Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'The Structure and Content of Truth' and 'Speaking of Objects'

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14 ideas

3. Truth / C. Correspondence Truth / 3. Correspondence Truth critique
Correspondence theories can't tell you what truths correspond to [Davidson]
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 / 7. Abstract/Concrete / a. Abstract/concrete
We can only see an alien language in terms of our own thought structures (e.g. physical/abstract) [Quine]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / b. Commitment of quantifiers
"No entity without identity" - our ontology must contain items with settled identity conditions [Quine, by Melia]
8. Modes of Existence / B. Properties / 12. Denial of Properties
There is no proper identity concept for properties, and it is hard to distinguish one from two [Quine]
9. Objects / A. Existence of Objects / 2. Abstract Objects / b. Need for abstracta
Our conceptual scheme becomes more powerful when we posit abstract objects [Quine]
9. Objects / A. Existence of Objects / 5. Individuation / a. Individuation
I prefer 'no object without identity' to Quine's 'no entity without identity' [Lowe on Quine]
19. Language / F. Communication / 6. Interpreting Language / b. Indeterminate translation
You could know the complete behavioural conditions for a foreign language, and still not know their beliefs [Quine]
Translation of our remote past or language could be as problematic as alien languages [Quine]