Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Against Method' and 'Apprehension: reason in absence of Rules'

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9 ideas

1. Philosophy / G. Scientific Philosophy / 1. Aims of Science

6601	Science rules the globe because of colonising power, not inherent rationality [Feyerabend]

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]

12. Knowledge Sources / E. Direct Knowledge / 1. Common Sense

22668

Apprehension is a complex intellect grasping the essence of a complex object [Holt,L]

14. Science / B. Scientific Theories / 6. Theory Holism

2561	For Feyerabend the meaning of a term depends on a whole theory [Feyerabend, by Rorty]