Consanance is harmony; dissonance is disharmony or contradiction.
Cognitive dissonance is contradictory knowledge or ideas.
Yes, cognitive dissonance is an unhealthy state of mind wherein one tries to hold a belief in two or more ideas that contradict each other.
Here is an example of cognitive dissonance.
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Belief A: Any church started by a man is a false church.
Belief B: Our church was started by William Irvine in 1897.
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Trying to hold those two beliefs simultaneously is a state of cognitive dissonance, a state of psychological conflict. Since this psychological conflict is uncomfortable, even unhealthy, a person will try to resolve it. If one does not resolve it one risks mental illness. To resolve it one must modify either A or B or both.
One might modify A to say, "Any church started by a man is a false church unless that man has dedicated his life to be a homeless, poor preacher like the apostles."
Or one might modify B to say, "Our church was not really started by Willliam Irvine, because his sister told him about some people she had met from Switzerland who had meetings in their home; therefore William Irvine was just perpetuating the true faith that he had heard about about by word of mouth through his sister."
This is an example of how people will grasp at ways to resolve the turmoil of cognitive dissonance.