15896
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Cantor needed Power Set for the reals, but then couldn't count the new collections [Cantor, by Lavine]
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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.
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From:
report of George Cantor (The Theory of Transfinite Numbers [1897]) by Shaughan Lavine - Understanding the Infinite I
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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.
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9379
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A sentence is obvious if it is true, and any speaker of the language will instantly agree to it [Quine]
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Full Idea:
A sentence is obvious if (a) it is true and (b) any speaker of the language is prepared, for any reason or none, to assent to it without hesitation, unless put off by being asked so obvious a question.
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From:
Willard Quine (Reply to Hellman [1975], p.206), quoted by Paul Boghossian - Analyticity Reconsidered §III
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A reaction:
This comes from someone who is keen to deny a priori knowledge, but what are we to make of the expostulations "It's obvious, you idiot!", and "Now I see it, it's obvious!", and "It seemed obvious, but I was wrong!"?
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