Boltzmann on Mathematics |
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Authors: | Tanaka Setsuko |
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Institution: | (1) 4932 Sentinel Drive, Apartment 201, Bethesda, MA, 20816, U.S.A. |
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Abstract: | Boltzmann’s lectures on natural philosophy point out how the principles of mathematics are both an improvement on traditional
philosophy and also serve as a necessary foundation of physics or what the English call “Natura Philosophy”, a title which
he will retain for his own lectures. We start with lecture #3 and the mathematical contents of his lectures plus a few philosophical
comments. Because of the length of the lectures as a whole we can only give the main points of each but organized into a coherent
study. Behind his mathematics stands his support of Darwinian evolution interpreted in a partly Lamarckian way. He also supported
non-Euclidean geometry. Much of Boltzmann’s analysis of mathematics is an attempt to refute Kant’s static a priori categories
and his identification of space with “non-sensuous intuition”. Boltzmann’s strong attention toward discreteness in mathematics
can be seen throughout the lectures. Part II of this paper will touch on the historical background of atomism and focus on
the discrete way of thinking with which Boltzmann approaches problems in mathematics and beyond. Part III briefly points out
how Boltzmann related mathematics and discreteness to music.
This revised version was published online in June 2006 with corrections to the Cover Date. |
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