Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'fragments/reports' and 'Evidentialism'

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9 ideas

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 / 4. Belief / c. Aim of beliefs

19525

If the only aim is to believe truths, that justifies recklessly believing what is unsupported (if it is right) [Conee/Feldman]

13. Knowledge Criteria / A. Justification Problems / 2. Justification Challenges / c. Knowledge closure

19524

We don't have the capacity to know all the logical consequences of our beliefs [Conee/Feldman]

13. Knowledge Criteria / A. Justification Problems / 3. Internal or External / a. Pro-internalism

604	Knowledge is mind and knowing 'cohabiting' [Lycophron, by Aristotle]