Switch to: References

Citations of:

Lakatos' philosophy of mathematics: a historical approach

New York, N.Y., U.S.A.: Distributors for the U.S. and Canada, Elsevier Science Pub. Co. (1991)

Add citations

You must login to add citations.
  1. Beyond the methodology of mathematics research programmes.Corfield David - 1998 - Philosophia Mathematica 6 (3):272-301.
    In this paper I assess the obstacles to a transfer of Lakatos's methodology of scientific research programmes to mathematics. I argue that, if we are to use something akin to this methodology to discuss modern mathematics with its interweaving theoretical development, we shall require a more intricate construction and we shall have to move still further away from seeing mathematical knowledge as a collection of statements. I also examine the notion of rivalry within mathematics and claim that this appears to (...)
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  • Towards Paraconsistent Inquiry.Can Baskent - 2016 - Australasian Journal of Logic 13 (2).
    In this paper, we discuss Hintikka’s theory of interrogative approach to inquiry with a focus on bracketing. First, we dispute the use of bracketing in the interrogative model of inquiry arguing that bracketing provides an indispensable component of an inquiry. Then, we suggest a formal system based on strategy logic and logic of paradox to describe the epistemic aspects of an inquiry, and obtain a naturally paraconsistent system. We then apply our framework to some cases to illustrate its use.
    Download  
     
    Export citation  
     
    Bookmark  
  • Lakatos’ Quasi-empiricism in the Philosophy of Mathematics.Michael J. Shaffer - 2015 - Polish Journal of Philosophy 9 (2):71-80.
    Imre Lakatos' views on the philosophy of mathematics are important and they have often been underappreciated. The most obvious lacuna in this respect is the lack of detailed discussion and analysis of his 1976a paper and its implications for the methodology of mathematics, particularly its implications with respect to argumentation and the matter of how truths are established in mathematics. The most important themes that run through his work on the philosophy of mathematics and which culminate in the 1976a paper (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • A missing link: The influence of László Kalmár's empirical view on Lakatos' philosophy of mathematics.Dezső Gurka - 2006 - Perspectives on Science 14 (3):263-281.
    . The circumstance, that the text of Imre Lakatos' doctoral thesis from the University of Debrecen did not survive, makes the evaluation of his career in Hungary and the research of aspects of continuity of his lifework difficult. My paper tries to reconstruct these newer aspects of continuity, introducing the influence of László Kalmár the mathematician and his fellow student, and Sándor Karácsony the philosopher and his mentor on Lakatos' work. The connection between the understanding of the empirical basis of (...)
    Download  
     
    Export citation  
     
    Bookmark   6 citations  
  • Towards an Evolutionary Account of Conceptual Change in Mathematics: Proofs and Refutations and the Axiomatic Variation of Concepts.Thomas Mormann - 2002 - In G. Kampis, L: Kvasz & M. Stöltzner (eds.), Appraising Lakatos: Mathematics, Methodology and the Man. Kluwer Academic Publishers. pp. 1--139.
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  • Mathematics as a quasi-empirical science.Gianluigi Oliveri - 2004 - Foundations of Science 11 (1-2):41-79.
    The present paper aims at showing that there are times when set theoretical knowledge increases in a non-cumulative way. In other words, what we call ‘set theory’ is not one theory which grows by simple addition of a theorem after the other, but a finite sequence of theories T1, ..., Tn in which Ti+1, for 1 ≤ i < n, supersedes Ti. This thesis has a great philosophical significance because it implies that there is a sense in which mathematical theories, (...)
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  • Legendre’s Revolution (1794): The Definition of Symmetry in Solid Geometry.Bernard R. Goldstein & Giora Hon - 2005 - Archive for History of Exact Sciences 59 (2):107-155.
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  • (1 other version)Editor's Introduction: Hungarian Studies in Lakatos' Philosophies of Mathematics and Science.Stefania R. Jha - 2006 - Perspectives on Science 14 (3):257-262.
    Download  
     
    Export citation  
     
    Bookmark  
  • Proof-analysis and continuity.Michael Otte - 2004 - Foundations of Science 11 (1-2):121-155.
    During the first phase of Greek mathematics a proof consisted in showing or making visible the truth of a statement. This was the epagogic method. This first phase was followed by an apagogic or deductive phase. During this phase visual evidence was rejected and Greek mathematics became a deductive system. Now epagoge and apagoge, apart from being distinguished, roughly according to the modern distinction between inductive and deductive procedures, were also identified on account of the conception of generality as continuity. (...)
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  • Criticism and growth of mathematical knowledge.Gianluigi Oliveri - 1997 - Philosophia Mathematica 5 (3):228-249.
    This paper attempts to show that mathematical knowledge does not grow by a simple process of accumulation and that it is possible to provide a quasi-empirical (in Lakatos's sense) account of mathematical theories. Arguments supporting the first thesis are based on the study of the changes occurred within Eudidean geometry from the time of Euclid to that of Hilbert; whereas those in favour of the second arise from reflections on the criteria for refutation of mathematical theories.
    Download  
     
