Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'The Ages of the World' and 'The Problem of the Essential Indexical'

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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]
11. Knowledge Aims / A. Knowledge / 4. Belief / b. Elements of beliefs
Indexicals are a problem for beliefs being just subject-proposition relations [Perry]
19. Language / C. Assigning Meanings / 9. Indexical Semantics
If we replace 'I' in sentences about me, they are different beliefs and explanations of behaviour [Perry]
Indexicals individuate certain belief states, helping in explanation and prediction [Perry]
19. Language / D. Propositions / 6. Propositions Critique
Indexicals reveal big problems with the traditional idea of a proposition [Perry]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / e. Character
We don't choose our characters, yet we still claim credit for the actions our characters perform [Schelling]
27. Natural Reality / D. Time / 2. Passage of Time / c. Tenses and time
Tense is essential for thought and action [Perry, by Le Poidevin]
Actual tensed sentences cannot be tenseless, because they can cite their own context [Perry, by Le Poidevin]