Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Pacidius Philalethi dialogue' and 'Does Emp.Knowledge have Foundation?'

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10 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]
9. Objects / C. Structure of Objects / 8. Parts of Objects / a. Parts of objects
12697 Indivisibles are not parts, but the extrema of parts [Leibniz]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / c. Empirical foundations
8793 If observation is knowledge, it is not just an experience; it is a justification in the space of reasons [Sellars]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / f. Foundationalism critique
8792 Observations like 'this is green' presuppose truths about what is a reliable symptom of what [Sellars]
18. Thought / D. Concepts / 4. Structure of Concepts / f. Theory theory of concepts
8791 The concept of 'green' involves a battery of other concepts [Sellars]