An Examination of Counterexamples in Proofs and Refutations
Abstract: Lakatos’s seminal work Proofs and Refutations introduced the methods of proofs and refutations by discussing the history and methodological development of Euler’s formula V — E+F = 2 for three dimensional polyhedra. Lakatos considered the history of polyhedra illustrating a good example fo...
| Main Authors: | , |
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| Format: | Article |
| Language: | deu |
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Éditions Kimé
2009-10-01
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| Series: | Philosophia Scientiæ |
| Online Access: | http://journals.openedition.org/philosophiascientiae/228 |
| Summary: | Abstract: Lakatos’s seminal work Proofs and Refutations introduced the methods of proofs and refutations by discussing the history and methodological development of Euler’s formula V — E+F = 2 for three dimensional polyhedra. Lakatos considered the history of polyhedra illustrating a good example for his philosophy and methodology of mathematics and geometry. In this study, we focus on the mathematical and topological properties which play a role in Lakatos’s methodological approach. For each example and counterexample given by Lakatos, we briefly outline its topological counterpart. We thus present the mathematical background and basis of Lakatos’s philosophy of mathematical methodology in the case of Euler’s formula, and thereby develop some intuitions about the function of his notions of positive and negative heuristics. |
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| ISSN: | 1281-2463 1775-4283 |