This book develops a naturalistic aesthetic theory that accounts for aesthetic phenomena in mathematics in the same terms as it accounts for more traditional aesthetic phenomena. Building upon a view advanced by James McAllister, the assertion is that beauty in science does not confine itself to anecdotes or personal idiosyncrasies, but rather that it had played a role in shaping the development of science. Mathematicians often evaluate certain pieces of mathematics using words like beautiful, elegant, or even ugly. Such evaluations (...) are prevalent, however, rigorous investigation of them, of mathematical beauty, is much less common. The volume integrates the basic elements of aesthetics, as it has been developed over the last 200 years, with recent findings in neuropsychology as well as a good knowledge of mathematics. The volume begins with a discussion of the reasons to interpret mathematical beauty in a literal or non-literal fashion, which also serves to survey historical and contemporary approaches to mathematical beauty. The author concludes that literal approaches are much more coherent and fruitful, however, much is yet to be done. In this respect two chapters are devoted to the revision and improvement of McAllister’s theory of the role of beauty in science. These antecedents are used as a foundation to formulate a naturalistic aesthetic theory. The central idea of the theory is that aesthetic phenomena should be seen as constituting a complex dynamical system which the author calls the aesthetic as process theory. The theory comprises explications of three central topics: aesthetic experience, aesthetic value and aesthetic judgment. The theory is applied in the final part of the volume and is used to account for the three most salient and often used aesthetic terms often used in mathematics: beautiful, elegant and ugly. This application of the theory serves to illustrate the theory in action, but also to further discuss and develop some details and to showcase the theory’s explanatory capabilities. (shrink)

The aim of this work is to account for expressions like “Cantor’s diagonal proof is elegant” or “Euler identity is the most beautiful formula of mathematics”. This type of expressions is common among mathematicians; however, they may result in two kinds of puzzled reactions: first, the non mathematician may find the use of the word ‘beautiful’ strange in this context. Second, the mathematician may try to reinterpret mathematical beauty in terms of the principles and precepts of mathematics itself. I present (...) an account of mathematical beauty that offers a way to avoid these puzzled reactions: mathematical beauty is just a type of “normal” beauty and no reinterpretation is necessary. To support this claim, I devise an aesthetic theory -by using insights and findings from experimental psychology, neurology, philosophical and psychological theories of emotion in art, philosophy of music and philosophy of science- that shows that aesthetic judgments in mathematics are genuine aesthetic judgments. (shrink)

I argue for an enactive account of musical experience — that is, the experience of listening ‘deeply’(i.e., sensitively and understandingly) to a piece of music. The guiding question is: what do we do when we listen ‘deeply’to music? I argue that these music listening episodes are, in fact, doings. They are instances of active perceiving, robust sensorimotor engagements with and manipulations of sonic structures within musical pieces. Music is thus experiential art, and in Nietzsche’s words, ‘we listen to music with (...) our muscles’. This paper attempts to explicate and defend this claim. First, I discuss enactive approaches to consciousness and cognition generally. Next, I apply an enactive model of perceptual consciousness to the experience of listening to music. To clarify what is at stake, I use Peter Kivy’s ‘enhanced formalism’ as a philosophical foil. I then look at how the animate body shapes musical experience. (shrink)

The present work aims at providing an evaluation of musical formalism, as it was intended by Eduard Hanslick in his treatise On the Musically Beautiful, in the light of Ludwig Wittgenstein's remarks on aesthetics and music. After a short historical introduction concerning the origins of the concept of absolute music within the framework of Romantic aesthetics and the writings of authors such as Wilhelm Heinrich Wackenroder, E. T. A. Hoffmann and Arthur Schopenhauer, I suggest a definition of formalism on the (...) basis of Hanslick's account of music. I compare, then, Hanslick's view on music with Wittgenstein's reflections on music and aesthetics, referring to both Wittgenstein's early philosophy – especially to the Tractatus Logico-Philosophicus – and to the later writings – namely to the Philosophical Investigations and the Lectures on Aesthetics. The outcome of the comparison between Hanslick's and Wittgenstein's views on music leads the discussion to an evaluation of the plausibility of the dichotomy between formalism and anti-formalism, and to a reflection on the objects, aims and methods of aesthetics. (shrink)