Combining Texts

All the ideas for 'Mahaprajnaparamitashastra', 'The Beautiful in Music' and 'The Theory of Transfinite Numbers'

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4 ideas

4. Formal Logic / F. Set Theory ST / 1. Set Theory

9616	A set is a collection into a whole of distinct objects of our intuition or thought [Cantor]
	Full Idea: A set is any collection into a whole M of definite, distinct objects m ... of our intuition or thought.
	From: George Cantor (The Theory of Transfinite Numbers [1897], p.85), quoted by James Robert Brown - Philosophy of Mathematics Ch.2
	A reaction: This is the original conception of a set, which hit trouble with Russell's Paradox. Cantor's original definition immediately invites thoughts about the status of vague objects.

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / f. Uncountable infinities

15896	Cantor needed Power Set for the reals, but then couldn't count the new collections [Cantor, by Lavine]
	Full Idea: Cantor grafted the Power Set axiom onto his theory when he needed it to incorporate the real numbers, ...but his theory was supposed to be theory of collections that can be counted, but he didn't know how to count the new collections.
	From: report of George Cantor (The Theory of Transfinite Numbers [1897]) by Shaughan Lavine - Understanding the Infinite I
	A reaction: I take this to refer to the countability of the sets, rather than the members of the sets. Lavine notes that counting was Cantor's key principle, but he now had to abandon it. Zermelo came to the rescue.

21. Aesthetics / C. Artistic Issues / 4. Emotion in Art

20344	Music is not an expressive art, because it expresses no familiar emotions [Hanslick, by Wollheim]
	Full Idea: Hanslick concluded from the fact that music doesn't express definite feelings like piety, love, joy, or sadness, that it isn't an art of expression.
	From: report of Eduard Hanslick (The Beautiful in Music [1854]) by Richard Wollheim - Art and Its Objects 48
	A reaction: Whether music is 'expressive' (which it may not be) should not be confused with whether it is emotional, which it clearly is, even in its coolest examples. Hanslick viewed music as a code, not a language.

23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues

7903	The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna]
	Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom.
	From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88)
	A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate').