Combining Texts

All the ideas for 'Semantics, Conceptual Role', 'Of Liberty and Necessity' and 'Principles of Arithmetic, by a new method'

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7 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]
10. Modality / B. Possibility / 5. Contingency
6215 'Contingent' means that the cause is unperceived, not that there is no cause [Hobbes]
19. Language / A. Nature of Meaning / 7. Meaning Holism / c. Meaning by Role
18033 The meaning of a representation is its role in thought, perception or decisions [Block]