Lakatos: An Introduction provides a thorough overview of both Lakatos's thought and his place in twentieth century philosophy. It is an essential and insightful read for students and anyone… Expand

It is argued in this study that (i) progress in the philosophy of mathematical practice requires a general positive account of informal proof; (ii) the best candidate is to think of informal proofs as arguments that depend on their matter as well as their logical form; (iii) articulating the dependency of informal inferences on their content requires a redefinition of logic as the general study of inferential actions, thereby supplying a partial characterisation of normal research in the field.Expand

Abstract After the publication of The structure of scientific revolutions, Kuhn attempted to fend off accusations of extremism by explaining that his allegedly “relativist” theory is little more than… Expand

This is a pre-copyedited, author-produced PDF of an article accepted for publication in Philosophia Mathematica following peer review. Under embargo. Embargo end date: 7 July 2018 The version of… Expand

This paper assumes the success of arguments against the view that informal mathematical proofs secure rational conviction in virtue of their relations with corresponding formal derivations.Expand

Lakatos argued that a proof, when presented in the usual “Euclidian” style, may leave the choice of theorem, definitions and proof-idea mysterious. To remove these mysteries, he recommended a… Expand

Mathematics has universal standards of validity. Nevertheless, there are local styles in mathematics. These may be the legacy of a dominant individual (e.g., the Newtonianism of 18th century British… Expand