Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'The Logical Basis of Metaphysics' and 'Event Causation: counterfactual analysis'

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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 / E. Structures of Logic / 2. Logical Connectives / c. not
Classical negation is circular, if it relies on knowing negation-conditions from truth-conditions [Dummett]
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 / B. Change in Existence / 4. Events / a. Nature of events
Maybe each event has only one possible causal history [Bennett]
Maybe an event's time of occurrence is essential to it [Bennett]
26. Natural Theory / C. Causation / 1. Causation
Delaying a fire doesn't cause it, but hastening it might [Bennett]
Either cause and effect are subsumed under a conditional because of properties, or it is counterfactual [Bennett]
26. Natural Theory / C. Causation / 2. Types of cause
Causes are between events ('the explosion') or between facts/states of affairs ('a bomb dropped') [Bennett]
26. Natural Theory / C. Causation / 9. General Causation / c. Counterfactual causation
The full counterfactual story asserts a series of events, because counterfactuals are not transitive [Bennett]
A counterfactual about an event implies something about the event's essence [Bennett]