Mathematicians often say that their theorems, proofs, and theories can be beautiful. They say mathematics can be like art. They know how to move creatively and freely in their domains. But ordinary people usually cannot do this and do not share this view. They often have unpleasant memories from school and do not have this experience of freedom and creativity in doing mathematics. I myself have been a mathematician, and I wish to highlight some of the creative aspects in doing (...) mathematics. I always had the feeling that there is much freedom in mathematics and that one can do as one pleases as long as one avoids contradictions (and one can even live with contradictions for a while). In mathematics one only needs to define something and there it is! Just imagine it, and it immediately exists. Where else, besides fiction, does one have such power? --- This essay has three parts. In the first, I lay out some historical facts and views that I will need later. Second, I insert an interlude with Kant, pointing out some of his claims and insights in aesthetics, and some aspects in mathematics that I think he overlooked or underestimated. Third, I will bring out some aspects of higher mathematics that I will show are similar to art. These aspects are in the doing and creating of mathematics, not in the finished theories. They are usually not found in textbooks. I want to show that a researcher in mathematics is like a painter or composer, exploring and creating. To see this, one has to adopt a first-person perspective. In this way I will show that aesthetics plays a role and leaves its traces also in mathematics. (shrink)

This essay introduces ideas from Confucius, Xunzi, the Six Dynasties, and Kant about beauty, music, morality, and what we might today call “aesthetic education.” It asks how beauty and morality are related and how they ideally should be related to each other. We know that beauty and morality can drift apart, and we may wonder how aesthetic education might work best. Should the arts be a means for developing morality? Or should it be the other way around? These questions are (...) still relevant today. But our world has changed, not only since Confucius, but also since Kant. We may ask what to make of their ideas in our present time. I argue that there are good reasons for keeping morality and aesthetics apart, somewhat in the spirit of Kant, and in opposition to the idea of “fusing” the two. (shrink)

In _An Introduction to Kant’s Aesthetics_, Christian Wenzel discusses and demystifies Kant’s Critique of the Power of Judgment, guiding the reader each step of the way and placing key points of discussion in the context of Kant’s other work. Explains difficult concepts in plain language, using numerous examples and a helpful glossary. Proceeds in the same order as Kant’s text for ease of reference and comprehension. Includes an illuminating foreword by Henry E. Allison. Offers twenty-six further-reading sections, commenting (...) briefly on books and articles from the English, German, and French, that are relevant for each topic Provides an extensive bibliography and a chapter summarizing Kant's main points. (shrink)

Ob die Kategorien schon bei der Wahrnehmung eine Rolle spielen, wird von Kant-Interpreten unterschiedlich gesehen. Peter Rohs etwa argumentiert für eine Unabhängigkeit und Selbständigkeit der Wahrnehmung gegenüber dem Verstand. Die intuitive Synthesis der Einbildungskraft müsse auf eigenen Füßen stehen können und Bilder und „singuläre Sinne“ der Anwendung der Begriffe vorausgehen. McDowell hingegen spricht sich gegen eine solche Selbständigkeit der Wahrnehmung aus. Setzte man sie voraus, käme der Verstand immer zu spät . Die Argumente beider Seiten sollen am Text Kants untersucht (...) werden . Es liegt hier ein echtes Sachproblem vor. Die gegenwärtige, hauptsächlich amerikanische Diskussion um eine etwaige Notwendigkeit kognitiver Funktionen bei der Wahrnehmung stößt auf ganz ähnliche Probleme wie wir sie schon bei Kant finden, nur daß man sich dieser Ähnlichkeit außerhalb von Kantkreisen oft nicht bewußt zu sein scheint. (shrink)

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. (shrink)

In der Reihe werden herausragende monographische Untersuchungen und Sammelbände zu allen Aspekten der Philosophie Kants veröffentlicht, ebenso zum systematischen Verhältnis seiner Philosophie zu anderen philosophischen Ansätzen in Geschichte und Gegenwart. Veröffentlicht werden Studien, die einen innovativen Charakter haben und ausdrückliche Desiderate der Forschung erfüllen. Die Publikationen repräsentieren damit den aktuellsten Stand der Forschung.

