An examination of counterexamples in proofs and refutations

Article


Bagce, S. and Baskent, C. 2009. An examination of counterexamples in proofs and refutations. Philosophia Scientiae. https://doi.org/10.4000/philosophiascientiae.228
TypeArticle
TitleAn examination of counterexamples in proofs and refutations
AuthorsBagce, S. and Baskent, C.
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.

Research GroupFoundations of Computing group
PublisherOpenEdition
JournalPhilosophia Scientiae
ISSN1281-2463
Electronic1775-4283
Publication dates
Print01 Oct 2009
Publication process dates
Deposited16 Sep 2022
Accepted03 Jan 2008
Output statusPublished
Digital Object Identifier (DOI)https://doi.org/10.4000/philosophiascientiae.228
LanguageEnglish
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