Combining Texts

All the ideas for 'fragments/reports', 'Intros to Russell's 'Essays in Analysis'' and 'The Discourses'

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5 ideas

5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / b. Cantor's paradox

21554	Sets always exceed terms, so all the sets must exceed all the sets [Lackey]
	Full Idea: Cantor proved that the number of sets in a collection of terms is larger than the number of terms. Hence Cantor's Paradox says the number of sets in the collection of all sets must be larger than the number of sets in the collection of all sets.
	From: Douglas Lackey (Intros to Russell's 'Essays in Analysis' [1973], p.127)
	A reaction: The sets must count as terms in the next iteration, but that is a normal application of the Power Set axiom.

5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / c. Burali-Forti's paradox

21553	It seems that the ordinal number of all the ordinals must be bigger than itself [Lackey]
	Full Idea: The ordinal series is well-ordered and thus has an ordinal number, and a series of ordinals to a given ordinal exceeds that ordinal by 1. So the series of all ordinals has an ordinal number that exceeds its own ordinal number by 1.
	From: Douglas Lackey (Intros to Russell's 'Essays in Analysis' [1973], p.127)
	A reaction: Formulated by Burali-Forti in 1897.

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?

25. Social Practice / E. Policies / 2. Religion in Society

19813	All legislators invoke God in support of extraordinary laws, because their justification is not obvious [Machiavelli]
	Full Idea: There has never been a single legislator who, in proposing extraordinary laws, did not have recourse to God, for otherwise they would not be accepted, since many benefits known to a prudent man do not have evident persuasive reasons.
	From: Niccolo Machiavelli (The Discourses [1520], 1.11), quoted by Jean-Jacques Rousseau - The Social Contract (tr Cress) II.7 n8
	A reaction: It does seem to be an important role for God and state religion, to give support to decisions and laws which might not be intrinsically popular.

7126	Rulers should preserve the foundations of religion, to ensure good behaviour and unity [Machiavelli]
	Full Idea: It is the duty of the rulers of a republic or a kingdom to preserve the foundations of the religion they hold; if they do this, it will be an easy thing for them to keep their state religious, and consequently good and united.
	From: Niccolo Machiavelli (The Discourses [1520], I.12)
	A reaction: This is the germ of Marx's view, that the sole role of religion is political, as a tool used by the ruling classes to keep the populace in their place. The same idea can be found in Critias (Idea 542). But what is wrong with some central moral guidance?