Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Panpsychism' and 'Definitiones cogitationesque metaphysicae'

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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]
8. Modes of Existence / B. Properties / 7. Emergent Properties
3291 Emergent properties appear at high levels of complexity, but aren't explainable by the lower levels [Nagel]
9. Objects / B. Unity of Objects / 2. Substance / d. Substance defined
12712 Substance is that which can act [Leibniz]
14. Science / D. Explanation / 3. Best Explanation / b. Ultimate explanation
12737 Nature can be fully explained by final causes alone, or by efficient causes alone [Leibniz]
26. Natural Theory / C. Causation / 9. General Causation / d. Causal necessity
3290 Given the nature of heat and of water, it is literally impossible for water not to boil at the right heat [Nagel]