Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Reflections on Knowledge, Truth and Ideas' and 'How to Russell a Frege-Church'

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14 ideas

2. Reason / D. Definition / 1. Definitions
'Nominal' definitions just list distinguishing characteristics [Leibniz]
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 / 2. Descriptions / c. Theory of definite descriptions
For Russell, expressions dependent on contingent circumstances must be eliminated [Kaplan]
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]
10. Modality / E. Possible worlds / 3. Transworld Objects / d. Haecceitism
'Haecceitism' says that sameness or difference of individuals is independent of appearances [Kaplan]
'Haecceitism' is common thisness under dissimilarity, or distinct thisnesses under resemblance [Kaplan]
If quantification into modal contexts is legitimate, that seems to imply some form of haecceitism [Kaplan]
11. Knowledge Aims / A. Knowledge / 1. Knowledge
Knowledge needs clarity, distinctness, and adequacy, and it should be intuitive [Leibniz]
18. Thought / C. Content / 2. Ideas
True ideas represent what is possible; false ideas represent contradictions [Leibniz]
26. Natural Theory / C. Causation / 2. Types of cause
In the schools the Four Causes are just lumped together in a very obscure way [Leibniz]