John Locke’s treatment of quantity in the Essay Concerning Human Understanding is not nearly as extensive or as well-known as his treatment of quality and his distinction between primary and secondary qualities. Yet I contend that a close examination of Locke’s comments on quantity in the Essay reveals that he endorses a general theory of quantity that not only distinguishes quantities from qualities, but also plays several other important roles in his overall philosophy—particularly in his treatments of infinity and demonstrative (...) knowledge. Moreover, I argue that this theory does not appear out of thin air, but is in certain respects one and the same as the approach to quantity found in Aristotle and developed by medieval Aristotelian thinkers. Identifying the core tenets of this approach in the texts of Aristotle and medieval Aristotelians, and formulating them clearly enough to shed light on Locke’s theory of quantity in the Essay, is the principal task of this paper. (shrink)

According to Newton and Clarke, Leibniz’s relationalism cannot make sense of distance quantities. Although the core of Newton and Clarke’s “argument from quantity” is clear enough, its details remain unclear because we do not know what its key term “quantity” means. This key term is still unsettled because, unlike Leibniz, who loudly voices his view of quantity in both his correspondence with Clarke and in his philosophical essays on quantity, Newton and Clarke are frustratingly terse when it comes to defining (...) quantity. Nevertheless, I think that it would be hasty to conclude that there is no way to expand our understanding of the term “quantity” as it appears in their argument. Although Newton and Clarke do not pursue a theory of quantity, their colleagues do, and the theory of quantity developed by their peers promises to deliver a historically rich perspective on Newton and Clarke’s argument from quantity. In this article, I aim to provide some historical context for Newton and Clarke’s argument from quantity by examining two criteria for quantity that were popular among their peers—what I call the “divisibility” and “precise increase and diminution” conditions. (shrink)

The physical sciences include highly developed fields that investigate intensities in the form of intensive quantities like speeds, temperatures, pressures and altitudes. Some contemporary readers of Deleuze interested in the physical sciences at times attribute to Deleuze a common, contemporary scientific concept of intensive magnitude. These readings identify Deleuze's philosophical conception of intensity with an existing scientific conception of intensity. The essay argues that Deleuze does not in fact lift a conception of intensity from the physical sciences to embed it (...) as the fundamental term in his differential ontology. (shrink)

La théorie russellienne des relations est ordinairement conçue comme le résultat d'une réflexion logique et ontologique sur l'ordre et l'asymétrie. Le présent article vise à présenter une autre généalogie, centrée sur les concepts de grandeur et de vecteur. Nous montrons en premier lieu que la thèse de l'irréductibilité des relations est avancée pour la première fois en 1897, à l'occasion d'une reformulation de la dialectique hégélienne de la quantité. Nous soulignons, en second lieu, que la notion de grandeur fait, autour (...) des années 1898-1899, l'objet d'une formalisation mathématique, complètement indépendante de la théorie des relations et fondée exclusivement sur les algèbres vectorielles. Nous montrons enfin que Russell, en possession de sa nouvelle doctrine logique, développe dès 1901 une théorie relationnelle des grandeurs vectorielles. Tout se passe donc comme si un des intérêts de la nouvelle théorie était, pour le philosophe, de permettre la substitution des relations aux grandeurs. (shrink)

This article presents an interpretation of Deleuze’s concept of difference-in-itself. I argue that this is best understood as an adption of Duns Scotus’s concept of ultimate difference. After suggesting that the influence of Scotus on Deleuze extends beyond their shared commitment to the univocity of being, I turn to briefly review Deleuze’s notion of absolute difference. I proceed from there to explain Scotus’s accounts of univocity and ultimate difference, throughout noting the many stark parallels with Deleuze. On the basis of (...) this Scotistic reading of Deleuzian difference, I then show how Deleuze’s synthesis of univocal being and difference-in-itself can be uniquely situated within the fourteenth-century Scotistic disputations on the predicability of univocal being to ultimate difference. I conclude with some suggestions on possible further connections between Deleuze and medieval metaphysics which are opened up through this association of Deleuze with Scotus and the Scotistic tradition. (shrink)