Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Pacidius Philalethi dialogue' and 'Elusive Knowledge'

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12 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]
11. Knowledge Aims / A. Knowledge / 4. Belief / a. Beliefs
12899 The timid student has knowledge without belief, lacking confidence in their correct answer [Lewis]
11. Knowledge Aims / B. Certain Knowledge / 3. Fallibilism
12897 To say S knows P, but cannot eliminate not-P, sounds like a contradiction [Lewis]
13. Knowledge Criteria / A. Justification Problems / 1. Justification / b. Need for justification
12898 Justification is neither sufficient nor necessary for knowledge [Lewis]
13. Knowledge Criteria / C. External Justification / 6. Contextual Justification / a. Contextualism
12895 Knowing is context-sensitive because the domain of quantification varies [Lewis, by Cohen,S]
19562 We have knowledge if alternatives are eliminated, but appropriate alternatives depend on context [Lewis, by Cohen,S]