Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Deriving Kripkean Claims with Abstract Objects' and 'The Case for Contextualism'

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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]
9. Objects / A. Existence of Objects / 2. Abstract Objects / a. Nature of abstracta
Abstract objects are actually constituted by the properties by which we conceive them [Zalta]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / a. Coherence as justification
A contextualist coherentist will say that how strongly a justification must cohere depends on context [DeRose]
13. Knowledge Criteria / C. External Justification / 6. Contextual Justification / a. Contextualism
Classical invariantism combines fixed truth-conditions with variable assertability standards [DeRose]
We can make contextualism more precise, by specifying the discrimination needed each time [DeRose]
In some contexts there is little more to knowledge than true belief. [DeRose]
Contextualists worry about scepticism, but they should focus on the use of 'know' in ordinary speech [DeRose]
13. Knowledge Criteria / C. External Justification / 6. Contextual Justification / b. Invariantism
If contextualism is about knowledge attribution, rather than knowledge, then it is philosophy of language [DeRose]
18. Thought / E. Abstraction / 2. Abstracta by Selection
Abstract objects are captured by second-order modal logic, plus 'encoding' formulas [Zalta]