Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Philosophy of Mind (Encylopedia III)' and 'From Stimulus to Science'

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9 ideas

2. Reason / B. Laws of Thought / 3. Non-Contradiction

6564	To affirm 'p and not-p' is to have mislearned 'and' or 'not' [Quine]

4. Formal Logic / F. Set Theory ST / 1. Set Theory

17884

Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner]

17893

'Reflection principles' say the whole truth about sets can't be captured [Koellner]

5. Theory of Logic / K. Features of Logics / 5. Incompleteness

17894

We have no argument to show a statement is absolutely undecidable [Koellner]

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity

17890

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

17887

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

17891

Arithmetical undecidability is always settled at the next stage up [Koellner]

16. Persons / F. Free Will / 2. Sources of Free Will

22040

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

22039

Geist is distinct from nature, not as a substance, but because of its normativity [Hegel, by Pinkard]