Combining Philosophers

All the ideas for Douglas Lackey, Richard Bentley and Einstein,A/Infeld,L

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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.

17. Mind and Body / A. Mind-Body Dualism / 3. Panpsychism

23224	That all matter thinks is absurd, and would make each part of our bodies a distinct self-consciousness [Bentley]
	Full Idea: [Belief in thinking matter] leads to monstrous absurdities. …Every stock and stone would be a percipient and rational creature. …every single Atom of our bodies would be a distinct Animal, endued with self-consciousness and personal sensation of its own.
	From: Richard Bentley (Matter and Motion Cannot Think [1692], p.14-15), quoted by Matthew Cobb - The Idea of the Brain 2
	A reaction: Sounds correct, though presumably panpsychists don't think the flickers of consciousness in my toenails and hair constitute full-blown persons. I can't imagine what awareness is being claimed for my toenails.

27. Natural Reality / B. Modern Physics / 2. Electrodynamics / b. Fields

18202	The concept of a field gradually replaced the substances in explaining relations between charges [Einstein/Infeld]
	Full Idea: In the beginning the field concept was no more than a means of facilitating the understanding of phenomena. ...In the new field language it is the field and not the charges themselves which is essential. The substance was overshadowed by the field.
	From: Einstein,A/Infeld,L (The Evolution of Physics [1938], p.151), quoted by Penelope Maddy - Naturalism in Mathematics II.4
	A reaction: This is very important for philosophical metaphysicians, especially those like me who want to explain the universe by the nature of the stuff that composes it. The 'stuff' had better not be simplistic individual 'substances'.