Combining Texts

All the ideas for 'fragments/reports', 'Principles of Arithmetic, by a new method' and 'The Case for Contextualism'

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12 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]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / a. Coherence as justification
19513 A contextualist coherentist will say that how strongly a justification must cohere depends on context [DeRose]
13. Knowledge Criteria / C. External Justification / 6. Contextual Justification / a. Contextualism
19514 Classical invariantism combines fixed truth-conditions with variable assertability standards [DeRose]
19515 We can make contextualism more precise, by specifying the discrimination needed each time [DeRose]
19510 In some contexts there is little more to knowledge than true belief. [DeRose]
19516 Contextualists worry about scepticism, but they should focus on the use of 'know' in ordinary speech [DeRose]
13. Knowledge Criteria / C. External Justification / 6. Contextual Justification / b. Invariantism
19511 If contextualism is about knowledge attribution, rather than knowledge, then it is philosophy of language [DeRose]
13. Knowledge Criteria / E. Relativism / 2. Knowledge as Convention
1556 By nature people are close to one another, but culture drives them apart [Hippias]