There are a number of interesting potential PhD projects in this area:
- Indeterminate belief and belief in indeterminacy.
- Nonclassical decision theory.
- Generalized confirmation theory.
Philosophy of logic
- The cognitive significance of nonlinear truth values.
- Intuitionism, rejection and agnosticism
- Rational uncertainty about logic.
Please contact me to discuss your ideas—on these or other topics in the area!