Combining Texts
Ideas for
'Parmenides', 'Varieties of Ontological Dependence' and 'Principles of Arithmetic, by a new method'
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7 ideas
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
17312
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It is more explanatory if you show how a number is constructed from basic entities and relations [Koslicki]
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6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
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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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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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6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
16150
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One is, so numbers exist, so endless numbers exist, and each one must partake of being [Plato]
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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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