Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Substances without Substrata' and 'On Wisdom'

expand these ideas     |    start again     |     specify just one area for these texts

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9 ideas

1. Philosophy / A. Wisdom / 1. Nature of Wisdom

19396

Wisdom is knowing all of the sciences, and their application [Leibniz]

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]

11. Knowledge Aims / A. Knowledge / 1. Knowledge

19397

Perfect knowledge implies complete explanations and perfect prediction [Leibniz]

19. Language / F. Communication / 6. Interpreting Language / c. Principle of charity

6316	We translate in a way that makes the largest possible number of statements true [Wilson,NL]