Combining Texts

All the ideas for 'Idealism: a critical survey', 'Without Immediate Justification' and 'Principles of Arithmetic, by a new method'

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12 ideas

6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
All models of Peano axioms are isomorphic, so the models all seem equally good for natural numbers [Cartwright,R on Peano]
PA concerns any entities which satisfy the axioms [Peano, by Bostock]
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
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
Arithmetic can have even simpler logical premises than the Peano Axioms [Russell on Peano]
13. Knowledge Criteria / A. Justification Problems / 2. Justification Challenges / a. Agrippa's trilemma
Coherentists say that regress problems are assuming 'linear' justification [Williams,M]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / a. Foundationalism
Traditional foundationalism is radically internalist [Williams,M]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / b. Basic beliefs
Basic judgements are immune from error because they have no content [Williams,M]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / c. Empirical foundations
Sensory experience may be fixed, but it can still be misdescribed [Williams,M]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / b. Pro-coherentism
We can no more expect a precise definition of coherence than we can of the moral ideal [Ewing]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / c. Coherentism critique
If undetailed, 'coherence' is just a vague words that covers all possible arguments [Ewing]
13. Knowledge Criteria / C. External Justification / 10. Anti External Justification
In the context of scepticism, externalism does not seem to be an option [Williams,M]