Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Metaphysics as a Guide to Morals' and 'The Essence of Reference'

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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 / F. Referring in Logic / 1. Naming / e. Empty names
It is best to say that a name designates iff there is something for it to designate [Sainsbury]
5. Theory of Logic / F. Referring in Logic / 2. Descriptions / b. Definite descriptions
Definite descriptions may not be referring expressions, since they can fail to refer [Sainsbury]
Definite descriptions are usually rigid in subject, but not in predicate, position [Sainsbury]
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]
15. Nature of Minds / C. Capacities of Minds / 6. Idealisation
We know perfection when we see what is imperfect [Murdoch]
19. Language / B. Reference / 3. Direct Reference / b. Causal reference
A new usage of a name could arise from a mistaken baptism of nothing [Sainsbury]
19. Language / B. Reference / 5. Speaker's Reference
Even a quantifier like 'someone' can be used referentially [Sainsbury]
26. Natural Theory / A. Speculations on Nature / 3. Natural Function
Things are thought to have a function, even when they can't perform them [Sainsbury]