 So one way of applying the PoI leads to inductive skepticism, the other yields the inductive optimism that seems so indispensable to science and daily life. If we could clarify how the PoI should be applied, and justify its use, we would have our answer to Hume’s problem (or at least the first half—we still have to address the issue of using conditional probabilities as a guide to new, unconditional probabilities). Can it be clarified and justified?