In the present day and age, Bob and Carl are hunting for emeralds. All the emeralds they find are green. Bob takes this as strong inductive support for the general conclusion that all emeralds are green. Carl takes this as strong inductive support for the conclusion that all emeralds are grue₂₀₂₂ (i.e. x is grue₂₀₂₂ iff x is first observed prior to Jan. 2022 and is green, or x is not first observed prior to Jan. 2022 and is blue).

1. (i) According to the standard Bayesian framework, what is required in order for Bob to be fully rational? How about Carl?

2. (ii) According to the standard Bayesian framework, is it possible for both Bob and Carl to be right about how the evidence supports their hypotheses? How?

3. (iii) Is this a problem for the Bayesian analysis of induction and confirmation theory? Explain why or why not.