Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Material Constitution' and 'Principles of Arithmetic, by a new method'

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16 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]
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
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]
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
15653 We can add Reflexion Principles to Peano Arithmetic, which assert its consistency or soundness [Halbach on Peano]
17891 Arithmetical undecidability is always settled at the next stage up [Koellner]
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]
9. Objects / C. Structure of Objects / 6. Constitution of an Object
16065 Constitution is identity (being in the same place), or it isn't (having different possibilities) [Wasserman]
16067 Constitution is not identity, because it is an asymmetric dependence relation [Wasserman]
16069 There are three main objections to seeing constitution as different from identity [Wasserman]
9. Objects / C. Structure of Objects / 8. Parts of Objects / a. Parts of objects
16068 The weight of a wall is not the weight of its parts, since that would involve double-counting [Wasserman]
9. Objects / F. Identity among Objects / 3. Relative Identity
16074 Relative identity may reject transitivity, but that suggests that it isn't about 'identity' [Wasserman]