Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Summula philosophiae naturalis' and 'Reality without Reference'

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14 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 / E. Categories / 5. Category Anti-Realism
Ockham was an anti-realist about the categories [William of Ockham, by Pasnau]
9. Objects / C. Structure of Objects / 4. Quantity of an Object
Ockham says matter must be extended, so we don't need Quantity [William of Ockham, by Pasnau]
Matter gets its quantity from condensation and rarefaction, which is just local motion [William of Ockham]
19. Language / A. Nature of Meaning / 1. Meaning
A minimum requirement for a theory of meaning is that it include an account of truth [Davidson]
19. Language / A. Nature of Meaning / 4. Meaning as Truth-Conditions
A theory of truth tells us how communication by language is possible [Davidson]
19. Language / B. Reference / 1. Reference theories
Is reference the key place where language and the world meet? [Davidson]
With a holistic approach, we can give up reference in empirical theories of language [Davidson]
19. Language / B. Reference / 4. Descriptive Reference / b. Reference by description
To explain the reference of a name, you must explain its sentence-role, so reference can't be defined nonlinguistically [Davidson]