What is defined as a belief with no basis in reality?

A belief with no basis in reality is accurately defined as a delusion. Delusions are fixed, false beliefs that are resistant to reasoning or confrontation with actual facts. These beliefs often stem from various psychological conditions and can significantly impair an individual's ability to function normally.

Delusions can manifest in many forms, such as beliefs of persecution, grandeur, or control. The critical feature that distinguishes delusions from other types of false perceptions or beliefs is their persistence and the individual's conviction in their truth, despite clear evidence to the contrary.

In contrast, hallucinations involve perceiving something (e.g., hearing voices or seeing things) that isn't present in the environment, which does not pertain to beliefs but rather to sensory experiences. Melancholia refers to a state of deep sadness or severe depression, and mania is characterized by an abnormally elevated mood, energy levels, and impulsivity. These terms do not capture the essence of a false belief as well as delusion does.