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Catching Glimpses: Perceiving Infinitesimals in the Scientific Revolution
CHUM 339
Spring 2021
Section: 01  
Crosslisting: COL 351, GRST 249, PHIL 302, SISP 339

The rise of mathematical natural science in the early modern period marked the dissolution of objective reality as it had previously been known. Since Aristotle, perceptible objects had been understood to be enduring substances whose identities were inscribed in their very being and which retained these identities through change. The mechanistic worldview of the 17th and 18th centuries exploded this stable order into a telescoping multiplicity of material systems, from the infinitesimally small to the infinitely large. Rather than encountering a world of enduring and identifiable substances--animals, vegetables, and minerals; people and artifacts--the perceiver was instead confronted with fleeting constellations of homogeneous matter in a perpetual flux, no sooner glimpsed than gone. This metaphysical picture of infinitary flux was complemented by a new branch of mathematics, the infinitesimal calculus, which proved immensely successful both in uncovering new theorems and in modeling empirical phenomena.

Both the metaphysics and the mathematics of the new science were, however, rife with paradox. If material objects not only harbor a microscopic substructure but are, in fact, divisible without end, then we are faced with pluralities of pluralities without any underlying unities--parts of parts of parts...and not a whole among them. Conceptual instability afflicted the infinitesimals used in calculus, as well. In some contexts they were treated as very small but non-zero quantities, in others as strictly zero--provoking one critic to call them "ghosts of departed quantities."

In conjunction with the CHUM theme "Ephemera," this class will study the philosophical turbulence induced by the new science--in particular, by the mechanical philosophy and infinitesimal calculus. We will pay special attention to its consequences for the philosophy of perception. Aristotle compared perceptible objects to signet rings impressing their distinctive forms on the receptive wax of the human sensorium. But if there are no enduring substances or determinate forms, how are we to understand our perceptual relation to the world? How must perceptual experience be reconceived so as to accommodate the fleetingness and flux of material phenomena? And how is it that, though we are awash in ephemera, we nevertheless enjoy an (illusory?) impression of endurance and stability?
Credit: 1 Gen Ed Area Dept: HA CHUM
Course Format: SeminarGrading Mode: Student Option
Level: UGRD Prerequisites: None
Fulfills a Major Requirement for: (COL)(GRST)(PHIL)(PHIL-Philosophy)(PHIL-Social Jus)(STS)
Past Enrollment Probability: 90% or above

Last Updated on APR-24-2024
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