Combining Texts

All the ideas for 'fragments/reports', 'The Raft and the Pyramid' and 'Mathematical logic and theory of types'

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16 ideas

2. Reason / A. Nature of Reason / 6. Coherence
The negation of all my beliefs about my current headache would be fully coherent [Sosa]
4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
Classes can be reduced to propositional functions [Russell, by Hanna]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / d. Russell's paradox
The class of classes which lack self-membership leads to a contradiction [Russell, by Grayling]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
Type theory seems an extreme reaction, since self-exemplification is often innocuous [Swoyer on Russell]
Russell's improvements blocked mathematics as well as paradoxes, and needed further axioms [Russell, by Musgrave]
Type theory means that features shared by different levels cannot be expressed [Morris,M on Russell]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
Ramified types can be defended as a system of intensional logic, with a 'no class' view of sets [Russell, by Linsky,B]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
A set does not exist unless at least one of its specifications is predicative [Russell, by Bostock]
Russell is a conceptualist here, saying some abstracta only exist because definitions create them [Russell, by Bostock]
Vicious Circle says if it is expressed using the whole collection, it can't be in the collection [Russell, by Bostock]
12. Knowledge Sources / E. Direct Knowledge / 1. Common Sense
There are very few really obvious truths, and not much can be proved from them [Sosa]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / e. Pro-foundations
A single belief can trail two regresses, one terminating and one not [Sosa]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / f. Foundationalism critique
If mental states are not propositional, they are logically dumb, and cannot be foundations [Sosa]
Mental states cannot be foundational if they are not immune to error [Sosa]
13. Knowledge Criteria / C. External Justification / 2. Causal Justification
Vision causes and justifies beliefs; but to some extent the cause is the justification [Sosa]
13. Knowledge Criteria / E. Relativism / 2. Knowledge as Convention
By nature people are close to one another, but culture drives them apart [Hippias]