Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Review of Bob Hale's 'Abstract Objects'' and 'fragments/reports'

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12 ideas

1. Philosophy / F. Analytic Philosophy / 4. Conceptual Analysis
We can't presume that all interesting concepts can be analysed [Williamson]
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]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
Platonism claims that some true assertions have singular terms denoting abstractions, so abstractions exist [Williamson]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / j. Ethics by convention
We should follow the law in public, and nature in private [Antiphon]
To gain the greatest advantage only treat law as important when other people are present [Antiphon]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / e. Character
The way you spend your time will form your character [Antiphon]
24. Political Theory / D. Ideologies / 2. Anarchism
Nothing is worse for mankind than anarchy [Antiphon]