Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Panpsychism' and 'Summa Contra Gentiles'

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11 ideas

1. Philosophy / A. Wisdom / 2. Wise People
Wise people should contemplate and discuss the truth, and fight against falsehood [Aquinas]
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]
8. Modes of Existence / B. Properties / 7. Emergent Properties
Emergent properties appear at high levels of complexity, but aren't explainable by the lower levels [Nagel]
17. Mind and Body / A. Mind-Body Dualism / 4. Occasionalism
Without God's influence every operation would stop, so God causes everything [Aquinas]
26. Natural Theory / C. Causation / 9. General Causation / d. Causal necessity
Given the nature of heat and of water, it is literally impossible for water not to boil at the right heat [Nagel]
27. Natural Reality / D. Time / 1. Nature of Time / f. Eternalism
Eternity coexists with passing time, as the centre of a circle coexists with its circumference [Aquinas]