Combining Texts

All the ideas for 'Aristotle and Descartes on Matter', 'Principles of Arithmetic, by a new method' and 'What is innate and why'

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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]
18. Thought / B. Mechanics of Thought / 4. Language of Thought
2605 If everything uses mentalese, ALL concepts must be innate! [Putnam]
2606 No machine language can express generalisations [Putnam]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / b. Prime matter
19399 Prime matter is nothing when it is at rest [Leibniz]