Results for 'Foundations of mathematics Grundlagen der Mathematik'

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  1. Hermann von Helmholtz, Philosophische und populärwissenschaftliche Schriften. 3 Bände.Gregor Schiemann, Michael Heidelberger & Helmut Pulte (eds.) - 2017 - Hamburg: Meiner.
    Aus dem vielfältigen Werk von Hermann von Helmholtz versammelt diese Ausgabe die im engeren Sinne philosophischen Abhandlungen, vor allem zur Wissenschaftsphilosophie und Erkenntnistheorie, sowie Vorträge und Reden, bei denen der Autor seine Ausnahmestellung im Wissenschaftsbetrieb nutzte, um die Wissenschaften und ihre Institutionen in der bestehenden Form zu repräsentieren und zu begründen. Ein Philosoph wollte Helmholtz nicht sein, aber er legte der philosophischen Reflexion wissenschaftlicher Erkenntnis und wissenschaftlichen Handelns große Bedeutung bei. Vor allem bezog er, in der Regel ausgehend von seinen (...)
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  2. Die Grundlagen der Arithmetik, 82-3.George Boolos & Richard G. Heck - 1998 - In Matthias Schirn (ed.), The Philosophy of mathematics today. New York: Clarendon Press.
    A close look at Frege's proof in "Foundations of Arithmetic" that every number has a successor. The examination reveals a surprising gap in the proof, one that Frege would later fill in "Basic Laws of Arithmetic".
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  3. Foundations of Ancient Ethics/Grundlagen Der Antiken Ethik.Jörg Hardy & George Rudebusch - 2014 - Göttingen, Germany: Vandenhoek.
    This book is an anthology with the following themes. Non-European Tradition: Bussanich interprets main themes of Hindu ethics, including its roots in ritual sacrifice, its relationship to religious duty, society, individual human well-being, and psychic liberation. To best assess the truth of Hindu ethics, he argues for dialogue with premodern Western thought. Pfister takes up the question of human nature as a case study in Chinese ethics. Is our nature inherently good (as Mengzi argued) or bad (Xunzi’s view)? Pfister ob- (...)
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  4. Altruismus, Jesus und das Ende der Welt – wie die Templeton Foundation eine Harvard-Professur kaufte und Evolution, Rationalität und Zivilisation angriff. Ein Rezension von E.O. Wilson 'Die soziale Eroberung der Erde' (The Social Conquest of Earth) (2012) und Nowak and Highfield 'SuperCooperators' (2012).Michael Richard Starks - 2020 - In Willkommen in der Hölle auf Erden: Babys, Klimawandel, Bitcoin, Kartelle, China, Demokratie, Vielfalt, Dysgenie, Gleichheit, Hacker, Menschenrechte, Islam, Liberalismus, Wohlstand, Internet, Chaos, Hunger, Krankheit, Gewalt, Künstliche Intelligenz, Krieg. Reality Press. pp. 272-285.
    Der berühmte Ameisenmann E.O. Wilson war schon immer einer meiner Helden - nicht nur ein hervorragender Biologe, sondern eine der winzigen und verschwindenden Minderheit von Intellektuellen, die es zumindest wagt, die Wahrheit über unsere Natur anzudeuten, die andere nicht verstehen oder, soweit sie es verstehen, aus politischen Gründen unermüdlich vermeiden. Leider beendet er seine lange Karriere auf äußerst schäbige Weise als Partei eines ignoranten und arroganten Angriffs auf die Wissenschaft, der zumindest teilweise durch die religiöse Inbrunst seiner Harvard-Kollegenmotiviertist. Es zeigt (...)
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  5. Rezension von "Die äußeren Grenzen der Vernunft " (The Outer Limits of Reason) von Noson Yanofsky 403p (2013) ( Überprüfung überarbeitet 2019).Michael Richard Starks - 2020 - In Willkommen in der Hölle auf Erden: Babys, Klimawandel, Bitcoin, Kartelle, China, Demokratie, Vielfalt, Dysgenie, Gleichheit, Hacker, Menschenrechte, Islam, Liberalismus, Wohlstand, Internet, Chaos, Hunger, Krankheit, Gewalt, Künstliche Intelligenz, Krieg. Reality Press. pp. 191-206.
