Hungarian Studies in Lakatos' Philosophies of Mathematics and Science -- Editor's Introduction

The broad outlines of Lakatos' life (1922–1974) are fairly well known. He was born in Hungary, educated at the University of Debrecen and lived in Hungary until the 1956 anti-Soviet revolution, at which time he fled to Vienna. From there he went to Cambridge England on a Rockefeller scholarship, received a Ph.D. in 1961 advised by George Polya (in mathematics) and R.B. Braithwaite (in philosophy of science), and was influenced by K. Popper. He wrote his dissertation "Essays in the Logic of Mathematical Discovery," which was serialized in the British Journal for the Philosophy of Science in 1963–64 as "Proofs and Refutations," and published as a book posthumously edited by J. Worrall and E. Zahar. Lakatos joined Popper at the London School of Economics in 1960, was very active in philosophy of science circles and labeled a Popperian. His best known essay in the philosophy of science, "Falsification and the Methodology of Scientific Research Programs" (MSRP) was published in 1970. He succeeded Popper in the chair of Logic in 1969–70, and was also editor of British Journal for the Philosophy of Science until his death.

Why another collection of essays on Lakatos? There have been several volumes on the life and work of Lakatos since his death—most, until recently, examining the development of his work emphasizing the Popperian Lakatos—dutiful or rebellious. An exception seems to be Koetsier's book, steering clear of these issues and focusing on Lakatos' philosophy of mathematics, which he carries beyond Lakatos' papers to execute what Lakatos reputedly wanted to develop: an application of the MSRP to mathematics. Koetsier found a large gap between MSRP and mathematics, handicapping such an endeavor. Two other recent books, one of which (Kadvany) takes its clue for his theme from Hacking's remark about 'the Hungarian Lakatos', meaning Lakatos as a (Hegelian?) Marxist-Lukacsian in Hungary. The other, a collection by Kvasz represents a wider critical examination of Lakatos' main themes, but also includes many papers carrying on either the Popperian-Lakatos or the Hegelian-Lakatos frameworks.

This special issue, authored by Hungarians, aims to avoid previously employed frameworks, and presents a fresh look at research done in Hungary previously not published in English (first three papers), as well as a paper presented at the 2004 HOPOS conference (last paper). Papers in this issue show Lakatos's growth as an academic and his reliance on Hungarian mathematicians and scientists beginning from his undergraduate years in Debrecen, and trace in detail, analyze and interpret the roots of his intellectual anchor: an engagement with understanding scientific discovery. These papers 'excavate' what seems to be buried in much of Lakatos' work: heuristics as logic of discovery and a quasi-empirical view of mathematics and science. His work has implicit references to 'intuitive evidence,' the 'knowing subject,' and 'the way of seeing' not drawn out in earlier studies.

Although Koetsier mentions two of the figures (Szabo and Kalmar) who are subjects of studies in this issue, for Koetsier they seem to be no more that occasions for Lakatos' response. That unexpressed 'way of seeing' is investigated within this issue through the missing link of Lakatos' mentor the philosopher Karacsony, the influences of his colleague the mathematician Kalmar, his teacher in classics Szabo, and his correspondent the philosopher Polanyi. In "Proofs and Refutations" Lakatos does not simply give a rational reconstruction of Euler's theorem, neither does he offer a definitive method for mathematical discovery. Rather, he explores patterns of thinking using the device of classroom dialogue. Dialogue, in the manner of witty Socratic questioning—even in mathematics—has been a pedagogic device at Debrecen University since the early 19^th century. This form of questioning shows ideas in the process of birth. The point of this exercise is not to be true to history, but to represent the role of particular types of ideas. (His sponsor, Renyi was a master of this.) To understand mathematical thinking and participating in the process is the key. And as Lakatos gradually came to see at the end what he 'knew' at...