Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'The Barcan Formula and Metaphysics' and 'Apriority as an Evaluative Notion'

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17 ideas

2. Reason / F. Fallacies / 4. Circularity
Maybe reasonableness requires circular justifications - that is one coherentist view [Field,H]
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]
12. Knowledge Sources / A. A Priori Knowledge / 6. A Priori from Reason
Lots of propositions are default reasonable, but the a priori ones are empirically indefeasible [Field,H]
12. Knowledge Sources / A. A Priori Knowledge / 7. A Priori from Convention
We treat basic rules as if they were indefeasible and a priori, with no interest in counter-evidence [Field,H]
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / a. Reliable knowledge
Reliability only makes a rule reasonable if we place a value on the truth produced by reliable processes [Field,H]
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / b. Anti-reliabilism
Believing nothing, or only logical truths, is very reliable, but we want a lot more than that [Field,H]
13. Knowledge Criteria / C. External Justification / 6. Contextual Justification / a. Contextualism
People vary in their epistemological standards, and none of them is 'correct' [Field,H]
14. Science / C. Induction / 1. Induction
If we only use induction to assess induction, it is empirically indefeasible, and hence a priori [Field,H]