Combining Texts

All the ideas for 'A Puzzle about Belief', 'Metaphysics as a Guide to Morals' and 'works'

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5 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
3340 Von Neumann defines each number as the set of all smaller numbers [Neumann, by Blackburn]
     Full Idea: Von Neumann defines each number as the set of all smaller numbers.
     From: report of John von Neumann (works [1935]) by Simon Blackburn - Oxford Dictionary of Philosophy p.280
4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
3355 Von Neumann wanted mathematical functions to replace sets [Neumann, by Benardete,JA]
     Full Idea: Von Neumann suggested that functions be pressed into service to replace sets.
     From: report of John von Neumann (works [1935]) by José A. Benardete - Metaphysics: the logical approach Ch.23
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
22716 Von Neumann defined ordinals as the set of all smaller ordinals [Neumann, by Poundstone]
     Full Idea: At age twenty, Von Neumann devised the formal definition of ordinal numbers that is used today: an ordinal number is the set of all smaller ordinal numbers.
     From: report of John von Neumann (works [1935]) by William Poundstone - Prisoner's Dilemma 02 'Sturm'
     A reaction: I take this to be an example of an impredicative definition (not predicating something new), because it uses 'ordinal number' in the definition of ordinal number. I'm guessing the null set gets us started.
15. Nature of Minds / C. Capacities of Minds / 6. Idealisation
22591 We know perfection when we see what is imperfect [Murdoch]
     Full Idea: We know of perfection as we look upon what is imperfect.
     From: Iris Murdoch (Metaphysics as a Guide to Morals [1992], 13)
     A reaction: This is in the context of a discussion of the ontological argument for God's existence, but I seize on it as a nice expression of the idealisation capacity of our minds. The alternative is that perfection is innate idea, since we aren't seeing it.
18. Thought / B. Mechanics of Thought / 5. Mental Files
16383 Puzzled Pierre has two mental files about the same object [Recanati on Kripke]
     Full Idea: In Kripke's puzzle about belief, the subject has two distinct mental files about one and the same object.
     From: comment on Saul A. Kripke (A Puzzle about Belief [1979]) by François Recanati - Mental Files 17.1
     A reaction: [Pierre distinguishes 'London' from 'Londres'] The Kripkean puzzle is presented as very deep, but I have always felt there was a simple explanation, and I suspect that this is it (though I will leave the reader to think it through, as I'm very busy…).