The mathematical form of measurement and the argument for Proposition I in Newton’s Principia

Locke's Aristotelian theory of quantity

“…36 Among the metaphysical questions are those concerning the ontological status of quantities (recall notes 4 and 8), as well as questions regarding whether and how Locke's approach to measure can encompass rational, irrational, and negative numbers (see Klein 1992, ch. 12 andDunlop 2012). Pertinent epistemological and practical questions include how to choose an appropriate unit of measure, and how to ascertain that the chosen unit is constant and unchanging through the process of measuring, given that the only way to ascertain this would presumably be to measure it-thereby engendering a regress (see Locke's Draft B §41-42, Essay II.xiv.18; for commentary, see Dunlop 2009 andAnstey 2016).…”

“…47 See Essay, "Epistle to the Reader". For the centrality of measurement to Newton's own conception of the project of the Principia, see Dunlop (2012). 48 For discussions of Locke's view of the limited scope of demonstrative knowledge in natural philosophy that stress our lack of epistemic access to real essences, see, e.g., Phemister (1993) and Rogers (2000).…”