Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Philosophical Implications of Mathematical logic' and 'Critique of Judgement II: Teleological'

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12 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 / C. Ontology of Logic / 1. Ontology of Logic
22329 Logic is highly general truths abstracted from reality [Russell, by Glock]
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]
15. Nature of Minds / C. Capacities of Minds / 5. Generalisation by mind
21569 It is good to generalise truths as much as possible [Russell]
22. Metaethics / B. Value / 1. Nature of Value / f. Ultimate value
18239 What is contemplated must have a higher value than contemplation [Kant, by Korsgaard]
18238 Only a good will can give man's being, and hence the world, a final purpose [Kant]
26. Natural Theory / A. Speculations on Nature / 1. Nature
22053 The Critique of Judgement aims for a principle that unities humanity and nature [Kant, by Bowie]
26. Natural Theory / A. Speculations on Nature / 2. Natural Purpose / b. Limited purposes
18237 Without men creation would be in vain, and without final purpose [Kant]