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Ideas for 'fragments/reports', 'My Philosophical Development' and 'On the Question of Absolute Undecidability'

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7 ideas

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]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
6423 We tried to define all of pure maths using logical premisses and concepts [Russell]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
6424 Formalists say maths is merely conventional marks on paper, like the arbitrary rules of chess [Russell]
6425 Formalism can't apply numbers to reality, so it is an evasion [Russell]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
6426 Intuitionism says propositions are only true or false if there is a method of showing it [Russell]