Species evolve by natural selection. Lemurs have toes. Both of these propositions are true, but the first is far more important to science because, as Darwin himself stated, it explains a great number of previously unconnected facts. It is obvious that explanatory coherence furthers the adoption of theories that encourage explanatory unification, because its principle of data priority, E4, encourages the acceptance of observation propositions, and its principle of explanation, E2, encourages the acceptance of hypotheses that explain many observations. Scientists have achieved theories that are at least approximately true.
Scientists use explanatory coherence.
So explanatory coherence leads to theories that are at least approximately true. Premise 1 is supported primarily by the technological applicability of theories in the natural sciences, and premise 2 is supported by computational modeling of many important historical cases of scientific reasoning. We should not expect a direct defense of the truth achievement of any non-trivial inductive method, so the indirectness of the defense of explanatory coherence as a generator of scientific truths does not undermine coherentism. Let me now address several of Millgram's minor objections to coherence construed as constraint satisfaction. According to principle E2b, hypotheses that together explain a proposition cohere with each other, so there is a positive constraint between them.