Combining Texts

All the ideas for 'fragments/reports', 'The Foundations of Mathematics' and 'The Foundations of Mathematics (2nd ed)'

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3 ideas

5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle

18844	You would cripple mathematics if you denied Excluded Middle [Hilbert]
	Full Idea: Taking the principle of Excluded Middle away from the mathematician would be the same, say, as prohibiting the astronomer from using the telescope or the boxer from using his fists.
	From: David Hilbert (The Foundations of Mathematics [1927], p.476), quoted by Ian Rumfitt - The Boundary Stones of Thought 9.4
	A reaction: [p.476 in Van Heijenoort]

8. Modes of Existence / A. Relations / 4. Formal Relations / b. Equivalence relation

18465	An 'equivalence' relation is one which is reflexive, symmetric and transitive [Kunen]
	Full Idea: R is an equivalence relation on A iff R is reflexive, symmetric and transitive on A.
	From: Kenneth Kunen (The Foundations of Mathematics (2nd ed) [2012], I.7.1)

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?