Combining Texts

All the ideas for 'Leibniz: Guide for the Perplexed', 'On the Basis of Morality' and 'On the Question of Absolute Undecidability'

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10 ideas

4. Formal Logic / F. Set Theory ST / 1. Set Theory
17884 Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner]
17893 'Reflection principles' say the whole truth about sets can't be captured [Koellner]
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
17894 We have no argument to show a statement is absolutely undecidable [Koellner]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
17890 There are at least eleven types of large cardinal, of increasing logical strength [Koellner]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
17887 PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
17891 Arithmetical undecidability is always settled at the next stage up [Koellner]
9. Objects / B. Unity of Objects / 2. Substance / d. Substance defined
19347 Substance needs independence, unity, and stability (for individuation); also it is a subject, for predicates [Perkins]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / b. Rational ethics
21375 Reason can be vicious, and great crimes have to be rational [Schopenhauer]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / e. Human nature
21379 Man's three basic ethical incentives are egoism, malice and compassion [Schopenhauer]
25. Social Practice / F. Life Issues / 6. Animal Rights
21376 Philosophy treats animals as exploitable things, ignoring the significance of their lives [Schopenhauer]