Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Philosophy of Mind (Encylopedia III)' and 'Intuitionism'

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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]
16. Persons / F. Free Will / 2. Sources of Free Will
Freedom is produced by the activity of the mind, and is not intrinsically given [Hegel]
17. Mind and Body / A. Mind-Body Dualism / 1. Dualism
Geist is distinct from nature, not as a substance, but because of its normativity [Hegel, by Pinkard]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / c. Ethical intuitionism
If there are intuited moral facts, why should we care about them? [Dancy,J]
Internalists say that moral intuitions are motivating; externalist say a desire is also needed [Dancy,J]
Obviously judging an action as wrong gives us a reason not to do it [Dancy,J]
Moral facts are not perceived facts, but perceived reasons for judgements [Dancy,J]