    Ich gebe einen ausführlichen Überblick über 'The Outer Limits of Reason' von Noson Yanofsky aus einer einheitlichen Perspektive von Wittgenstein und Evolutionspsychologie. Ich weise darauf hin, dass die Schwierigkeit bei Themen wie Paradoxon in Sprache und Mathematik, Unvollständigkeit, Unbedenklichkeit, Berechenbarkeit, Gehirn und Universum als Computer usw. allesamt auf das Versäumnis zurückzuführen ist, unseren Sprachgebrauch im geeigneten Kontext sorgfältig zu prüfen, und daher das Versäumnis, Fragen der wissenschaftlichen Tatsache von Fragen der Funktionsweise von Sprache zu trennen. Ich bespreche Wittgensteins Ansichten (...)
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  6. Stance Pluralism, Scientology and the Problem of Relativism.Ragnar van der Merwe - 2024 - Foundations of Science 29 (3):625–644.
    Inspired by Bas van Fraassen’s Stance Empiricism, Anjan Chakravartty has developed a pluralistic account of what he calls epistemic stances towards scientific ontology. In this paper, I examine whether Chakravartty’s stance pluralism can exclude epistemic stances that licence pseudo-scientific practices like those found in Scientology. I argue that it cannot. Chakravartty’s stance pluralism is therefore prone to a form of debilitating relativism. I consequently argue that we need (1) some ground or constraint in relation to which epistemic stances can be (...)
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  7. Ostwald, Weber und die 'energetischen Grundlagen' der Kulturwissenschaft.Matthias Neuber - 2015 - In Gerhard Wagner & Claudius Härpfer (eds.), Max Webers vergessene Zeitgenossen. Studien zur Genese der Wissenschaftslehre. Wiesbaden: Harrassowitz Verlag..
    Wilhelm Ostwald’s program of a physical energetics is the attempt at a comprehensive description of nature on the basis of the concept of energy. In his book Energetische Grundlagen der Kulturwissenschaft, first published in 1909, Ostwald applies this conception to the area of culture. His central assumption is that cultural phenomena should be described by the energetic notion of “efficiency relation” (Güteverhältnis). His systematic thesis is that science, when organized according to the Machian “principle of economy,” proves as the (...)
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  8. The Beyträge at 200: Bolzano's quiet revolution in the philosophy of mathematics.Jan Sebestik & Paul Rusnock - 2013 - Journal for the History of Analytical Philosophy 1 (8).
    This paper surveys Bolzano's Beyträge zu einer begründeteren Darstellung der Mathematik (Contributions to a better-grounded presentation of mathematics) on the 200th anniversary of its publication. The first and only published issue presents a definition of mathematics, a classification of its subdisciplines, and an essay on mathematical method, or logic. Though underdeveloped in some areas (including,somewhat surprisingly, in logic), it is nonetheless a radically innovative work, where Bolzano presents a remarkably modern account of axiomatics and the epistemology of (...)
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  9. Physical Foundations of Mathematics (In Russian).Andrey Smirnov - manuscript
    The physical foundations of mathematics in the theory of emergent space-time-matter were considered. It is shown that mathematics, including logic, is a consequence of equation which describes the fundamental field. If the most fundamental level were described not by mathematics, but something else, then instead of mathematics there would be consequences of this something else.
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  10. Categorical foundations of mathematics or how to provide foundations for abstract mathematics.Jean-Pierre Marquis - 2013 - Review of Symbolic Logic 6 (1):51-75.
    Fefermans argument is indeed convincing in a certain context, it can be dissolved entirely by modifying the context appropriately.
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  11. The foundations of mathematics from a historical viewpoint.Antonino Drago - 2015 - Epistemologia 38 (1):133-151.
    A new hypothesis on the basic features characterising the Foundations of Mathematics is suggested. By means of them the entire historical development of Mathematics before the 20th Century is summarised through a table. Also the several programs, launched around the year 1900, on the Foundations of Mathematics are characterised by a corresponding table. The major difficulty that these programs met was to recognize an alternative to the basic feature of the deductive organization of a theory (...)
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  12. Hyperintensional Foundations of Mathematical Platonism.David Elohim - manuscript
    This paper aims to provide hyperintensional foundations for mathematical platonism. I examine Hale and Wright's (2009) objections to the merits and need, in the defense of mathematical platonism and its epistemology, of the thesis of Necessitism. In response to Hale and Wright's objections to the role of epistemic and metaphysical modalities in providing justification for both the truth of abstraction principles and the success of mathematical predicate reference, I examine the Necessitist commitments of the abundant conception of properties endorsed (...)
