Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Principles of Theoretical Logic' and 'Short History of Modern Philosophy'

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11 ideas

4. Formal Logic / C. Predicate Calculus PC / 1. Predicate Calculus PC

17750

The first clear proof of the consistency of the first order predicate logic was in 1928 [Hilbert/Ackermann, by Walicki]

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 / A. Overview of Logic / 2. History of Logic

5637	Nowadays logic is seen as the science of extensions, not intensions [Scruton]

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]

18. Thought / C. Content / 2. Ideas

5636	Cartesian 'ideas' confuse concepts and propositions [Scruton]

24. Political Theory / A. Basis of a State / 3. Natural Values / c. Natural rights

5660	Allegiance is prior to the recognition of individual rights [Scruton]

25. Social Practice / C. Rights / 1. Basis of Rights

5653	A right is a power which is enforced in the name of justice [Scruton]