Mind wandering is typically operationalized as task-unrelated thought. Some argue for the need to distinguish between unintentional and intentional mind wandering, where an agent voluntarily shifts attention from task-related to task-unrelated thoughts. We reveal an inconsistency between the standard, task-unrelated thought definition of mind wandering and the occurrence of intentional mind wandering (together with plausible assumptions about tasks and intentions). This suggests that either the standard definition of mind wandering should be rejected or that intentional mind wandering is an incoherent category. Solving this puzzle is critical for advancing theoretical frameworks of mind wandering.