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  13. Grundlagen der Logik und Mathematik: Der Standpunkt Wittgensteins.Timm Lampert - 2003 - In Lampert Timm (ed.), Knowledge and Belief. pp. 44-51.
    Es wird gezeigt, dass Wittgenstein in seiner Frühphilosophie ein nicht-axiomatisches Beweisverständnis entwickelt, für das sich das Problem der Begründung der Axiome nicht stellt. Nach Wittgensteins Beweisverständnis besteht der Beweis einer formalen Eigenschaft einer Formel – z.B. der logischen Wahrheit einer prädikatenlogischen Formel oder der Gleichheit zweier arithmetischer Ausdrücke – in der Transformation der Formel in eine andere Notation, an deren Eigenschaften sich entscheiden lässt, ob die zu beweisende formale Eigenschaft besteht oder nicht besteht. Dieses Verständnis grenzt Wittgenstein gegenüber einem axiomatischen (...)
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  14. Wittgenstein And Labyrinth Of ‘Actual Infinity’: The Critique Of Transfinite Set Theory.Valérie Lynn Therrien - 2012 - Ithaque 10:43-65.
    In order to explain Wittgenstein’s account of the reality of completed infinity in mathematics, a brief overview of Cantor’s initial injection of the idea into set- theory, its trajectory and the philosophic implications he attributed to it will be presented. Subsequently, we will first expound Wittgenstein’s grammatical critique of the use of the term ‘infinity’ in common parlance and its conversion into a notion of an actually existing infinite ‘set’. Secondly, we will delve into Wittgenstein’s technical critique of the (...)
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  15. Category theory and the foundations of mathematics: Philosophical excavations.Jean-Pierre Marquis - 1995 - Synthese 103 (3):421 - 447.
    The aim of this paper is to clarify the role of category theory in the foundations of mathematics. There is a good deal of confusion surrounding this issue. A standard philosophical strategy in the face of a situation of this kind is to draw various distinctions and in this way show that the confusion rests on divergent conceptions of what the foundations of mathematics ought to be. This is the strategy adopted in the present paper. It (...)
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  16. (1 other version)Wittgenstein on the Foundations of Mathematics.Andrew McLean-Inglis - 1992 - Dissertation, Oxford University
    In Part I, an attempt is made to survey the original source material on which any detailed assessment of Wittgenstein's remarks on the foundations of mathematics from his middle and later periods ought to be based. This survey is presented within the context of a sketch of Wittgenstein's biography, which also mentions some of the major developments in his thinking. In addition, certain main themes are emphasized; these have to do primarily with the Kantian aspects of Wittgenstein's thought (...)
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  17. Descriptive Complexity, Computational Tractability, and the Logical and Cognitive Foundations of Mathematics.Markus Pantsar - 2021 - Minds and Machines 31 (1):75-98.
    In computational complexity theory, decision problems are divided into complexity classes based on the amount of computational resources it takes for algorithms to solve them. In theoretical computer science, it is commonly accepted that only functions for solving problems in the complexity class P, solvable by a deterministic Turing machine in polynomial time, are considered to be tractable. In cognitive science and philosophy, this tractability result has been used to argue that only functions in P can feasibly work as computational (...)
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  18. Wittgenstein on Gödelian 'Incompleteness', Proofs and Mathematical Practice: Reading Remarks on the Foundations of Mathematics, Part I, Appendix III, Carefully.Wolfgang Kienzler & Sebastian Sunday Grève - 2016 - In Sebastian Sunday Grève & Jakub Mácha (eds.), Wittgenstein and the Creativity of Language. Palgrave Macmillan. pp. 76-116.
    We argue that Wittgenstein’s philosophical perspective on Gödel’s most famous theorem is even more radical than has commonly been assumed. Wittgenstein shows in detail that there is no way that the Gödelian construct of a string of signs could be assigned a useful function within (ordinary) mathematics. — The focus is on Appendix III to Part I of Remarks on the Foundations of Mathematics. The present reading highlights the exceptional importance of this particular set of remarks and, (...)
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  19. The Quantum Strategy of Completeness: On the Self-Foundation of Mathematics.Vasil Penchev - 2020 - Cultural Anthropology eJournal (Elsevier: SSRN) 5 (136):1-12.
