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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16698
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Days exist, and yet they seem to be made up of parts which don't exist [Burley]
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Full Idea:
I grant that a successive being is composed out of non-beings, as is clear of a day, which is composed of non-entities. Some part of this day is past and some future, and yet this day is.
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From:
Walter Burley (Commentary on 'Physics' [1325], III text 11,f.65rb), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 18.3
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A reaction:
The dilemma of Aristotle over time infected the scholastic attempt to give an account of successive entities. A day is a wonderfully elusive entity for a metaphysician.
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16690
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Unlike permanent things, successive things cannot exist all at once [Burley]
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Full Idea:
This is the difference between permanent and successive things: that a permanent thing exists all at once, or at least can exist all at once, whereas it is incompatible with a successive thing to exist all at once.
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From:
Walter Burley (Commentary on 'Physics' [1325], III txt 11,f.65rb), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 18.1
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A reaction:
Permanent things sound like what are now called 'three-dimensional' objects, but scholastic 'entia successiva' are not the same as spacetime 'worms' or collections of temporal stages.
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