Aaron Wells

There is a relatively overlooked problem with Kant’s claim that in inquiry we must treat nature as if it were actually infinite in extent: he also states that the concept of an actually infinite world is self-contradictory. This threatens to make the command to treat the world as infinite incoherent; the problem also affects his error theory for traditional metaphysics and his account of the sublime. After laying out this worry in greater detail than has been done so far, I consider and reject readings on which Kant either does not consider this case a violation of ought-implies-can or allows that in this case, following an incoherent demand is epistemically acceptable on consequentialist grounds. Then I turn to my preferred solution, which takes the relevant regulative principle to concern Kant’s noumena (understood as intensionally distinct from things in themselves), whereas the contradiction is provoked only by representations of phenomena.

On an influential reading, Leibniz's eighteenth-century followers, such as Wolff and Baumgarten, were proto-logicists who sought to transform all propositions into analytic truths. Kant's main innovation, on this reading, lies in asserting that there are synthetic a priori truths. Against this, I establish the importance of a line of thought in Leibniz, Wolff, and Baumgarten that stresses the role of perception for determinate knowledge of magnitudes, such as the objects of geometry. (I also consider Crusius, who hews much closer to an analytic or conceptual account of magnitude.) I argue that these thinkers fail to solve a family of philosophical problems arising from a conflict between (1) their commitment to the objectivity and necessity of mathematics, and (2) their view that a determinate grasp of magnitude partly depends on relations to a perceiver. I then contend that Kant is also a participant in the debate about these problems, that he is closer to his predecessors than usually assumed (though partly rejecting their emphasis on empirical perception), and that at least two problems for his account remain unsolved.

Relationalism about space faces well-known objections if it is limited to relations between actual bodies. These problems might be avoided through so-called modal relationalism, on which the relevant relata include possible entities. Leibniz is considered a founder of modal relationalism, appealing to relations among possible situations. This article argues that for the central type of relation in question, namely congruence, Leibniz cannot give an adequate basis for modal relationalism. This is because his criteria for determining congruence rely on actual perception, and because attempts to modalize this perception requirement conflict with his other commitments.

Nomic essentialism is the surprising view that properties of particulars are importantly dependent on laws. In this paper, I consider what I call a moderate nomic essentialist reading of Kant, on which the thesis of dependence on law is restricted to properties of empirical objects. I argue that this reading is more plausible than it might seem, and can be textually motivated by the relational character of empirical objects, the role of laws in determinism, and Kant’s laws-first account of what it is to be a material particular. I also compare this reading with more familiar contemporary arguments for nomic essentialism. Finally, I consider two problems for nomic essentialism—the problem of circularity and the problem of nomic governance—and outline some possible responses on Kant’s behalf.

In the Metaphysical Foundations of Natural Science, Kant attempts to argue a priori from the indefinite divisibility of space to the indefinite metaphysical divisibility of matter. This is one type of argument from the continuity of space – purportedly established by Euclidean geometry – to the continuity of matter. I compare Kant’s argument to parallel reasoning in Du Châtelet, whose work he knew. Both philosophers appeal to idealism about matter in their reasoning, yet also face difficulties in explaining why continuity, though not some other properties from geometry, applies to matter. Both also risk inconsistency in adopting potentialist accounts of material parts, while also committing to realism about infinitesimals. An important difference between them is that Du Châtelet deploys at least three definitions of continuity; only one of these, amounting to indefinite divisibility, is shared with Kant.

For Kant, inquiry into nature properly requires seeking to explain all material wholes merely mechanically, in terms of their parts. There is no consensus on how he justifies this Principle of Mechanism. I argue that Kant seeks to derive this claim about part and wholes neither from his laws or mechanics, nor from the mere discursivity of our understanding (two standard options in the literature), but instead from a priori principles laid out in the first Critique, which govern parts, wholes, and magnitudes. These principles are also fundamental to Kant’s account of mathematics. Therefore, Kant’s Principle of Mechanism and his philosophy of mathematics have common foundations.

