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Ideas for
'On the Question of Absolute Undecidability', 'Of the First Principles of Government' and 'Principles of Arithmetic, by a new method'
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8 ideas
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
17890
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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
13949
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All models of Peano axioms are isomorphic, so the models all seem equally good for natural numbers [Cartwright,R on Peano]
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18113
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PA concerns any entities which satisfy the axioms [Peano, by Bostock]
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17634
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Peano axioms not only support arithmetic, but are also fairly obvious [Peano, by Russell]
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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
15653
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We can add Reflexion Principles to Peano Arithmetic, which assert its consistency or soundness [Halbach on Peano]
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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 / 6. Logicism / a. Early logicism
17635
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Arithmetic can have even simpler logical premises than the Peano Axioms [Russell on Peano]
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