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.

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)

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)

Most social scientists and philosophers claim that sociology and philosophy are disjoint fields of inquiry. Some have wondered how to trace the precise boundary between them. Mario Bunge argues that the two fields are so entangled with one another that no demarcation is possible or, indeed, desirable. In fact, sociological research has demonstrably philosophical pre-suppositions. In turn, some findings of sociology are bound to correct or enrich the philosophical theories that deal with the world, our knowledge of it, or (...) the ways of acting upon it. While Bunge's thesis would hardly have shocked Mill, Marx, Durkheim, or Weber, it is alien to the current sociological mainstream and dominant philosophical schools. Bunge demonstrates that philosophical problematics arise in social science research. A fertile philosophy of social science unearths critical presuppositions, analyzes key concepts, refines effective research strategies, crafts coherent and realistic syntheses, and identifies important new problems. Bunge examines Marx's and Durkheim's thesis that social facts are as objective as physical facts; the so-called Thomas theorem that refutes the behaviorist thesis that social agents react to social stimuli rather than to the way we perceive them; and Merton's thesis on the ethos of basic science which shows that science and morality are intertwined. He considers selected philosophical problems raised by contemporary social studies and argues forcefully against tolerance of shabby work in academic social science and philosophy alike. (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)

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)

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)

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)

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)

This fascinating exploration of the great discoveries of history's most important mathematicians seeks an answer to the eternal question: Does mathematics hold the key to understanding the mysteries of the physical world?

It is generally argued that if the wave-function in the de Broglie–Bohm theory is a physical field, it must be a field in configuration space. Nevertheless, it is possible to interpret the wave-function as a multi-field in three-dimensional space. This approach hasn’t received the attention yet it really deserves. The aim of this paper is threefold: first, we show that the wave-function is naturally and straightforwardly construed as a multi-field; second, we show why this interpretation is superior to other interpretations (...) discussed in the literature; third, we clarify common misconceptions. (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.

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)

Machine generated contents note: I. METAPHYSICS -- 1. How Do Realism, Materialism, and Dialectics Fare in Contemporary Science? -- 2. New Dialogues between Hylas and Philonous -- 3. Energy: Between Physics and Metaphysics -- 4. The Revival of Causality -- 5. Emergence and the Mind -- 6 SCIENTIFIC REALISM -- 6. The Status of Concepts -- 7. Popper's Unworldly World 3 --II. METHODOLOGY AND PHILOSOPHY OF SCIENCE -- 8. On Method in the Philosophy of Science -- 9. Induction in Science (...) -- 10. The GST Challenge to the Classical Philosophies of Science -- 11. The Power and Limits of Reduction -- 12. Thinking in Metaphors --III. PHILOSOPHY OF MATHEMATICS -- 13. Moderate Mathematical Fictionism -- 14. The Gap between Mathematics and Reality -- 15. Two Faces and Three Masks of Probability --IV. PHILOSOPHY OF PHYSICS -- 16. Physical Relativity and Philosophy -- 17. Hidden Variables, Separability, and Realism -- 18. Schrodinger's Cat Is Dead --V. PHILOSOPHY OF PSYCHOLOGY -- 19. From Mindless Neuroscience and Brainless Psychology to Neuropsychology -- 20. Explaining Creativity -- VI. PHILOSOPHY OF SOCIAL SCIENCE -- 21. Analytic Philosophy of Society and Social Science: -- The Systemic Approach as an Alternative to Holism and Individualism -- 22. Rational Choice Theory: A Critical Look at Its Foundations -- 23. Realism and Antirealism in Social Science --VII. PHILOSOPHY OF TECHNOLOGY -- 24. The Nature of Applied Science and Technology -- 25. The Technology-Science-Philosophy Triangle in Its Social Context -- 26. The Technologies in Philosophy --VIII. MORAL PHILOSOPHY -- 27. A New Look at Moral Realism -- 28. Rights Imply Duties --IX. SOCIAL AND POLITICAL PHILOSOPHY -- 29. Morality Is the Basis of Legal and Political Legitimacy -- 30. Technoholodemocracy: An Alternative to -- Capitalism and Socialism -- Bibliography -- Index of Names -- Index of Subjects. (shrink)

