Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'De arcanus motus' and 'Collins Dictionary of Philosophy'

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9 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 / C. Powers and Dispositions / 1. Powers

12733

Because of the definitions of cause, effect and power, cause and effect have the same power [Leibniz]

10. Modality / A. Necessity / 2. Nature of Necessity

12734

Every necessary proposition is demonstrable to someone who understands [Leibniz]

12. Knowledge Sources / B. Perception / 4. Sense Data / b. Nature of sense-data

6457	Sensations are mental, but sense-data could be mind-independent [Vesey]