The problem of free will as it is know in Western philosophical traditions is hardly known in China. Considering how central the problem is in the West, this is a remarkable fact. We try to explain this, and we offer insights into discussions within Chinese traditions that we think are related, not historically but regarding the issues discussed. Thus we introduce four central Chinese concepts, namely: (1) xīn 心 (heart, heart-mind), (2) xìng 性 (human nature, characteristic tendencies, inborn capacity), (3) (...) mìng 命 (lifespan, fate, command, allotment, endowment), and (4) zìrán 自然 (self-so, so of itself, nature, spontaneity), and we indicate how these concepts and their discussions can be related to discussions on free will. (shrink)

When contrasting something with its opposite, such as positive numbers with negative numbers, repulsion with attraction, good and evil, beauty and ugliness, Kant some-times says the latter are not merely cases of negation or privation of the former, but that they have their own, independent grounds. But do negative judgments of taste really have a priori grounds? There are two kinds of negative judgments of taste: “This is not beautiful” and “This is ugly.” Can they be a priori judgments? Or (...) are they always impure and without a priori basis? In this essay, I argue that they can be pure a priori judgments. I will give detailed analyses of examples involving part-whole relationships, objects of art, and aesthetic ideas. In addition, detailed discussions of opposing interpretations will be offered. (shrink)

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 .. (shrink)

In the framework of his transcendental philosophy, Kant strictly separates morality from aesthetics. The pleasure in the good and the pleasure in the beautiful are two different kinds of pleasure (Arten des Wohlgefallens). As a consequence, a moral act as such cannot be beautiful. It is only in a second step that Kant indicates possible connections, in his comments on aesthetic ideas, symbolism, the sensus communis, and education in general. In Confucius on the other hand we do not find such (...) a radical separation between beauty and morality. Ritual is a source of both. Moral acts can be beautiful. One might wonder whether Confucius missed a point, or whether Kant overdid the separation. Or is it that their conceptions are so fundamentally different that they cannot easily be translated and identified across different philosophical traditions? (shrink)

Wittgenstein in his later years thought about experiences of meaning and aspect change. Do such experiences matter? Or would a meaning- or aspect-blind person not lose much? Moreover, is this a matter of aesthetics or epistemology? To get a better perspective on these matters, I will introduce distinctions between certain subjective and objective aspects, namely feelings of our inner psychological states versus fine-tuned objective experiences of the outer world. It seems to me that in his discussion of meaning-blindness, Wittgenstein unhappily (...) floats between these two extremes, the subjective and the objective. I will also introduce some notions from Kant's aesthetics, to get a better understanding of the interplay between feeling and meaning. This will shed some new light on Wittgenstein's enquiry into meaning- and aspect-blindness. (shrink)

This essay is about Wittgenstein, first about his views on ethics, second about his conception of language games. Third, it combines the two and shows how problems arise from this. Wittgenstein rejects theories of ethics and emphasises the variety of language games. Such language games are marked by what I call “inner relativity”. Wittgenstein himself was not a relativist, but it seems to me his views easily lead to what I call “outer relativism”. In matters of ethics this is particularly (...) problematic. (shrink)

In 1930, the British economist John Maynard Keynes predicted that by 2030 people would work only fifteen hours per week and enjoy more free time and leisure, that we would return to “principles of religion and traditional virtue,” declaring “love of money morbid, semi-criminal, and semi-pathological,” and that “we shall once more value ends above means.” But today, we do not see that this prophesy has proven true. Something must have gone wrong. We do not sufficiently know the distinction between (...) needs and wants, absolute values and relative values, what a good life is, and how to live it. In this essay, I will present and discuss ideas from Confucius, Aristotle, Zhuangzi, and the Stoics that I think are deep and meaningful and can help us free ourselves from evolutionary programming and blind belief in economic and technological growth. (shrink)

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. (shrink)