Predictivists use the no miracle argument to argue that “novel” predictions are decisive evidence for theories, while mere accommodation of “old” data cannot confirm to a significant degree. But deductivists claim that since confirmation is a logical theory-data relationship, predicted data cannot confirm more than merely deduced data, and cite historical cases in which known data confirmed theories quite strongly. On the other hand, the advantage of prediction over accommodation is needed by scientific realists to resist Laudan’s criticisms of the (...) no miracle argument. So, if the deductivists are right, the most powerful argument for realism collapses. There seems to be an inescapable contradiction between these prima facie plausible arguments of predictivists and deductivists; but this puzzle can be solved by understanding what exactly counts as novelty, if novel predictions must support the no miracle argument, i.e., if they must be explainable only by the truth of theories. Taking my cues from the use-novelty tradition, I argue that (1) the predicted data must not be used essentially in building the theory or choosing the auxiliary assumptions. This is possible if the theory and its auxiliary assumptions are plausible independently of the predicted data, and I analyze the consequences of this requirement in terms of best explanation of diverse bodies of data. Moreover, the predicted data must be (2) a priori improbable, and (3) heterogeneous to the essentially used data. My proposed notion of novelty, therefore, is not historical, but functional. Hence, deductivists are right that confirmation is independent of time and of historical contingencies such as if the theorist knew a datum, used it, or intended to accommodate it. Predictivists, however, are right that not all consequences confirm equally, and confirmation is not purely a logical theory-data relation, as it crucially involves background epistemic conditions and the notion of best explanation. Conditions (1)–(3) make the difference between prediction and accommodation, and account for the confirming power of theoretical virtues such as non ad-hocness, non-fudging, non-overfitting, independence and consilience. I thus show that functional novelty (a) avoids the deductivist objections to predictivism, (b) is a gradual notion, in accordance with the common intuition that confirmation comes in degrees, and (c) supports the no miracle argument, so vindicating scientific realism. (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.

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)

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)

There are two possible realist defense strategies against the pessimistic meta-induction and Laudan’s meta-modus tollens: the selective strategy, claiming that discarded theories are partially true, and the discontinuity strategy, denying that pessimism about past theories can be extended to current ones. A radical version of discontinuity realism is proposed by Gerald Doppelt: rather than discriminating between true and false components within theories, he holds that superseded theories cannot be shown to be even partially true, while present best theories are demonstrably (...) completely true. I argue that this position, running counter both the cumulativity of science and fallibilism, is untenable; it cannot account for the success of past theories, nor for the failures of current theories, and rather than shutting the door to the pessimistic historical objections it opens it wide. The best strategy, instead, joins the selective idea there was both some truth and some falsity in discarded theories, like in current ones, with the moderate discontinuity idea that the truth rate in present best theories is much greater than in past ones. (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)

I want to combine two hitherto largely independent research projects, scientific understanding and mechanistic explanations. Understanding is not only achieved by answering why-questions, that is, by providing scientific explanations, but also by answering what-questions, that is, by providing what I call scientific descriptions. Based on this distinction, I develop three forms of understanding: understanding-what, understanding-why, and understanding-how. I argue that understanding-how is a particularly deep form of understanding, because it is based on mechanistic explanations, which answer why something happens in (...) virtue of what it is made of. I apply the three forms of understanding to two case studies: first, to the historical development of thermodynamics and, second, to the differences between the Clausius and the Boltzmann entropy in explaining thermodynamic processes. (shrink)

The ontological models framework distinguishes ψ-ontic from ψ-epistemic wave- functions. It is, in general, quite straightforward to categorize the wave-function of a certain quantum theory. Nevertheless, there has been a debate about the ontological status of the wave-function in the statistical interpretation of quantum mechanics: is it ψ-epistemic and incomplete or ψ-ontic and complete? I will argue that the wave- function in this interpretation is best regarded as ψ-ontic and incomplete.

