Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Philosophical Theology' and 'Substance'

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9 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
15391 A substance is, roughly, a basic being or subject at the foundation of reality [Robb]
9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts
15392 If an object survives the loss of a part, complex objects can have autonomy over their parts [Robb]
28. God / B. Proving God / 3. Proofs of Evidence / b. Teleological Proof
1451 Design is seen in the way ideas match the world, in the mechanisms of evolution, and in values [Tennant,FR, by PG]