In the preface to On Certainty Anscombe and von Wright say that in 1949 Malcolm suggested to Wittgenstein to think again about Moore’s “Defense of Common Sense” (1925) and “Proof of an External World” (1939). Malcolm himself had written on the issue in “Defending Common Sense” (1949). In the preface to the Philosophical Investigations Wittgenstein quotes Nestroy saying that there is usually very little progress in philosophy. But I think some progress has been made from Moore and Malcolm to Wittgenstein (...) regarding skepticism. There is more awareness of practice and perspective and this opens the discussion in novel ways. But it also gives rise to new problems, in particular of morality and relativity. (shrink)

In this essay I point out parallels between Kant’s theory of aesthetics and Wittgenstein’s discussion of rule following. Although Wittgenstein did not write an aesthetics and Kant did not discuss Wittgensteinian rule-following problems, and although both Kant and Wittgenstein begin at very different starting points and use different methods, they end up dealing with similar issues, namely issues about rules, particularity, exemplarity, objectivity, practice, and as-if statements.

There has been recent dispute between Putnam and Searle over whether meanings are “in the head”. Putnam makes use of Twin-Earth thought experiments to show that our mental states alone cannot determine what we refer to (and thus “mean”) and that we rely also on external factors, which are not “in the head”. This suggests to me that we in some way mean more than we actually know. Searle on the other hand makes use of what he calls “Intentional contents”, (...) “conditions of satisfaction”, and “self-referentiality”, to show that meanings can be said to be in the head. It seems to me that an internalist account as we find it in Husserl or Searle is closer to what is going on when we mean something. (shrink)

What is the nature of thought? Is thought linguistic and some kind of silent speech? Or is it pre-linguistic and some kind of association of ideas and images in the mind? Does it happen in the brain? I will focus on the last question, but also say something about the other two. I will present a simple thought experiment to show that thought must somehow happen in the brain. But then I will soften the impression this might give by pointing (...) out what is needed to read those thoughts. Simply put, ontologically thought is in the brain, epistemologically it is not. (shrink)

There are mathematical structures with elements that cannot be distinguished by the properties they have within that structure. For instance within the field of complex numbers the two square roots of −1, i and −i, have the same algebraic properties in that field. So how do we distinguish between them? Imbedding the complex numbers in a bigger structure, the quaternions, allows us to algebraically tell them apart. But a similar problem appears for this larger structure. There seems to be always (...) a background and a context that we rely upon. Thus mathematicians naturally make use of Kantian intuition and references fixed by names and denotations. I argue that such features cannot be avoided. (shrink)

It has often been said that the Chinese script is pictorial or ideographic, and that this is one of the reasons why Chinese tend to think more analogically than logically, and why in the past the natural sciences developed to a lesser degree in China than in the West. These are strong claims. They have often been oversimplified and exaggerated, but I think there is something to be said for them. Here I will focus on the first question. I will (...) argue that Chinese characters still have semantic features that create image-like qualities in a wider sense: not mere resemblances between sign and object, but family resemblances in semantic fields. The fact that Chinese is an isolating and monosyllabic language is essential in this. (shrink)

This essay is about the inner and the outer in Wittgenstein, in particular his notion of “meaning experience”. Wittgenstein reminds us that we should not think of the inner, psychological the way we think about the outer, physical world. Again and again he keeps returning to certain views about the soul and our mental states. I think that it is not only therapy he has in mind. I will contrast certain aesthetic and ethical aspects of his thoughts with views from (...) Kant. (shrink)

The notion of “representation” is central to Kant’s transcendental philosophy. But naturalism and mind-body reductionism tend to reduce talk of (first-person) representation to stories of (third-person) causality and evolution. How does Kant fare in this context?

