The Muller-Luyer diagram  has been a favorite of psychology textbooks for many years. The two figures are usually presented as a visual illusion. The upper line looks longer than the bottom. If you take ruler and measure both lines, they are the same.  Even when you know the lines are the same length, they continue to look different. The apparent line-length difference is stable and enduring over time and all observers who see these two figures come to the same conclusion.

Illusions are clues to the deeply imbedded features of perception and cognition. On one level, we recognize that our visual systems can misrepresent the world. On another level, we can appreciate what built-in bias or preconception produces the illusion. We can also recognize that there is a natural level of perception  and cognition that is burdened with illusions and other errors and a meta level of knowledge that detects and understands these illusions and errors.

A belief  is hard to define with any accuracy because beliefs are necessarily fuzzy. Beliefs are usually expressed in words and supported by stories. The word “belief “describes a fuzzy cognitive state, which can vary from an arbitrary story with little or no basis in experience, to a somewhat reasonable conclusion derived from limited information. The expression "seeing is believing" suggests that direct experience is more convincing than facsimiles of experiences such as a story; but what then is a belief?

A scientist who has measured the amount of mercury in drinking water will state that he found so many micrograms per milliliter. He does not talk in terms of belief, but of fact. If the scientist is less certain of the significance of his measurement, he may suggest a normal range or he may decline to have an opinion. A scientist stating his position among a group of querulous peers may state " I believe" when he or she wants to declare a personal position without incurring a frontal assault from his critics. The scientist’s belief is opinion - a reasoned conclusion with some uncertainty attached. 

The world "belief" is more often used by people who belong to religious organizations; for them belief is an expression of loyalty to a group and its predetermined creeds and stories. Religious beliefs involve unreasoned opinions that arbitrarily reduce uncertainty within the chosen group. Religious beliefs are often attached to the worst of human behaviors and are often used to justify hatred and killing. The word “faith” is used to describe unquestioning acceptance of the beliefs of the local group. Groups that base their existence on local beliefs attach great importantance to declarations of faith since their beliefs are arbitrary and cannot be tested. To a religious fanatic, faith is a virtue. To a reasonable scientist, faith is an obstacle and a vice.

Delusions are false beliefs. Obviously, the term “delusion’ is relative to the beliefs of the person who decides to use the term. If a person looks at the Muller-Luyer diagram (above) and believes, as every reasonable person should, that the upper line is longer, a second observer with a ruler may conclude that the first observer is deluded.  The two observers may never agree. The two beliefs arising from the Muller-Luyer diagram are prototypes of differing beliefs that lead to conflicts that disturb human groups everyday.  While seeing might be believing, not all seeing reveals an accurate picture of what is really going and most beliefs are arbitrary opinions that have little or nothing to do with what is really going on out there.

The notion of “false” is easy if you believe one thing and confront another human who believes something else. Obviously, the other guy is deluded. The notion of “false” is more difficult if you are philosopher and notice that different vantage points, illusions, errors, memory limitations and other cognitive problems are typical of humans and that no two humans will ever agree on what they saw and what it means. You might conclude that there is no fixed and enduring truth . We tune into selected features of what is really going on out there. Our efforts generate a range of beliefs about what is really going on out there. Many beliefs are simply memes or stories that are repeated without understanding or review. Fixed beliefs persist beyond any reasonable currency, resist revision and review, and are always false when you stand outside the group that perpetuates the belief.