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Explaining Beauty in Mathematics: An Aesthetic Theory of Mathematics

Part of the Synthese Library Book Series (volume 370)

DOI: 10.1007/978-3-319-03452-2

ISBN: 978-3-319-03451-5

Publisher: Springer International Publishing - Springer Journals

Nov 27, 2014

1 - 10 of 15 Chapters

Available

On Non-literal Approaches

Montano, Ulianov

Pages: 3 –19

[This chapter discusses in detail the idea that mathematical beauty should be reinterpreted to preserve mathematics’ stand among the sciences. Three reasons to reinterpret mathematical beauty are examined; the two cultures split, the epistemic character of mathematics, and its rational character....
Available

Beautiful, Literally

Montano, Ulianov

Pages: 21 –31

[This chapter discusses literal interpretations of beauty in science and mathematics. First, a principled argument against reinterpreting mathematical beauty is presented: aesthetic terms cannot be interpreted metaphorically. Next we discuss how James McAllister’s literal interpretation of beauty...
Available

Ugly, Literally

Montano, Ulianov

Pages: 33 –43

[In this chapter computer-assisted proofs are discussed. This discussion allows the introduction of multiple issues. The perceived ugliness of such proofs is the main subject of analysis; this further serves to highlight some limitations of the idea of the aesthetic induction. We conclude that an...
Available

Problems of the Aesthetic Induction

Montano, Ulianov

Pages: 45 –56

[This chapter explores problems of the mechanism of aesthetic induction. The aesthetic induction has conceptual problems as wells as significant explanatory anomalies. In particular, historical evidence supports the existence of historical constants—properties whose preferences remain relatively...
Available

Naturalizing the Aesthetic Induction

Montano, Ulianov

Pages: 57 –69

[In this chapter I propose to naturalize the aesthetic induction in order to solve its problems. We shall see that this course of action has been suggested by Theo Kuipers’ approach to the aesthetic induction. Kuipers interprets the aesthetic induction in terms of the mere exposure effect. The...
Available

Introduction to a Naturalistic Aesthetic Theory

Montano, Ulianov

Pages: 73 –83

[This chapter lays down the foundations of a naturalistic aesthetic theory based on the notion of aesthetic-process. The aesthetic theory advanced here proposes to see the different kinds of aesthetic things—such as aesthetic experience, aesthetic value, aesthetic descriptions, etc.—as...
Available

Aesthetic Experience

Montano, Ulianov

Pages: 85 –116

[This chapter addresses aesthetic experience. Aesthetic experience is interpreted as a subprocess that involves changes in the focus and content of our attention and the eliciting of affective responses. A conception of the characteristic intentional object involved in aesthetic experiences of...
Available

Aesthetic Value

Montano, Ulianov

Pages: 117 –130

[This chapter addresses aesthetic value. Aesthetic value is interpreted as a relation between sets of properties and mental activities, and subjective reactions. By interpreting aesthetic evaluation as consisting on concurrent affective and propositional evaluations it is possible to model the...
Available

Aesthetic Judgement I: Concept

Montano, Ulianov

Pages: 131 –148

[This chapter address the nature of aesthetic terms and judgments. Aesthetic judgements are interpreted as expressions of subjective states, characterized by the application of aesthetic terms. Their functions are to articulate aesthetic experience and to share the result of such articulation....
Available

Aesthetic Judgement II: Functions

Montano, Ulianov

Pages: 149 –159

[In this chapter the functions that aesthetic terms and judgements play in aesthetic-processes are examined. The use of aesthetic terms not only expresses a subjective state but it helps constitute the experience itself, this function is labelled articulation. A second function is to broadcast...

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