Assaying lakatos's philosophy of mathematics

Justifying Definitions in Mathematics--Going Beyond Lakatos

“…Thus Lakatos indeed thought that his ideas could apply to substantial parts of established branches of mathematics of the twentieth century up to the present day. But I agree with Corfield's [1997] main point that Lakatos failed to see that his ideas are also relevant for highly formalised mathematics. For this reason this paper is not restricted to informal mathematics.…”

The Argument of Mathematics

“…Commentators and critics, for instance (Corfield, 1997) or (Feferman, 1978), usually share this view, often seeing the rest of the book as a 5 The name incorporates HR (Colton, 2002), which is a system named after mathematicians Godfrey Harold Hardy and Srinivasa Aiyangar Ramanujan and forms a key part of our model, and the letter "L", which reflects the deep influence of Lakatos's work on our model. Commentators and critics, for instance (Corfield, 1997) or (Feferman, 1978), usually share this view, often seeing the rest of the book as a 5 The name incorporates HR (Colton, 2002), which is a system named after mathematicians Godfrey Harold Hardy and Srinivasa Aiyangar Ramanujan and forms a key part of our model, and the letter "L", which reflects the deep influence of Lakatos's work on our model.…”

Bridging the Gap Between Argumentation Theory and the Philosophy of Mathematics

“…7 Since Lakatos's work (1976) was the first attempt to characterise informal mathematics (see Corfield, 1997 andFeferman, 1978), it is likely to be incomplete, and hence be open to criticism and extension. Lakatos himself neither considered the methods complete nor definitive, arguing only that they provide a more realistic and helpful portrayal of mathematical discovery than Euclidean (deductive) methodology.…”

“…Commentators and critics, for instance Corfield (1997) or Feferman (1978, usually share this view, often seeing the rest of the book as a prelude to this method. 8 The method works on a putative proof of a conjecture: the main example in (Lakatos, 1976) is Cauchy's (1813) proof of Euler's conjecture that for all polyhedra, V − E + F is 2.…”