Why is keeping a diary a crime?

Keeping a diary isn't actually a crime. Oceania has no laws, thus the government doesn't have to keep any laws. They have the freedom to make things up as they go along..... and to punish anyone for anything.

The thing that he was about to do was to open a diary. This was not illegal (nothing was illegal, since there were no longer any laws), but if detected it was reasonably certain that it would be punished by death, or at least by twentyfive years in a forced-labour camp.

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His pen had slid voluptuously over the smooth paper, printing in large neat capitals—DOWN WITH BIG BROTHER DOWN WITH BIG BROTHER DOWN WITH BIG BROTHER DOWN WITH BIG BROTHER DOWN WITH BIG BROTHER over and over again, filling half a page. He could not help feeling a twinge of panic. It was absurd, since the writing of those particular words was not more dangerous than the initial act of opening the diary, but for a moment he was tempted to tear out the spoiled pages and abandon the enterprise altogether.

He did not do so, however, because he knew that it was useless. Whether he wrote DOWN WITH BIG BROTHER, or whether he refrained from writing it, made no difference. Whether he went on with the diary, or whether he did not go on with it, made no difference. The Thought Police would get him just the same. He had committed—would still have committed, even if he had never set pen to paper—the essential crime that contained all others in itself. Thoughtcrime, they called it.