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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20723
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Only when working people are poor do they remain obedient to God [Calvin, by Weber]
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Full Idea:
Calvin made the much-quoted statement that only when the people, i.e. the mass of labourers and craftsmen, were poor did they remain obedient to God.
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From:
report of Jean Calvin (works [1549]) by Max Weber - The Protestant Ethic and the Spirit of Capitalism 5
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A reaction:
This is only one aspect of Christian influence. The alternative is John Wesley's exhortation to work diligently, live modestly, save, invest and get rich. Most people want a comfortable intermediate state, but who proclaims that?
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