When a particular explanation is both good and much better than any competitor, and when the explained observation is accurate, then an inference to the best explanation will provide strong inductive support. At other times, no clear winner or even reasonable contender emerges. In such cases, an inference to the best explanation will be correspondingly weak.
Whether an inference to the best explanation is strong enough depends on the context. As contexts shift, standards of rigor can change. Evidence that is strong enough to justify my belief that my spouse took our car might not be strong enough to convict our neighbor of stealing our car. Good judgment is often required to determine whether a certain degree of strength is adequate for the purposes at hand.
Context can also affect the rankings of various factors. Many explanations, for example, depend on universal premises. In such cases, compatibility with observation is usually the primary test. The universal principle should not be refuted by counterexamples. But sometimes explanatory power will take precedence: If a principle has strong explanatory power, we may accept it even in the face of clear disconfirming evidence. We do not give up good explanations lightly—nor should we. To understand why, recall (from Chapter 9) that we do not test single propositions in isolation from other propositions in our system of beliefs. When faced with counterevidence to our beliefs, we often have a choice between what to give up and what to continue to hold on to.