Import of Background Assumptions. The characterization result draws a line between the solvable and unsolvable problems. Background knowledge reduces the inductive complexity of a problem; with enough background knowledge, the problem crosses the threshold between the unsolvable and the solvable. In many domains of empirical inquiry, the pivotal background assumptions are those that make reliable inquiry feasible. (Kuhn [1970] makes related points about the importance of background assumptions embodied in a “paradigm”).