Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'German Philosophy: a very short introduction' and 'Introduction to 'Language Truth and Logic''

expand these ideas     |    start again     |     specify just one area for these texts


17 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 / C. Knowing Reality / 3. Idealism / b. Transcendental idealism
Transcendental idealism aims to explain objectivity through subjectivity [Bowie]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / d. Absolute idealism
The Idealists saw the same unexplained spontaneity in Kant's judgements and choices [Bowie]
German Idealism tried to stop oppositions of appearances/things and receptivity/spontaneity [Bowie]
Crucial to Idealism is the idea of continuity between receptivity and spontaneous judgement [Bowie]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / c. Empirical foundations
Basic propositions refer to a single experience, are incorrigible, and conclusively verifiable [Ayer]
15. Nature of Minds / A. Nature of Mind / 4. Other Minds / c. Knowing other minds
The argument from analogy fails, so the best account of other minds is behaviouristic [Ayer]
19. Language / A. Nature of Meaning / 5. Meaning as Verification
A statement is meaningful if observation statements can be deduced from it [Ayer]
Directly verifiable statements must entail at least one new observation statement [Ayer]
The principle of verification is not an empirical hypothesis, but a definition [Ayer]
19. Language / D. Propositions / 1. Propositions
Sentences only express propositions if they are meaningful; otherwise they are 'statements' [Ayer]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / i. Prescriptivism
Moral approval and disapproval concerns classes of actions, rather than particular actions [Ayer]