Combining Texts

All the ideas for 'In Praed.', 'Principles of Arithmetic, by a new method' and 'Inventing Logical Necessity'

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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]
9. Objects / B. Unity of Objects / 2. Substance / a. Substance
16776 Substance is an intrinsic thing, so parts of substances can't also be intrinsic things [Duns Scotus]
10. Modality / A. Necessity / 6. Logical Necessity
12189 Logical necessity involves a decision about usage, and is non-realist and non-cognitive [Wright,C, by McFetridge]
19. Language / A. Nature of Meaning / 7. Meaning Holism / b. Language holism
7320 Holism cannot give a coherent account of scientific methodology [Wright,C, by Miller,A]