Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Against Method' and 'Individuation'

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12 ideas

1. Philosophy / G. Scientific Philosophy / 1. Aims of Science
Science rules the globe because of colonising power, not inherent rationality [Feyerabend]
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 / E. Nominalism / 3. Predicate Nominalism
Not all predicates can be properties - 'is non-self-exemplifying', for example [Lowe]
9. Objects / A. Existence of Objects / 5. Individuation / a. Individuation
Neither mere matter nor pure form can individuate a sphere, so it must be a combination [Lowe]
14. Science / B. Scientific Theories / 6. Theory Holism
For Feyerabend the meaning of a term depends on a whole theory [Feyerabend, by Rorty]
14. Science / D. Explanation / 1. Explanation / c. Direction of explanation
If the flagpole causally explains the shadow, the shadow cannot explain the flagpole [Lowe]
15. Nature of Minds / C. Capacities of Minds / 3. Abstraction by mind
Properties are facets of objects, only discussable separately by an act of abstraction [Lowe]