Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Reply to Fourth Objections' and 'Explanation and 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 / a. Names
Using proper names properly doesn't involve necessary and sufficient conditions [Putnam]
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 / D. Essence of Objects / 5. Essence as Kind
Putnam bases essences on 'same kind', but same kinds may not share properties [Mackie,P on Putnam]
14. Science / B. Scientific Theories / 2. Aim of Science
Science aims at truth, not at 'simplicity' [Putnam]
17. Mind and Body / E. Mind as Physical / 6. Conceptual Dualism
The concept of mind excludes body, and vice versa [Descartes]
19. Language / B. Reference / 3. Direct Reference / b. Causal reference
I now think reference by the tests of experts is a special case of being causally connected [Putnam]
26. Natural Theory / B. Natural Kinds / 5. Reference to Natural Kinds
Natural kind stereotypes are 'strong' (obvious, like tiger) or 'weak' (obscure, like molybdenum) [Putnam]
Express natural kinds as a posteriori predicate connections, not as singular terms [Putnam, by Mackie,P]