Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Lecture on Nominalism' and 'What is Art?'

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16 ideas

2. Reason / F. Fallacies / 1. Fallacy
The Struthionic Fallacy is that of burying one's head in the sand [Quine]
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 / E. Structures of Logic / 6. Relations in Logic
All relations, apart from ancestrals, can be reduced to simpler logic [Quine]
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]
6. Mathematics / C. Sources of Mathematics / 3. Mathematical Nominalism
Nominalism rejects both attributes and classes (where extensionalism accepts the classes) [Quine]
21. Aesthetics / B. Nature of Art / 4. Art as Expression
True works of art transmit completely new feelings [Tolstoy]
Art is when one man uses external signs to hand on his feelings to another man [Tolstoy]
The highest feelings of mankind can only be transmitted by art [Tolstoy]
21. Aesthetics / C. Artistic Issues / 4. Emotion in Art
The purpose of art is to help mankind to evolve better, more socially beneficial feelings [Tolstoy]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
People estimate art according to their moral values [Tolstoy]
The upper classes put beauty first, and thus freed themselves from morality [Tolstoy]
We separate the concept of beauty from goodness, unlike the ancients [Tolstoy]