Combining Texts

All the ideas for 'fragments/reports', 'Principles of Arithmetic, by a new method' and 'Warrant and Proper Function'

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8 ideas

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]
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / a. Reliable knowledge
6356 Maybe a reliable justification must come from a process working with its 'proper function' [Plantinga, by Pollock/Cruz]
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
1748 Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius]
27. Natural Reality / G. Biology / 3. Evolution
5989 Archelaus said life began in a primeval slime [Archelaus, by Schofield]