Introduction -- Aesthetic judgements, aesthetic principles, and aesthetic properties -- Aesthetic essence -- The acquaintance principle -- The intersubjective validity of aesthetic judgements -- The pure judgement of taste as an aesthetic reflective judgement -- Understanding music -- The characterization of aesthetic qualities by essential metaphors and quasi-metaphors -- Musical movement and aesthetic metaphors -- Aesthetic realism and emotional qualities of music -- On looking at a picture -- The look of a picture -- Wollheim on correspondence, projective properties, and (...) expressive perception -- Wittgenstein on aesthetics. (shrink)

We propose that aesthetic pleasure is a function of the perceiver's processing dynamics: The more fluently perceivers can process an object, the more positive their aesthetic response. We review variables known to influence aesthetic judgments, such as figural goodness, figure-ground contrast, stimulus repetition, symmetry, and prototypicality, and trace their effects to changes in processing fluency. Other variables that influence processing fluency, like visual or semantic priming, similarly increase judgments of aesthetic pleasure. Our proposal provides an integrative framework for the study (...) of aesthetic pleasure and sheds light on the interplay between early preferences versus cultural influences on taste, preferences for both prototypical and abstracted forms, and the relation between beauty and truth. In contrast to theories that trace aesthetic pleasure to objective stimulus features per se, we propose that beauty is grounded in the processing experiences of the perceiver, which are in part a function of stimulus properties. (shrink)

Aesthetic Formalism has fallen on hard times. At best it receives unsympathetic discussion and swift rejection. At worst it is the object of abuse and derision. But I think that there is something to be said for it. In this paper, I shall try to find and secure the truth in formalism. I shall not try to defend formalism against all of the objections to it.1 Instead I shall articulate a moderate formalist view that draws on aesthetic0nonaesthetic determination and Kant’s (...) distinction between free and dependent beauty. I shall examine four central art forms—painting, sculpture, lit-. (shrink)

This paper explores the role of aesthetic judgements in mathematics by focussing on the relationship between the epistemic and aesthetic criteria employed in such judgements, and on the nature of the psychological experiences underpinning them. I claim that aesthetic judgements in mathematics are plausibly understood as expressions of what I will call ‘aesthetic-epistemic feelings’ that serve a genuine cognitive and epistemic function. I will then propose a naturalistic account of these feelings in terms of sub-personal processes of representing and assessing (...) the relation between cognitive processes and certain properties of the stimuli at which they are directed. (shrink)

ABSTRACT This paper explores the role of aesthetic judgements in mathematics by focussing on the relationship between the epistemic and aesthetic criteria employed in such judgements, and on the nature of the psychological experiences underpinning them. I claim that aesthetic judgements in mathematics are plausibly understood as expressions of what I will call ‘aesthetic-epistemic feelings’ that serve a genuine cognitive and epistemic function. I will then propose a naturalistic account of these feelings in terms of sub-personal processes of representing and (...) assessing the relation between cognitive processes and certain properties of the stimuli at which they are directed. (shrink)

This survey chapter focuses on two questions concerning the nature of beauty. First, can “beauty” be defined, and if so, how? Second, what is the relation between beauty and the mind; for example, between being beautiful and being judged beautiful, or between being beautiful and being the object of pleasure?

In a very influential paper Rota stresses the relevance of mathematical beauty to mathematical research, and claims that a piece of mathematics is beautiful when it is enlightening. He stops short, however, of explaining what he means by ‘enlightening’. This paper proposes an alternative approach, according to which a mathematical demonstration or theorem is beautiful when it provides understanding. Mathematical beauty thus considered can have a role in mathematical discovery because it can guide the mathematician in selecting which hypothesis to (...) consider and which to disregard. Thus aesthetic factors can have an epistemic role qua aesthetic factors in mathematical research. (shrink)

In chapters ranging from "The Beautiful, the Dainty, and the Dumpy" to "Skin-deep or In the Eye of the Beholder?" Nick Zangwill investigates the nature of beauty as we conceive it, and as it is in itself. The notion of beauty is currently attracting increased interest, particularly in philosophical aesthetics and in discussions of our experiences and judgments about art. In The Metaphysics of Beauty, Zangwill argues that it is essential to beauty that it depends on the ordinary features of (...) things. He uses this principle to defend the notion of the aesthetic, to call for a version of aesthetic formalism, and to reconsider the reality of beauty. The Metaphysics of Beauty brings beauty to the center of intellectual consciousness in a manner informed by contemporary metaphysics and engages with beauty as an enduring object of human thought and experience. (shrink)

In this concise survey, intended for advanced undergraduate students of aesthetics, Alan Goldman focuses on the question of aesthetic value, using many practical examples from painting, music, and literature to make his case. Although he treats a wide variety of views, he argues for a nonrealist view of aesthetic value, showing that the personal element can never be factored out of evaluative aesthetic judgments and explaining why this is so.

Aesthetics in philosophy of mathematics is too narrowly construed. Beauty is not the only feature in mathematics that is arguably aesthetic. While not the highest aesthetic value, being interesting is a sine qua non for publishability. Of the many ways to be interesting, being explanatory has recently been discussed. The motivational power of what is interesting is important for both directing research and stimulating education. The scientific satisfaction of curiosity and the artistic desire for beautiful results are complementary but both (...) aesthetic. (shrink)

In this article I examine the status of putative aesthetic judgements in science and mathematics. I argue that if the judgements at issue are taken to be genuinely aesthetic they can be divided into two types, positing either a disjunction or connection between aesthetic and epistemic criteria in theory/proof assessment. I show that both types of claim face serious difficulties in explaining the purported role of aesthetic judgements in these areas. I claim that the best current explanation of this role, (...) McAllister's 'aesthetic induction' model, fails to demonstrate that the judgements at issue are genuinely aesthetic. I argue that, in light of these considerations, there are strong reasons for suspecting that many, and perhaps all, of the supposedly aesthetic claims are not genuinely aesthetic but are in fact 'masked' epistemic assessments. (shrink)

Mathematicians sometimes judge a mathematical proof to be beautiful and in doing so seem to be making a judgement of the same kind as aesthetic judgements of works of visual art, music or literature. Mathematical proofs are also appraised for explanatoriness: some proofs merely establish their conclusions as true, while others also show why their conclusions are true. This paper will focus on the prima facie plausible assumption that, for mathematical proofs, beauty and explanatoriness tend to go together. To make (...) headway we need to have some grip on what it is for a proof to be beautiful, and for that we need some account of judgements of beauty in general. That is the concern of the first section. The second section faces the problem that it is far from obvious how abstract entities, such as mathematical proofs, can be beautiful, strictly and literally speaking. Reasons are given for the view that they can be. The third section introduces the distinction between proofs which explain their conclusions and proofs which do not. Finally, the question whether, for mathematical proofs, the beautiful and the explanatory tend to coincide is addressed. It is argued that we have reason to doubt that explanatory proofs tend to be beautiful, and insufficient reason to believe or disbelieve that beautiful proofs tend to be explanatory. (shrink)

Cet article cherche à montrer comment la pratique mathématique, particulièrement celle admettant des représentations visuelles, peut conduire à de nouveaux résultats mathématiques. L'argumentation est basée sur l'étude du cas d'un domaine des mathématiques relativement récent et prometteur: la théorie géométrique des groupes. L'article discute comment la représentation des groupes par les graphes de Cayley rendit possible la découverte de nouvelles propriétés géométriques de groupes.