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Explaining beauty in mathematics: an aesthetic theory of mathematics
Author
Publisher
Springer
Publication Date
[2014]
Language
English
Description
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Table of Contents
From the Manuscript
Antecedents
On non-literal approaches
The two cultures, Shaftesbury and Hutchenson
Unsound divide
Shaftesbury
Hutchenson
The epistemic character of mathematics
Rota's interpretation of mathematical beauty
Rota's problems
The rational character of mathematics
Rational reinterpretations
Beautiful, literally
Metaphor and aesthetic terms
McAllister's approach
McAllister's aesthetic theory
Aesthetic properties, aesthetic criteria and aesthetic canon
The aesthetic canon
The aesthetic induction
Aesthetic induction in mathematics
McAllister in summary
Ugly, literally
Ugliness in mathematics
Computer-assisted proofs
Phenomenological factors
Intentional objects
Intentional proofs
Why the conflict?
Problems of the aesthetic induction
Two kinds of problems
Anomalies
Theoretical tensions
Induction
Beauty and aesthetic
Objectivism/projectivism inconsistency
Theory and modelling
Naturalizing the aesthetic induction
The mere-exposure effect and the nature of the aesthetic induction
Naturalizing preference evolution
Naturalizing the aesthetic induction
Preference, affection and emotion
Constraints of affective plasticity
Conceptualizing preference evolution
The aesthetic canon as a system
Critical adequacy
Robustness of critical adequacy
Dynamics of the new model
The new model : constrained aesthetic induction
Constrained Aesthetic Induction (CAI)
Problems addressed
An aesthetics of mathematics
Introduction to a naturalistic aesthetic theory
The mark of the aesthetic
Phases of an aesthetic-process
Aesthetic experience
Characterizing aesthetic experience
Aesthetic intentional objects
Mathematical intentional objects
A notion of aesthetic mathematical intentional object
Dimensions and properties
Activities and relations
A model of aesthetic mathematical intentional objects
Aesthetic form
Types of experience
Basic appreciation response
Non "inductive" response
Performative appreciation responses
Adaptive appreciation response
The pleasure-relation
Formalization
Aesthetic value
Extension of aesthetic value
Typical positive aesthetic criterion
Dynamics
Value and aesthetic canon
Aesthetic canon evolution
Naturalistic Evolution Rule II (NERII)
Positive value
Negative value
Aesthetic experience and the application of value repositories
Aesthetic judgement I : concept
On aesthetic terms
Sibley
Hungerland
Kivy
Declercq
Zangwill
A new model of aesthetic terms
Metaphor
Metaphorical terms and aesthetic terms
Experience and response spaces
A new model of aesthetic terms
Genuine aesthetic terms
Definitions of aesthetic term, description and judgement
Always and only aesthetic terms : the spectrum of aesthetic terms
Aesthetic judgement II : functions
Concept and function
Emphases and perspectives
Articulation
Definition of articulation
Broadcasting function
Locally terminal aesthetic terms
Unifying approaches
Mathematical aesthetic judgements
Applications
Case analysis I : beauty
Knowledge, beauty and "isolated pearls"
Case 1, beauty : y = ex
Experience
Value
Dynamics
Judgement
The process in summary
Case analysis II : elegance
Experience
Step-series interpretation
Single-object interpretation
Affective response in step-series interpretation
Affective response in the single-object interpretation
Value
Judgement
The process in summary
Case analysis III : ugliness, revisited
The proof
Experience
Value
Scenario 1 : change by aesthetic induction
Scenario 2 : change in the nature of our experience
Closing remarks
Issues of mathematical beauty, revisited
Conclusion
Bibliography.
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ISBN
9783319034515
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