Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'The Varieties of Necessity' and 'Public Text and Common Reader'

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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 / 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]
10. Modality / C. Sources of Modality / 1. Sources of Necessity
Each area of enquiry, and its source, has its own distinctive type of necessity [Fine,K]
13. Knowledge Criteria / C. External Justification / 7. Testimony
Unsupported testimony may still be believable [Fine,K]
21. Aesthetics / A. Aesthetic Experience / 3. Taste
Literary meaning emerges in comparisons, and tradition shows which comparisons are relevant [Scruton]
21. Aesthetics / B. Nature of Art / 5. Art as Language
In literature, word replacement changes literary meaning [Scruton]
21. Aesthetics / C. Artistic Issues / 1. Artistic Intentions
Without intentions we can't perceive sculpture, but that is not the whole story [Scruton]
21. Aesthetics / C. Artistic Issues / 3. Artistic Representation
In aesthetic interest, even what is true is treated as though it were not [Scruton]
21. Aesthetics / C. Artistic Issues / 5. Objectivism in Art
We can be objective about conventions, but love of art is needed to understand its traditions [Scruton]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / a. Scientific essentialism
Causation is easier to disrupt than logic, so metaphysics is part of nature, not vice versa [Fine,K]