LAKATOS' PHILOSOPHY OF MATHEMATICS A Historical Approach (Studies in the History and Philosophy of Mathematics Volume 3)

In this book, which is both a philosophical and historiographical study, the author investigates the fallibility and the rationality of mathematics by means of rational reconstructions of developments in mathematics. The initial chapters are devoted to a critical discussion of Lakatos' philosophy of mathematics. In the remaining chapters several episodes in the history of mathematics are discussed, such as the appearance of deduction in Greek mathematics and the transition from Eighteenth-Century to Nineteenth-Century analysis. The author aims at developing a notion of mathematical rationality that agrees with the historical facts. A modified version of Lakatos' methodology is proposed. The resulting constructions show that mathematical knowledge is fallible, but that its fallibility is remarkably weak.

A.M. Coyne
...very clearly written and can be understood by advanced undergraduates in either mathematics or philosophy. The bibliography is extensive. It will interest all philosophers of mathematics and any mathematician interested in reflecting on the methodology of mathematics.
Zentralblatt für Mathematik