Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'works' and 'Nietzsche's System'

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12 ideas

1. Philosophy / E. Nature of Metaphysics / 3. Metaphysical Systems
Metaphysics aims at the essence of things, and a system to show how this explains other truths [Richardson]
Metaphysics needs systems, because analysis just obsesses over details [Richardson]
Metaphysics generalises the data, to get at the ontology [Richardson]
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]
24. Political Theory / A. Basis of a State / 1. A People / a. Human distinctiveness
Humans dominate because, unlike other animals, they have a synthesis of conflicting drives [Richardson]
24. Political Theory / D. Ideologies / 1. Ideology
Ideology is 'socially necessary illusion' or 'socially necessary false-consciousness' [Adorno, by Finlayson]
26. Natural Theory / C. Causation / 7. Eliminating causation
A mind that could see cause and effect as a continuum would deny cause and effect [Richardson]