Kirsten Walsh

Descartes and Roberval: Physics and Simple Machines

 

This presentation deals with an episode of the interaction between Descartes and Roberval: the debate about the center of gravity and the center of oscillation of a physical body. I aim to show how this debate about a mathematical science, i.e. mechanics, is informed by metaphysical commitments regarding the properties of matter. Descartes and Roberval disagreed upon the definitions and particularities of the centers of gravity and oscillation. Descartes regarded them as two relative and complementary features of bodies. For Roberval, the centers would act on one another: measuring the center of oscillation would have to include the directionality of movement imposed by the center of gravity on each part of the moving body.

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I argue that the best explanation of this disagreement goes back to the metaphysical commitments about weight and/or gravity (gravité ou pesanteur). Roberval believes that each part of matter has an intrinsic property of uniting with other parts. This intrinsic property grounds the absolute character of the center of gravity and oscillation, which, in turn, accounts for Roberval’s geometrical treatment of the two notions.

Early Modern Vice Epistemology

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In this talk, I make a case for the existence of an early modern English tradition of vice epistemology. In its modern form, vice epistemology names the study of the identity and significance of epistemic vices, such as arrogance and closed-mindedness. Unfortunately vice epistemology tends not to evince an historical sensibility nor to engage significantly with the work of intellectual or cultural historians. This is a shame, since it obscures a variety of earlier projects in vice epistemology and their practitioners. A particularly rich period is 16th and 17th century English natural philosophy, where a latent sensitivity to epistemic vice is evident in prevailing talk of the ‘infirmities’, ‘defects’, and ‘weaknesses’ of the mind. Although the best example is Francis Bacon’s account of the ‘Idols of the Mind’, similar themes run through writings by Boyle, Glanvil and other natural philosophers. Such nascent vice-epistemological projects were rooted in a variety of wider cultural and intellectual developments - the revival of scepticism, the enduring legacy of postlapsarian anthropologies, and Renaissance humanist emphasis on humility frailty. If this is broadly right, contemporary vice epistemologists and scholars of early modern philosophy can and should have productive conversations.

The Non-Mathematical Ambitions of Antoine Arnauld

 

This paper will examine the Nouveaux éléments de Géométrie of 1667, a seemingly unlikely intervention in the mathematical culture of the mid-seventeenth century for Antoine Arnauld, a firebrand theologian and author of works on topics in logic and grammar. The aim of this paper is to examine Arnauld’s reasons for penning a revised edition of Euclid’s Elements particularly given the hostile attitudes of fellow theologians who insisted that the practice of mathematics was a futile, trivial, and vainglorious misuse of time. In this talk I show that Arnauld created a geometry that he hoped would serve in the cultivation of moral, spiritual and intellectual virtues. The account of Arnauld’s mathematical interventions I offer connects his mathematical treatise to concerns in moral philosophy, theology and epistemology. These reflections, I argue, are indispensable to developing any account of mathematical practice in the early modern era.

Microscopes and Mechanism: What was the limit of Hooke’s empiricism?

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In this paper I set the limits of Robert Hooke’s empiricism. A well established narrative in the history of science has connected his much-loved microscope with mechanical, anti-Aristotelian natural philosophy: it was used to seek visual confirmation of corpuscles, particles, effluvia, and other replacements for hylomorphic causal explanations. This paper complicates the general story by showing that Hooke was at best ambiguous about the existence of such entities, and never hoped to see them with his magnifying lenses.

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Considering his famous Micrographia as well as later lectures from the middle and twilight of his career, I draw a distinction between two types of mechanical philosophy in Hooke’s thought, and claim that he sorted the causes of phenomena into the visible and the invisible. When dealing with the visible, he searched for a kind of functional minima, the ‘machines of nature’. His search was motivated more by the metaphor of nature as a machine than by the metaphysical belief in atomistic philosophy, and he used lenses much as artisans and jewellers had for years previously to produce detailed work. When he discussed the invisible causes of the motions of these machines, he hypothesised parts of matter that would always remain strictly invisible.

‘Quick wit and good understanding’: Newtonian Certainty and ‘Compelled Assent’

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Newton claims his laws of motion are certainly true, and yet his justification looks surprisingly weak.  He writes, “The principles I have set forth are accepted by mathematicians and confirmed by experiments of many kinds” (Newton, 1999: 424), and yet he merely cites a handful of experiments—which only support the laws for a limited domain.  Why, then, does Newton claim certainty?  I’ll argue that this case is revelatory of Newton’s notion of certainty—a central idea in his distinctive methodology.  Drawing on his other methodological statements, I characterise Newton’s certainty as ‘compelled assent’: Newton thought the evidence, properly understood, compelled the observer towards an undeniable conclusion.