<p>Curiosity raises a basic problem: how can a mind represent what it does not yet know so that inquiry can begin and be guided? I propose Indefinite Targeting, a flexible template of the form “an F that meets condition C”. It licenses search while allowing parameters and even kind labels to be revised as evidence accrues. The account explains three stable features of practice that strain the idea that a definite description is the basic target format: large initial misdescription (Neptune), principled negative endings (Vulcan), and non-unique outcomes (a two-thieves scenario). To avoid trivializing inquiry, I formulate norms for topic continuity and stopping: preserve a core causal or explanatory role; license changes by evidence; prefer minimal disturbance; and count empty or multiple extensions as completion under adequate tests. From this base, I derive two attitude types with distinct success conditions: Object Curiosity, which aims at property fixation, and Network Curiosity, which aims at building a holistic, interconnected model of a topic.</p>