Let's take the case of a fictional John.
John expresses the following viewpoint.
If a proposition about reality can't be proved or disproved, it is rational to be completely uncommitted on the likelihood of the truth of that proposition.
It is irrational to describe a proposition that cannot be proved or disproved as "very unlikely to be true" unless one can do the necessary mathematical calculations to determine its probability.
Mary disagrees, and thinks that these views of John's will contradict other views that he has, and also the way he behaves, so she attempts to stimulate cognitive dissonance in John in order to encourage a change of mind. She suggests to John:
"Don't you think it's very unlikely that there's a treasure worth more than one million dollars buried under the middle of your backyard?.".
John considers the question, and replies:
"no, I don't know how likely it is, so I'm completely uncommitted on the question".
Mary then asks John why he doesn't dig a hole in the centre of his backyard, as that would seem worth doing for anyone who didn't think the proposition very unlikely. After all, she points out, even at a one in ten chance, the effort would surely be worth it.
John expresses annoyance, and leaves the room.
Why?
It's quite likely that Mary has successfully stimulated some dissonance in John. Assuming he knows that holes are dug frequently for a variety of reasons, and that a random hole can be reasonably regarded as very unlikely to uncover a million dollar treasure because these turn up very rarely, he would actually consider the treasure proposition to be very unlikely. But because of his expressed views on the irrationality of such an estimate, he finds himself with conflicting cognitions.
John is a geologist, and Mary knows that he strongly disagrees with creationists who declare the planet to be less than 10,000 years old. So, on their next meeting, she asks him about omphalism, pointing out that the proposition cannot be conclusively proved or disproved. John sticks to his guns, and declares himself completely uncommitted on whether omphalism is true or false. Mary then points out that he must then be completely uncommitted on the age of the earth.
John expresses annoyance, and storms out of the room.
And so it goes.