Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'The Barcan Formula and Metaphysics' and 'An American Indian model of the Universe'

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13 ideas

4. Formal Logic / D. Modal Logic ML / 7. Barcan Formula
The Barcan Formulas express how to combine modal operators with classical quantifiers [Simchen]
The Barcan Formulas are orthodox, but clash with the attractive Actualist view [Simchen]
BF implies that if W possibly had a child, then something is possibly W's child [Simchen]
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]
10. Modality / E. Possible worlds / 1. Possible Worlds / d. Possible worlds actualism
Serious Actualism says there are no facts at all about something which doesn't exist [Simchen]
13. Knowledge Criteria / E. Relativism / 5. Language Relativism
Hopi consistently prefers verbs and events to nouns and things [Whorf]
14. Science / B. Scientific Theories / 4. Paradigm
Scientific thought is essentially a specialised part of Indo-European languages [Whorf]
27. Natural Reality / D. Time / 2. Passage of Time / e. Tensed (A) series
The Hopi have no concept of time as something flowing from past to future [Whorf]