Lakatos' Philosophy of Mathematics: A Historical Approach
Hardbound. 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.
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The Methodology of Scientific Research
Cauchy and the continuum
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algebraic Archimedes Archimedes's argue axioms Cauchy Cauchy's Chapter characterize concerning conformal mapping conjectures considered construction continuous functions continuum curve deductive defined definition derivative differential divergent series Elements equal equations Euclidean Tradition Euler Euler's formula Euler's theorem example existence expression fact fallibility thesis finite follows Fontaine Formalist Tradition formula geometrical Giorello Greek mathematics hard core heuristic heuristic unity implies infinitely large infinitely small infinitesimals interchangeability theorem L'Huilier Lagrange Lakatos Lakatos's MSRP Lakatosian Laudan's lemma limit mathe mathematical research traditions mathematicians matical means method methodology of mathematical methodology of proof MMRT MP&R MSRP natural science nineteenth century non-standard interpretation notion paper parabola particular philosophy of mathematics point of view polygon polyhedra polyhedron positive heuristic possible principle progress Proofs and Refutations proved quasi-empirical rational reconstruction research programmes research projects respect Riemann Schlomilch sense shows solved Spalt's tion triangle uniform convergence valeur variable zero