    Gentzen’s approach by transfinite induction and that of intuitionist Heyting arithmetic to completeness and the self-foundation of mathematics are compared and opposed to the Gödel incompleteness results as to Peano arithmetic. Quantum mechanics involves infinity by Hilbert space, but it is finitist as any experimental science. The absence of hidden variables in it interpretable as its completeness should resurrect Hilbert’s finitism at the cost of relevant modification of the latter already hinted by intuitionism and Gentzen’s approaches for completeness. This (...)
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  20. Die toten Hände der Gruppenauswahl und Phänomenologie -Ein Rückblick auf "Individualität und Verstrickung" (Individuality and Entanglement) von Herbert Gintis 357p (2017) (Rezension überarbeitet 2019).Michael Richard Starks - 2020 - In Willkommen in der Hölle auf Erden: Babys, Klimawandel, Bitcoin, Kartelle, China, Demokratie, Vielfalt, Dysgenie, Gleichheit, Hacker, Menschenrechte, Islam, Liberalismus, Wohlstand, Internet, Chaos, Hunger, Krankheit, Gewalt, Künstliche Intelligenz, Krieg. Reality Press. pp. 259-271.
    Da Gintis ein leitender Ökonom ist und ich einige seiner früheren Bücher mit Interesse gelesen habe, erwartete ich einige weitere Einblicke in das Verhalten. Leider, macht er die toten Hände der Gruppenauswahl und Phänomenologie in die Herzstücke seiner Verhaltenstheorien, und das macht die Arbeit weitgehend ungültig. Schlimmer noch, da er hier ein so schlechtes Urteilsvermögen an den Tag stellt, stellt er all seine bisherigen Arbeiten in Frage. Der Versuch, die Gruppenauswahl seiner Freunde in Harvard, Nowak und Wilson wiederzubeleben, vor ein (...)
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  21.  70
    (1 other version)Fichtes Wissenschaftslehre im Aufbrechen der Paradigmen mechanizistischen Denkens.Jürgen Stahl - 1993 - Fichte-Studien 5:149-158.
    Im Artikel wird der Fortschritt von Fichtes Methodenverständnis gegenüber den enzyklopädischen Wissenssystemen – wie beispielsweise bei Wolff, Zeller oder Lambert – herausgearbeitet. Anfang des 19. Jahrhunderts hatte sich die Erkenntnis durchgesetzt, dass weder die Philosophie noch die aufkeimenden Sozialwissenschaften und auch nicht die Naturforschung, wo sie es mit dem Leben zu tun hat, als bloßer Formalismus nach dem Modell der Mathematik oder Physik aufzubauen waren. Fichte gelang es demgegenüber mit seiner Ich-Konstruktion nicht nur das innere Verhältnis der differenzierten Vermögen (...)
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  22. Hilbert's different aims for the foundations of mathematics.Besim Karakadılar - manuscript
    The foundational ideas of David Hilbert have been generally misunderstood. In this dissertation prospectus, different aims of Hilbert are summarized and a new interpretation of Hilbert's work in the foundations of mathematics is roughly sketched out. Hilbert's view of the axiomatic method, his response to criticisms of set theory and intuitionist criticisms of the classical foundations of mathematics, and his view of the role of logical inference in mathematical reasoning are briefly outlined.
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  23. Axioms, Definitions, and the Pragmatic a priori: Peirce and Dewey on the “Foundations” of Mathematical Science.Bradley C. Dart - 2024 - European Journal of Pragmatism and American Philosophy 16 (1).
    Peirce and Dewey were generally more concerned with the process of scientific activity than purely mathematical work. However, their accounts of knowledge production afford some insights into the epistemology of mathematical postulates, especially definition and axioms. Their rejection of rationalist metaphysics and their emphasis on continuity in inquiry provides the pretext for the pragmatic a priori – hypothetical and operational assumptions whose justification relies on their fruitfulness in the long run. This paper focuses on the application of this idea to (...)
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  24. A Pluralist Foundation of the Mathematics of the First Half of the Twentieth Century.Antonino Drago - 2017 - Journal of the Indian Council of Philosophical Research 34 (2):343-363.
