On the Impact of Philosophical Conceptions on Mathematical Research: The Case of Condillac and Babbage
DOI:
https://doi.org/10.48160/18532330me1.35Keywords:
philosophy, mathematics , Condillac , BabbageAbstract
The possible impact of general philosophical ideas on the choice of research subjects in mathematics is the topic of this paper. I examine a specific case in which the philosophical background is provided by a discussion on the role of language in science, which is associated with the work of Condillac. The area of mathematics considered is functional equations, a difficult chapter of mathematical analysis that began to be developed between the end of the eighteenth and the beginning of the nineteenth century. The researcher is Charles Babbage (1791-1871), a young British mathematician deeply interested in the recent work of French mathematicians and philosophers of science.
In a series of papers published in 1815-1816 Babbage developed a ‘language’ specifically designed for the treatment of functional equations. However, the dynamic debate on the relationship between language, science and the possibilities of a theory of signs, along the first two decades of the nineteenth century, as well as shortcomings in Babbage’s approach, conspired against his interesting research approach progressing further. Finally, on the basis of the previous discussion, I make some historical remarks on the transmission of scientific information between France and Britain in these two interesting decades.
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