This chapter highlights the central importance of modal dimensions of the nature of knowledge. It focuses on several value problems regarding knowledge, describing the logical landscape of value issues and identifying a special value problem that concerns the relationship between knowledge and its parts. The chapter uses this problem to motivate taking seriously probabilistic accounts of truth-tracking and sensitivity over standard counterfactual approaches. This approaches described here rely on the three-place relation, since they offer stories that are at least initially plausible concerning the nature of knowledge. The probabilistic approach to truth-tracking shows significant promise, and can be used as well to address the original Meno problem concerning the value of knowledge over true opinion. The conclusion to draw from the discussion is that theories of knowledge that rely on sensitivity and truth-tracking conditions can go some distance toward explaining the value of knowledge, but not the entire distance.