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18189
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ZFC could contain a contradiction, and it can never prove its own consistency [MacLane]
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Full Idea:
We have at hand no proof that the axioms of ZFC for set theory will never yield a contradiction, while Gödel's second theorem tells us that such a consistency proof cannot be conducted within ZFC.
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From:
Saunders MacLane (Mathematics: Form and Function [1986], p.406), quoted by Penelope Maddy - Naturalism in Mathematics
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A reaction:
Maddy quotes this, while defending set theory as the foundation of mathematics, but it clearly isn't the most secure foundation that could be devised. She says the benefits of set theory do not need guaranteed consistency (p.30).
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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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7903
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The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna]
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Full Idea:
The six perfections are of giving, morality, patience, vigour, meditation, and wisdom.
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From:
Nagarjuna (Mahaprajnaparamitashastra [c.120], 88)
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A reaction:
What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate').
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