Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Reflections on Knowledge, Truth and Ideas' and 'On the Law of War and Peace'

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19 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]
18. Thought / C. Content / 2. Ideas
True ideas represent what is possible; false ideas represent contradictions [Leibniz]
20. Action / C. Motives for Action / 5. Action Dilemmas / c. Omissions
Nations are not obliged to help one-another, but are obliged not to harm one another [Grotius, by Tuck]
24. Political Theory / A. Basis of a State / 3. Natural Values / c. Natural rights
Everyone has a right of self-preservation, and harming others is usually unjustifiable [Grotius, by Tuck]
24. Political Theory / D. Ideologies / 5. Democracy / a. Nature of democracy
Democracy needs respect for individuality, but the 'community of friends' implies strict equality [Grotius]
25. Social Practice / A. Freedoms / 7. Freedom to leave
A person is free to renounce their state, as long as it is not a moment of crisis [Grotius, by Rousseau]
25. Social Practice / D. Justice / 2. The Law / c. Natural law
Grotius and Pufendorf based natural law on real (rather than idealised) humanity [Grotius, by Ford,JD]
A natural right of self-preservation is balanced by a natural law to avoid unnecessary harm [Grotius, by Tuck]
25. Social Practice / D. Justice / 2. The Law / d. Legal positivism
Grotius ignored elaborate natural law theories, preferring a basic right of self-preservation [Grotius, by Tuck]
25. Social Practice / E. Policies / 1. War / b. Justice in war
It is permissible in a just cause to capture a place in neutral territory [Grotius]
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]
28. God / A. Divine Nature / 6. Divine Morality / b. Euthyphro question
Moral principles have some validity without a God commanding obedience [Grotius, by Mautner]