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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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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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424Williams 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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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
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203Proof in C17 AlgebraPhilosophia Scientiae 43-59. 2005.By the middle of the seventeenth century we that find that algebra is able to offer proofs in its own right. That is, by that time algebraic argument had achieved the status of proof. How did this transformation come about?
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58Lakatos: An IntroductionRoutledge. 1998._Lakatos: An Introduction_ provides a thorough overview of both Lakatos's thought and his place in twentieth century philosophy. It is an essential and insightful read for students and anyone interested in the philosophy of science.
Areas of Specialization
Philosophy of Mathematics |
Areas of Interest
Logic and Philosophy of Logic |
Philosophy of Mathematics |