Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'De arcanus motus' and 'Entity and Identity'

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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 / C. Powers and Dispositions / 1. Powers
12733 Because of the definitions of cause, effect and power, cause and effect have the same power [Leibniz]
9. Objects / A. Existence of Objects / 2. Abstract Objects / b. Need for abstracta
16980 We need a logical use of 'object' as predicate-worthy, and an 'ontological' use [Strawson,P]
9. Objects / D. Essence of Objects / 3. Individual Essences
16979 It makes no sense to ask of some individual thing what it is that makes it that individual [Strawson,P]
10. Modality / A. Necessity / 2. Nature of Necessity
12734 Every necessary proposition is demonstrable to someone who understands [Leibniz]