When people make inferences about other people's minds, called theory of mind (ToM), a network in the cerebral cortex becomes active. ToM experiments sometimes use the false belief task, in which subjects decide whether a story character believes A or B. The "false" belief occurs if the character believes A when B is true. We devised a version in which subjects judged whether a cartoon head "believed" a ball to be in box 1 or box 2. The task was a visual, reaction time version of a ToM task. We proposed two alternative hypotheses. In hypothesis 1, cortical regions of interest within the ToM network should distinguish between false and true belief trials, reflecting outside information that the subjects have about the cartoon character. In hypothesis 2, the ToM network should distinguish between conditions only if the subjects think that the cartoon character can distinguish between the conditions, thus reflecting a model of the internal contents of the cartoon character's mind. The results supported hypothesis 2. Events that the cartoon could not "see" did not affect activity in the ToM network; the same events, when the cartoon could apparently "see" them, significantly affected activity in the right temporoparietal junction (TPJ). The results support the view that the right TPJ participates in modeling the mental states of others, rather than in evaluating the accuracy of the beliefs of others, and may help explain why previous experiments showed mixed results when directly comparing false belief to true belief conditions.