A falsely held belief that persists in spite of evidence contrary to the belief is formally called a:

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A delusion is a false belief that is not based in reality and persists despite evidence to the contrary. Hallucinations involve perceiving things that are not actually present, negative symptoms of schizophrenia refer to a lack or decrease in normal behaviors or emotions, and dissociation refers to a detachment from reality.

A Falsely Held Belief That Persists in Spite of Evidence