Combining Texts

All the ideas for 'Theory of Knowledge (2nd edn)', 'The Actual and the Virtual' and 'On the Question of Absolute Undecidability'

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9 ideas

1. Philosophy / C. History of Philosophy / 4. Later European Philosophy / b. Seventeenth century philosophy

2945	Most philosophers start with reality and then examine knowledge; Descartes put the study of knowledge first [Lehrer]

1. Philosophy / F. Analytic Philosophy / 4. Conceptual Analysis

2946	You cannot demand an analysis of a concept without knowing the purpose of the analysis [Lehrer]

4. Formal Logic / F. Set Theory ST / 1. Set Theory

17884

Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner]

17893

'Reflection principles' say the whole truth about sets can't be captured [Koellner]

5. Theory of Logic / K. Features of Logics / 5. Incompleteness

17894

We have no argument to show a statement is absolutely undecidable [Koellner]

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity

17890

There are at least eleven types of large cardinal, of increasing logical strength [Koellner]

6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic

17887

PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner]

6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic

17891

Arithmetical undecidability is always settled at the next stage up [Koellner]

7. Existence / E. Categories / 5. Category Anti-Realism

21907

We don't want another new set of categories; we want a variety of flexible categories [Deleuze, by May]