[deciplex]

If it negates it for the majority of inputs, but you insist it negates it for very few or no inputs, I would call that cognitive dissonance as well. In other words, if it's highly unlikely that two things are both true, but you consider it very likely they are both true, that's probably cognitive dissonance even if the two propositions are not logical contradictions.

[dancompton]

Do you disagree that given a bag of all functions which accept N inputs, it is unlikely that 2 chosen at random would negate each other across all N inputs?

[deciplex]

Obviously I don't disagree with that. Where are you going with this? People don't formulate their beliefs by picking randomly from a collection of all theoretically-possible beliefs. To expand on your example, if you are selecting from a bag of beliefs according to some criteria (based on some combination of morality, desire, etc) which are themselves in conflict (e.g. "I wish to be feared; I wish to be loved") then I think you are more likely to pick some beliefs which happen to contradict each other (again, if not logically, then for most inputs) than you would just by selecting randomly. Or, probably, if your criteria are more in tune with one another.

[dancompton]

How do people formulate their beliefs?