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Poincaré's philosophy of mathematics
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dc.contributor.advisor | Clark, Peter | |
dc.contributor.author | Folina, Janet | |
dc.coverage.spatial | 248 | en_US |
dc.date.accessioned | 2012-06-08T14:12:15Z | |
dc.date.available | 2012-06-08T14:12:15Z | |
dc.date.issued | 1986 | |
dc.identifier.uri | https://hdl.handle.net/10023/2703 | |
dc.description.abstract | The primary concern of this thesis is to investigate the explicit philosophy of mathematics in the work of Henri Poincare. In particular, I argue that there is a well-founded doctrine which grounds both Poincare's negative thesis, which is based on constructivist sentiments, and his positive thesis, via which he retains a classical conception of the mathematical continuum. The doctrine which does so is one which is founded on the Kantian theory of synthetic a priori intuition. I begin, therefore, by outlining Kant's theory of the synthetic a priori, especially as it applies to mathematics. Then, in the main body of the thesis, I explain how the various central aspects of Poincare's philosophy of mathematics - e.g. his theory of induction; his theory of the continuum; his views on impredicativiti his theory of meaning - must, in general, be seen as an adaptation of Kant's position. My conclusion is that not only is there a well-founded philosophical core to Poincare's philosophy, but also that such a core provides a viable alternative in contemporary debates in the philosophy of mathematics. That is, Poincare's theory, which is secured by his doctrine of a priori intuitions, and which describes a position in between the two extremes of an "anti-realist" strict constructivism and a "realist" axiomatic set theory, may indeed be true. | en_US |
dc.language.iso | en | en_US |
dc.publisher | University of St Andrews | |
dc.subject.lcsh | QA9.P7F7 | |
dc.subject.lcsh | Mathematics--Philosophy | en_US |
dc.title | Poincaré's philosophy of mathematics | en_US |
dc.type | Thesis | en_US |
dc.type.qualificationlevel | Doctoral | en_US |
dc.type.qualificationname | PhD Doctor of Philosophy | en_US |
dc.publisher.institution | The University of St Andrews | en_US |
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