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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23981
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Rage is inconceivable without bodily responses; so there are no disembodied emotions [James]
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Full Idea:
Can one fancy a state of rage and picture no flushing of the face, no dilation of the nostrils, no clenching of the teeth, no impulse to vigorous action? …A purely disembodied human emotion is a nonentity.
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From:
William James (What is an Emotion? [1884], p.194), quoted by Peter Goldie - The Emotions 3 'Bodily'
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A reaction:
Plausible for rage, but less so for irritation or admiration. Goldie thinks James is wrong. James says if intellectual feelings don't become bodily then they don't qualify as emotions. No True Scotsman!
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