Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'fragments/reports' and 'The Road to Serfdom'

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13 ideas

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]
7. Existence / A. Nature of Existence / 3. Being / a. Nature of Being
Being is one [Melissus, by Aristotle]
24. Political Theory / D. Ideologies / 8. Socialism
Socialist economics needs a very strong central power, virtually leading to slavery [Hayek, by Oksala]
25. Social Practice / A. Freedoms / 4. Free market
Hayek was a liberal, but mainly concerned with market freedom [Hayek, by Dunt]
Impeding the market is likely to lead to extensive state control [Hayek]
27. Natural Reality / A. Classical Physics / 1. Mechanics / a. Explaining movement
There is no real motion, only the appearance of it [Melissus, by Diog. Laertius]
27. Natural Reality / C. Space / 1. Void
The void is not required for change, because a plenum can alter in quality [Aristotle on Melissus]
27. Natural Reality / E. Cosmology / 2. Eternal Universe
Nothing could come out of nothing [Melissus]