Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Principles of Theoretical Logic' and 'Causal Structuralism'

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15 ideas

4. Formal Logic / C. Predicate Calculus PC / 1. Predicate Calculus PC
17750 The first clear proof of the consistency of the first order predicate logic was in 1928 [Hilbert/Ackermann, by Walicki]
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 / C. Powers and Dispositions / 2. Powers as Basic
15127 A categorical basis could hardly explain a disposition if it had no powers of its own [Hawthorne]
8. Modes of Existence / C. Powers and Dispositions / 5. Powers and Properties
15123 Is the causal profile of a property its essence? [Hawthorne]
15122 Could two different properties have the same causal profile? [Hawthorne]
15124 If properties are more than their powers, we could have two properties with the same power [Hawthorne]
9. Objects / C. Structure of Objects / 2. Hylomorphism / b. Form as principle
15128 We can treat the structure/form of the world differently from the nodes/matter of the world [Hawthorne]
9. Objects / D. Essence of Objects / 3. Individual Essences
15121 An individual essence is a necessary and sufficient profile for a thing [Hawthorne]
26. Natural Theory / C. Causation / 7. Eliminating causation
15126 Maybe scientific causation is just generalisation about the patterns [Hawthorne]
26. Natural Theory / D. Laws of Nature / 6. Laws as Numerical
15125 We only know the mathematical laws, but not much else [Hawthorne]