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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1422
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God's existence is either necessary or impossible, and no one has shown that the concept of God is contradictory [Malcolm]
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Full Idea:
God's existence is either impossible or necessary. It can be the former only if the concept of such a being is self-contradictory or in some way logically absurd. Assuming that this is not so, it follows that He necessarily exists.
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From:
Norman Malcolm (Anselm's Argument [1959], §2)
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A reaction:
The concept of God suggests paradoxes of omniscience, omnipotence and free will, so self-contradiction seems possible. How should we respond if the argument suggests God is necessary, but evidence suggests God is highly unlikely?
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