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'On the Question of Absolute Undecidability', 'Concluding Unscientific Postscript' and 'Mathematics and the Metaphysicians'
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5 ideas
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
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In mathematic we are ignorant of both subject-matter and truth [Russell]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / b. Mark of the infinite
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A collection is infinite if you can remove some terms without diminishing its number [Russell]
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6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
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There are at least eleven types of large cardinal, of increasing logical strength [Koellner]
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6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
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PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner]
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6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
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Arithmetical undecidability is always settled at the next stage up [Koellner]
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