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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6608
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Strong sense, delicate sentiment, practice, comparisons, and lack of prejudice, are all needed for good taste [Hume]
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Full Idea:
Strong sense, united to delicate sentiment, improved by practice, perfected by comparison, and cleared of all prejudice, can alone entitle critics to the valuable character of having 'taste'.
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From:
David Hume (Of the standard of taste [1757]), quoted by Robert Fogelin - Walking the Tightrope of Reason Ch.6
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A reaction:
I agree entirely with this, but then I am a very politically incorrect elitist when it comes to taste. It just seems screamingly obvious that professional wine-tasters have a better appreciation of wine than me, and so on for the rest of the arts.
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