Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Theology and Verification' and 'Many, but almost one'

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13 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 / D. Theories of Reality / 10. Vagueness / d. Vagueness as linguistic
Semantic indecision explains vagueness (if we have precisifications to be undecided about) [Lewis]
9. Objects / B. Unity of Objects / 3. Unity Problems / b. Cat and its tail
If cats are vague, we deny that the many cats are one, or deny that the one cat is many [Lewis]
9. Objects / B. Unity of Objects / 3. Unity Problems / e. Vague objects
We have one cloud, but many possible boundaries and aggregates for it [Lewis]
19. Language / F. Communication / 6. Interpreting Language / c. Principle of charity
Basic to pragmatics is taking a message in a way that makes sense of it [Lewis]
29. Religion / D. Religious Issues / 1. Religious Commitment / c. Religious Verification
Belief in an afterlife may be unverifiable in this life, but it will be verifiable after death [Hick, by PG]
It may be hard to verify that we have become immortal, but we could still then verify religious claims [Hick, by PG]
29. Religion / D. Religious Issues / 1. Religious Commitment / d. Religious Falsification
Some things (e.g. a section of the expansion of PI) can be verified but not falsified [Hick, by PG]