Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', '68: Generation of the soul in 'Timaeus'' and 'Does moral phil rest on a mistake?'

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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]
18. Thought / A. Modes of Thought / 3. Emotions / f. Emotion and reason
Some say emotion is a sort of reason, and others say virtue concerns emotion [Plutarch]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / c. Purpose of ethics
The 'Ethics' is disappointing, because it fails to try to justify our duties [Prichard]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / c. Particularism
The mistake is to think we can prove what can only be seen directly in moral thinking [Prichard]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / d. Virtue theory critique
Virtues won't generate an obligation, so it isn't a basis for morality [Prichard]
23. Ethics / D. Deontological Ethics / 2. Duty
We feel obligations to overcome our own failings, and these are not relations to other people [Prichard]
23. Ethics / E. Utilitarianism / 1. Utilitarianism
If pain were instrinsically wrong, it would be immoral to inflict it on ourselves [Prichard]