Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Mathematics, Science and Language' and 'A Specimen of Discoveries'

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11 ideas

2. Reason / A. Nature of Reason / 4. Aims of Reason
5035 The two basics of reasoning are contradiction and sufficient reason [Leibniz]
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 / 1. Mathematics
18119 Mathematics is a mental activity which does not use language [Brouwer, by Bostock]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / g. Applying mathematics
18118 Brouwer regards the application of mathematics to the world as somehow 'wicked' [Brouwer, by Bostock]
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]
17. Mind and Body / A. Mind-Body Dualism / 5. Parallelism
5038 Assume that mind and body follow their own laws, but God has harmonised them [Leibniz]
29. Religion / D. Religious Issues / 3. Problem of Evil / b. Human Evil
5037 God doesn't decide that Adam will sin, but that sinful Adam's existence is to be preferred [Leibniz]