Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Ars Magna' and 'Three-Dimensionalism v Four-Dimensionalism'

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12 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 / A. Overview of Logic / 2. History of Logic
Lull's combinatorial art would articulate all the basic concepts, then show how they combine [Lull, by Arthur,R]
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 / B. Unity of Objects / 3. Unity Problems / a. Scattered objects
If we accept scattered objects such as archipelagos, why not think of cars that way? [Hawthorne]
9. Objects / E. Objects over Time / 4. Four-Dimensionalism
Four-dimensionalists say instantaneous objects are more fundamental than long-lived ones [Hawthorne]
10. Modality / A. Necessity / 11. Denial of Necessity
A modal can reverse meaning if the context is seen differently, so maybe context is all? [Hawthorne]
27. Natural Reality / C. Space / 6. Space-Time
Modern metaphysicians tend to think space-time points are more fundamental than space-time regions [Hawthorne]
28. God / A. Divine Nature / 3. Divine Perfections
Nine principles of God: goodness, greatness, eternity, power, wisdom, will, virtue, truth and glory [Lull, by Arthur,R]