Which term refers to a continued belief despite proof against it?

The term that best describes a continued belief despite evidence contradicting it is "delusion." Delusions are fixed false beliefs that are resistant to reason or confrontation with actual fact, often seen in various mental health disorders, including schizophrenia. A person experiencing a delusion firmly maintains this belief even in the face of compelling evidence that should logically lead them to alter their view.

In contrast, hallucinations involve perceiving things that are not present in reality, such as hearing voices or seeing things that do not exist. Illusions refer to misinterpretations of real sensory stimuli, where the perception is distorted but the object is present. Mood disorders encompass a broader category of mental health issues that primarily influence a person's emotional state, such as depression or bipolar disorder, but are not directly related to belief systems like delusions are. Understanding these distinctions clarifies why "delusion" is the most appropriate term for the question posed.