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34EMILY R. GROSHOLZ. Representation and Productive Ambiguity in Mathematics and the Sciences. Oxford: Oxford University Press, 2007. ISBN 978-0-19-929973-7. Pp. viii + 313 (review)Philosophia Mathematica 20 (2): 245-252. 2012.
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48Michel Serfati. La Révolution Symbolique: La Constitution de l'Ecriture Symbolique Mathématique. Preface by Jacques Bouverasse. Paris: Éditions Petra, 2005. Pp. ix + 427. ISBN 2-84743-006-7 (review)Philosophia Mathematica 15 (1): 122-126. 2007.It is difficult to imagine mathematics without its symbolic language. It is especially difficult to imagine doing mathematics without using mathematical notation. Nevertheless, that is how mathematics was done for most of human history. It was only at the end of the sixteenth century that mathematicians began to develop systems of mathematical symbols . It is startling to consider how rapidly mathematical notation evolved. Viète is usually taken to have initiated this development with his Isagog…Read more
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47Paolo Mancosu, ed. The Philosophy of Mathematical Practice. Oxford: Oxford University Press, 2008. ISBN 978-0-19-929645-3. Pp. xi + 447: Critical Studies/Book Reviews (review)Philosophia Mathematica 18 (3): 350-360. 2010.(No abstract is available for this citation)
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90What can the Philosophy of Mathematics Learn from the History of Mathematics?Erkenntnis 68 (3): 393-407. 2008.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 historic…Read more
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339Two CulturesCogito 12 (1): 13-16. 1998.The schism between analytic and continental philosophy resists repair because it is not confined to philosophers. It is a local manifestation of a far more profound and pervasive division. In 1959 C.P. Snow lamented the partition of intellectual life in to `two cultures': that of the scientist and that of the literary intellectual. If we follow the practice of most universities and bundle historical and literary studies together in the faculty of humanities on the one hand, and count pure mathem…Read more
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129Moral particularism and scientific practiceMetaphilosophy 39 (4-5): 492-507. 2008.Abstract: Particularism is usually understood as a position in moral philosophy. In fact, it is a view about all reasons, not only moral reasons. Here, I show that particularism is a familiar and controversial position in the philosophy of science and mathematics. I then argue for particularism with respect to scientific and mathematical reasoning. This has a bearing on moral particularism, because if particularism about moral reasons is true, then particularism must be true with respect to reas…Read more
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123Imre Lakatos and Paul Feyerabend for and against method: Including Lakatos's lectures on scientific method and the Lakatos–Feyerabend correspondence (review)British Journal for the Philosophy of Science 51 (4): 919-922. 2000.
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15Book reviews (review)International Studies in the Philosophy of Science 7 (2): 191-207. 1993.The Chances of Explanation: Causal Explanation in the Social, Medical, and Physical Sciences Paul Humphreys, 1989 Princeton University Press x+170 pp., £12.95 (paperback) ISBN 0 691 020286 8; £25.00 (hardback) ISBN 0 69107353 8In Search of a Better World: Lectures and Essays from Thirty Years Karl Popper London, Routledge £25.00 (hardback)Artificial Morality: Virtuous Robots for Virtual Games Peter Danielson, 1992 London, Routledge £35.00 (hardback) ISBN 0 415 034841; £10.99 (paperback) ISBN 0 4…Read more
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367Tales of wonder: Ian Hacking: Why is there philosophy of mathematics at all? Cambridge University Press, 2014, 304pp, $80 HBMetascience 24 (3): 471-478. 2015.Why is there Philosophy of Mathematics at all? Ian Hacking. in Metascience (2015)
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Michael Detlefsen, ed., "Proof and Knowledge in Mathematics" (review)International Journal of Philosophical Studies 2 (1): 149. 1994.
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92What is dialectical philosophy of mathematics?Philosophia Mathematica 9 (2): 212-229. 2001.The late Imre Lakatos once hoped to found a school of dialectical philosophy of mathematics. The aim of this paper is to ask what that might possibly mean. But Lakatos's philosophy has serious shortcomings. The paper elaborates a conception of dialectical philosophy of mathematics that repairs these defects and considers the work of three philosophers who in some measure fit the description: Yehuda Rav, Mary Leng and David Corfield.
