 Condition-independence says that the mere addition of a new observation condition \(c_{k+1}\), without specifying one of its outcomes, does not alter the likelihood of the outcomes \(e^k\) of other experiments \(c^k\). To appreciate the significance of this condition, imagine what it would be like if it were violated. Suppose hypothesis \(h_j\) is some statistical theory, say, for example, a quantum theory of superconductivity. The conditions expressed in \(c^k\) describe a number of experimental setups, perhaps conducted in numerous labs throughout the world, that test a variety of aspects of the theory (e.g., experiments that test electrical conductivity in different materials at a range of temperatures). An outcome sequence \(e^k\) describes the results of these experiments. The violation of condition-independence would mean that merely adding to \(h_{j}\cdot b\cdot c^{k}\) a statement \(c_{k+1}\) describing how an additional experiment has been set up, but with no mention of its outcome, changes how likely the evidence sequence \(e^k\) is taken to be. What \((h_j\cdot b)\) says via likelihoods about the outcomes \(e^k\) of experiments \(c^k\) differs as a result of merely supplying a description of another experimental arrangement, \(c_{k+1}\). Condition-independence, when it holds, rules out such strange effects.