Combining Texts

All the ideas for 'fragments/reports', 'Immortality of the Soul' and 'Paradoxes of the Infinite'

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5 ideas

4. Formal Logic / F. Set Theory ST / 1. Set Theory
9987 An aggregate in which order does not matter I call a 'set' [Bolzano]
     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'.
     From: Bernard Bolzano (Paradoxes of the Infinite [1846], §4), quoted by William W. Tait - Frege versus Cantor and Dedekind IX
     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.
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
10856 A truly infinite quantity does not need to be a variable [Bolzano]
     Full Idea: A truly infinite quantity (for example, the length of a straight line, unbounded in either direction) does not by any means need to be a variable.
     From: Bernard Bolzano (Paradoxes of the Infinite [1846]), quoted by Brian Clegg - Infinity: Quest to Think the Unthinkable §10
     A reaction: This is an important idea, followed up by Cantor, which relegated to the sidelines the view of infinity as simply something that could increase without limit. Personally I like the old view, but there is something mathematically stable about infinity.
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / e. Character
541 Virtue comes more from habit than character [Critias]
     Full Idea: More men are good through habit than through character.
     From: Critias (fragments/reports [c.440 BCE], B09), quoted by John Stobaeus - Anthology 3.29.41
28. God / C. Attitudes to God / 5. Atheism
542 Fear of the gods was invented to discourage secret sin [Critias]
     Full Idea: When the laws forbade men to commit open crimes of violence, and they began to do them in secret, a wise and clever man invented fear of the gods for mortals, to frighten the wicked, even if they sin in secret.
     From: Critias (fragments/reports [c.440 BCE], B25), quoted by Sextus Empiricus - Against the Professors (six books) 9.54
29. Religion / B. Monotheistic Religion / 4. Christianity / c. Angels
16689 The schools said spirits lack extension, and wonder how many could dance on a needle's point [More,H]
     Full Idea: Many, not without reason, laugh at those ridiculous fancies of the schools, that rashly take away all extensions from spirits, whether souls or angels, and then dispute how many of them booted and spurred may dance on a needle's point at once.
     From: Henry More (Immortality of the Soul [1659], III.2.1), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 17.3
     A reaction: This famous idea originated with William Chillingworth. More's version is the classic one. Pasnau cites Aquinas Summa 1a 52.3 as discussing the actual question (and says this couldn't happen).