I reconstruct J. H. Lambert’s views on how practical grounds relate to epistemic features, such as certainty. I argue, first, that Lambert’s account of moral certainty does not involve any distinctively practical influence on theoretical belief. However, it does present an interesting form of fallibilism about justification as well as a denial of a tight link between knowledge and action. Second, I argue that for Lambert, the persistence principle that underwrites induction is supported by practical reasons to believe; this indicates that Lambert is a moderate pragmatist about reasons for theoretical belief.

Draft for presentation at the 14th International Kant-Congress, September 2024. Abstract: Kant claims we intuit infinite space. There’s a problem: Kant thinks full awareness of infinite space requires synthesis—the act of putting representations together and comprehending them as one. But our ability to synthesize is finite. Tobias Rosefeldt has argued in a recent paper that Kant’s notion of decomposing synthesis offers a solution. This talk criticizes Rosefeldt’s approach. First, Rosefeldt is committed to nonconceptual yet determinate awareness of (potentially) infinite space, but I argue that such awareness is (1) prima facie implausible, as well as contravened by textual evidence from Kant’s (2a) definitions of ‘infinity’ and (2b) account of geometrical construction. Second, scrutiny of how Kant thinks awareness of potential infinity is afforded by geometrical construction (e.g., extending a line segment ad indefinitum) indicates no essential role for decomposing synthesis. Familiar synthesis from parts to wholes is sufficient.

I examine Du Châtelet’s methodology for physics and metaphysics through the lens of her engagement with Newton’s Rules for Reasoning in Natural Philosophy. I first show that her early manuscript writings discuss and endorse these Rules. Then, I argue that her famous published account of hypotheses continues to invoke close analogues of Rules 3 and 4, despite various developments in her position. Once relevant experimental evidence and some basic constraints are met, it is legitimate to inductively generalize from observations; general hypotheses can thereafter be assumed as true until contrary experiments show otherwise. I conclude by arguing that this account of induction plays an essential role in her metaphysics, both in an argument for simple substances—which has an inductive premise—and in her attempt to distinguish acceptable and unacceptable metaphysical commitments.

I distinguish three ways in which early modern rationalists seek to apply the principle of sufficient reason to empirical science, and critically assess some of their attempts to do so. I focus especially on how these thinkers assume substantive theories of explanation and intelligibility--which are indebted to the mechanist and experimentalist traditions--in many of their deployments of this rationalist principle. A recurring problem is that these philosophers deploy their standards of intelligibility inconsistently: some of their own favored explanations do not always live up to their standards. I argue that the problem is especially acute for Leibniz and Euler, given their enthusiasm for final-causal explanations.

I first aim to sketch the institutional and historical route that the first four women admitted to the Bologna Academy--Laura Bassi, Faustina Pignatelli, Emilie Du Châtelet, and Maria Gaetana Agnesi-- took to membership (section 2). I bring out some of the institutional and sociological connections between them: one of Bassi’s students befriended Du Châtelet, for example. I then turn to two major themes in Du Châtelet’s work on philosophy and science. One is the attempt to unify disparate phenomena through analogical reasoning, manifest in her Dissertation on fire (section 3). A second theme is her insistence that scientific hypotheses can and should be constrained by extra-empirical principles: these include the principle of sufficient reason, the principle of the identity of indiscernibles, principles of continuity, and a theological principle of perfection (section 4).

Du Châtelet holds that mathematical representations play an explanatory role in natural science. Moreover, she writes that 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 material 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 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 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.

For Émilie Du Châtelet, I argue, a central role of the principle of sufficient reason is to discriminate between better and worse explanations. Her principle of sufficient reason does not play this role for just any conceivable intellect: it specifically enables understanding for minds like ours. She develops this idea in terms of two criteria for the success of our explanations: “understanding how” and “understanding why.” These criteria can respectively be connected to the determinateness and contrastivity of explanations. The crucial role Du Châtelet’s principle of sufficient reason plays in identifying good explanations is often overlooked in the literature, or else run together with questions about the justification and likelihood of explanations. An auxiliary goal of the article is to situate Du Châtelet’s principle of sufficient reason with respect to some of the general epistemological and metaphysical commitments of her Institutions de Physique, clarifying how it fits into the broader project of that work.

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.