Aaron Wells

Du Châtelet holds that mathematical representations play an explanatory role in natural science. Moreover, things proceed in nature as they do in geometry. How should we square these assertions with Du Châtelet’s idealism about mathematical objects, on which they are ‘fictions’ dependent on acts of abstraction? The question is especially pressing because some of her important interlocutors (Wolff, Maupertuis, and Voltaire) denied that mathematics informs us about the properties of real things. After situating Du Châtelet in this debate, this chapter argues, first, that her account of the origins of mathematical objects is less subjectivist than it might seem. Mathematical objects are non-arbitrary, public entities. While mathematical objects are partly mind-dependent, so too are material things. Mathematical objects can approximate the material. Second, it is argued that this moderate metaphysical position underlies Du Châtelet’s persistent claims that mathematics is required for certain kinds of general knowledge, including in natural science. The chapter concludes with an illustrative example: an analysis of Du Châtelet’s argument that matter is continuous. A key but overlooked premise in the argument is that mathematical representations and material nature correspond.

There is a growing consensus that Emilie Du Châtelet’s challenging essay “On Freedom” defends compatibilism. I offer an alternative, libertarian reading of the essay. I lay out the prima facie textual evidence for such a reading. I also explain how apparently compatibilist remarks in “On Freedom” can be read as aspects of a sophisticated type of libertarianism that rejects blind or arbitrary choice. To this end, I consider the historical context of Du Châtelet’s essay, and especially the dialectic between various strands of eighteenth-century libertarianism and compatibilism.

The consensus is that in his 1755 Nova Dilucidatio, Kant endorsed broadly Leibnizian compatibilism, then switched to a strongly incompatibilist position in the early 1760s. I argue for an alternative, incompatibilist reading of the Nova Dilucidatio. On this reading, actions are partly grounded in indeterministic acts of volition, and partly in prior conative or cognitive motivations. Actions resulting from volitions are determined by volitions, but volitions themselves are not fully determined. This move, which was standard in medieval treatments of free choice, explains why Kant is so critical of Crusius’s version of libertarian freedom: Kant understands Crusius as making actions entirely random. In defense of this reading, I offer a new analysis of the version of the principle of sufficient reason that appears in the Nova Dilucidatio. This principle can be read as merely guaranteeing grounds for the existence of things or substances, rather than efficient causes for states and events. As such, the principle need not exclude libertarian freedom. Along the way, I seek to illuminate obscure aspects of Kant’s 1755 views on moral psychology, action theory, and the threat of theological determinism.

I begin by outlining Du Châtelet’s ontology of mathematical objects: she is an idealist, and mathematical objects are fictions dependent on acts of abstraction. Next, I consider how this idealism can be reconciled with her endorsement of necessary truths in mathematics, which are grounded in essences that we do not create. Finally, I discuss how mathematics and physics relate within Du Châtelet’s idealism. Because the primary objects of physics are partly grounded in the same kinds of acts as yield mathematical objects, she thinks we are sometimes licensed in drawing conclusions about physical things from mathematical premises.

It is widely held that, in his pre-Critical works, Kant endorsed a necessitation account of laws of nature, where laws are grounded in essences or causal powers. Against this, I argue that the early Kant endorsed the priority of laws in explaining and unifying the natural world, as well as their irreducible role in in grounding natural necessity. Laws are a key constituent of Kant’s explanatory naturalism, rather than undermining it. By laying out neglected distinctions Kant draws among types of natural law, grounding relations, and ontological levels, I show that his early works present a coherent and sophisticated laws-first account of the natural order.

There is a tension in Emilie Du Châtelet’s thought on mathematics. The objects of mathematics are ideal or fictional entities; nevertheless, mathematics is presented as indispensable for an account of the physical world. After outlining Du Châtelet’s position, and showing how she departs from Christian Wolff’s pessimism about Newtonian mathematical physics, I show that the tension in her position is only apparent. Du Châtelet has a worked-out defense of the explanatory and epistemic need for mathematical objects, consistent with their metaphysical nonfundamentality. I conclude by sketching how Du Châtelet’s conception of mathematical indispensability differs interestingly from many contemporary approaches.

Ecology arguably has roots in eighteenth-century natural histories, such as Linnaeus's economy of nature, which pressed a case for holistic and final-causal explanations of organisms in terms of what we'd now call their environment. After sketching Kant's arguments for the indispensability of final-causal explanation merely in the case of individual organisms, and considering the Linnaean alternative, this paper examines Kant's critical response to Linnaean ideas. I argue that Kant does not explicitly reject Linnaeus's holism. But he maintains that the indispensability of final-causal explanation depends on robust modal connections between types of organism and their functional parts; relationships in Linnaeus's economy of nature, by contrast, are relatively contingent. Kant's framework avoids strong metaphysical assumptions, is responsive to empirical evidence, and can be fruitfully compared with some contemporary approaches to biological organization.