Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Two treatises' and 'What is the Basis of Moral Obligation?'

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12 ideas

1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / d. Philosophy as puzzles
In philosophy the truth can only be reached via the ruins of the false [Prichard]
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]
9. Objects / C. Structure of Objects / 4. Quantity of an Object
Quantity is the capacity to be divided [Digby]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / c. Particularism
I see the need to pay a debt in a particular instance, and any instance will do [Prichard]
The complexities of life make it almost impossible to assess morality from a universal viewpoint [Prichard]
23. Ethics / D. Deontological Ethics / 2. Duty
Seeing the goodness of an effect creates the duty to produce it, not the desire [Prichard]
26. Natural Theory / A. Speculations on Nature / 7. Later Matter Theories / b. Corpuscles
Colours arise from the rarity, density and mixture of matter [Digby]