Combining Texts
Ideas for
'On the Question of Absolute Undecidability', 'Regressive Method for Premises in Mathematics' and 'Introduction to the Philosophy of Mind'
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5 ideas
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 / 2. Proof in Mathematics
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It seems absurd to prove 2+2=4, where the conclusion is more certain than premises [Russell]
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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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6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
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Arithmetic was probably inferred from relationships between physical objects [Russell]
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