Christian Wenzel

This essay will inform the reader about Kant’s views on mathematics and aesthetics. It will also critically discuss these views and offer further suggestions and personal opinions from the author’s side. Kant (1724-1804) was not a mathematician, nor was he an artist. One must even admit that he had little understanding of higher mathematics and that he did not have much of a theory that could be called a “philosophy of mathematics” either. But he formulated a very influential aesthetic theory that is contained in his “Critique of the Power of Aesthetic Judgment” (1790), and his views on mathematics, especially those that compare it with philosophy, are distinctive and worthy of our attention. Hence, combining mathematics and aesthetics, asking whether mathematics can be beautiful and why and how it can or cannot be so called, according to Kant’s theory, will be particularly interesting. This essay has three parts: it discusses mathematics, aesthetics, and the aesthetics of mathematics, primarily in Kantian perspectives but also in ways that critically evaluate those perspectives.

This is an essay about language, thought, and culture in general, and about Ancient Greek and Classical Chinese in particular. It is about the Sapir-Whorf hypothesis, which says that language influences the mind, and applies this hypothesis to Greek and Chinese. It is also an essay in comparative philosophy as well as a contribution to the history of ideas. From the language side, I rely on the nineteenth-century German linguist Wilhelm von Humboldt, and from the culture side on the contemporary French sinologist François Jullien. Combining their ideas, I give substance to the Sapir-Whorf hypothesis and explain some of Jullien's claims about the historical and political developments of Chinese culture. The central ..

In this essay I to do three things. First, I discuss a statement from the Tractatus which says that our free will consists in our ignorance of future actions: “The freedom of the will consists in the impossibility of knowing actions that still lie in the future. We could know them only if causality were an inner necessity like that of logical inference.” (5.1362) I think this statement might well be inspired by a claim Moore made in connection with free will in his 1912 book Ethics: “We can hardly ever know for certain beforehand, which choice we actually shall make”. But I think Moore’s claim in favor of free will is not convincing. Second, I discuss a question raised in Philosophical Investigations. Wittgenstein asks what remains if we “subtract” the fact that my arm goes up from the fact that I raise my arm, and he adds in brackets: “Are the kinaesthetic sensations my willing?” (621) This added reflection is a reaction to ideas put forward by William James. Wittgenstein opposes these ideas. He argues that we should not think of the will as a cause at all, kinaesthetic or not, but rather as something embedded in, and constituted by, certain contexts of learning, expectation, practice, and lack of surprise. This is a strong claim. He also returns to the question about the predictability of the future: “When people talk about the possibility of foreknowledge of the future they always forget the fact of the prediction of one’s own voluntary movements” (629). The question is whether Wittgenstein has solved, or dissolved, the problem of free will. Some think that this is the case. I doubt it is. This is the third point I wish to discuss.