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9987
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An aggregate in which order does not matter I call a 'set' [Bolzano]
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Full Idea:
An aggregate whose basic conception renders the arrangement of its members a matter of indifference, and whose permutation therefore produces no essential difference, I call a 'set'.
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From:
Bernard Bolzano (Paradoxes of the Infinite [1846], §4), quoted by William W. Tait - Frege versus Cantor and Dedekind IX
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A reaction:
The idea of 'sets' was emerging before Cantor formalised it, and clarified it by thinking about infinite sets. Nowadays we also have 'ordered' sets, which rather contradicts Bolzano, and we also expect the cardinality to be determinate.
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7669
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We cannot attain all the ideals of every culture, so there cannot be a perfect life [Herder, by Berlin]
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Full Idea:
For Herder, we cannot attain to the highest ideals of all the centuries and all the places at once, and since we cannot do that, the whole notion of the perfect life collapses.
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From:
report of Johann Gottfried Herder (works [1784]) by Isaiah Berlin - The Roots of Romanticism Ch.3
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A reaction:
Herder seems to be the father of modern cultural relativism. The idea is hard to challenge, but the ideals of some cultures should be ignored, if they diminish rather than enhance the good life for all.
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7668
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Herder invented the idea of being rooted in (or cut off from) a home or a group [Herder, by Berlin]
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Full Idea:
The whole notion of being at home, or being cut off from one's natural roots, the whole idea of roots, the whole idea of belonging to a group, a sect, a movement, was largely invented by Herder.
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From:
report of Johann Gottfried Herder (works [1784], Ch.3) by Isaiah Berlin - The Roots of Romanticism
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A reaction:
Hm. Broad generalisations are an awful temptation in the history of ideas. As a corrective to this, trying reading the two Anglo-Saxon poems 'The Wanderer' and 'The Seafarer'. Very Germanic, I suppose. Interesting, though. Leads to Hegel's politics.
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