Combining Texts

All the ideas for 'Through the Looking Glass', 'The Theory of Transfinite Numbers' and 'Matter and Motion Cannot Think'

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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.

7. Existence / A. Nature of Existence / 3. Being / e. Being and nothing

21982	I only wish I had such eyes as to see Nobody! It's as much as I can do to see real people. [Carroll,L]
	Full Idea: "I see nobody on the road," said Alice. - "I only wish I had such eyes," the King remarked. ..."To be able to see Nobody! ...Why, it's as much as I can do to see real people."
	From: Lewis Carroll (C.Dodgson) (Through the Looking Glass [1886], p.189), quoted by A.W. Moore - The Evolution of Modern Metaphysics 07.7
	A reaction: [Moore quotes this, inevitably, in a chapter on Hegel] This may be a better candidate for the birth of philosophy of language than Frege's Groundwork.

17. Mind and Body / A. Mind-Body Dualism / 3. Panpsychism

23224	That all matter thinks is absurd, and would make each part of our bodies a distinct self-consciousness [Bentley]
	Full Idea: [Belief in thinking matter] leads to monstrous absurdities. …Every stock and stone would be a percipient and rational creature. …every single Atom of our bodies would be a distinct Animal, endued with self-consciousness and personal sensation of its own.
	From: Richard Bentley (Matter and Motion Cannot Think [1692], p.14-15), quoted by Matthew Cobb - The Idea of the Brain 2
	A reaction: Sounds correct, though presumably panpsychists don't think the flickers of consciousness in my toenails and hair constitute full-blown persons. I can't imagine what awareness is being claimed for my toenails.