Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Letters to Russell' and 'Five Milestones of Empiricism'

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14 ideas

1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined
The main problem of philosophy is what can and cannot be thought and expressed [Wittgenstein, by Grayling]
2. Reason / D. Definition / 7. Contextual Definition
Contextual definition shifted the emphasis from words to whole sentences [Quine]
Bentham's contextual definitions preserved terms after their denotation became doubtful [Quine]
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]
7. Existence / C. Structure of Existence / 6. Fundamentals / d. Logical atoms
Atomic facts correspond to true elementary propositions [Wittgenstein]
12. Knowledge Sources / D. Empiricism / 1. Empiricism
In scientific theories sentences are too brief to be independent vehicles of empirical meaning [Quine]
Empiricism improvements: words for ideas, then sentences, then systems, then no analytic, then naturalism [Quine]
19. Language / D. Propositions / 4. Mental Propositions
A thought is mental constituents that relate to reality as words do [Wittgenstein]
19. Language / E. Analyticity / 4. Analytic/Synthetic Critique
Holism in language blurs empirical synthetic and empty analytic sentences [Quine]