A paradoxical intervention is a non-hypnosis way of treating people. It seems to be the opposite of what you would think is needed.
Paradoxical Intervention for Smoking
For example, the late Alan Carr wrote a book about stopping smoking. One of the first rules in the book was that the reader was not to stop smoking now, and make no attempt to give up. They have to keep smoking until they have finished the whole book. Now, I have no idea what he intended with this instruction, but the result is that the smoker starts reading the book, and then feels pressured to keep smoking. They didn't want to smoke, but must. You can't stop until you have finished the book.
That means that every time you turn a page you are reminded that you are not allowed to stop smoking yet. That increases the desire to not be forbidden to stop, which increased the desire to want to stop. Which is precisely the feeling you want the smoker to have. So paradoxically, by ordering them to not stop, you increase their desire to stop.
Paradoxical Intervention theory
The basic idea in a paradoxical intervention to reduce the resistance of the client. Normally a client wants to do the problem behavior because they have some unconscious programming or need that needs to be fulfilled. Normally the unconscious need is outside of awareness. If you give the client permission to go on doing the problem behavior, then the client is able to get some awareness of why they want to do it. By thinking about that, the client becomes aware that they actually do have some control over their own behavior.
Paradoxical Intervention examples
The interventions can be anything. For example, telling a child that they should scream some more and see where it gets them. Or telling a person threatening suicide to go ahead. There is of course a danger in this, so in practice things are usually less dramatic. A typical paradoxical intervention would be to tell a procrastinator to set aside an hour a day to do procrastination. Tell them to get really good at it. This forces the individual to think about the consequences of their action, and possibly to reconsider its usefulness.
Milton Erickson Paradoxical Intervention
Milton Erickson described many paradoxical interventions. His best known is probably the case where a couple were having sexual problems. The wife didn't want to initiate sex. He told them to go home and to not have any sex, to never have sex again. The result was that the couple lay in bed and for the first time, didn't feel any pressure to have sex. Which soon resulted in them thinking about sex more, and in actually having sex again. Together they proved the therapist wrong.