Combining Philosophers

All the ideas for Herodotus, Douglas Lackey and Kretzmann/Stump

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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.
14. Science / A. Basis of Science / 2. Demonstration
22110 Demonstration provides depth of understanding and explanation (rather than foundations) [Kretzmann/Stump]
     Full Idea: According to Aquinas, what demonstration provides is not so much knowledge as conceived by foundationalists as depth of understanding and explanatory insight.
     From: Kretzmann/Stump (Aquinas, Thomas [2005]), quoted by Kretzmann/Stump - Aquinas, Thomas 11
     A reaction: It was noticeable that Aristotle didn't make clear what demonstration aims to achieve, and he didn't employ it elsewhere in his writings. We aim for understanding, not for well grounded propositions. Understanding needs implications and mechanisms.
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)