Guiding Questions for Picollo & Schindler's "Disquotation and Infinite Conjunctions"
1. What is the infinite conjunction function of truth?
2. When does the truth predicate play a logical role? When does it play an epistemic role? Are they mutually exclusive?
3. Why wouldn’t it be entirely correct to talk about logics of truth?
4. What are the main questions the paper focuses on? Is there any connection between them?
5. What is the usual answer to questions 1?
6. What does the equivalence answer to question 2 consist in?
7. Why is the equivalence account not satisfactory? Can it be patched turning to the omega-rule or the standard model? Why?
8. What’s the finite axiomatisation account consist in? Does it work in the typed case? What about the untyped case?
9. Does the finite axiomatisation account support the adoption of introduction principles for truth? Why?
10. What is the elimination property of truth?
11. What are the minimal requirements a formal theory of truth should satisfy to have this property? Could the underlying logic be classical?
12. Could the theory contain elimination truth principles but not the elimination property? Give an example.
13. How do the authors deal with Jones’ counterexample given by Field?
14. Can the strategy from the previous question be applied to cases like (6) and (9)? What are the drawbacks?
15. Can elimination principles alone handle infinite disjunctions as they handle infinite conjunctions? How?
16. What is deflationism?
17. What are the constrains a deflationist formal theory of truth must obey? Are the paradoxes a special problem for deflationism?
18. Why can’t classical truth theories that have the elimination property express agreement with their own theorems via a reflection principle? How can this be done otherwise?