Combining Texts

All the ideas for 'Philosophical Explanations', 'On Note L to Bayle's 'Rorarius'' and 'Principles of Arithmetic, by a new method'

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10 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]
11. Knowledge Aims / A. Knowledge / 4. Belief / c. Aim of beliefs
3570 Maybe knowledge is belief which 'tracks' the truth [Nozick, by Williams,M]
13. Knowledge Criteria / C. External Justification / 4. Tracking the Facts
2748 A true belief isn't knowledge if it would be believed even if false. It should 'track the truth' [Nozick, by Dancy,J]
15. Nature of Minds / B. Features of Minds / 2. Unconscious Mind
19355 The soul doesn't understand many of its own actions, if perceptions are confused and desires buried [Leibniz]
17. Mind and Body / A. Mind-Body Dualism / 5. Parallelism
19350 We should say that body is mechanism and soul is immaterial, asserting their independence [Leibniz]
26. Natural Theory / A. Speculations on Nature / 4. Mathematical Nature
19356 Minds unconsciously count vibration beats in music, and enjoy it when they coincide [Leibniz]