Combining Texts

All the ideas for 'fragments/reports', 'Perceptual experience has conceptual content' and 'Paradoxes of the Infinite'

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4 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.

13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / c. Empirical foundations

8875	Sense experiences must have conceptual content, since they are possible reasons for judgements [Brewer,B]
	Full Idea: Given that sense experiential states do provide reasons for empirical beliefs, they must have conceptual content, ...where a mental state with conceptual content is one where the content is of a possible judgement by the subject.
	From: Bill Brewer (Perceptual experience has conceptual content [2005], I)
	A reaction: This is, I believe, wrong. Even complex observations, like a pool of blood, only become reasons when they have been interpreted. Otherwise they are just the raw ingredients of evidence. How could an uninterpreted red patch be a 'reason'?

21. Aesthetics / C. Artistic Issues / 7. Art and Morality

468	Musical performance can reveal a range of virtues [Damon of Ath.]
	Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice.
	From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where?