Combining Texts

All the ideas for 'What is Mathematical Truth?', 'Principles of Arithmetic, by a new method' and 'Introduction to the Philosophy of Mind'

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16 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]
7. Existence / C. Structure of Existence / 5. Supervenience / c. Significance of supervenience
3523 Shadows are supervenient on their objects, but not reducible [Maslin]
7. Existence / D. Theories of Reality / 1. Ontologies
3517 'Ontology' means 'study of things which exist' [Maslin]
10. Modality / B. Possibility / 1. Possibility
10269 Mathematics eliminates possibility, as being simultaneous actuality in sets [Putnam]
15. Nature of Minds / A. Nature of Mind / 4. Other Minds / d. Other minds by analogy
3538 Analogy to other minds is uncheckable, over-confident and chauvinistic [Maslin]
16. Persons / B. Nature of the Self / 7. Self and Body / b. Self as brain
3540 If we are brains then we never meet each other [Maslin]
16. Persons / C. Self-Awareness / 3. Limits of Introspection
3518 I'm not the final authority on my understanding of maths [Maslin]
17. Mind and Body / D. Property Dualism / 2. Anomalous Monism
3530 Denial of purely mental causation will lead to epiphenomenalism [Maslin]
17. Mind and Body / D. Property Dualism / 3. Property Dualism
3520 Token-identity removes the explanatory role of the physical [Maslin]
26. Natural Theory / C. Causation / 9. General Causation / b. Nomological causation
3528 Causality may require that a law is being followed [Maslin]
26. Natural Theory / D. Laws of Nature / 7. Strictness of Laws
3525 Strict laws make causation logically necessary [Maslin]
3527 Strict laws allow no exceptions and are part of a closed system [Maslin]