Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'The Basing Relation' and 'Introduction to a Secret Encyclopaedia'

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10 ideas

1. Philosophy / F. Analytic Philosophy / 2. Analysis by Division
13099 Analysing right down to primitive concepts seems beyond our powers [Leibniz]
3. Truth / A. Truth Problems / 8. Subjective Truth
5022 We hold a proposition true if we are ready to follow it, and can't see any objections [Leibniz]
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]
11. Knowledge Aims / A. Knowledge / 4. Belief / a. Beliefs
19696 There are reasons 'for which' a belief is held, reasons 'why' it is believed, and reasons 'to' believe it [Neta]
19697 The basing relation of a reason to a belief should both support and explain the belief [Neta]