TY - JOUR
T1 - Infinitesimals as an issue in neo-Kantian philosophy of science
AU - Mormann, T.
AU - Katz, M.
N1 - HOPOS publishes international, peer-reviewed scholarship examining the development of the philosophical analysis of science in history, and how that development informs and influences the philosophy of science. The journal provides an outlet for work that helps to explain the historical links between philosophy and science, the social, economic, and political context in which both are situated, and the problems and debates that have shaped philosophy and science. It is published by University of Chicago Press
PY - 2013
Y1 - 2013
N2 - We seek to elucidate the philosophical context in which one of the most important conceptual transformations of modern mathematics took place, namely, the so-called revolution in rigor in infinitesimal calculus and mathematical analysis. Some of the protagonists of the said revolution were Cauchy, Cantor, Dedekind, and Weierstrass. The dominant current of philosophy in Germany at the time was neo-Kantianism. Among its various currents, the Marburg school (Cohen, Natorp, Cassirer, and others) was the one most interested in matters scientific and mathematical. Our main thesis is that Marburg neo-Kantian philosophy formulated a sophisticated position toward the problems raised by the concepts of limits and infinitesimals. The Marburg school neither clung to the traditional approach of logically and metaphysically dubious infinitesimals nor Whiggishly subscribed to the new orthodoxy of the “great triumvirate” of Cantor, Dedekind, and Weierstrass that declared infinitesimals conceptus nongrati in mathematical discourse. Rather, following Cohen’s lead, the Marburg philosophers sought to clarify Leibniz’s principle of continuity and to exploit it in making sense of infinitesimals and related concepts.
AB - We seek to elucidate the philosophical context in which one of the most important conceptual transformations of modern mathematics took place, namely, the so-called revolution in rigor in infinitesimal calculus and mathematical analysis. Some of the protagonists of the said revolution were Cauchy, Cantor, Dedekind, and Weierstrass. The dominant current of philosophy in Germany at the time was neo-Kantianism. Among its various currents, the Marburg school (Cohen, Natorp, Cassirer, and others) was the one most interested in matters scientific and mathematical. Our main thesis is that Marburg neo-Kantian philosophy formulated a sophisticated position toward the problems raised by the concepts of limits and infinitesimals. The Marburg school neither clung to the traditional approach of logically and metaphysically dubious infinitesimals nor Whiggishly subscribed to the new orthodoxy of the “great triumvirate” of Cantor, Dedekind, and Weierstrass that declared infinitesimals conceptus nongrati in mathematical discourse. Rather, following Cohen’s lead, the Marburg philosophers sought to clarify Leibniz’s principle of continuity and to exploit it in making sense of infinitesimals and related concepts.
UR - https://www.journals.uchicago.edu/doi/abs/10.1086/671348
M3 - Article
SN - 2152-5188
VL - 3
SP - 236
EP - 280
JO - HOPOS
JF - HOPOS
IS - 2
ER -