Alan J. Cain

In retrospect, modern aesthetics is seen to have emerged at the end of the 17th and in the 18th centuries, with the term ‘aesthetic’ being coined by Alexander Gottlieb Baumgarten (1714–62) in 1735 from the Greek aisthētikos [αἰσθητικός].

Many of the early thinkers considered mathematical beauty to be an archetypical form of beauty and integrated it into their theories.

For example, Jean-Pierre de Crousaz (1663–1750) and Francis Hutcheson (1694–1746) both analysed beauty in terms of ‘unity (or uniformity) amidst variety’. Hutcheson thought that this explained why regular polyhedra were more beautiful than irregular ones, and that Archimedes' celebrated theorem

‘The ratios of volumes of a cylinder, its inscribed sphere, and a cone of equal base and height are 3 ∶ 2 ∶ 1’

was more beautiful than the less precise

‘A cylinder has greater volume than an inscribed sphere, which in turn has greater volume than a cone of equal base and height’

because they had equal variety (since they applied to the same objects), but the first theorem had greater unity.

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#aesthetics #HistPhil #Baumgarten #Crousaz #Hutcheson #UnityAmidstVariety #UniformityAmidstVariety #MathematicalBeauty

Feb 22 at 12:23pmWeb
Show threadAlan J. CainFeb 22

Denis Diderot (1713–84) criticized Hutcheson's application of uniformity amidst variety to geometrical objects and to theorems in his article on ‘Beautiful’ in the ‘Encyclopédie’.

Diderot preferred the system of Yves-Marie André (1675–1764), whose book ‘Essai sur le Beau’ was famous in its time. (I produced an open-access annotated translation in 2010; see the references in the next post.) André thought that in mathematics there was an essential geometrical beauty that was prior even to God and which had been used in the creation of the world. André saw beauty as a motivation for mathematicians from Euclid and Archimedes to Kepler and Huygens:

‘In a word, there is no academy in Europe where the love of mathematical beauty has not given in our days new conquests to the kingdom of truth.’

The attention paid to mathematical beauty in philosophical aesthetics seems to have dwindled in the 19th century with the domination in aesthetics of the philosophy of *art*, rather than of *beauty*, especially under G.W.F. Hegel's (1770–1831) influence. It revived in the first half of the 20th century in the work of philosophers like David Wight Prall (1886–1940) and Louis Arnaud Reid (1895–1986).

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#Diderot #YvesMarieAndre #Hegel

Show threadAlan J. CainFeb 22

References

• Y.-M. André. ‘Essay on Beauty’. Trans. from the French and annotated by A.J. Cain Porto: Ebook, 2010. URL: https://archive.org/details/EssayOnBeauty

• A.J. Cain. ‘Form & Number: A History of Mathematical Beauty’. Lisbon, 2024. URL: https://archive.org/details/cain_formandnumber_ebook_large chs 10–11, 20.

• J.P. de Crousaz. Traité du Beau. Amsterdam: François L'Honoré, 1715. URL: https://gallica.bnf.fr/ark:/12148/bpt6k1510777m

• D. Diderot. ‘Beau’. In: ‘Encyclopédie, ou Dictionnaire Raisonné des Sciences, des Arts et des Métiers’. vol.2. Ed. by D. Diderot & J. le R. d'Alembert. Paris, 1752. URL: https://artflsrv04.uchicago.edu/philologic4.7/encyclopedie0922/navigate/2/1354*

• F. Hutcheson. ‘An Inquiry Concerning Beauty, Order &c.’. In: ‘An Inquiry into the Original of Our Ideas of Beauty and Virtue in Two Treatises.’ Ed. by W. Leidhold.
Indianapolis: Liberty Fund, 2004. ISBN: 978-0-86597-428-9. URL: https://oll.libertyfund.org/titles/2462

• D.W. Prall. ‘Æsthetic Judgement’. New York: Thomas Y. Crowell Company, 1967.

• L.A. Reid. ‘A Study in Aesthetics’. London: George Allen & Unwin, 1931.

Image sources:

• Crousaz, ‘Traité du Beau’. Gallica, Bibliothèque Nationale de France. https://gallica.bnf.fr/ark:/12148/bpt6k1510777m [Public domain]

• L'Encyclopédie. Volume 02. L’Institut de France. URL: https://bibnum.institutdefrance.fr/ark:/61562/mz2085 [Public domain]

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Essay on Beauty : Yves-Marie André : Free Download, Borrow, and Streaming : Internet Archive

This is an annotated translation into English of the extended edition of Essai sur le beau (Paris: Ganeau 1770) by Yves-Marie André (‘le Père André’),...

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