    MethodologyA new hypothesis on the basic features characterizing the Foundations of Mathematics is suggested.Application of the methodBy means of it, the several proposals, launched around the year 1900, for discovering the FoM are characterized. It is well known that the historical evolution of these proposals was marked by some notorious failures and conflicts. Particular attention is given to Cantor's programme and its improvements. Its merits and insufficiencies are characterized in the light of the new conception of the FoM. (...)
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  25. Logic. of Descriptions. A New Approach to the Foundations of Mathematics and Science.Joanna Golińska-Pilarek & Taneli Huuskonen - 2012 - Studies in Logic, Grammar and Rhetoric 27 (40):63-94.
    We study a new formal logic LD introduced by Prof. Grzegorczyk. The logic is based on so-called descriptive equivalence, corresponding to the idea of shared meaning rather than shared truth value. We construct a semantics for LD based on a new type of algebras and prove its soundness and completeness. We further show several examples of classical laws that hold for LD as well as laws that fail. Finally, we list a number of open problems. -/- .
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  26. Grete Hermann as Neo-Kantian Philosopher of Space and Time Representation.Erik C. Banks - 2018 - Journal for the History of Analytical Philosophy 6 (3).
    Grete Hermann’s essay “Die naturphilosophischen Grundlagen der Quantenmechanik” has received much deserved scholarly attention in recent years. In this paper, I follow the lead of Elise Crull who sees in Hermann’s work the general outlines of a neo-Kantian interpretation of quantum theory. In full support of this view, I focus on Hermann’s central claim that limited spatio-temporal, and even analogically causal, representations of events exist within an overall relational structure of entangled quantum mechanical states that defy any unified spatio-temporal (...)
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  27. WHAT IS THE "x" WHICH OCCURS IN "sin x"? Being an Essay Towards a Conceptual Foundations of Mathematics.Mohamed Amer - manuscript
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  28. Marriages of Mathematics and Physics: A Challenge for Biology.Arezoo Islami & Giuseppe Longo - 2017 - Progress in Biophysics and Molecular Biology 131:179-192.
    The human attempts to access, measure and organize physical phenomena have led to a manifold construction of mathematical and physical spaces. We will survey the evolution of geometries from Euclid to the Algebraic Geometry of the 20th century. The role of Persian/Arabic Algebra in this transition and its Western symbolic development is emphasized. In this relation, we will also discuss changes in the ontological attitudes toward mathematics and its applications. Historically, the encounter of geometric and algebraic perspectives enriched the (...)
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  29. Aksjologiczne podstawy polskiego prawa [The Axiological Basis of Polish Law].Marek Piechowiak - 2013 - In Tadeusz Guz, Jan Głuchowski & Maria Pałubska (eds.), Synteza prawa polskiego od 1989 roku. C. H. Beck. pp. 39-70.
    An axiological analysis of the basis of the 1997 Constitution of the Republic of Poland, determined mainly in the Preamble, makes it possible to put forward a thesis that this axiology is not, at least in reference to the principle, eclectic. In respect of the meta-axiological settlements, this is a tradition of natural-law type, recognizing the objective grounding of values and law. The accepted solutions are also convergent with the axiology typical of the international protection of human rights. -/- Résumé (...)
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  30. A NEW PHILOSOPHICAL FOUNDATION OF CONSTRUCTIVE MATHEMATICS.Antonino Drago - manuscript
    The current definition of Constructive mathematics as “mathematics within intuitionist logic” ignores two fundamental issues. First, the kind of organization of the theory at issue. I show that intuitionist logic governs a problem-based organization, whose model is alternative to that of the deductive-axiomatic organization, governed by classical logic. Moreover, this dichotomy is independent of that of the kind of infinity, either potential or actual, to which respectively correspond constructive mathematical and classical mathematical tools. According to this view a (...)
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  31. The "Unreasonable" Effectiveness of Mathematics: The Foundational Approach of the Theoretic Alternatives.Catalin Barboianu - 2015 - Revista de Filosofie 62 (1):58-71.
    The attempts of theoretically solving the famous puzzle-dictum of physicist Eugene Wigner regarding the “unreasonable” effectiveness of mathematics as a problem of analytical philosophy, started at the end of the 19th century, are yet far from coming out with an acceptable theoretical solution. The theories developed for explaining the empirical “miracle” of applied mathematics vary in nature, foundation and solution, from denying the existence of a genuine problem to structural theories with an advanced level of mathematical formalism. Despite (...)
