the philosophy of mathematical practice

[...]... was to account for the rationality of the growth of mathematics in terms of transitions between mathematical practices Among the patterns of mathematical change, Kitcher discussed generalization, rigorization, and systematization One of the features of the ‘maverick’ tradition was the polemic against the ambitions of mathematical logic as a canon for philosophy of mathematics Mathematical logic, which... one centered on the foundations of mathematics and the other centered on articulating the methodology of mathematics Kitcher (1984) had already put forward an account of the growth of mathematical knowledge that is one of the earliest, and still one of the most impressive, studies in the methodology of mathematics in the analytic literature Starting from the notion of a mathematical practice, ² Kitcher’s... in the changes in mathematical practice, or a theory of mathematical growth, the case studies she investigated have led her to consider portions of the history of analysis and of set theory The history of set theory (up to its present state) is the ‘laboratory’ for the distillation of the naturalistic model of the practice Finally, a major difference in attitude between Maddy and the ‘mavericks’ is the. .. for the philosophy of mathematics, tasks that arise either from the current practice of mathematics or from the history of the subject A small number of philosophers (including one of us) believe that the answer is yes Despite large disagreements among the members of this group, proponents of the minority tradition share the view that philosophy of mathematics ought to concern itself with the kinds of. .. relations between the philosophy of mathematics and the practice of mathematics Similar 12 paolo mancosu sentiments appear in the writings of many philosophers of mathematics who hold that the goal of philosophy of mathematics is to account for mathematics as it is practiced, not to recommend reform (Maddy, 1997, p.161) Naturalism, in the Maddian sense, recognizes the autonomy of mathematics from natural... pursues, among other things, the dialectical nature of mathematical developments, the logic of discovery in mathematics, the applicability of mathematics to the natural sciences, the nature of mathematical modeling, and what accounts for the fruitfulness of certain concepts in mathematics More precisely, here is a list of topics that motivate large chunks of Corfield’s book: 1) Why are some mathematical. .. Associate Professor in the Philosophy Department of the University of Michigan He completed a B.A (Mathematics and Philosophy) at the University of Toronto and a Ph.D (Philosophy) at Princeton His current research interests include the history of 17th century mathematics, especially geometry and complex analysis, both as subjects in their own right and as illustrations of themes in the philosophy of mathematical. .. study the other branches of human knowledge (most obviously the natural sciences) Philosophers should pose such questions as: How does mathematical knowledge grow? What is mathematical progress? What makes some mathematical ideas (or theories) better than others? What is mathematical explanation? (p 17) They concluded the introduction by claiming that the current state of the philosophy of mathematics... his desire to move into philosophy of mathematics to the discovery of Lakatos’ Proofs and Refutations (1976) and he takes as the motto for his introduction Lakatos’ famous paraphrasing of Kant: The history of mathematics, lacking the guidance of philosophy, has become blind, while the philosophy of mathematics, turning its back on the most intriguing phenomena in the history of mathematics, has become... means of a case study from real algebraic geometry Related to the topic of epistemic virtues of different mathematical proofs is the ideal of Purity of methods in mathematics The notion of purity has played an important role in the history of mathematics—consider, for instance, the elimination of geometrical intuition from the development of analysis in the 19th century—and in a way it underlies all the . He is the author of Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century (OUP 1996) and editor of From Brouwer to Hilbert. The debate on the foundations of mathematics. some mathematical ideas (or theories) better than others? What is mathematical explanation? (p. 17) They concluded the introduction by claiming that the current state of the philosophy of mathematics. systematization. One of the features of the ‘maverick’ tradition was the polemic against the ambitions of mathematical logic as a canon for philosophy of mathemat- ics. Mathematical logic, which