Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Against Coherence' and 'Reference and Generality (3rd ed)'

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17 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 / 4. Using Numbers / d. Counting via concepts
12154 Are 'word token' and 'word type' different sorts of countable objects, or two ways of counting? [Geach, by Perry]
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 / A. Existence of Objects / 6. Nihilism about Objects
8969 We should abandon absolute identity, confining it to within some category [Geach, by Hawthorne]
9. Objects / F. Identity among Objects / 3. Relative Identity
16075 Denial of absolute identity has drastic implications for logic, semantics and set theory [Wasserman on Geach]
12152 Identity is relative. One must not say things are 'the same', but 'the same A as' [Geach]
9. Objects / F. Identity among Objects / 8. Leibniz's Law
16073 Leibniz's Law is incomplete, since it includes a non-relativized identity predicate [Geach, by Wasserman]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / a. Coherence as justification
21515 Incoherence may be more important for enquiry than coherence [Olsson]
21514 Coherence is the capacity to answer objections [Olsson]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / c. Coherentism critique
21496 Mere agreement of testimonies is not enough to make truth very likely [Olsson]
21499 Coherence is only needed if the information sources are not fully reliable [Olsson]
21502 A purely coherent theory cannot be true of the world without some contact with the world [Olsson]
21512 Extending a system makes it less probable, so extending coherence can't make it more probable [Olsson]