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  32. Das kosmische Gedächtnis. Kosmologie, Semiotik und Gedächtnistheorie im Werke von Giordano Bruno (1548-1600), Series: Philosophie und Geschichte der Wissenschaften, Studien und Quellen, Lang, Frankfurt (The introduction can be downloaded from: pdf.) [The Cosmic Memory. Cosmology, Semiotics and Art of Memory in the Work of Giordano Bruno (1548-1600)].Wolfgang Wildgen - 1998 - Frankfurt am Main, Deutschland: Lang.
    Abstract (German) Dieses Buch faßt meine Forschungen zur Semiotik Giordano Brunos und zu deren Grundlagen in der Kosmologie und in der Gedächtnistheorie zusammen, wobei sowohl die Heterogenität als auch der Universalität des Denkers den Charakter dieses Buches geprägt haben. Es wird kein glattes Bild seiner Person oder seines Werkes angeboten, kein bejahender Jubel über eine epochale Leistung; wichtiger war mir die bis ins Detail gehende, manchmal mühselige Interpretation seiner Systementwürfe, wobei ich versucht habe, auch deren formales und technisches Niveau (...)
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  33. Die Grundlagen der Normativität bei Kant und Spener.Anna Szyrwińska - 2011 - Argument: Biannual Philosophical Journal 1 (2):225-238.
    English title: The Fundations of Normativity by Kant and Spener. In one of the chapters in Conflict of Faculties, Kant presents so-called “Spener’s problem”. Kant refers to the conception of the 17th century theologian Philipp Jakob Spener, concerning the problem of radical moral transformation of individuals. Spener became famous as one of the founders and main exponents of pietistic theology, which in the 18th century became one of the most significant intellectual trends at the University of Königsberg and about which (...)
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  34. Die Grundlagen der Arithmetik, §§ 82-3. [REVIEW]William Demopoulos - 1998 - Bulletin of Symbolic Logic 6 (4):407-28.
    This paper contains a close analysis of Frege's proofs of the axioms of arithmetic §§70-83 of Die Grundlagen, with special attention to the proof of the existence of successors in §§82-83. Reluctantly and hesitantly, we come to the conclusion that Frege was at least somewhat confused in those two sections and that he cannot be said to have outlined, or even to have intended, any correct proof there. The proof he sketches is in many ways similar to that given (...)
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  35. Schopenhauers Logikdiagramme in den Mathematiklehrbüchern Adolph Diesterwegs.Jens Lemanski - 2022 - Siegener Beiträge Zur Geschichte Und Philosophie der Mathematik 16:97-127.
    Ein Beispiel für die Rezeption und Fortführung der schopenhauerschen Logik findet man in den Mathematiklehrbüchern Friedrich Adolph Wilhelm Diesterwegs (1790–1866), In diesem Aufsatz werden die historische und systematische Dimension dieser Anwendung von Logikdiagramme auf die Mathematik skizziert. In Kapitel 2 wird zunächst die frühe Rezeption der schopenhauerschen Logik und Philosophie der Mathematik vorgestellt. Dabei werden einige oftmals tradierte Vorurteile, die das Werk Schopenhauers betreffen, in Frage gestellt oder sogar ausgeräumt. In Kapitel 3 wird dann die Philosophie der (...) und der Logik Schopenhauers vorgestellt. Es wird gezeigt, dass Schopenhauers Logikdiagramme auf Ideen der Mathematiker Leonhard Euler (1707–1783), Bernhard Friedrich Thibaut (1775–1832) und Franz Ferdinand Schweins (1780–1856) zurückgehen und dass Schopenhauer diese Logikdiagramme auch bereits zur Analyse mathematischer Begriffe verwendet. Kapitel 4 beschäftigt sich mit der Schopenhauer-Rezeption Diesterwegs. Es wird die Frage behandelt, inwieweit Diesterweg in der Mathematik von Schopenhauer beeinflusst war und welche Rolle dieser Einfluss auf sein Verständnis von Logik und Mathematik hatte. In Kapitel 5 wird schließlich gezeigt, dass Diesterweg die schopenhauersche Begriffsanalyse der Mathematik mit Hilfe von Logikdiagrammen aufgreift und weiterführt. Da Diesterweg einer der einflussreichsten Pädagogen und Mathematikdidaktiker des 20. Jahrhunderts war, ist anzunehmen, dass sich Spuren dieser Methode noch heute finden lassen. Inwiefern dies wahrscheinlich ist, wird in der Zusammenfassung (Kapitel 6) thematisiert. (shrink)
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  36. Computability. Computable functions, logic, and the foundations of mathematics[REVIEW]R. Zach - 2002 - History and Philosophy of Logic 23 (1):67-69.