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21Review of Imre Lakatos, Paul Feyerabend and Matteo Motterlini: For and Against Method: Including Lakatos's Lectures on Scientific Method and the Lakatos-Feyerabend Correspondence (review)British Journal for the Philosophy of Science 51 (4): 919-922. 2000.
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39The formalising tendency in philosophy and experimental psychologyPhenomenology and the Cognitive Sciences 2 (4): 337-352. 2003.This paper is an exercise in the phenomenology of science. It examines the tendency to prefer formal accounts in a familiar body of experimental psychology. It will argue that, because of this tendency, psychologists of this school neglect those forms of human cognition typical of the humanities disciplines. This is not a criticism of psychology, however. Such neglect is compatible with scientific rigour, provided it does not go unnoticed. Indeed, reflection on the case in hand allows us to refi…Read more
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24Old Maps, Crystal Spheres, and the Cartesian CircleGraduate Faculty Philosophy Journal 22 (2): 13-27. 2001.It would be a mistake to imagine that the problem of the Cartesian circle lies in Descartes’ suggestion that we cannot know anything unless we know God. It is true that this thought seems fatal to his enterprise; for if we cannot know anything prior to knowing that God exists, then it follows that we cannot know the arguments that prove God’s existence. However the problem of the Cartesian circle does not consist in this logical error. It consists, rather, in the fact that Descartes’ attempts to…Read more
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78Lakatos as historian of mathematicsPhilosophia Mathematica 5 (1): 42-64. 1997.This paper discusses the connection between the actual history of mathematics and Lakatos's philosophy of mathematics, in three parts. The first points to studies by Lakatos and others which support his conception of mathematics and its history. In the second I suggest that the apparent poverty of Lakatosian examples may be due to the way in which the history of mathematics is usually written. The third part argues that Lakatos is right to hold philosophy accountable to history, even if Lakatos'…Read more
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Proceedings of the Symposium on Mathematical Practice and Cognition Ii: A Symposium at the Aisb/Iacap World Congress 2012 (edited book)Society for the Study of Artificial Intelligence and the Simulation of Behaviour. 2012.
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Bransen, JAM and Slors, M.(eds.)-The Problematic Reality of ValuesPhilosophical Books 39 61-61. 1998.
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The Philosophy of Mathematics of Imre LakatosDissertation, Oxford University. 1995.DPhil dissertation, University of Oxford.
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55Re-reading soviet philosophy: Bakhurst on ilyenkovStudies in East European Thought 44 (1): 1-31. 1992.
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29History, methodology and early algebra 1International Studies in the Philosophy of Science 8 (2): 113-124. 1994.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 proved. The…Read more
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428Williams on Dawkins – responseThink 9 (26): 21-27. 2010.Peter Williams complains that Richard Dawkins wraps his naturalism in ‘a fake finery of counterfeit meaning and purpose’. For his part, Williams has wrapped his complaint in an unoriginal and inapt analogy. The weavers in Hans Christian Andersen's fable announce that the Emperor's clothes are invisible to stupid people; almost the whole population pretends to see them for fear of being thought stupid . Fear of being thought stupid does not seem to trouble Richard Dawkins. Moreover, Williams offe…Read more
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25Albert Lautman, ou la dialectique dans les mathématiquesPhilosophiques 37 (1): 75-94. 2010.Dans cet article, j’explore dans un premier temps la conception que se fait Lautman de la dialectique en examinant ses références à Platon et Heidegger. Je compare ensuite les structures dialectiques identifiées par Lautman dans les mathématiques contemporaines avec celles qui émergent de ses sources philosophiques. Enfin, je soutiens que les structures qu’il a découvertes dans les mathématiques sont plus riches que le suggère son modèle platonicien, et que la distinction « ontologique » de Heid…Read more
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66Three is a magic numberThe Philosophers' Magazine 44 (44): 83-88. 2009.Logical theory – and philosophical theory generally – is just that, theory. Generations of logic students felt a sort of unease about it without knowing what to do about it. Nowadays, students of mathematical logic feel a similar unease when faced with the fact that in standard predicate calculus, “All unicorns are sneaky” is true precisely because there are no unicorns. Blanché’s analysis reminds us that such feelings of unease may indicate a shortcoming in the theory rather than in the student…Read more
Areas of Specialization
Philosophy of Mathematics |
Areas of Interest
Logic and Philosophy of Logic |
Philosophy of Mathematics |