Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Conceptions of Truth' and 'Virtue Epistemology'

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10 ideas

2. Reason / D. Definition / 12. Paraphrase
The idea of 'making' can be mere conceptual explanation (like 'because') [Künne]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner]
'Reflection principles' say the whole truth about sets can't be captured [Koellner]
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
We have no argument to show a statement is absolutely undecidable [Koellner]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
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
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
Arithmetical undecidability is always settled at the next stage up [Koellner]
13. Knowledge Criteria / B. Internal Justification / 1. Epistemic virtues
Epistemic virtues: love of knowledge, courage, caution, autonomy, practical wisdom... [Kvanvig]
If epistemic virtues are faculties or powers, that doesn't explain propositional knowledge [Kvanvig]
The value of good means of attaining truth are swamped by the value of the truth itself [Kvanvig]