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020 _a9783319034522
_9978-3-319-03452-2
024 7 _a10.1007/978-3-319-03452-2
_2doi
050 4 _aBC1-199
072 7 _aHPL
_2bicssc
072 7 _aPHI011000
_2bisacsh
082 0 4 _a160
_223
100 1 _aMontano, Ulianov.
_eauthor.
245 1 0 _aExplaining Beauty in Mathematics: An Aesthetic Theory of Mathematics
_h[electronic resource] /
_cby Ulianov Montano.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2014.
300 _aXVIII, 220 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aSynthese Library, Studies in Epistemology, Logic, Methodology, and Philosophy of Science ;
_v370
505 0 _aIntroduction -- Part 1. Antecedents -- Chapter 1. On Non-literal Approaches -- Chapter 2. Beautiful, Literally -- Chapter 3. Ugly, Literally -- Chapter 4. Problems of the Aesthetic Induction -- Chapter 5. Naturalizing the Aesthetic Induction -- Part 2. An Aesthetics of Mathematics -- Chapter 6. Introduction to a Naturalistic Aesthetic Theory -- Chapter 7. Aesthetic Experience -- Chapter 8. Aesthetic Value -- Chapter 9. Aesthetic Judgement I: Concept -- Chapter 10. Aesthetic Judgement II: Functions -- Chapter 11. Mathematical Aesthetic Judgements -- Part 3. Applications -- Chapter 12. Case Analysis I: Beauty -- Chapter 13. Case Analysis II: Elegance -- Chapter 14. Case Analysis III: Ugliness, Revisited -- Chapter 15. Issues of Mathematical Beauty, Revisited.
520 _aThis 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 (in mathematics), 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.
650 0 _aPhilosophy (General).
650 0 _aAesthetics.
650 0 _aLogic.
650 0 _aLogic, Symbolic and mathematical.
650 1 4 _aPhilosophy.
650 2 4 _aLogic.
650 2 4 _aMathematical Logic and Foundations.
650 2 4 _aAesthetics.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783319034515
830 0 _aSynthese Library, Studies in Epistemology, Logic, Methodology, and Philosophy of Science ;
_v370
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-319-03452-2
912 _aZDB-2-SHU
999 _c92993
_d92993