Combining Philosophers

All the ideas for Herodotus, Speussipus and Douglas Lackey

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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.
9. Objects / B. Unity of Objects / 2. Substance / c. Types of substance
594 Speusippus suggested underlying principles for every substance, and ended with a huge list [Speussipus, by Aristotle]
     Full Idea: Speusippus suggested principles for each substance, including principles for numbers, magnitude and the soul. He thus arrived at no mean list of substances.
     From: report of Speussipus (thirty titles (lost) [c.367 BCE]) by Aristotle - Metaphysics 1028b
28. God / C. Attitudes to God / 5. Atheism
2632 Speusippus said things were governed by some animal force rather than the gods [Speussipus, by Cicero]
     Full Idea: Speusippus, following his uncle Plato, held that all things were governed by some kind of animal force, and tried to eradicate from our minds any notion of the gods.
     From: report of Speussipus (thirty titles (lost) [c.367 BCE]) by M. Tullius Cicero - On the Nature of the Gods ('De natura deorum') I.33
29. Religion / D. Religious Issues / 2. Immortality / a. Immortality
1513 The Egyptians were the first to say the soul is immortal and reincarnated [Herodotus]
     Full Idea: The Egyptians were the first to claim that the soul of a human being is immortal, and that each time the body dies the soul enters another creature just as it is being born.
     From: Herodotus (The Histories [c.435 BCE], 2.123.2)