Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Mathematical Explanation' and 'The Sublime and the Good'

expand these ideas     |    start again     |     specify just one area for these texts


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]
9. Objects / D. Essence of Objects / 3. Individual Essences
Particular essence is often captured by generality [Steiner,M]
14. Science / D. Explanation / 2. Types of Explanation / e. Lawlike explanations
Maybe an instance of a generalisation is more explanatory than the particular case [Steiner,M]
14. Science / D. Explanation / 2. Types of Explanation / m. Explanation by proof
Explanatory proofs rest on 'characterizing properties' of entities or structure [Steiner,M]
21. Aesthetics / B. Nature of Art / 1. Defining Art
We should first decide what are the great works of art, with aesthetic theory following from that [Murdoch]
21. Aesthetics / C. Artistic Issues / 6. Value of Art
Great art proves the absurdity of art for art's sake [Murdoch]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
Because art is love, it improves us morally [Murdoch]
Art and morals are essentially the same, and are both identical with love [Murdoch]
22. Metaethics / B. Value / 2. Values / g. Love
Love is realising something other than oneself is real [Murdoch]