It is a common thought that mathematics can be not only true but also beautiful, and many of the greatest mathematicians have attached central importance to the aesthetic merit of their theorems, proofs and theories. But how, exactly, should we conceive of the character of beauty in mathematics? In this paper I suggest that Kant's philosophy provides the resources for a compelling answer to this question. Focusing on §62 of the ‘Critique of Aesthetic Judgment’, I argue against the common view (...) that Kant's aesthetics leaves no room for beauty in mathematics. More specifically, I show that on the Kantian account beauty in mathematics is a non-conceptual response felt in light of our own creative activities involved in the process of mathematical reasoning. The Kantian proposal I thus develop provides a promising alternative to Platonist accounts of beauty widespread among mathematicians. While on the Platonist conception the experience of mathematical beauty consists in an intellectual insight into the fundamental structures of the universe, according to the Kantian proposal the experience of beauty in mathematics is grounded in our felt awareness of the imaginative processes that lead to mathematical knowledge. The Kantian account I develop thus offers to elucidate the connection between aesthetic reflection, creative imagination and mathematical cognition. (shrink)
Laws of nature play a central role in Kant's theoretical philosophy and are crucial to understanding his philosophy of science in particular. In this volume of new essays, the first systematic investigation of its kind, a distinguished team of scholars explores Kant's views on the laws of nature in the physical and life sciences. Their essays focus particularly on the laws of physics and biology, and consider topics including the separation in Kant's treatment of the physical and life sciences, the (...) relation between universal and empirical laws of nature, and the role of reason and the understanding in imposing order and lawful unity upon nature. The volume will be of great interest to advanced students and scholars of Kant's philosophy of science, and to historians and philosophers of science more generally. (shrink)
I argue for the unity of imagination in two prima facie diverse contexts: experiences of beauty and achievements of understanding. I develop my argument in three steps. First, I begin by describing a type of aesthetic experience that is grounded in a set of imaginative activities on the part of the person having the experience. Second, I argue that the same set of imaginative activities that grounds this type of aesthetic experience also contributes to achievements of understanding. Third, I show (...) that my unified account of imagination has important implications: it sheds light on two puzzling phenomena, the aesthetic value of science and the cognitive value of art. (shrink)
Can aesthetic judgements legitimately be linked to the success of scientific theories? I suggest that a satisfactory answer to this question should account for the persistent attraction that aesthetic considerations seem to have for scientists, while also explaining the apparent instability of the link between the beauty of a theory and its truth. I argue that two widespread tendencies in the literature, Pythagorean and subjectivist approaches, have difficulties meeting this twofold challenge. I propose a Kantian conception of aesthetic judgements as (...) second‐order considerations, related to our own intellectual capacities for making sense of the world, and argue that it fares better. (shrink)
In this paper I discuss two questions. What does Kant understand by mechanical explanation in the Critique of judgment? And why does he think that mechanical explanation is the only type of the explanation of nature available to us? According to the interpretation proposed, mechanical explanations in the Critique of judgment refer to a particular species of empirical causal laws. Mechanical laws aim to explain nature by reference to the causal interaction between the forces of the parts of matter and (...) the way in which they form into complex material wholes. Just like any other empirical causal law, however, mechanical laws can never be known with full certainty. The conception according to which we can explain all of nature by means of mechanical laws, it turns out, is based on what Kant calls ‘regulative’ or ‘reflective’ considerations about nature. Nothing in Kant’s Critique of judgment suggests that these considerations can ever be justified by reference to how the natural world really is. I suggest that what, upon first consideration, appears to be a thoroughly mechanistic conception of nature in Kant is much more limited than one might have expected. (shrink)
it is common to praise the beauty of theories, the elegance of proofs, and the pleasing simplicity of explanations. We may admire, for example, the beauty of Einstein’s theory of general relativity, the simplicity of Darwin’s idea of natural selection, and the elegance of a geometrical proof of Pythagoras’s theorem. Aesthetic judgments such as these have much currency among scientists, and they are employed in the search for knowledge more broadly. But while the use of aesthetic judgments in science is (...) widespread, it is not uncontroversial.1 On one side, such judgments are often inspired by the Platonic vision that beauty and truth are ultimately one. As Henri Poincaré saw it, science is the “disinterested pursuit... (shrink)
We can observe a connection between some serious environmental problems caused by the overexploitation of environmental resources and the particular conceptions of property rights that are claimed to hold with regard to these resources. In this paper, I investigate whether Kant’s conception of property rights might constitute a basis for justifying property regimes that would overcome some of these environmental problems. Kant’s argument for the right to property, put forward in his Doctrine of right, is complex. In Section 2, I (...) attempt an interpretation. Section 3 works out the defining characteristics of the conception of property rights that Kant’s argument establishes and investigates their implications for determining property regimes in environmental resources. Kant proposes a minimalist notion of the right to property as a triadic relation between persons with regard to an object, justified only on the condition that it is universalizable in the given circumstances. I argue that this notion offers a promising account for determining property relations with regard to environmental resources. By way of illustration, in Section 4, I focus on an example of Kantian property rights in one type of environmental resource: the marine fisheries. (shrink)
First, I raise two objections against Ginsborg’s interpretation of natural teleology. I argue that Ginsborg’s notion of primitive normativity is too thin to account for Kant’s more substantive conception of the organism. Furthermore, I question whether Kant has room for a notion of purposiveness that is entirely divorced from intentional activity. Second, I ask about the implications of Ginsborg’s account of the relationship between aesthetic judgement and cognition. I suggest that her reading can easily be extended to allow for aesthetic (...) pleasure in empirical reflection. (shrink)
In his Kant on Laws, Eric Watkins presents an account of reason on which the principles of specification and continuity are regulative instructions to search for different kinds of the unconditioned. I suggest that we correct Watkins’ account in two ways. First, we need to complete Watkins’ claim to the plurality of the unconditioned: reason aims for three kinds of the unconditioned, associated with the lowest, next and highest concepts. Second, we need to look beyond reason’s search for the unconditioned (...) in order to properly understand the nature of the aim of reason. I argue that we construe reason’s aim as the systematic unity of cognition considered as a whole or, in Kant’s teleological terms, as the realization of an ‘idea’, or a ‘purposive unity’. (shrink)
Kant is often characterised as the chief exponent of an anthropocentric ethics that can ascribe to nature only a purely instrumental value. By contrast, this paper argues that Kant′s teleological conception of nature provides the basis for a promising account of environmental ethics. According to this account we can attribute to nature a value that is independent of its usefulness to human beings without making this value independent from the judgment of the rational valuer.
