Combining Texts

All the ideas for 'Through the Looking Glass', 'The Poetics' and 'The Theory of Transfinite Numbers'

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5 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.
10. Modality / B. Possibility / 1. Possibility
22518 The actual must be possible, because it occurred [Aristotle]
     Full Idea: Actual events are evidently possible, otherwise they would not have occurred.
     From: Aristotle (The Poetics [c.347 BCE], 1451b18)
     A reaction: [quoted online by Peter Adamson] Seems like common sense, but it's important to have Aristotle assert it.
21. Aesthetics / B. Nature of Art / 8. The Arts / b. Literature
16566 Poetry is more philosophic than history, as it concerns universals, not particulars [Aristotle]
     Full Idea: Poetry is something more philosophic and of graver import than history, since its statements are rather of universals, whereas those of history are singulars.
     From: Aristotle (The Poetics [c.347 BCE], 1451b05)
     A reaction: Hm. Characters in great novels achieve universality by being representated very particularly. Great depth of mind seems required to be a poet, but less so for a historian (though there is, I presume, no upward limit on the possible level of thought).