Combining Texts
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'On the Question of Absolute Undecidability', 'A Discourse on Method' and 'Theory of Science (Wissenschaftslehre, 4 vols)'
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5 ideas
6. Mathematics / A. Nature of Mathematics / 2. Geometry
9618
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Bolzano wanted to reduce all of geometry to arithmetic [Bolzano, by Brown,JR]
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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
17891
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Arithmetical undecidability is always settled at the next stage up [Koellner]
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6. Mathematics / C. Sources of Mathematics / 2. Intuition of Mathematics
9830
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Bolzano began the elimination of intuition, by proving something which seemed obvious [Bolzano, by Dummett]
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