Combining Texts

All the ideas for 'The Evolution of Modern Metaphysics', 'The Theory of Transfinite Numbers' and 'Morals and Modals'

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6 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.

10. Modality / C. Sources of Modality / 1. Sources of Necessity

14629	If we are told the source of necessity, this seems to be a regress if the source is not already necessary [Blackburn]
	Full Idea: If we ask why A must be the case, and A is then proved from B, that explains it if B must be so. If the eventual source cites some truth F, then if F just is so, there is strong pressure to feel that the original necessity has not been explained.
	From: Simon Blackburn (Morals and Modals [1987], 1)
	A reaction: [compressed] Ross Cameron wrote a reply to this which I like. I'm fishing for the idea that essence is the source of necessity (as Kit Fine says), but that essence itself is not necessary (as only I say, apparently!).

14529	If something underlies a necessity, is that underlying thing necessary or contingent? [Blackburn, by Hale/Hoffmann,A]
	Full Idea: Blackburn asks of what theorists propose as underlying the necessity of a proposition, the question whether they themselves are conceived as obtaining of necessity or merely contingently.
	From: report of Simon Blackburn (Morals and Modals [1987], p.120-1) by Bob Hale/ Aviv Hoffmann - Introduction to 'Modality' 1
	A reaction: I've seen a reply to this somewhere: I think the thought was that a necessity wouldn't be any less necessary if it had a contingent source, any more than the father of a world champion boxer has to be a world champion boxer.

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)