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)

In his early writings, Kant says that the solution to the puzzle of how morality can serve as a motivating force in human life is nothing less than the “philosophers’ stone.” In this dissertation I show that for years Kant searched for the philosophers’ stone in the concept of “respect” (Achtung), which he understood as the complex effect practical reason has on feeling. -/- I sketch the history of that search in Chapters 1-2. In Chapter 3 I show that Kant’s (...) analysis in Groundwork I is incomplete because it does not explain how respect functions as a feeling in motivating choice. In Chapter 4 I argue that Kant’s subsequent attempt to sidestep this explanation in Groundwork III is unsuccessful, and that his position remains open to a skeptical threat. The argument in the second Critique, which I reconstruct in Chapters 5-6, overcomes this threat, and in doing so explains how the feeling of respect is both painful and pleasurable. -/- In the course of defending these claims, I provide an alternative reading of the shift in Kant’s ethical project from the Groundwork of 1785 to the second Critique of 1788 Against a common view in the literature, I argue that the shift does not concern the direction of Kant’s deduction (from freedom to morality, or morality to freedom); rather, it concerns his view of human sensibility and the resources he thinks we have to make our practical self-understanding intelligible. In the second Critique, I argue, Kant develops a novel approach to moral feeling from the perspective of the human agent; and this in turn clears room in his ethics for a new kind of a priori knowledge—namely, knowledge of what the activity of practical reason must feel like. By way of conclusion, I offer a few reasons for why the form of Kant’s argument in the second Critique is still relevant today, as it shows why we can only address moral skepticism from a first-personal perspective. (shrink)

The aim of this research is to explore what relations self-affection bears to the intuitions of inner sense. I propose that self-affection makes some contribution to formal intuitions and empirical consciousness by arguing that the functions of self-affection consist respectively in conceptualising and conscious-making. I begin by examining Kant’s concept of inner sense and point out that inner sense as a receptive faculty depends on self-affection. In so doing, I emphasise that self-affection includes both a pure and an empirical aspect (...) which corresponds to Kant’s distinction between the transcendental synthesis of imagination and the empirical synthesis of apprehension. Then, I focus on the pure aspect and argue that the conceptualising function involved in the pure self-affection is decisive for the generation of formal intuition. In particular, I explain why the formal intuition of time depends on the intuition of space and how it is constituted by drawing a line. After that, I turn to analysing the empirical aspect of self-affection and show that by virtue of the empirical synthesis of apprehension one is aware of both the empirical contents of representations and the mental actions performed on them, whereby I suggest that this empirical conscious-making function can be understood as an act of distinguishing from a mereological point of view. (shrink)

In many of his writings, Castoriadis argues that ‘the discovery of the imagination’ occurs in the works of Aristotle, Kant, Fichte, Freud, Heidegger and Merleau-Ponty. Although he has systematically encountered and interrogated the works of Aristotle, Kant, Freud, and Merleau-Ponty, the work of Fichte remains an enigmatic absence within the orbit of Castoriadis' work. This study is an attempt to address this enigma through a close reading of Fichte’s The Science of Knowledge.

In 1764, Kant published his Observations on the Feeling of the Beautiful and the Sublime and in 1790 his influential third Critique, the Critique of the Power of Judgment. The latter contains two parts, the ‘Critique of the Aesthetic Power of Judgment’ and the ‘Critique of the Teleological Power of Judgment’. They reveal a new principle, namely the a priori principle of purposiveness (Zweckmäßigkeit) of our power of judgment, and thereby offer new a priori grounds for beauty and biology within (...) the framework of Kant's transcendental philosophy. They also unite the previous two Critiques, the Critique of Pure Reason and the Critique of Practical Reason. Besides contributing to general and systematic aspects within his transcendental philosophy, Kant's aesthetics also offers new insights into old problems. It deals with feeling versus experience, subjectivity versus objectivity, disinterested pleasure, aesthetic universality, free and adherent beauty, the sensus communis, genius, aesthetic ideas, beauty as the symbol of morality, beauty of nature versus beauty of art, the sublime, and the supersensible. In this article I will limit myself to this critical aesthetics of Kant. But I will also discuss the ugly and the possibility of beauty in mathematics and see whether Kant's theory can successfully explain or deal with them. I will also compare his theory with philosophical ideas from a very different tradition, namely from Confucius, not only as a challenge to Kant's theory, but also because there is a growing interest from the Chinese side in combining ideas from Confucius and Kant, an interest that might well become influential in both East and West during the 21st century. (shrink)