From the Logic of Mathematical Discovery to the Methodology of Scientific Research Programmes

Abstract

ions), but also that we can to some extent use the formal method to set up new formal theories. Thus, we have to move from the opposition and correlation between formal and informal theories to those between mathematics and empirical activities much clearer. In conclusion, although there are some important ideas and possibilities for further development in Lakatos' philosophy of mathematics, his quasiempirical view of mathematics is not a thorough theory and also has some defects. This conclusion is in no sense strange, for even Lakatos himself thought his philosophy of mathematics needed further improvement, and it is in fact an inescapable result of his basic idea, i.e. to extend Popper's fallibilism to the domain of mathematics. Fortunately, although Lakatos did not have time to do what he wanted to do in the field of philosophy of mathematics, he made a new important advance in the field of philosophy of science, and this is his methodology of scientific research programmes. 2 FROM THE LOGIC OF MATHEMATICAL DISCOVERY TO THE METHODOLOGY OF SCIENTIFIC RESEARCH PROGRAMMES As an exponent of the methodology of scientific research programmes, Lakatos made quite clear the relationship between this theory and Popper's fallibilism (especially with what is called 'sophisticated methodological falsificationism'. However, as there is some 'corresponding relationship' between the basic elements of scientific research programmes and Kuhn's theory of paradigm (e.g., Kuhn points out: 'Though his terminology is different, his analytic apparatus is as close to mine as need be: hard core, work in the protective belt, and degenerating phase are close parallels for my paradigms, normal science, and crisis' (Lakatos and Musgrave (eds) [1970], p. 256). 'Someone said that the methodology of scientific research programmes could be regarded as a synthesis of Popper's fallibilism and Kuhn's theory of philosophy of science' (Lakatos and Musgrave (eds) [1970], p. 211). This analysis is in some sense correct; but, as there are still important differences between Lakatos' methodology and that of the other two it would be more appropriate to say that Lakatos developed his methodology against the background of both Popper's and Kuhn's theories of philosophy of science. This is what Lakatos says: 'In the last few years, I have been advocating a methodology of scientific research This content downloaded from 207.46.13.169 on Sat, 01 Oct 2016 06:18:59 UTC All use subject to http://about.jstor.org/terms