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)

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)

El objetivo de este artículo consiste en caracterizar la finalidad de las figuras geométricas. El concepto de tal finalidad se desarrolla en la segunda parte de la Crítica del Juicio. Considero que ese concepto permite a Kant especificar la relación entre los conceptos y la resolución de problemas en el ámbito de la matemática. El artículo contiene tres partes. En primer lugar, se explican algunos aspectos de la concepción kantiana de los conceptos geométricos. En segundo término, se detalla la función (...) de la finalidad geométrica en el marco de la "Crítica del Juicio teleológico". Finalmente, se comentan las características propias de esa finalidad. (shrink)