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  1. Two Dogmas of Empiricism.W. Quine - 1951 - [Longmans, Green].
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  • Collected Papers of Charles Sanders Peirce: Pragmatism and pragmaticism and Scientific metaphysics.Charles Sanders Peirce - 1960 - Cambridge: Belknap Press.
    Charles Sanders Peirce has been characterized as the greatest American philosophic genius. He is the creator of pragmatism and one of the founders of modern logic. James, Royce, Schroder, and Dewey have acknowledged their great indebtedness to him. A laboratory scientist, he made notable contributions to geodesy, astronomy, psychology, induction, probability, and scientific method. He introduced into modern philosophy the doctrine of scholastic realism, developed the concepts of chance, continuity, and objective law, and showed the philosophical significance of the theory (...)
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  • Non-standard Analysis.Gert Heinz Müller - 2016 - Princeton University Press.
    Considered by many to be Abraham Robinson's magnum opus, this book offers an explanation of the development and applications of non-standard analysis by the mathematician who founded the subject. Non-standard analysis grew out of Robinson's attempt to resolve the contradictions posed by infinitesimals within calculus. He introduced this new subject in a seminar at Princeton in 1960, and it remains as controversial today as it was then. This paperback reprint of the 1974 revised edition is indispensable reading for anyone interested (...)
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  • Argumentation schemes for presumptive reasoning.Douglas N. Walton - 1996 - Mahwah, N.J.: L. Erlbaum Associates.
    This book identifies 25 argumentation schemes for presumptive reasoning and matches a set of critical questions to each.
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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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  • Is there a logic of scientific discovery?Norwood Russell Hanson - 1960 - Australasian Journal of Philosophy 38 (2):91 – 106.
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  • Managing Informal Mathematical Knowledge: Techniques from Informal Logic.Andrew Aberdein - 2006 - Lecture Notes in Artificial Intelligence 4108:208--221.
    Much work in MKM depends on the application of formal logic to mathematics. However, much mathematical knowledge is informal. Luckily, formal logic only represents one tradition in logic, specifically the modeling of inference in terms of logical form. Many inferences cannot be captured in this manner. The study of such inferences is still within the domain of logic, and is sometimes called informal logic. This paper explores some of the benefits informal logic may have for the management of informal mathematical (...)
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  • (1 other version)Proofs and refutations (I).Imre Lakatos - 1963 - British Journal for the Philosophy of Science 14 (53):1-25.
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  • Proofs and refutations (II).Imre Lakatos - 1963 - British Journal for the Philosophy of Science 14 (54):120-139.
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  • A Computational Model Of Lakatos-style Reasoning.Alison Pease - 2013 - Philosophy of Mathematics Education Journal 27.
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  • Mathematical explanation: Problems and prospects.Paolo Mancosu - 2001 - Topoi 20 (1):97-117.
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  • The Uses of Argument in Mathematics.Andrew Aberdein - 2005 - Argumentation 19 (3):287-301.
    Stephen Toulmin once observed that ”it has never been customary for philosophers to pay much attention to the rhetoric of mathematical debate’ [Toulmin et al., 1979, An Introduction to Reasoning, Macmillan, London, p. 89]. Might the application of Toulmin’s layout of arguments to mathematics remedy this oversight? Toulmin’s critics fault the layout as requiring so much abstraction as to permit incompatible reconstructions. Mathematical proofs may indeed be represented by fundamentally distinct layouts. However, cases of genuine conflict characteristically reflect an underlying (...)
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  • Translating Toulmin Diagrams: Theory Neutrality in Argument Representation.Chris Reed & Glenn Rowe - 2005 - Argumentation 19 (3):267-286.
    The Toulmin diagram layout is very familiar and widely used, particularly in the teaching of critical thinking skills. The conventional box-and-arrow diagram is equally familiar and widespread. Translation between the two throws up a number of interesting challenges. Some of these challenges (such as the relationship between Toulmin warrants and their counterparts in traditional diagrams) represent slightly different ways of looking at old and deep theoretical questions. Others (such as how to allow Toulmin diagrams to be recursive) are diagrammatic versions (...)
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  • Proofs and refutations (III).Imre Lakatos - 1963 - British Journal for the Philosophy of Science 14 (55):221-245.
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  • (1 other version)Proofs and Refutations.Imre Lakatos - 1980 - Noûs 14 (3):474-478.
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  • Analysis in greek geometry.Richard Robinson - 1936 - Mind 45 (180):464-473.
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  • Proofs and refutations (IV).I. Lakatos - 1963 - British Journal for the Philosophy of Science 14 (56):296-342.
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  • What's there to know? A Fictionalist Approach to Mathematical Knowledge.Mary Leng - 2007 - In Mary Leng, Alexander Paseau & Michael D. Potter (eds.), Mathematical Knowledge. Oxford, England: Oxford University Press.
    Defends an account of mathematical knowledge in which mathematical knowledge is a kind of modal knowledge. Leng argues that nominalists should take mathematical knowledge to consist in knowledge of the consistency of mathematical axiomatic systems, and knowledge of what necessarily follows from those axioms. She defends this view against objections that modal knowledge requires knowledge of abstract objects, and argues that we should understand possibility and necessity in a primative way.
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