Combining Texts

All the ideas for 'Confessions of a Philosopher', 'works' and 'Epistemic Operators'

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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.
13. Knowledge Criteria / A. Justification Problems / 2. Justification Challenges / c. Knowledge closure
6445 You have knowledge if you can rule out all the relevant alternatives to what you believe [Dretske, by DeRose]
     Full Idea: The 'Relevant Alternatives' theory of knowledge said the main ingredient that must be added to true belief to make knowledge is that one be in a position to rule out all the relevant alternatives to what one believes.
     From: report of Fred Dretske (Epistemic Operators [1970]) by Keith DeRose - Intro: Responding to Skepticism §6
     A reaction: Dretske and Nozick are associated with this strategy. There will obviously be a problem in defining 'relevant'. Otherwise it sounds quite close to Plato's suggestion that we need true belief with 'logos'.
16. Persons / C. Self-Awareness / 3. Limits of Introspection
3102 Why don't we experience or remember going to sleep at night? [Magee]
     Full Idea: As a child it was incomprehensible to me that I did not experience going to sleep, and never remembered it. When my sister said 'Nobody remembers that', I just thought 'How does she know?'
     From: Bryan Magee (Confessions of a Philosopher [1997], Ch.I)
     A reaction: This is actually evidence for something - that we do not have some sort of personal identity which is separate from consciousness, so that "I am conscious" would literally mean that an item has a property, which it can lose.