Journal of Indian Philosophy 35 (5-6):469-485 (2007)

One of the ways in which the artificial languages of mathematics are “generous”, that is, in which they assists the advance of thought, is through its establishment of advanced operatory structures that permit an even further advance of intuition. However, this generosity may be delusive, suggest ideas which in the longer run turn out to be untenable. The paper analyses two cases of “honest generosity”, namely a “proof” of the sign rule “less times less makes plus” from the 1340s and a result in partition theory obtained by Euler by means of rash manipulations of infinite series and products, case-Cantor’s introduction of transfinite numbers from 1895-and (in modern terms) a failed attempt to extend the semi-group of algebraic powers into a complete group, also from c. 1340. Gewöhnlich glaubt der Mensch, wenn er nur Worte hört es müsse sich dabei wohl auch was denken lassen Goethe, Faust I, 2565-2566He gives the kids free samples because he knows full well that today’s young innocent faces will be tomorrow’s clientele Tom Lehrer, “The Old Dope Peddler”
Keywords Philosophy
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Reprint years 2008
DOI 10.1007/s10781-007-9028-2
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References found in this work BETA

The Psychology of Intelligence.Rex Knight, Jean Piaget, M. Piercy & D. E. Berlyne - 1951 - Philosophical Quarterly 1 (5):470.
Artificial Languages Across Sciences and Civilizations.Frits Staal - 2006 - Journal of Indian Philosophy 34 (1-2):89-141.
The Concept of Existence and the Role of Constructions in Euclid's Elements.Orna Harari - 2003 - Archive for History of Exact Sciences 57 (1):1-23.
The Korean Adaptation of the Chinese-Islamic Astronomical Tables.Yunli Shi - 2003 - Archive for History of Exact Sciences 57 (1):25-60.

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