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  1. The ‘Popperian Programme’ And Mathematics: Part II: From Quasi-Empiricism to Mathematical Research Programmes.Eduard Glas - 2001 - Studies in History and Philosophy of Science Part A 32 (2):355-376.
    In the first part of this article I investigated the Popperian roots of Lakatos's Proofs and Refutations, which was an attempt to apply, and thereby to test, Popper's theory of knowledge in a field—mathematics—to which it had not primarily been intended to apply. While Popper's theory of knowledge stood up gloriously to this test, the new application gave rise to new insights into the heuristic of mathematical development, which necessitated further clarification and improvement of some Popperian methodological maxims. In the (...)
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  • 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 (...)
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  • Bridging the Gap Between Argumentation Theory and the Philosophy of Mathematics.Alison Pease, Alan Smaill, Simon Colton & John Lee - 2009 - Foundations of Science 14 (1-2):111-135.
    We argue that there are mutually beneficial connections to be made between ideas in argumentation theory and the philosophy of mathematics, and that these connections can be suggested via the process of producing computational models of theories in these domains. We discuss Lakatos’s work (Proofs and Refutations, 1976) in which he championed the informal nature of mathematics, and our computational representation of his theory. In particular, we outline our representation of Cauchy’s proof of Euler’s conjecture, in which we use work (...)
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  • O filozofii matematyki Imre Lakatosa.Krzysztof Wójtowicz - 2007 - Roczniki Filozoficzne 55 (1):229-247.
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  • Mathematical Engineering and Mathematical Change.Jean‐Pierre Marquis - 1999 - International Studies in the Philosophy of Science 13 (3):245 – 259.
    In this paper, I introduce and examine the notion of “mathematical engineering” and its impact on mathematical change. Mathematical engineering is an important part of contemporary mathematics and it roughly consists of the “construction” and development of various machines, probes and instruments used in numerous mathematical fields. As an example of such constructions, I briefly present the basic steps and properties of homology theory. I then try to show that this aspect of contemporary mathematics has important consequences on our conception (...)
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  • Objects and Processes in Mathematical Practice.Uwe V. Riss - 2011 - Foundations of Science 16 (4):337-351.
    In this paper it is argued that the fundamental difference of the formal and the informal position in the philosophy of mathematics results from the collision of an object and a process centric perspective towards mathematics. This collision can be overcome by means of dialectical analysis, which shows that both perspectives essentially depend on each other. This is illustrated by the example of mathematical proof and its formal and informal nature. A short overview of the employed materialist dialectical approach is (...)
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  • 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, (...)
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  • The 'Popperian Programme' and Mathematics.Eduard Glas - 2001 - Studies in History and Philosophy of Science Part A 32 (1):119-137.
    Lakatos's Proofs and Refutations is usually understood as an attempt to apply Popper's methodology of science to mathematics. This view has been challenged because despite appearances the methodology expounded in it deviates considerably from what would have been a straightforward application of Popperian maxims. I take a closer look at the Popperian roots of Lakatos's philosophy of mathematics, considered not as an application but as an extension of Popper's critical programme, and focus especially on the core ideas of this programme (...)
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