    Epstein and Carnielli's fine textbook on logic and computability is now in its second edition. The readers of this journal might be particularly interested in the timeline `Computability and Undecidability' added in this edition, and the included wall-poster of the same title. The text itself, however, has some aspects which are worth commenting on.
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  37. Poincaré’s Philosophy of Mathematics.A. P. Bird - 2021 - Cantor's Paradise (00):00.
    It is undeniable Poincaré was a very famous and influential scientist. So, possibly because of it, it was relatively easy for him to participate in the heated discussions of the foundations of mathematics in the early 20th century. We can say it was “easy” because he didn't get involved in this subject by writing great treatises, or entire books about his own philosophy of mathematics (as other authors from the same period did). Poincaré contributed to the philosophy (...)
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  38. Artificial Evil and the Foundation of Computer Ethics.Luciano Floridi & J. W. Sanders - 2001 - Springer Netherlands. Edited by Luciano Floridi & J. W. Sanders.
    Moral reasoning traditionally distinguishes two types of evil:moral (ME) and natural (NE). The standard view is that ME is the product of human agency and so includes phenomena such as war,torture and psychological cruelty; that NE is the product of nonhuman agency, and so includes natural disasters such as earthquakes, floods, disease and famine; and finally, that more complex cases are appropriately analysed as a combination of ME and NE. Recently, as a result of developments in autonomous agents in cyberspace, (...)
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  39. (1 other version)System und Methode.Jürgen Stahl - 1997 - Fichte-Studien 10:99-113.
    Der Autor analysiert die methodologische Grundlegung der Transzendentalphilosophie durch Fichte. Als entscheidenden Punkt arbeitet er den durch Fichte vollzogenen Paradigmenwechsel heraus Danach kommt der Systembegründung nicht mehr ein vorwissenschaftlicher Status zu, sondern diese wird Moment der Systemkonstitution und Systemkonstruktion. Das erlaubt Fichte, die philosophische Methode in ihrer Strenge von der Methode der Mathematik abzuheben. -/- The author analyzes the methodological basis of Fichte's transcendental philosophy. As a decisive point, he works out the paradigm shift that Fichte carried out. According (...)
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  40. Foundations of Relational Realism: A Topological Approach to Quantum Mechanics and the Philosophy of Nature.Michael Epperson & Elias Zafiris - 2013 - Lanham: Lexington Books. Edited by Elias Zafiris.
    Foundations of Relational Realism presents an intuitive interpretation of quantum mechanics, based on a revised decoherent histories interpretation, structured within a category theoretic topological formalism. -/- If there is a central conceptual framework that has reliably borne the weight of modern physics as it ascends into the twenty-first century, it is the framework of quantum mechanics. Because of its enduring stability in experimental application, physics has today reached heights that not only inspire wonder, but arguably exceed the limits of (...)
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  41. Univalent Foundations as a Foundation for Mathematical Practice.Harry Crane - 2018
    I prove that invoking the univalence axiom is equivalent to arguing 'without loss of generality' (WLOG) within Propositional Univalent Foundations (PropUF), the fragment of Univalent Foundations (UF) in which all homotopy types are mere propositions. As a consequence, I argue that practicing mathematicians, in accepting WLOG as a valid form of argument, implicitly accept the univalence axiom and that UF rightly serves as a Foundation for Mathematical Practice. By contrast, ZFC is inconsistent with WLOG as it is applied, (...)
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  42. Reconstructing the Unity of Mathematics circa 1900.David J. Stump - 1997 - Perspectives on Science 5 (3):383-417.
    Standard histories of mathematics and of analytic philosophy contend that work on the foundations of mathematics was motivated by a crisis such as the discovery of paradoxes in set theory or the discovery of non-Euclidean geometries. Recent scholarship, however, casts doubt on the standard histories, opening the way for consideration of an alternative motive for the study of the foundations of mathematics—unification. Work on foundations has shown that diverse mathematical practices could be integrated into (...)
