By Edmund Burke
An eloquent and infrequently even erotic booklet, the Philosophical Enquiry was once lengthy brushed off as a section of mere juvenilia. despite the fact that, Burke's research of the connection among emotion, good looks, and artwork shape is now famous as not just a big and influential paintings of aesthetic conception, but in addition one of many first significant works in ecu literature at the chic, a topic that has interested thinkers from Kant and Coleridge to the philosophers and critics of this day.
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Extra info for A Philosophical Enquiry into the Origin of our Ideas of the Sublime and Beautiful
22]. McAllister points out that, in recent decades, two new types of proofs have appeared: long proofs, such as Wiles’ 108-page-long proof of Fermat’s last theorem; and computer-assisted proofs, such as Appel and Haken’s proof of the four-colour theorem. These types of proof challenge the classical conception of proof, since they are not graspable in the classical sense, and may even exhibit a logical structure different from the classical proof. McAllister speculates that they might even alter our conception of beautiful proof.
In general, the predicate ‘beautiful’ can be employed very naturally in comparative judgements; there is nothing wrong with sentences like ‘A is more (or less) beautiful than B’. Furthermore, in actuality some mathematical results are regarded as more beautiful than others: David Wells  even offers a ranking of some of the most beautiful theorems, based on a poll of mathematicians. In summary, beauty is a concept that does admit degrees; it is a fuzzy concept. If Rota were correct in arguing that mathematicians dislike fuzzy concepts, they would try to avoid the predicate ‘beautiful’ as much as the predicate ‘enlightening’.
Such anthologies are seldom to be found on any mathematician’s bookshelf [78, p. 180]. He is also aware of the fact that a common strategy in anecdotal accounts is to try to reduce mathematical beauty to some unproblematical property. This is why he addresses, although without mentioning names or sources, G. H. Hardy’s view that the properties of unexpectedness and inevitability are the sources of beauty. Rota seems less concerned with the fact that unexpectedness and inevitability are not sufficient conditions for beauty than with the fact that those properties have no relevant epistemic role.