Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Inventing Logical Necessity' and 'Summula philosophiae naturalis'

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11 ideas

4. Formal Logic / F. Set Theory ST / 1. Set Theory
17884 Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner]
17893 'Reflection principles' say the whole truth about sets can't be captured [Koellner]
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
17894 We have no argument to show a statement is absolutely undecidable [Koellner]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
17890 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
17887 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
17891 Arithmetical undecidability is always settled at the next stage up [Koellner]
7. Existence / E. Categories / 5. Category Anti-Realism
16608 Ockham was an anti-realist about the categories [William of Ockham, by Pasnau]
9. Objects / C. Structure of Objects / 4. Quantity of an Object
16599 Ockham says matter must be extended, so we don't need Quantity [William of Ockham, by Pasnau]
16681 Matter gets its quantity from condensation and rarefaction, which is just local motion [William of Ockham]
10. Modality / A. Necessity / 6. Logical Necessity
12189 Logical necessity involves a decision about usage, and is non-realist and non-cognitive [Wright,C, by McFetridge]
19. Language / A. Nature of Meaning / 7. Meaning Holism / b. Language holism
7320 Holism cannot give a coherent account of scientific methodology [Wright,C, by Miller,A]