Combining Texts

All the ideas for 'General Draft', 'Properties' and 'Principles of Arithmetic, by a new method'

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11 ideas

1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / a. Philosophy as worldly
22026 Philosophy is homesickness - the urge to be at home everywhere [Novalis]
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]
8. Modes of Existence / B. Properties / 2. Need for Properties
18430 We accept properties because of type/tokens, reference, and quantification [Edwards]
8. Modes of Existence / B. Properties / 10. Properties as Predicates
18432 Quineans say that predication is primitive and inexplicable [Edwards]
8. Modes of Existence / E. Nominalism / 2. Resemblance Nominalism
18437 Resemblance nominalism requires a second entity to explain 'the rose is crimson' [Edwards]
9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts
18434 That a whole is prior to its parts ('priority monism') is a view gaining in support [Edwards]
15. Nature of Minds / C. Capacities of Minds / 6. Idealisation
19591 Desire for perfection is an illness, if it turns against what is imperfect [Novalis]