Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'The Middle Works (15 vols, ed Boydston)' and 'Why Propositions cannot be concrete'

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16 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 / 3. Value of Knowledge
The value and truth of knowledge are measured by success in activity [Dewey]
16. Persons / B. Nature of the Self / 1. Self and Consciousness
Habits constitute the self [Dewey]
18. Thought / E. Abstraction / 1. Abstract Thought
The idea of abstract objects is not ontological; it comes from the epistemological idea of abstraction [Plantinga]
Theists may see abstract objects as really divine thoughts [Plantinga]
19. Language / D. Propositions / 3. Concrete Propositions
If propositions are concrete they don't have to exist, and so they can't be necessary truths [Plantinga]
19. Language / D. Propositions / 4. Mental Propositions
Propositions can't just be in brains, because 'there are no human beings' might be true [Plantinga]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / e. Character
The good people are those who improve; the bad are those who deteriorate [Dewey]
24. Political Theory / D. Ideologies / 5. Democracy / a. Nature of democracy
Democracy is the development of human nature when it shares in the running of communal activities [Dewey]
Democracy is not just a form of government; it is a mode of shared living [Dewey]
24. Political Theory / D. Ideologies / 6. Liberalism / b. Liberal individualism
Individuality is only developed within groups [Dewey]