adjacency (...) matrix. To quantify changes of functional network efficiency during an exhaustive cycling task, we computed three graph theoretical indices: local efficiency (LE), global efficiency (GE) and Density (D) in two different frequency bands, Alpha and Beta bands, that indicate alertness processes and motor binding/fatigue respectively. This analysis was conducted for six different task intervals: pre-cycling, initial, intermediate and final stages of cycling, active recovery and passive recovery. Fourteen participants performed an incremental cycling task with simultaneous EEG recording and RPE monitoring to detect participants’ exhaustion. LE remained constant during the endurance cycling task in both bands. Therefore, we speculate that fatigue processes did not affect segregated neural processing. We observed an increase of GE in the Alpha band only during cycling, that could be due to greater alertness processes and preparedness to stimuli during exercise. Conversely, although D did not change significantly over time in the Alpha band, its general reduction in the Beta bands during cycling could be interpreted within the framework of the neural efficiency hypothesis, which posits a reduced neural activity for expert/automated performances. We argue that the use of graph theoretical indices represents a clear methodological advancement in studying endurance performance. (shrink)

Dans son Apologie, Justin structure son discours selon un double plan: il se prononce en faveur des chrétiens injustement haïs, mais aussi, de manière plus personnelle, comme quelqu�un qui pressent l�approche de sa condamnation et s�y prépare en assumant le rôle du sage qui, sur le point de mourir, fustige l�autorité politique, sans en craindre les conséquences. En recourant à un topos littéraire très connu dans l�Antiquité, Justin se «construit» une image de mort honorable au sein de sa communauté.

NOVO CÓDIGO DE PROCESSO CIVIL: REFLEXÕES SOBRE LIBERDADE, IGUALDADE E MUDANÇAS DE PARADIGMAS.