In this paper it is argued that the fundamental difference of the formal and the informal position in the philosophy of mathematics results from the collision of an object and a process centric perspective towards mathematics. This collision can be overcome by means of dialectical analysis, which shows that both perspectives essentially depend on each other. This is illustrated by the example of mathematical proof and its formal and informal nature. A short overview of the employed materialist dialectical approach is (...) given that rationalises mathematical development as a process of model production. It aims at placing more emphasis on the application aspects of mathematical results. Moreover, it is shown how such production realises subjective capacities as well as objective conditions, where the latter are mediated by mathematical formalism. The approach is further sustained by Polanyi’s theory of problem solving and Stegmaier’s philosophy of orientation. In particular, the tool and application perspective illuminates which role computer-based proofs can play in mathematics. (shrink)

This paper attempts to present a general picture of the most important philosophical elements found in the Hungarian writings of Imre Lakatos, later the famous philosopher of science in England, with a focus on his views on science and its social context. In the first section, Lakatos' life in Hungary is summarized, with a special emphasis on those few years when most of the Hungarian works were written. The second section offers a list of his Hungarian publications, each item accompanied (...) by a brief description. Then we examine the lost doctoral dissertation and its possible contents as reconstructed from the reports of the readers and the published texts. Finally we identify the main philosophical sources the young Lakatos could have used, and give a summary of his basic views on science. (shrink)

This paper attempts to present a general picture of the most important philosophical elements found in the Hungarian writings of Imre Lakatos, later the famous philosopher of science in England, with a focus on his views on science and its social context. In the first section, Lakatos' life in Hungary is summarized, with a special emphasis on those few years when most of the Hungarian works were written. The second section offers a list of his Hungarian publications, each item accompanied (...) by a brief description. Then we examine the lost doctoral dissertation and its possible contents as reconstructed from the reports of the readers and the published texts. Finally we identify the main philosophical sources the young Lakatos could have used, and give a summary of his basic views on science. (shrink)

. The circumstance, that the text of Imre Lakatos' doctoral thesis from the University of Debrecen did not survive, makes the evaluation of his career in Hungary and the research of aspects of continuity of his lifework difficult. My paper tries to reconstruct these newer aspects of continuity, introducing the influence of László Kalmár the mathematician and his fellow student, and Sándor Karácsony the philosopher and his mentor on Lakatos' work. The connection between the understanding of the empirical basis of (...) exact ideas—which is a common feature in the papers of the members of the Karácsonycircle—and Lakatos' way of thinking regarding mathematics is more direct and can be documented through his connection to Kalmár. The central element of Lakatos' philosophy of mathematics is criticism of formalism and his tendency is to use the empirical view. Discussions at the 1965 International Colloquium in the Philosophy of Science in London were very helpful in clarifying the quasi-empirical conception. Kalmár's lecture in London, based on one of his papers published by Karácsony in 1942, emphasized the empirical character of mathematics. After this colloquium some elements of the heritage of the Karácsony-circle were integrated again in the development of Lakatos' way of thinking. First I will analyze the Kalmár lecture of 1965 at the Colloquium of Philosophy of Science and Lakatos's reflections on the problem of the foundation of mathematics. Then I will present their common Hungarian background, their education and the beginning of their career, which have many important common features; third I draw attention to the network of contacts of Karácsony-disciples. (shrink)

Imre Lakatos gained fame in the English-speaking world as a follower and critic of philosopher of science Karl Popper. However, Lakatos’ background involved other philosophical and scientific sources from his native Hungary. Lakatos surreptitiously used Hegelian Marxism in his works on philosophy of science and mathematics, disguising it with the rhetoric of the Popper school. He also less surreptitiously incorporated, particularly in his treatment of mathematics, work of the strong tradition of heuristics in twentieth century Hungary. Both his Marxism and (...) his emphasis on heuristics contained a view of science and mathematics that contrasted with the mainstream of Anglo-American philosophy of science. Both involved a dynamic view of science, whether historical or psychological, and an emphasis on practice as opposed to static, formal representations of scientific theories. (shrink)