Combining Philosophers

All the ideas for Eubulides, E Conee / R Feldman and Peter Koellner

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13 ideas

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]
5. Theory of Logic / L. Paradox / 1. Paradox
6007 If you know your father, but don't recognise your father veiled, you know and don't know the same person [Eubulides, by Dancy,R]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
6006 If you say truly that you are lying, you are lying [Eubulides, by Dancy,R]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / b. The Heap paradox ('Sorites')
6008 Removing one grain doesn't destroy a heap, so a heap can't be destroyed [Eubulides, by Dancy,R]
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]
11. Knowledge Aims / A. Knowledge / 4. Belief / c. Aim of beliefs
19525 If the only aim is to believe truths, that justifies recklessly believing what is unsupported (if it is right) [Conee/Feldman]
13. Knowledge Criteria / A. Justification Problems / 2. Justification Challenges / c. Knowledge closure
19524 We don't have the capacity to know all the logical consequences of our beliefs [Conee/Feldman]
13. Knowledge Criteria / B. Internal Justification / 3. Evidentialism / b. Evidentialism
19518 Evidentialism says justifications supervene on the available evidence [Conee/Feldman]
20. Action / C. Motives for Action / 3. Acting on Reason / c. Reasons as causes
19519 Rational decisions are either taken to be based on evidence, or to be explained causally [Conee/Feldman]