Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Lectures on Jurisprudence' and 'Human Knowledge: its scope and limits'

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


12 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 / E. Structures of Logic / 2. Logical Connectives / c. not
Is it possible to state every possible truth about the whole course of nature without using 'not'? [Russell]
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]
10. Modality / A. Necessity / 6. Logical Necessity
Some facts about experience feel like logical necessities [Russell]
12. Knowledge Sources / D. Empiricism / 5. Empiricism Critique
It is hard to explain how a sentence like 'it is not raining' can be found true by observation [Russell]
19. Language / F. Communication / 3. Denial
If we define 'this is not blue' as disbelief in 'this is blue', we eliminate 'not' as an ingredient of facts [Russell]
25. Social Practice / D. Justice / 2. The Law / d. Legal positivism
The existence of law is one thing, its merits and demerits another [Austin,J]
27. Natural Reality / A. Classical Physics / 1. Mechanics / a. Explaining movement
Russell's 'at-at' theory says motion is to be at the intervening points at the intervening instants [Russell, by Psillos]