What are the best works summarizing, discussing or criticizing the work of Imre Lakatos? What are the pros and cons of said works? Which would you recommend picking up first if one has read some but not all of his books?
I cannot do pros/cons because I am not a specialist in this field, but I am aware of the basic literature, as follows:
- Essays in Memory of Imre Lakatos (1976)
- A notable critique of Lakatos: Ian Hacking, "Imre Lakatos’s Philosophy of Science" (1979)
- Partial review integrating and responding to Hacking's critiques: Matteo Motterlini, "Reconstructing Lakatos: a reassessment of Lakatos’ epistemological project in the light of the Lakatos Archive" (2002)
- Motterlini also wrote a 1999 book introducing Lakatos' letters to Feyerabend (although these letters are not particularly deep in their philosophy).
- A larger review of Lakatos' work: Appraising Lakatos: Mathematics, Methodology, and the Man (2002)
The famous Proofs and Refutations by Lakatos contains an appendix on Cauchy's infinitesimals. Later Lakatos revisited the subject, offering a rather different viewpoint in
Lakatos, Imre. Cauchy and the continuum: the significance of nonstandard analysis for the history and philosophy of mathematics. Math. Intelligencer 1 (1978), no. 3, 151–161.
Lakatos' perspective on Cauchy got a rather shoddy treatment in
Schubring, Gert. Conflicts between generalization, rigor, and intuition. Number concepts underlying the development of analysis in 17–19th Century France and Germany. Sources and Studies in the History of Mathematics and Physical Sciences. Springer-Verlag, New York, 2005.
This was in turn analyzed in the 2013 publication
Błaszczyk, Piotr; Katz, Mikhail G.; Sherry, David. Ten misconceptions from the history of analysis and their debunking. Found. Sci. 18 (2013), no. 1, 43–74
as well as the 2017 publication
Błaszczyk, Piotr; Kanovei, Vladimir; Katz, Mikhail G.; Sherry, David Controversies in the foundations of analysis: comments on Schubring's Conflicts. Found. Sci. 22 (2017), no. 1, 125–140.