Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Metaphysical Foundations of Mathematics' and 'Persistence, Change and Explanation'

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15 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]
5. Theory of Logic / L. Paradox / 2. Aporiai
By using aporiai as his start, Aristotle can defer to the wise, as well as to the many [Haslanger]
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 / 1. Ontologies
Ontology disputes rest on more basic explanation disputes [Haslanger]
9. Objects / E. Objects over Time / 3. Three-Dimensionalism
The persistence of objects seems to be needed if the past is to explain the present [Haslanger]
Persistence makes change and its products intelligible [Haslanger]
9. Objects / E. Objects over Time / 5. Temporal Parts
We must explain change amongst 'momentary entities', or else the world is inexplicable [Haslanger]
If the things which exist prior to now are totally distinct, they need not have existed [Haslanger]
14. Science / D. Explanation / 2. Types of Explanation / g. Causal explanations
Natural explanations give the causal interconnections [Haslanger]
14. Science / D. Explanation / 2. Types of Explanation / j. Explanations by reduction
Best explanations, especially natural ones, need grounding, notably by persistent objects [Haslanger]
27. Natural Reality / D. Time / 2. Passage of Time / g. Time's arrow
When one element contains the grounds of the other, the first one is prior in time [Leibniz]