Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'fragments/reports' and 'Frege on Apriority (with ps)'

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11 ideas

1. Philosophy / C. History of Philosophy / 2. Ancient Philosophy / c. Classical philosophy

21336

Crates lived in poverty, and treated his whole life as a joke [Crates of Thebes, by Plutarch]

1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / a. Philosophy as worldly

1767	Everyone should study philosophy until they see all people in the same light [Crates of Thebes, by Diog. Laertius]

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 / 2. Geometry

16901

The equivalent algebra model of geometry loses some essential spatial meaning [Burge]

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

16902

Peano arithmetic requires grasping 0 as a primitive number [Burge]

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]

12. Knowledge Sources / A. A Priori Knowledge / 1. Nature of the A Priori

16892

Is apriority predicated mainly of truths and proofs, or of human cognition? [Burge]