Zobrazeno 1 - 10
of 153
pro vyhledávání: '"Katz, Karin"'
Publikováno v:
Journal of Humanistic Mathematics, Volume 8 Issue 1 (January 2018), pages 108-119
Felix Klein and Abraham Fraenkel each formulated a criterion for a theory of infinitesimals to be successful, in terms of the feasibility of implementation of the Mean Value Theorem. We explore the evolution of the idea over the past century, and the
Externí odkaz:
http://arxiv.org/abs/1802.01972
Autor:
Bair, Jacques, Blaszczyk, Piotr, Ely, Robert, Henry, Valerie, Kanovei, Vladimir, Katz, Karin U., Katz, Mikhail G., Kudryk, Taras, Kutateladze, Semen S., McGaffey, Thomas, Mormann, Thomas, Schaps, David M., Sherry, David
Publikováno v:
Mat. Stud. 47 (2017), no. 2, 115-144
Procedures relying on infinitesimals in Leibniz, Euler and Cauchy have been interpreted in both a Weierstrassian and Robinson's frameworks. The latter provides closer proxies for the procedures of the classical masters. Thus, Leibniz's distinction be
Externí odkaz:
http://arxiv.org/abs/1712.00226
Autor:
Bair, Jacques, Blaszczyk, Piotr, Katz, Karin U., Katz, Mikhail G., Kudryk, Taras, Sherry, David
Philosopher Benardete challenged both the conventional wisdom and the received mathematical treatment of zero, dot, nine recurring. An initially puzzling passage in Benardete on the intelligibility of the continuum reveals challenging insights into n
Externí odkaz:
http://arxiv.org/abs/1706.00191
Autor:
Bascelli, Tiziana, Blaszczyk, Piotr, Borovik, Alexandre, Kanovei, Vladimir, Katz, Karin U., Katz, Mikhail G., Kutateladze, Semen S., McGaffey, Thomas, Schaps, David M., Sherry, David
Cauchy's sum theorem is a prototype of what is today a basic result on the convergence of a series of functions in undergraduate analysis. We seek to interpret Cauchy's proof, and discuss the related epistemological questions involved in comparing di
Externí odkaz:
http://arxiv.org/abs/1704.07723
Autor:
Bascelli, Tiziana, Blaszczyk, Piotr, Kanovei, Vladimir, Katz, Karin U., Katz, Mikhail G., Kutateladze, Semen S., Nowik, Tahl, Schaps, David M., Sherry, David
In relation to a thesis put forward by Marx Wartofsky, we seek to show that a historiography of mathematics requires an analysis of the ontology of the part of mathematics under scrutiny. Following Ian Hacking, we point out that in the history of mat
Externí odkaz:
http://arxiv.org/abs/1612.05944
Autor:
Blaszczyk, Piotr, Kanovei, Vladimir, Katz, Karin U., Katz, Mikhail G., Kutateladze, Semen S., Sherry, David
Abraham Robinson's framework for modern infinitesimals was developed half a century ago. It enables a re-evaluation of the procedures of the pioneers of mathematical analysis. Their procedures have been often viewed through the lens of the success of
Externí odkaz:
http://arxiv.org/abs/1609.04531
Autor:
Blaszczyk, Piotr, Kanovei, Vladimir, Katz, Karin U., Katz, Mikhail G., Kudryk, Taras, Mormann, Thomas, Sherry, David
To explore the extent of embeddability of Leibnizian infinitesimal calculus in first-order logic (FOL) and modern frameworks, we propose to set aside ontological issues and focus on procedural questions. This would enable an account of Leibnizian pro
Externí odkaz:
http://arxiv.org/abs/1605.03501
Autor:
Bair, Jacques, Blaszczyk, Piotr, Ely, Robert, Henry, Valerie, Kanovei, Vladimir, Katz, Karin U., Katz, Mikhail G., Kutateladze, Semen S., McGaffey, Thomas, Reeder, Patrick, Schaps, David M., Sherry, David, Shnider, Steven
We apply Benacerraf's distinction between mathematical ontology and mathematical practice (or the structures mathematicians use in practice) to examine contrasting interpretations of infinitesimal mathematics of the 17th and 18th century, in the work
Externí odkaz:
http://arxiv.org/abs/1605.00455
Publikováno v:
Quantum Studies: Mathematics and Foundations 3 (2016), no. 3, 231-236
Small oscillations evolved a great deal from Klein to Robinson. We propose a concept of solution of differential equation based on Euler's method with infinitesimal mesh, with well-posedness based on a relation of adequality following Fermat and Leib
Externí odkaz:
http://arxiv.org/abs/1604.06663
Autor:
Bascelli, Tiziana, Blaszczyk, Piotr, Kanovei, Vladimir, Katz, Karin U., Katz, Mikhail G., Schaps, David M., Sherry, David
Publikováno v:
HOPOS (Journal of the International Society for the History of Philosophy of Science) Volume 6, Number 1, Spring 2016, pp. 117-147
Did Leibniz exploit infinitesimals and infinities `a la rigueur, or only as shorthand for quantified propositions that refer to ordinary Archimedean magnitudes? Chapter 5 in (Ishiguro 1990) is a defense of the latter position, which she reformulates
Externí odkaz:
http://arxiv.org/abs/1603.07209