Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Reflections on Knowledge, Truth and Ideas' and 'Method and Results'

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12 ideas

2. Reason / D. Definition / 1. Definitions
'Nominal' definitions just list distinguishing characteristics [Leibniz]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner]
'Reflection principles' say the whole truth about sets can't be captured [Koellner]
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
We have no argument to show a statement is absolutely undecidable [Koellner]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
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
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
Arithmetical undecidability is always settled at the next stage up [Koellner]
11. Knowledge Aims / A. Knowledge / 1. Knowledge
Knowledge needs clarity, distinctness, and adequacy, and it should be intuitive [Leibniz]
17. Mind and Body / A. Mind-Body Dualism / 6. Epiphenomenalism
T.H.Huxley gave the earliest clear statement of epiphenomenalism [Huxley, by Rey]
Brain causes mind, but it doesn't seem that mind causes actions [Huxley]
18. Thought / C. Content / 2. Ideas
True ideas represent what is possible; false ideas represent contradictions [Leibniz]
26. Natural Theory / C. Causation / 2. Types of cause
In the schools the Four Causes are just lumped together in a very obscure way [Leibniz]