We investigated the effect of goal specificity on a search in a hypothesis space based on the dual space search theory. Rule induction and scientific discovery have been studied based on the dual space search theory. The processes of scientific discovery and rule induction develop through the interaction between two types of searches in the two spaces: in a “hypothesis space” for searching hypotheses and in an “instance space” for testing hypotheses (Simon & Lea, 1974; Klahr & Dunbar, 1988). The search in a hypothesis space is crucial for scientific discovery. However, we tend not to search in a hypothesis space when we aim for a specific goal. In such case, we concentrate on a search in an instance space to achieve the goal. The earlier studies have shown that problem-solvers given a specific goal learn more poorly then problem-solvers given a nonspecific goal (e.g., Sweller & Levine, 1982). Burns and Vollmeyer (2002) explained that this difference was due to the effect of goal specificity on a search in a hypothesis space. A nonspecific goal encourages the participants to search actively in a hypothesis space. Therefore, a nonspecific goal may lead to better learning than a specific goal. In this study, we define the hypothesis space in which the participants initially search as an “initial hypothesis space,” and the hypothesis space containing a target rule to be discovered as a “target hypothesis space.” In the preceding studies, the initial hypothesis space was given by an experimenter. Furthermore, this initial hypothesis was identical to the target space because it contained a target rule to be discovered. It is a rare case that the factors to be considered are previously given. We used the task in which the participants needed to find the target hypothesis space in order to discover an appropriate rule. Using this task, we investigated the effect of goal specificity in the situations where a shift of a hypothesis space was needed to discover the target rule. In addition, the effect of an initial hypothesis space on the effect of goal specificity was investigated. Two hypotheses were considered in the two situations: the situation where the initial hypothesis space, but not the target space, was shown (initial space situation), and not shown (no initial space situation). Hypothesis 1: A nonspecific goal facilitates a search in a hypothesis space more than a specific goal does. Hypothesis 2: As a hypothesis space is more searched, the performance in discovering the target rule improves. We conducted four experiments manipulating goal specificity and an existence of the initial hypothesis space. As a result, we found that the effect of goal specificity on a search in a hypothesis space depended on whether or not the participants noticed an initial hypothesis space. When an initial hypothesis space was offered, a nonspecific goal actually facilitated a search in the hypothesis space. By contrast, the goal specificity effect was not confirmed when no initial hypothesis space was offered. We also found that the facilitation of the hypothesis space search improved the performance in discovering the target rule.