Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Life of Pythagoras' and 'There Are No Abstract Objects'

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10 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
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]
8. Modes of Existence / E. Nominalism / 1. Nominalism / c. Nominalism about abstracta
14596 Call 'nominalism' the denial of numbers, properties, relations and sets [Dorr]
8. Modes of Existence / E. Nominalism / 5. Class Nominalism
14597 Natural Class Nominalism says there are primitive classes of things resembling in one respect [Dorr]
10. Modality / A. Necessity / 11. Denial of Necessity
14598 Abstracta imply non-logical brute necessities, so only nominalists can deny such things [Dorr]
28. God / A. Divine Nature / 6. Divine Morality / b. Euthyphro question
1515 Pythagoreans believe it is absurd to seek for goodness anywhere except with the gods [Iamblichus]