Combining Texts

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

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14 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]
10. Modality / C. Sources of Modality / 2. Necessity as Primitive
Some necessary truths are brute, and others derive from final causes [Leibniz]
15. Nature of Minds / B. Features of Minds / 1. Consciousness / c. Parts of consciousness
Our large perceptions and appetites are made up tiny unconscious fragments [Leibniz]
18. Thought / A. Modes of Thought / 3. Emotions / c. Role of emotions
Passions reside in confused perceptions [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]
28. God / A. Divine Nature / 2. Divine Nature
God produces possibilities, and thus ideas [Leibniz]