Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Why Propositions cannot be concrete' and 'Dispositional Essentialism Grounds Laws of Nature?'

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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]
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]
8. Modes of Existence / C. Powers and Dispositions / 6. Dispositions / c. Dispositions as conditional
An 'antidote' allows a manifestation to begin, but then blocks it [Corry]
A 'finkish' disposition is one that is lost immediately after the appropriate stimulus [Corry]
8. Modes of Existence / C. Powers and Dispositions / 6. Dispositions / d. Dispositions as occurrent
If a disposition is never instantiated, it shouldn't be part of our theory of nature [Corry]
14. Science / A. Basis of Science / 3. Experiment
Maybe an experiment unmasks an essential disposition, and reveals its regularities [Corry]
18. Thought / E. Abstraction / 1. Abstract Thought
The idea of abstract objects is not ontological; it comes from the epistemological idea of abstraction [Plantinga]
Theists may see abstract objects as really divine thoughts [Plantinga]
19. Language / D. Propositions / 3. Concrete Propositions
If propositions are concrete they don't have to exist, and so they can't be necessary truths [Plantinga]
19. Language / D. Propositions / 4. Mental Propositions
Propositions can't just be in brains, because 'there are no human beings' might be true [Plantinga]
26. Natural Theory / D. Laws of Nature / 1. Laws of Nature
Dispositional essentialism says fundamental laws of nature are strict, not ceteris paribus [Corry]