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'On the Question of Absolute Undecidability', 'Empty Names' and 'Critique of Pure Reason'
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5 ideas
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
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3343
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Euclid's could be the only viable geometry, if rejection of the parallel line postulate doesn't lead to a contradiction [Benardete,JA on Kant]
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6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
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8737
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Kant suggested that arithmetic has no axioms [Kant, by Shapiro]
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5557
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Axioms ought to be synthetic a priori propositions [Kant]
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6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
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17887
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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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17891
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Arithmetical undecidability is always settled at the next stage up [Koellner]
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