Combining Texts

All the ideas for 'On Certainty', 'The Philosophical Culture' and 'Principles of Arithmetic, by a new method'

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

9 ideas

1. Philosophy / G. Scientific Philosophy / 3. Scientism
1489 Modern philosophy tends to be a theory-constructing extension of science, but there is also problem-solving [Nagel]
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]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / a. Foundationalism
3597 Foundations need not precede other beliefs [Wittgenstein]
13. Knowledge Criteria / D. Scepticism / 6. Scepticism Critique
3596 Total doubt can't even get started [Wittgenstein, by Williams,M]
19. Language / A. Nature of Meaning / 10. Denial of Meanings
4721 If you are not certain of any fact, you cannot be certain of the meaning of your words either [Wittgenstein]