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International Studies in Phenomenology and Philosophy

Book | Chapter

176841

A geometrical constructive approach to infinitesimal analysis

epistemological potential and boundaries of tractional motion

Pietro Milici

pp. 3-21

Abstract

Recent foundational approaches to Infinitesimal Analysis are essentially algebraic or computational, whereas the first approaches to such problems were geometrical. From this perspective, we may recall the seventeenth-century investigations of the "inverse tangent problem." Suggested solutions to this problem involved certain machines, intended as both theoretical and actual instruments, which could construct transcendental curves through so-called tractional motion. The main idea of this work is to further develop tractional motion to investigate if and how, at a very first analysis, these ideal machines (like the ancient straightedge and compass) can constitute the basis of a purely geometrical and finitistic axiomatic foundation (like Euclid's planar geometry) for a class of differential problems. In particular, after a brief historical introduction, a model of such machines (i.e., the suggested components) is presented. Then, we introduce some preliminary results about generable functions, an example of a "tractional" planar machine embodying the complex exponential function, and, finally, a didactic proposal for this kind of artifact.

Publication details

Published in:

Lolli Gabriele, Panza Marco, Venturi Giorgio (2015) From logic to practice: Italian studies in the philosophy of mathematics. Dordrecht, Springer.

Pages: 3-21

DOI: 10.1007/978-3-319-10434-8_1

Full citation:

Milici Pietro (2015) „A geometrical constructive approach to infinitesimal analysis: epistemological potential and boundaries of tractional motion“, In: G. Lolli, M. Panza & G. Venturi (eds.), From logic to practice, Dordrecht, Springer, 3–21.