Abstract Symbols and Concrete Magnitudes
speaker: Douglas Jesseph (University of South Florida)abstract: This paper concerns a foundational debate among seventeenth century philosophers and philosophically-minded mathematicians over the proper objects of mathematical investigation. Beginning with the polemics between Thomas Hobbes and John Wallis over the relative merits of algebra, I outline two very different conceptions of the foundations of mathematics: one that sees mathematics as fundamentally concerned with abstract symbols that are independent of the structure and contents of the actual world, and another that seeks the foundations of mathematics in concrete spatial magnitudes generated by motion. These two competing foundational programs depend on very different conceptions of the dependence between mathematical and physical concepts, and they result in two quite different conceptions of rigorous demonstration. Although I take Hobbes and Wallis as exemplifying these contrasting foundational programs, the issue was raised by other seventeenth century figures, including Descartes, Barrow, Leibniz, and Newton.
timetable:
Wed 15 Sep, 9:00 - 10:30, Sala Conferenze Centro De Giorgi
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