Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'On Duties ('De Officiis')' and 'works'

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11 ideas

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

21405

Cicero sees wisdom in terms of knowledge, but earlier Stoics saw it as moral [Cicero, by Long]

1. Philosophy / A. Wisdom / 2. Wise People

20871

Unfortunately we choose a way of life before we are old enough to think clearly [Cicero]

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 / D. Assumptions for Logic / 2. Excluded Middle

15941

For intuitionists excluded middle is an outdated historical convention [Brouwer]

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 / 3. Nature of Numbers / h. Reals from Cauchy

18247

Brouwer saw reals as potential, not actual, and produced by a rule, or a choice [Brouwer, by Shapiro]

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]

23. Ethics / D. Deontological Ethics / 3. Universalisability

6031	The essence of propriety is consistency [Cicero]