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  43. Sofia A. Yanovskaya: The Marxist Pioneer of Mathematical Logic in the Soviet Union.Dimitris Kilakos - 2019 - Transversal: International Journal for the Historiography of Science 6:49-64.
    K. Marx’s 200th jubilee coincides with the celebration of the 85 years from the first publication of his “Mathematical Manuscripts” in 1933. Its editor, Sofia Alexandrovna Yanovskaya (1896–1966), was a renowned Soviet mathematician, whose significant studies on the foundations of mathematics and mathematical logic, as well as on the history and philosophy of mathematics are unduly neglected nowadays. Yanovskaya, as a militant Marxist, was actively engaged in the ideological confrontation with idealism and its influence on modern (...) and their interpretation. Concomitantly, she was one of the pioneers of mathematical logic in the Soviet Union, in an era of fierce disputes on its compatibility with Marxist philosophy. Yanovskaya managed to embrace in an originally Marxist spirit the contemporary level of logico-philosophical research of her time. Due to her highly esteemed status within Soviet academia, she became one of the most significant pillars for the culmination of modern mathematics in the Soviet Union. In this paper, I attempt to trace the influence of the complex socio-cultural context of the first decades of the Soviet Union on Yanovskaya’s work. Among the several issues I discuss, her encounter with L. Wittgenstein is striking. (shrink)
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  44. Make It So: Imperatival Foundations for Mathematics.Neil Barton, Ethan Russo & Chris Scambler - manuscript
    This article articulates and assesses an imperatival approach to the foundations of mathematics. The core idea for the program is that mathematical domains of interest can fruitfully be viewed as the outputs of construction procedures. We apply this idea to provide a novel formalisation of arithmetic and set theory in terms of such procedures, and discuss the significance of this perspective for the philosophy of mathematics.
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  45. Expanding the notion of inconsistency in mathematics: the theoretical foundations of mutual inconsistency.Carolin Antos - forthcoming - From Contradiction to Defectiveness to Pluralism in Science: Philosophical and Formal Analyses.
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  46. A Structuralist Proposal for the Foundations of the Natural Numbers.Desmond Alan Ford - manuscript
    This paper introduces a novel object that has less structure than, and is ontologically prior to the natural numbers. As such it is a candidate model of the foundation that lies beneath the natural numbers. The implications for the construction of mathematical objects built upon that foundation are discussed.
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  47. Grounding the Selectionist Explanation for the Success of Science in the External Physical World.Ragnar van der Merwe - forthcoming - Foundations of Science: DOI: 10.1007/s10699-023-09907-y.
    I identify two versions of the scientific anti-realist’s selectionist explanation for the success of science: Bas van Fraassen’s original and K. Brad Wray’s newer interpretation. In Wray’s version, psycho-social factors internal to the scientific community – viz. scientists’ interests, goals, and preferences – explain the theory-selection practices that explain theory-success. I argue that, if Wray’s version were correct, then science should resemble art. In art, the artwork-selection practices that explain artwork-success appear faddish. They are prone to radical change over time. (...)
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  48. The Axiom of choice in Quine's New Foundations for Mathematical Logic.Ernst P. Specker - 1954 - Journal of Symbolic Logic 19 (2):127-128.
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  49. On the epistemological foundations of the law of the lever.Maarten Van Dyck - 2009 - Studies in History and Philosophy of Science Part A 40 (3):315-318.
    In this paper I challenge Paolo Palmieri’s reading of the Mach-Vailati debate on Archimedes’s proof of the law of the lever. I argue that the actual import of the debate concerns the possible epistemic (as opposed to merely pragmatic) role of mathematical arguments in empirical physics, and that construed in this light Vailati carries the upper hand. This claim is defended by showing that Archimedes’s proof of the law of the lever is not a way of appealing to a non-empirical (...)
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  50. (1 other version)Time and Information in the Foundations of Physics.Vasil Penchev - 2020 - Information Theory and Research eJournal (Elsevier: SSRN) 1 (25):1-12.
    The paper justifies the following theses: The totality can found time if the latter is axiomatically represented by its “arrow” as a well-ordering. Time can found choice and thus information in turn. Quantum information and its units, the quantum bits, can be interpreted as their generalization as to infinity and underlying the physical world as well as the ultimate substance of the world both subjective and objective. Thus a pathway of interpretation between the totality via time, order, choice, and information (...)
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