Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'A Short History of German Philosophy' and 'Proper Names'

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13 ideas

1. Philosophy / E. Nature of Metaphysics / 3. Metaphysical Systems
Early Romantics sought a plurality of systems, in a quest for freedom [Hösle]
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 / F. Referring in Logic / 1. Naming / b. Names as descriptive
We don't normally think of names as having senses (e.g. we don't give definitions of them) [Searle]
How can a proper name be correlated with its object if it hasn't got a sense? [Searle]
'Aristotle' means more than just 'an object that was christened "Aristotle"' [Searle]
Reference for proper names presupposes a set of uniquely referring descriptions [Searle]
Proper names are logically connected with their characteristics, in a loose way [Searle]
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]
25. Social Practice / E. Policies / 5. Education / d. Study of history
In the 18th century history came to be seen as progressive, rather than cyclical [Hösle]