    Export citation  
     
    Bookmark   5 citations  
  • Heuristic, methodology or logic of discovery? Lakatos on patterns of thinking.Olga Kiss - 2006 - Perspectives on Science 14 (3):302-317.
    . Heuristic is a central concept of Lakatos' philosophy both in his early works and in his later work, the methodology of scientific research programs. The term itself, however, went through significant change of meaning. In this paper I study this change and the ‘metaphysical’ commitments behind it. In order to do so, I turn to his mathematical heuristic elaborated in Proofs and Refutations. I aim to show the dialogical character of mathematical knowledge in his account, which can open a (...)
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  • Problems with Fallibilism as a Philosophy of Mathematics Education.Stuart Rowlands, Ted Graham & John Berry - 2011 - Science & Education 20 (7-8):625-654.
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  • A Burgessian Critique of Nominalistic Tendencies in Contemporary Mathematics and its Historiography.Karin Usadi Katz & Mikhail G. Katz - 2012 - Foundations of Science 17 (1):51-89.
    We analyze the developments in mathematical rigor from the viewpoint of a Burgessian critique of nominalistic reconstructions. We apply such a critique to the reconstruction of infinitesimal analysis accomplished through the efforts of Cantor, Dedekind, and Weierstrass; to the reconstruction of Cauchy’s foundational work associated with the work of Boyer and Grabiner; and to Bishop’s constructivist reconstruction of classical analysis. We examine the effects of a nominalist disposition on historiography, teaching, and research.
    Download  
     
    Export citation  
     
    Bookmark   18 citations  
  • History, methodology and early algebra 1.Brendan Larvor - 1994 - International Studies in the Philosophy of Science 8 (2):113-124.
    The limits of ‘criterial rationality’ (that is, rationality as rule‐following) have been extensively explored in the philosophy of science by Kuhn and others. In this paper I attempt to extend this line of enquiry into mathematics by means of a pair of case studies in early algebra. The first case is the Ars Magna (Nuremburg 1545) by Jerome Cardan (1501–1576), in which a then recently‐discovered formula for finding the roots of some cubic equations is extended to cover all cubics and (...)
    Download  
     
    Export citation  
     
    Bookmark  
  • Searching for the holy in the ascent of Imre Lakatos.John Wettersten - 2004 - Philosophy of the Social Sciences 34 (1):84-150.
    Bernard Lavor and John Kadvany argue that Lakatos’s Hegelian approach to the philosophy of mathematics and science enabled him to overcome all competing philosophies. His use of the approach Hegel developed in his Phenomenology enabled him to show how mathematics and science develop, how they are open-ended, and that they are not subject to rules, even though their rationality may be understood after the fact. Hegel showed Lakatos how to falsify the past to make progress in the present. A critique (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • Mathematical naturalism: Origins, guises, and prospects. [REVIEW]Bart Van Kerkhove - 2006 - Foundations of Science 11 (1-2):5-39.
    During the first half of the twentieth century, mainstream answers to the foundational crisis, mainly triggered by Russell and Gödel, remained largely perfectibilist in nature. Along with a general naturalist wave in the philosophy of science, during the second half of that century, this idealist picture was finally challenged and traded in for more realist ones. Next to the necessary preliminaries, the present paper proposes a structured view of various philosophical accounts of mathematics indebted to this general idea, laying the (...)
    Download  
     
    Export citation  
     
    Bookmark   4 citations  
  • Maxime Bôcher's concept of complementary philosophy of mathematics.Jerzy Dadaczyński & Robert Piechowicz - 2020 - Philosophical Problems in Science 68:9-36.
    The main purpose of the present paper is to demonstrate that as early as 1904 pre-eminent American mathematician Maxime Bôcher was an adherent to the presently relevant argument of reasonableness, or even necessity of parallel development of two philosophical methods of reflection on mathematics, so that its essence could be more fully comprehended. The goal of the research gives rise to the question: what two types of philosophical deliberation on mathematics were proposed by Bôcher?
    Download  
     
    Export citation  
     
    Bookmark  
  • Mathematical explanation: Problems and prospects.Paolo Mancosu - 2001 - Topoi 20 (1):97-117.
    Download  
     
    Export citation  
     
    Bookmark   51 citations  
  • What can the Philosophy of Mathematics Learn from the History of Mathematics?Brendan Larvor - 2008 - Erkenntnis 68 (3):393-407.
    This article canvasses five senses in which one might introduce an historical element into the philosophy of mathematics: 1. The temporal dimension of logic; 2. Explanatory Appeal to Context rather than to General Principles; 3. Heraclitean Flux; 4. All history is the History of Thought; and 5. History is Non-Judgmental. It concludes by adapting Bernard Williams’ distinction between ‘history of philosophy’ and ‘history of ideas’ to argue that the philosophy of mathematics is unavoidably historical, but need not and must not (...)
    Download  
     
    Export citation  
     
    Bookmark  
  • The Creative Growth of Mathematics.Jean Paul van Bendegem - 1999 - Philosophica 63 (1).
    Download  
     
    Export citation  
     
    Bookmark   5 citations  
  • O filozofii matematyki Imre Lakatosa.Krzysztof Wójtowicz - 2007 - Roczniki Filozoficzne 55 (1):229-247.
    Download  
     
    Export citation  
     
    Bookmark