Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Realism and Anti-Realism' and 'Why Constitution is not Identity'

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13 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 / D. Theories of Reality / 2. Realism
Metaphysical realists are committed to all unambiguous statements being true or not true [Dummett]
9. Objects / B. Unity of Objects / 3. Unity Problems / c. Statue and clay
Clay is intrinsically and atomically the same as statue (and that lacks 'modal properties') [Rudder Baker]
The clay is not a statue - it borrows that property from the statue it constitutes [Rudder Baker]
9. Objects / B. Unity of Objects / 3. Unity Problems / d. Coincident objects
Is it possible for two things that are identical to become two separate things? [Rudder Baker]
9. Objects / C. Structure of Objects / 6. Constitution of an Object
Constitution is not identity, as consideration of essential predicates shows [Rudder Baker]
The constitution view gives a unified account of the relation of persons/bodies, statues/bronze etc [Rudder Baker]
Statues essentially have relational properties lacked by lumps [Rudder Baker]