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  1. On the most open question in the history of mathematics: A discussion of Maddy.Adrian Riskin - 1994 - Philosophia Mathematica 2 (2):109-121.
    In this paper, I argue against Penelope Maddy's set-theoretic realism by arguing (1) that it is perfectly consistent with mathematical Platonism to deny that there is a fact of the matter concerning statements which are independent of the axioms of set theory, and that (2) denying this accords further that many contemporary Platonists assert that there is a fact of the matter because they are closet foundationalists, and that their brand of foundationalism is in radical conflict with actual mathematical practice.
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  • Euclid's elements and the axiomatic method.Ian Mueller - 1969 - British Journal for the Philosophy of Science 20 (4):289-309.
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  • The four-color theorem and mathematical proof.Michael Detlefsen & Mark Luker - 1980 - Journal of Philosophy 77 (12):803-820.
    I criticize a recent paper by Thomas Tymoczko in which he attributes fundamental philosophical significance and novelty to the lately-published computer-assisted proof of the four color theorem (4CT). Using reasoning precisely analogous to that employed by Tymoczko, I argue that much of traditional mathematical proof must be seen as resting on what Tymoczko must take as being "empirical" evidence. The new proof of the 4CT, with its use of what Tymoczko calls "empirical" evidence is therefore not so novel as he (...)
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  • Proclus: A Commentary on the First Book of Euclid's Elements.Glenn R. Morrow (ed.) - 1970 - Princeton University Press.
    In Proclus' penetrating exposition of Euclid's method's and principles, the only one of its kind extant, we are afforded a unique vantage point for understanding the structure and strenght of the Euclidean system. A primary source for the history and philosophy of mathematics, Proclus' treatise contains much priceless information about the mathematics and mathematicians of the previous seven or eight centuries that has not been preserved elsewhere.
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  • History and Philosophy of Modern Mathematics.William Aspray & Philip Kitcher - 1988 - U of Minnesota Press.
    History and Philosophy of Modern Mathematics was first published in 1988. Minnesota Archive Editions uses digital technology to make long-unavailable books once again accessible, and are published unaltered from the original University of Minnesota Press editions. The fourteen essays in this volume build on the pioneering effort of Garrett Birkhoff, professor of mathematics at Harvard University, who in 1974 organized a conference of mathematicians and historians of modern mathematics to examine how the two disciplines approach the history of mathematics. In (...)
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  • (4 other versions)Two Dogmas of Empiricism.Willard V. O. Quine - 1951 - Philosophical Review 60 (1):20–43.
    Modern empiricism has been conditioned in large part by two dogmas. One is a belief in some fundamental cleavage between truths which are analytic, or grounded in meanings independently of matters of fact, and truth which are synthetic, or grounded in fact. The other dogma is reductionism: the belief that each meaningful statement is equivalent to some logical construct upon terms which refer to immediate experience. Both dogmas, I shall argue, are ill founded. One effect of abandoning them is, as (...)
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  • The philosophy of mathematics of Imre Lakatos.Mark Steiner - 1983 - Journal of Philosophy 80 (9):502-521.
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  • Poincaré's conception of the objectivity of mathematics.Janet Folina - 1994 - Philosophia Mathematica 2 (3):202-227.
    There is a basic division in the philosophy of mathematics between realist, ‘platonist’ theories and anti-realist ‘constructivist’ theories. Platonism explains how mathematical truth is strongly objective, but it does this at the cost of invoking mind-independent mathematical objects. In contrast, constructivism avoids mind-independent mathematical objects, but the cost tends to be a weakened conception of mathematical truth. Neither alternative seems ideal. The purpose of this paper is to show that in the philosophical writings of Henri Poincaré there is a coherent (...)
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  • The logic of impossible quantities.David Sherry - 1991 - Studies in History and Philosophy of Science Part A 22 (1):37-62.
    In a ground-breaking essay Nagel contended that the controversy over impossible numbers influenced the development of modern logic. I maintain that Nagel was correct in outline only. He overlooked the fact that the controversy engendered a new account of reasoning, one in which the concept of a well-made language played a decisive role. Focusing on the new account of reasoning changes the story considerably and reveals important but unnoticed similarities between the development of algebraic logic and quantificational logic.
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  • The Wake of Berkeley's Analyst: Rigor Mathematicae?David Sherry - 1987 - Studies in History and Philosophy of Science Part A 18 (4):455.
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  • Polyhedra and the Abominations of Leviticus.David Bloor - 1978 - British Journal for the History of Science 11 (3):245-272.
    How are social and institutional circumstances linked to the knowledge that scientists produce? To answer this question it is necessary to take risks: speculative but testable theories must be proposed. It will be my aim to explain and then apply one such theory. This will enable me to propose an hypothesis about the connexion between social processes and the style and content of mathematical knowledge.
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  • (1 other version)The Logic of Mathematical Discovery vs. the Logical Structure of Mathematics.Solomon Feferman - 1978 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1978:309 - 327.
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  • The concept of function up to the middle of the 19th century.A. P. Youschkevitch - 1976 - Archive for History of Exact Sciences 16 (1):37-85.
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  • The ritual origin of geometry.A. Seidenberg - 1961 - Archive for History of Exact Sciences 1 (5):488-527.
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  • Meno. Plato & Lane Cooper - 1961 - In Edith Hamilton & Huntington Cairns (eds.), Plato: The Collected Dialogues. Princeton: New Jersey: Princeton University Press.
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  • Basic Works. Aristotle - 1942 - Philosophical Review 51:95.
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  • (1 other version)The Formal and the Informal.William Berkson - 1978 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1978:297 - 308.
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