Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Material Constitution' and 'Introduction - Ontology'

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16 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]
7. Existence / C. Structure of Existence / 3. Levels of Reality
Biologists see many organic levels, 'abstract' if seen from below, 'structural' if seen from above [Lycan]
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]
9. Objects / F. Identity among Objects / 6. Identity between Objects
'Lightning is electric discharge' and 'Phosphorus is Venus' are synthetic a posteriori identities [Lycan]
17. Mind and Body / C. Functionalism / 2. Machine Functionalism
Functionalism has three linked levels: physical, functional, and mental [Lycan]
17. Mind and Body / C. Functionalism / 5. Teleological Functionalism
A mental state is a functional realisation of a brain state when it serves the purpose of the organism [Lycan]
26. Natural Theory / A. Speculations on Nature / 2. Natural Purpose / c. Purpose denied
People are trying to explain biological teleology in naturalistic causal terms [Lycan]