Quantity and Extension in Suárez and Descartes

This paper compares the development of the notion of continuous quantity in the work of Francisco Suárez and René Descartes. The discussion begins with a consideration of Suárez’s rejection of the view – common to ‘realists’ such as Thomas Aquinas and ‘nominalists’ such as William of Ockham – that quantity is inseparable from the extension of material integral parts. Crucial here is Suárez’s view that quantified extension exhibits a kind of impenetrability that distinguishes it from other kinds of extension. This view sheds considerable light on initially obscure remarks on impenetrability in Descartes’ late correspondence with Henry More. Though Descartes differs from Suárez and other major scholastic figures in his understanding of the relation of quantity to material substance, he nonetheless requires in the end some version of the Suárezian distinction between quantified and unquantified extension.

Quantity, Integral Parts, and Boundaries

This chapter focuses on an aspect of Suárez’s metaphysics that is especially relevant to the non-scholastic identification of matter with extension in early modern thought, namely, his account of the nature of the Aristotelian accident of “continuous quantity.” The chapter begins with Suárez’s contribution to a debate within medieval scholasticism between “realist” and “nominalist” views of quantity. One distinctive feature of this contribution is Suárez’s insistence that this accident bears a special relation to impenetrability. There is then a consideration of Suárez’s contribution to a scholastic debate over the mereological relation between wholes and their “integral parts” that pits anti-reductionists against reductionists. The chapter ends with an examination of Suárez’s contribution to scholastic debates over the ontological status of the “indivisible” boundaries of parts, namely, points, lines, and surfaces. Suárez adopts a “moderate realism” that takes boundaries to be really distinct from the parts they limit.

The Metaphysics of the Material World

This book traces a particular development of the metaphysics of the material world in early modern thought. The route it follows derives from a critique of Spinoza in the work of Pierre Bayle. Bayle charged in particular that Spinoza’s monistic conception of the material world founders on the account of extension and its “modes” and parts that he inherited from Descartes, and that Descartes in turn inherited from late scholasticism, and ultimately from Aristotle. After an initial discussion of Bayle’s critique of Spinoza and its relation to Aristotle’s distinction between substance and accident, this study starts with the original re-conceptualization of Aristotle’s metaphysics of the material world that we find in the work of the early modern scholastic Suárez. What receives particular attention is Suárez’s introduction of the “modal distinction” and his distinctive account of the Aristotelian accident of “continuous quantity.” This examination of Suárez is followed by a treatment of the connections of his particular version of the scholastic conception of the material world to the very different conception that Descartes offered. Especially important is Descartes’s view of the relation of extended substance both to its modes and to the parts that compose it. Finally, there is a consideration of what these developments in Suárez and Descartes have to teach us about Spinoza’s monistic conception of the material world. Of special concern here is to draw on this historical narrative to provide a re-assessment of Bayle’s critique of Spinoza.

Commonalities for Numerical and Continuous Quantity Skills at Temporo-parietal Junction

How do our abilities to process number and other continuous quantities such as time and space relate to each other? Recent evidence suggests that these abilities share common magnitude processing and neural resources, although other findings also highlight the role of dimension-specific processes. To further characterize the relation between number, time, and space, we first examined them in a population with a developmental numerical dysfunction (developmental dyscalculia) and then assessed the extent to which these abilities correlated both behaviorally and anatomically in numerically normal participants. We found that (1) participants with dyscalculia showed preserved continuous quantity processing and (2) in numerically normal adults, numerical and continuous quantity abilities were at least partially dissociated both behaviorally and anatomically. Specifically, gray matter volume correlated with both measures of numerical and continuous quantity processing in the right TPJ; in contrast, individual differences in number proficiency were associated with gray matter volume in number-specific cortical regions in the right parietal lobe. Together, our new converging evidence of selective numerical impairment and of number-specific brain areas at least partially distinct from common magnitude areas suggests that the human brain is equipped with different ways of quantifying the outside world.