Combining Philosophers

All the ideas for Rescher,N/Oppenheim,P, Richard Posner and Douglas Lackey

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4 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.

9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts

12887	A whole must have one characteristic, an internal relation, and a structure [Rescher/Oppenheim]
	Full Idea: A whole must possess an attribute peculiar to and characteristic of it as a whole; there must be a characteristic relation of dependence between the parts; and the whole must have some structure which gives it characteristics.
	From: Rescher,N/Oppenheim,P (Logical Analysis of Gestalt Concepts [1955], p.90), quoted by Peter Simons - Parts 9.2
	A reaction: Simons says these are basically sensible conditions, and tries to fill them out. They seem a pretty good start, and I must resist the temptation to rush to borderline cases.

24. Political Theory / D. Ideologies / 5. Democracy / a. Nature of democracy

21131	Democracy is competition for support of the people, guided by self-interest on all sides [Posner]
	Full Idea: Democratic politics is a competition among self-interested politicians, constituting a ruling class, for the support of the people, also assumed to be self-interested, and none too interested or well informed about politics.
	From: Richard Posner (Law, Pragmatism and Democracy [2003], p.144), quoted by Andrew Shorten - Contemporary Political Theory 05
	A reaction: This articulates the 'competitive' view of democracy, as simply a technique for establishing legitimacy. Posner is also an economist, and they also assume that everyone is wholly self-interested, which may be why they are so frequently wrong.