Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'The Varieties of Necessity' and 'Gravity and Grace (9 extracts)'

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20 ideas

3. Truth / A. Truth Problems / 3. Value of Truth
We seek truth only because it is good [Weil]
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 / 1. Sources of Necessity
Each area of enquiry, and its source, has its own distinctive type of necessity [Fine,K]
13. Knowledge Criteria / C. External Justification / 7. Testimony
Unsupported testimony may still be believable [Fine,K]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / a. Idealistic ethics
Beauty, goodness and truth are only achieved by applying full attention [Weil]
22. Metaethics / C. The Good / 1. Goodness / a. Form of the Good
The good is a nothingness, and yet real [Weil]
There are two goods - the absolute good we want, and the reachable opposite of evil [Weil]
24. Political Theory / C. Ruling a State / 1. Social Power
The essence of power is illusory prestige [Weil]
24. Political Theory / D. Ideologies / 1. Ideology
A group is only dangerous if it endorses an abstract entity [Weil]
24. Political Theory / D. Ideologies / 2. Anarchism
Our only social duty is to try to limit evil [Weil]
24. Political Theory / D. Ideologies / 9. Communism
The collective is the one and only object of false idolatry [Weil]
24. Political Theory / D. Ideologies / 14. Nationalism
Charity is the only love, and you can feel that for a country (a place with traditions), but not a nation [Weil]
25. Social Practice / A. Freedoms / 1. Slavery
If effort is from necessity rather than for a good, it is slavery [Weil]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / a. Scientific essentialism
Causation is easier to disrupt than logic, so metaphysics is part of nature, not vice versa [Fine,K]
29. Religion / D. Religious Issues / 2. Immortality / b. Soul
The soul is the intrinsic value of a human [Weil]