Deployment Realism resists Laudan’s and Lyons’ objections to the “No Miracle Argument” by arguing that a hypothesis is most probably true when it is deployed essentially in a novel prediction. However, Lyons criticized Psillos’ criterion of essentiality, maintaining that Deployment Realism should be committed to all the actually deployed assumptions. But since many actually deployed assumptions proved false, he concludes that the No Miracle Argument and Deployment Realism fail. I reply that the essentiality condition is required by Occam’s razor. In (...) fact, there is a simpler formulation of essentiality which escapes Lyons’ criticisms and rescues the No Miracle Argument and Deployment Realism from their purported historical counterexamples: a hypothesis is essential when it has no proper parts (in Yablo’s sense) sufficient to derive the same prediction. Although essentiality so conceived cannot be detected prospectively, this is just natural, and it is not a problem but an advantage for Deployment Realism. (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.

Abstract We examine the construction of electromagnetism in its current form, and in an alternative form, from a point of view that combines a minimal realism with strict rational demands. We begin by discussing the requests of reason when constructing a theory and next, we follow the historical development as presented in the record of original publications, the underlying epistemology (often explained by the authors) and the mathematical constructions. The historical construction develops along socio-political disputes (mainly, the reunification of Germany (...) and the second industrial revolution), epistemic disputes (at least two demarcations of science in conflict) and several theories of electromagnetism. Such disputes resulted in the militant adoption of the ether by some, a position that expanded in parallel with the expansion of Prussia. This way of thinking was facilitated by the earlier adoption of a standpoint that required, as a condition for understanding, the use of physical hypothesis in the form of analogies; an attitude that is antithetic to Newton's “hypotheses non fingo”. While the material ether was finally abandoned, the epistemology survived in the form of “substantialism” and a metaphysical ether: the space. The militants of the ether attributed certainties regarding the ether to Faraday and Maxwell, when they only expressed doubts and curiosity. Thus, the official story is not the real history. This was achieved by the operation of detaching Maxwell's electromagnetism from its construction and introducing a new game of formulae and interpretations. Large and important parts of Maxwell work are today not known, as for example, the rules for the transformation of the electromagnetic potentials between moving systems. When experiments showed that all the theories based in the material ether were incorrect, a new interpretation was offered: Special Relativity (SR). At the end of the transformation period a pragmatic view of science, well adapted to the industrial society, had emerged, as well as a new protagonist: the theoretical physicist. The rival theory of delayed action at distance initiated under the influence of Gauss was forgotten in the midst of the intellectual warfare. The theory is indistinguishable in formulae from Maxwell's and its earlier versions are the departing point of Maxwell for the construction of his equations. We show in a mathematical appendix that such (relational) theory can incorporate Lorentz' contributions as well as Maxwell's transformations and C. Neumann's action, without resource to the ether. Demarcation criteria was further changed at the end of the period making room for habits and intuitions. When these intuited criteria are examined by critical reason (seeking for the fundaments) they can be sharpened with the use of the Non Arbitrariness Principle, which throws light over the arbitrariness in the construction of SR. Under a fully rational view SR is not acceptable, it requires to adopt a less demanding epistemology that detaches the concept from the conception, such as Einstein's own view in this respect, inherited from Hertz. In conclusion: we have shown in this relevant exercise how the reality we accept depends on earlier, irrational, decisions that are not offered for examination but rather are inherited from the culture. (shrink)

What does it take to understand a phenomenon ideally, or to the highest conceivable extent? In this paper, we answer this question by arguing for five necessary conditions for ideal understanding: (i) representational accuracy, (ii) intelligibility, (iii) truth, (iv) reasonable endorsement, and (v) fitting. Even if one disagrees that there is some form of ideal understanding, these five conditions can be regarded as sufficient conditions for a particularly deep level of understanding. We then argue that grasping, novel predictions, and transparency (...) are not reasonable conditions for ideal understanding. (shrink)

A re-evaluation of the notion of vacuum in quantum electrodynamics is presented, focusing on the vacuum of the quantized electromagnetic field. In contrast to the ‘nothingness’ associated to the idea of classical vacuum, subtle aspects are found in relation to the vacuum of the quantized electromagnetic field both at theoretical and experimental levels. These are not the usually called vacuum effects. The view defended here is that the so-called vacuum effects are not due to the ground state of the quantized (...) electromagnetic field. Nevertheless it is possible to maintain an empirically demonstrable notion of vacuum state that is consistent with the interpretation of the formalism of the theory. (shrink)