NEWTON AND HAMILTON: IN DEFENSE OF TRUTH IN ALGEBRA

Authors


  • Janet Folina is Professor of Philosophy at Macalester College. She is interested in the concept of mathematical proof and its relation to issues such as the use of diagrams in mathematics and Church's Thesis. She is the author of Poincaré and the Philosophy of Mathematics (Palgrave Macmillan, 1992), and, in general, enjoys research on the philosophies of working mathematicians from the nineteenth and twentieth centuries.

abstract

Although it is clear that Sir William Rowan Hamilton supported a Kantian account of algebra, I argue that there is an important sense in which Hamilton's philosophy of mathematics can be situated in the Newtonian tradition. Drawing from both Niccolo Guicciardini's (2009) and Stephen Gaukroger's (2010) readings of the Newton–Leibniz controversy over the calculus, I aim to show that the very epistemic ideals that underpin Newton's argument for the superiority of geometry over algebra also motivate Hamilton's philosophy of algebra. Namely, Hamilton's defense of algebra, like Newton's defense of geometry, is driven by the claim that a mathematical science must have a proper object and thus a basis in truth. In particular, Hamilton aims to show that algebra is not a mere language, or tool, or a mere “art”; instead, he argues, algebra is a bona fide mathematical science, like geometry, because its methods also provide true and accurate insight into a genuine subject matter, namely, the pure form of temporal intuition.

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