Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Explanations in reply to Mr Bradley' and 'The Doctrine of Necessity Examined'

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11 ideas

1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / a. Philosophy as worldly
Philosophers should be more inductive, and test results by their conclusions, not their self-evidence [Russell]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner]
'Reflection principles' say the whole truth about sets can't be captured [Koellner]
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
We have no argument to show a statement is absolutely undecidable [Koellner]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
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
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
Arithmetical undecidability is always settled at the next stage up [Koellner]
10. Modality / B. Possibility / 7. Chance
Is chance just unknown laws? But the laws operate the same, whatever chance occurs [Peirce]
22. Metaethics / B. Value / 2. Values / e. Death
Is there any such thing as death among the lower organisms? [Peirce]
26. Natural Theory / D. Laws of Nature / 4. Regularities / a. Regularity theory
If the world is just mechanical, its whole specification has no more explanation than mere chance [Peirce]
26. Natural Theory / D. Laws of Nature / 11. Against Laws of Nature
The more precise the observations, the less reliable appear to be the laws of nature [Peirce]