Combining Texts
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'On the Question of Absolute Undecidability', 'Introduction to the Theory of Logic' and 'Spinoza's Ethics'
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3 ideas
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 / f. Mathematical induction
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If a set is defined by induction, then proof by induction can be applied to it [Zalabardo]
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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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