Southern Journal of Philosophy 50 (3):504-527 (2012)
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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References found in this work BETA
From Kant to Hilbert: A Source Book in the Foundations of Mathematics.William Bragg Ewald (ed.) - 1996 - Oxford University Press.
The Collapse of Mechanism and the Rise of Sensibility: Science and the Shaping of Modernity, 1680-1760.Stephen Gaukroger - 2010 - Oxford University Press.
Kant on the `Symbolic Construction' of Mathematical Concepts.Lisa Shabel - 1998 - Studies in History and Philosophy of Science Part A 29 (4):589-621.
The Analyst: A Discourse Addressed to an Infidel Mathematician.George Berkeley - 1734 - Wilkins, David R..
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