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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16700
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In order to speak about time and successive entities, the 'present' must be enlarged [Wycliff]
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Full Idea:
It is clear from the way in which one must speak about time and other successive entities that talk about 'the present' must be enlarged. Otherwise it would have to be denied that any successive entity could exist, which is impossible.
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From:
John Wycliff (De ente praedicamentali [1375], 20 p.189), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 18.3
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A reaction:
This is a lovely idea, even if it is not quite clear what it means. The mind seems to stretch out the now anyway (as the 'specious present'), so why not embrace that in language and conscious thought?
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16701
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To be successive a thing needs parts, which must therefore be lodged outside that instant [Wycliff]
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Full Idea:
If something is successive, it is successive with respect to its individual parts, which cannot exist at the same instant. Therefore it follows that many of its parts are lodged outside that instant.
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From:
John Wycliff (De ente praedicamentali [1375], 20 p.189), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 18.3
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A reaction:
An obvious would be to say that there are therefore no successive entities, but Wycliff is appealing to our universal acceptance of them, and offering a transcendental argument. Nice move.
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