Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Letters to Foucher' and 'The Mozi'

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12 ideas

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 / C. Powers and Dispositions / 4. Powers as Essence
Essence is primitive force, or a law of change [Leibniz]
22. Metaethics / C. The Good / 1. Goodness / g. Consequentialism
Mohists desire wealth, population and social order as the best consequences [Mozi, by Norden]
23. Ethics / B. Contract Ethics / 2. Golden Rule
If people regarded other states as they did their own, they would never attack them [Mozi]
23. Ethics / D. Deontological Ethics / 3. Universalisability
Mozi condemns partiality, which is the cause of all the great harms in the world [Mozi]
Those who are against impartiality still prefer impartial protectors [Mozi]
26. Natural Theory / C. Causation / 9. General Causation / d. Causal necessity
The connection in events enables us to successfully predict the future, so there must be a constant cause [Leibniz]