Combining Texts

All the ideas for 'Laches', 'Syntactic Structure' and 'Principles of Arithmetic, by a new method'

expand these ideas     |    start again     |     specify just one area for these texts

9 ideas

1. Philosophy / A. Wisdom / 3. Wisdom Deflated
291 Don't assume that wisdom is the automatic consequence of old age [Plato]
2. Reason / F. Fallacies / 8. Category Mistake / c. Category mistake as semantic
18009 Chomsky established the view that category mistakes are well-formed but meaningless [Chomsky, by Magidor]
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]
19. Language / C. Assigning Meanings / 1. Syntax
18007 Syntax is independent of semantics; sentences can be well formed but meaningless [Chomsky, by Magidor]
23. Ethics / C. Virtue Theory / 3. Virtues / d. Courage
293 Being unafraid (perhaps through ignorance) and being brave are two different things [Plato]