Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Material Constitution' and 'The Varieties of Necessity'

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14 ideas

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]
9. Objects / C. Structure of Objects / 6. Constitution of an Object
Constitution is identity (being in the same place), or it isn't (having different possibilities) [Wasserman]
Constitution is not identity, because it is an asymmetric dependence relation [Wasserman]
There are three main objections to seeing constitution as different from identity [Wasserman]
9. Objects / C. Structure of Objects / 8. Parts of Objects / a. Parts of objects
The weight of a wall is not the weight of its parts, since that would involve double-counting [Wasserman]
9. Objects / F. Identity among Objects / 3. Relative Identity
Relative identity may reject transitivity, but that suggests that it isn't about 'identity' [Wasserman]
10. Modality / C. Sources of Modality / 1. Sources of Necessity
Each area of enquiry, and its source, has its own distinctive type of necessity [Fine,K]
13. Knowledge Criteria / C. External Justification / 7. Testimony
Unsupported testimony may still be believable [Fine,K]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / a. Scientific essentialism
Causation is easier to disrupt than logic, so metaphysics is part of nature, not vice versa [Fine,K]