Lakatos's philosophy of mathematics

✍ Scribed by Gregory Currie

• Publisher: Springer Netherlands
• Year: 1979
• Tongue: English
• Weight: 905 KB
• Volume: 42
• Category: Article
• ISSN: 0039-7857
• DOI: 10.1007/bf00413811

✦ Synopsis

In November of 1956, at the age of 31, Imre Lakatos left Hungary, going first to Vienna and then to Kings College, Cambridge, as a Ph.D. student. For his thesis he chose the topic of mathematical discovery and, at the suggestion of the Hungarian mathematician George Polyfi, he based his research on an historical case study; the development of a conjecture, due to Euler, about polyhedra. This part of the thesis is in the form of a dialogue, while other chapters, concerning the ancient method of analysis-synthesis and developments in 19th Century analysis are given in conventional, expository form. The thesis was completed in 1959,1 and later the first two chapters (concerning Euler's conjecture) were expanded into a series of articles, z After Lakatos's death in 1974 these articles, together with another two chapters from the thesis, were published in book form.

In this paper I shall examine some of the main theses of Proofs and Refutations, 3 and I shall try to put the views expressed there into the context of Lakatos's other writings, both on the philosophy of mathematics and the philosophy of science.

2. Lakatos was not interested in the sorts of problems in the philosophy of mathematics which concern many contemporary philosophers, such as questions about mathematical ontology (e.g. What are numbers?), or the relation between mathematics and set theory (Can mathematics be founded on set theory?). Rather his concern was with the growth of mathematical knowledge, and in particular with the way in which mathematics grows from informal conjectures and heuristic proofs into formalized or semi-formalized theories. He rejects the idea of foundations for mathematical knowledge and holds that it is Synthese 42 (1979) 335-351.