From what appears to be a reputable source:
Cognitive Dissonance Theory, developed by Leon Festinger (1957), is concerned with the relationships among cognitions. A cognition, for the purpose of this theory, may be thought of as a ³piece of knowledge.² The knowledge may be about an attitude, an emotion, a behavior, a value, and so on. For example, the knowledge that you like the color red is a cognition; the knowledge that you caught a touchdown pass is a cognition; the knowledge that the Supreme Court outlawed school segregation is a cognition. People hold a multitude of cognitions simultaneously, and these cognitions form irrelevant, consonant or dissonant relationships with one another.
[. . .]
Two cognitions are said to be dissonant if one cognition follows from the opposite of another. What happens to people when they discover dissonant cognitions? The answer to this question forms the basic postulate of Festinger¹s theory. A person who has dissonant or discrepant cognitions is said to be in a state of psychological dissonance, which is experienced as unpleasant psychological tension. This tension state has drivelike properties that are much like those of hunger and thirst. When a person has been deprived of food for several hours, he/she experiences unpleasant tension and is driven to reduce the unpleasant tension state that results. Reducing the psychological sate of dissonance is not as simple as eating or drinking however.
The above, taken strictly and literally, is incoherent. We are first told that a cognition is a bit of knowledge, and then in the second quoted paragraph that (in effect) some cognitions are dissonant, and that if one cognition follows from the opposite of another, then the two are dissonant. But surely it is logically impossible that any two bits of knowledge, K1 and K2, be such that K1 entails the negation of K2, or vice versa. Why? Because every cognition is true -- there cannot be false knowledge -- and no two truths are such that one follows from the opposite of the other.
The author is embracing an inconsistent pentad:
1. Every cognition is a bit of knowledge.
2. Every bit of knowledge is true.
3. Some, at least two, cognitions are dissonant.
4. If one cognition follows from the opposite (the negation) of another, then the two are dissonant.
5. It is logically impossible that two truths be such that one follows from the negation of the other: if a cognition is true, then its negation is false, and no falsehood follows from a truth.
The point, obviously, is that while beliefs can be dissonant, cognitions cannot be. There simply is no such thing as cognitive dissonance. What there is is doxastic dissonance.
"What a pedant you are! Surely what the psychologists mean is what you call doxastic dissonance."
Then they should say what they mean. Language matters. Confusing belief and knowledge and truth and related notions can lead to serious and indeed pernicious errors. A good deal of contemporary relativism is sired by a failure to make such distinctions.