According to the so-called Sapir-Whorf hypothesis, a language influences the mind of its user. This is more or less trivial, but the problems are in the details. It is difficult to make precise what those influences are, be it in general philosophical or in particular empirical-cultural terms. I will give an account of what I take to be basic aesthetic and grammatical features of the Chinese language compared with what we find in Western languages such as Latin or greek. Then (...) I will indicate what I take to be cultural differences and discuss whether these might be the result of differences in language structure. (shrink)

Wittgenstein wrote: “No supposition seems to me more natural than that there is no process in the brain correlated with associating or with thinking; so that it would be impossible to read off thought-processes from brain processes.” In general, he rejects what he calls “psycho-physical parallelism.” In Sect. 1, I explain Wittgenstein’s position on this topic and how his followers defend it. In Sect. 2, I argue against Wittgenstein, contending that there is “thought” in a wider sense and that it (...) can be “manifested” without expression. Thought does not need to be ordinarily expressed or even expressible, and it can be read off from the brain, provided one has sufficient technology, data, and understanding of the subject’s interaction with the environment. In Sect. 3, I offer results from brain-science in support of my claims. (shrink)

This paper has two parts. In the first I give a brief historical account of the a priori and point out the central and problematic role of 'Erfahrung überhaupt' in Kant’s transcendental philosophy. In the second and main part I offer a criticism of Kripke’s arguments for the contingent a priori and I thereby question his radical separation of metaphysics and epistemology.

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)

Hermann Schmitz has developed a “New Phenomenology.” It emphasizes fundamental conceptions that undercut traditional subject-object distinctions. In the Chinese classic The Zhuangzi we find stories that describe involvements and dialogue that can be seen as doing something similar. I will bring out some of these parallels. In particular I will focus on freedom and mutual understanding.

The main ideas in this paper can be summarized in the following three points. (1) Openness, indeterminacy, and exemplarity are elements of both Kant's aesthetics and Wittgenstein's notion of language games. (2) These elements are essential to what makes a person. They are necessary in processes of decision-making and in the development of a person. (3) Such aspects were in the center of discussion during the eighteenth and nineteenth centuries in Europe, especially in the tradition of the so-called Bildungsroman. Unfortunately, (...) they tend to be forgotten nowadays. (shrink)

In this essay I focus on Wittgenstein's discussion of how we understand and feel about people that come from cultures very different from our own. Wittgenstein writes about "guessing thoughts", "regularities", and "common human behaviour" (gemeinsame menschliche Handlungsweise) in this context. I argue that his idea about given forms of life that we should "accept", will be problematic if we want to find a meaningful way of relating to such people with whom we "cannot find our feet" (in die man (...) sich nicht finden kann). (shrink)

Kant sometimes compares human beings with animals and angels and grants human beings a middle position. But contrary to what one might expect, his transcendental philosophy does not apply well to animals or angels. The question of whether we share perception with animals has no good answer in his system that has to be taken as a single piece and does not allow for introducing steps of empirical, real developments. Differently from Kant, McDowell does compare human beings with animals, but (...) he is not a transcendental philosopher and his attempts to find support in Kant are problematic. Although McDowell says that concepts go "all the way out" and Kant says the categories go "all the way down," which sounds similar, Kant talks of a priori categories, not empirical concepts. Burge is definitely not a transcendental philosopher like Kant. Up front he strongly relies on empirical studies, especially animal perception. Nevertheless, his quest into mental content introduces first-person perspectives that have a metaphysical flavor, and this makes - at least to me - comparisons with Kant tempting again. (shrink)

In this essay I closely look at dialogues from the Daoist text Zhuangzi and examine their modes of reasoning. The observations, comments, and dialogues are often witty, surprising, and puzzling. Sometimes they are mystic and difficult to understand. But how “reasonable” are the answers given in these dialogues? I will focus on a dialogue from chapter 17, called “Autumn Floods.” I will closely follow and analyze the arguments and their twists. In particular, I will question the use of the word (...) “Dao.” I will also place this analysis in broader comparative frameworks regarding rationality, the Sapir-Whorf hypothesis, and Western traditions. (shrink)

This is a short, but complex and ambitious book. It is argumentative in style and in many places written in the first person. It appeared first in German in 2003, and in 2016 in English translation, to which the two translators added a detailed and informative introduction. The overall aim of the book is to describe and explain how human beings, as users of propositional language and with the ability to refer to themselves, develop into egocentric beings, who find themselves (...) confronted with the world as a whole, and who turn to mysticism or religion in order to find some peace of mind. A wide range of themes and arguments are interwoven along on the way from being an "I"-sayer to... (shrink)