Combining Texts

All the ideas for 'The Evolution of Modern Metaphysics', 'The Theory of Transfinite Numbers' and 'fragments/reports'

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5 ideas

1. Philosophy / E. Nature of Metaphysics / 1. Nature of Metaphysics

21959	Metaphysics is the most general attempt to make sense of things [Moore,AW]
	Full Idea: Metaphysics is the most general attempt to make sense of things.
	From: A.W. Moore (The Evolution of Modern Metaphysics [2012], Intro)
	A reaction: This is the first sentence of Moore's book, and a touchstone idea all the way through. It stands up well, because it says enough without committing to too much. I have to agree with it. It implies explanation as the key. I like generality too.

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.

11. Knowledge Aims / C. Knowing Reality / 3. Idealism / b. Transcendental idealism

21958	Appearances are nothing beyond representations, which is transcendental ideality [Moore,AW]
	Full Idea: Appearances in general are nothing outside our representations, which is just what we mean by transcendental ideality.
	From: A.W. Moore (The Evolution of Modern Metaphysics [2012], B535/A507)

15. Nature of Minds / A. Nature of Mind / 2. Psuche

5880	Xenocrates held that the soul had no form or substance, but was number [Xenocrates, by Cicero]
	Full Idea: Xenocrates denied that the soul had form or any substance, but said that it was number, and the power of number, as had been held by Pythagoras long before, was the highest in nature.
	From: report of Xenocrates (fragments/reports [c.327 BCE]) by M. Tullius Cicero - Tusculan Disputations I.x.20
	A reaction: This shows how strong the Pythagorean influence was in the Academy. This is not totally stupid. Dawkins holds that the essence of DNA is information, which can be expressed mathematically. Xenocrates was a functionalist.