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.

This is a review of CONDITIONALS: FROM PHILOSOPHY TO COMPUTER SCIENCE, edited by Crocco G., del Cerro L. Fariñas, and Herzig A., Studies in logic and computation, no. 5, Clarendon Press, Oxford University Press, Oxford and New York 1995.

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 considering the main theses of Alain Richardson's analysis of Carnap's Aufbau, and in particular Richardson's motivation for criticising the Quinean naturalisation of epistemology, we focus on the alleged neo-kantian influence on Carnap work. There is something lacking in Richardson rational reconstruction of Camap's work before 1939: the German logical tradition of Frege and Hilbert which Carnap was evidently confronted with. The themes of this tradition appear and disappear here and there in Richardson's book, but the real weight of its (...) epistemological consequences on the nature of logic and mathematics seems misplaced. (shrink)

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)

Kant’s critique/doctrine distinction tracks the difference between a canon for the understanding’s proper use and an organon for its dialectical misuse. The latter reflects the dogmatic use of reason to attain a doctrine of knowledge with no antecedent critique. In the 1790s, Fichte collapses Kant’s distinction and redefines dogmatism. He argues that deriving a canon is essentially dialectical and thus yields an organon: critical idealism is properly a doctrine of science or Wissenschaftslehre. Criticism is furthermore said to refute dogmatism, by (...) which Fichte means Spinozism. Schelling repudiates Fichte’s position in his Philosophical Letters by reviving Kant’s distinction. First, ‘critique’ for Schelling names a canon that is valid for all systems—including Spinozism—and thus favours none—not even the Wissenschaftslehre. Second, Schelling coins ‘dogmaticism’ to refer to what Kant calls ‘dogmatism’: reason’s uncritical claim to doctrine. Hence, he says all systems—even Fichte’s—are susceptible to the ‘enthusiasm’ of mistaking themselves for doctrines or ‘objects of knowledge’, instead of subjectively valid ‘objects of freedom’. I reconstruct Schelling’s argument for reviving Kant’s distinction, while noting two consequences for German idealism. First, if criticism favours no system, a system’s origin cannot be an act of knowledge, e.g., intellectual intuition, but only an act of endorsement. Second, if dogmaticism entails enthusiasm, a system’s goal cannot be absolute knowledge, but only infinite striving. Hence, by retrieving Schelling’s notion of dogmaticism, we can both gain a better understanding of the Letters and register the impact of a core Kantian distinction on the German idealist project. (shrink)

This paper addresses whether, how, and to what extent social studies student teachers who have been introduced to inquiry-oriented teaching (as manifest in the National Council for the Social Studies C3 Framework) in their secondary social studies methods course incorporate this approach into the planning for their practicum experience. Based on analysis of lesson plans used in the practicum and follow-up interviews with a small subset of student teachers, this paper analyzes the factors that promote or inhibit use of this (...) approach to teaching in their practicum experience. Results indicate the C3-oriented teaching approach, as taught in the methods course, did appear in the student teachers’ lesson plans. A small subset of student teachers used the framework competently while two smaller subsets were less adept in their application. The degree of application was affected by student teachers’ perceptions of their school placements and students’ needs. (shrink)

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)

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)

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)

Meillassoux seeks knowledge of transcendental reality, blaming Kant for the ‘correlationist’ proscription of independent access to either thought or being. For Meillassoux, correlationism blocks an account of the meaning of ‘ancestral statements’ regarding reality prior to humans. I examine three charges on which Meillassoux’s argument depends: (1) Kant distorts ancestral statements’ meaning; (2) Kant fallaciously infers causality’s necessity; (3) Kant’s transcendental idealism cannot grasp ‘the great outdoors’. I reject these charges: (1) imposes a Cartesian misreading, hence Meillassoux’s false assumption that, (...) for Kant, objects don’t exist without subjects; (2) misreads Kant, who infers causality’s necessity from the possibility of experience; (3) casts Kant’s idealism as subjective, ignoring his perspectival portrayal of it. (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)

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)

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.

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)

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)

This study examines high school students’ responses to a public policy discussion on the topic of Internet privacy. Specifically, students discussed the question of whether search engines and social media sites should be permitted to monitor, track, and share users’ personal data or whether such practices violate personal privacy. We observed discussions of the topic in four high school classrooms in 2015–2016, prior to the presidential election in 2016. We first explain why the topic failed to work as a controversial (...) public issue with high schoolers. We then explain their responses to the issue. We found (1) students displayed a surprising trust in Facebook and Google; (2) students framed the issue of Internet Privacy as a conflict in values and a set of trade-offs; and (3) students tended to put more weight on personal responsibility than implications for democracy in their assessment of the (acknowledged) erosion of privacy as a result of social media and Internet search engines. We conclude with implications for social studies education and teacher education. (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)

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.

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)

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.

Bazzocchi disposes the text of the Tractatus in a user-friendly manner, exactly as Wittgenstein's decimals advise. This discloses the logical form of the book by distinct reading units, linked into a fashioned hierarchical tree. The text becomes much clearer and every reader can enjoy, finally, its formal and literary qualities.