Combining Philosophers

All the ideas for Douglas Lackey, J.O. Urmson and Euripides

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4 ideas

1. Philosophy / D. Nature of Philosophy / 7. Despair over Philosophy

9283	Our ancient beliefs can never be overthrown by subtle arguments [Euripides]
	Full Idea: Teiresias: We have no use for theological subtleties./ The beliefs we have inherited, as old as time,/ Cannot be overthrown by any argument,/ Nor by the most inventive ingenuity.
	From: Euripides (The Bacchae [c.407 BCE], 201)
	A reaction: [trans. Philip Vellacott (Penguin)] Compare Idea 8243. While very conservative societies have amazing resilience in maintaining traditional beliefs, modern culture eats into them, not directly by argument, but by arguments at fifth remove.

1. Philosophy / F. Analytic Philosophy / 1. Nature of Analysis

13750	Analysis aims at the structure of facts, which are needed to give a rationale to analysis [Urmson, by Schaffer,J]
	Full Idea: Urmson explains the direction of analysis as 'towards a structure...more nearly similar to the structure of the fact', adding that this metaphysical picture is needed as a 'rationale of the practice of analysis'.
	From: report of J.O. Urmson (Philosophical Analysis [1956], p.24-5) by Jonathan Schaffer - On What Grounds What n30
	A reaction: In other words, only realists can be truly motivated to keep going with analysis. Merely analysing language-games is doable, but hardly exciting.

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.