A paradox or self-contradictory statement can work in two ways: first, a statement that seems logical on the surface can, in reality, make no sense. Perhaps the most famous of this type of paradox can be found in another work of Orwell's, Animal Farm. In this book, the pigs, once their power is secured, paint the following maxim on the side of the barn: "All animals are equal, but some are more equal than others." It deceives the simpler animals, but in essence it is nonsense. Other paradoxes, however, seem to be contradictory but actually can make sense when you think about them. They are meant to provoke thought. An example would be "lose your life to save it." What it means is that often we don't come into our own sense of self until we give up--"lose"--our preconceived notions of what our life "should" be.
In 1984, Orwell wants to communicate a lesson about how language, if not guarded carefully, can be manipulated to harm people. Therefore, he is most concerned in this novel with the first kind of paradox: nonsense parading as sense. The whole society of Oceania is built on paradoxes that allow a small ruling elite to maintain power at all costs, even at the cost of their own happiness. Therefore, the Party keeps most of the people in misery so that its inner elite can be, not happy, but a little less miserable. It uses paradox to keep the common people thinking life is improving when in fact it is getting worse: people are told, for instance, that chocolate rations are increasing when in fact, they are being decreased. People are taught that a constant state of warfare is needed to protect their ever "improving" (but really eroding) standard of living, when, in fact, the leaders of the Party need the war machine in order to use up the materials that otherwise would be available truly to offer people a better standard of living. "Improvements" in the language, likewise, actually diminish the language's richness in order to keep people from being able to think. By using language to dupe people, the Party controls an ever more dehumanized world.