Combining Texts

All the ideas for 'fragments/reports', '21: First Epistle of Peter' and 'An Axiomatization of Set Theory'

unexpand these ideas     |    start again     |     specify just one area for these texts

---

4 ideas

4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size

15943	Limitation of Size is not self-evident, and seems too strong [Lavine on Neumann]
	Full Idea: Von Neumann's Limitation of Size axiom is not self-evident, and he himself admitted that it seemed too strong.
	From: comment on John von Neumann (An Axiomatization of Set Theory [1925]) by Shaughan Lavine - Understanding the Infinite VII.1

6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory

13672	All the axioms for mathematics presuppose set theory [Neumann]
	Full Idea: There is no axiom system for mathematics, geometry, and so forth that does not presuppose set theory.
	From: John von Neumann (An Axiomatization of Set Theory [1925]), quoted by Stewart Shapiro - Foundations without Foundationalism 8.2
	A reaction: Von Neumann was doubting whether set theory could have axioms, and hence the whole project is doomed, and we face relativism about such things. His ally was Skolem in this.

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?

29. Religion / D. Religious Issues / 1. Religious Commitment / e. Fideism

17593	Always be ready to give reasons for your beliefs [Peter]
	Full Idea: Be ready to give an answer to every man that asketh you a reason of the hope that is in you with meekness and fear.
	From: St Peter (21: First Epistle of Peter [c.50], 3:15)
	A reaction: This quotation is the rational theologian's standard response to pure fideism.