Combining Texts

All the ideas for 'Cosmic Apprentice', 'The iterative conception of Set' and 'Principles of Arithmetic, by a new method'

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7 ideas

1. Philosophy / G. Scientific Philosophy / 3. Scientism
16567 Scientists know everything about nothing, philosophers nothing about everything [Sagan,D]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / h. Axiom of Replacement VII
18192 Do the Replacement Axioms exceed the iterative conception of sets? [Boolos, by Maddy]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
13949 All models of Peano axioms are isomorphic, so the models all seem equally good for natural numbers [Cartwright,R on Peano]
18113 PA concerns any entities which satisfy the axioms [Peano, by Bostock]
17634 Peano axioms not only support arithmetic, but are also fairly obvious [Peano, by Russell]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
15653 We can add Reflexion Principles to Peano Arithmetic, which assert its consistency or soundness [Halbach on Peano]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
17635 Arithmetic can have even simpler logical premises than the Peano Axioms [Russell on Peano]