Despite the opinion of David Hume, we find it possible to predict many things about the future. I will have breakfast tomorrow. Some people will celebrate New Year’s Day on January 1st, 2016. The Jehovah’s Witnesses will continue to modify their predictions for the end of the world.
Despite this ability to say a few things about the future, however, if our predictions are sufficiently detailed they are guaranteed to fail. In part this is true simply because our knowledge is not good enough, but there is another reason, one which would guarantee that such predictions would fail even if made by someone with perfect knowledge.
Suppose I have perfect knowledge of the future, and I write down in a book everything that I think you will do for the rest of your life, in nearly every detail, saying at what time of day you will perform various actions such as brushing your teeth, and so on. Then I give you the book. For the first few days, you do everything that is written there, in every detail.
At some point you are pretty sure to wonder whether you can do something different from what the book says. It says that you will eat breakfast at 7:10 AM one morning, so you decide to test violating that, and eat at 7:30 instead. Presumably, nothing will force you to eat breakfast earlier than you planned, and so the prediction will be falsified.
The situation here is very much like the Liar Game in the previous post. The statements have a truth value, and are not objectively paradoxical. But the player cannot get them right, because the truth value of the last statement is anti-correlated with his judgment. In the same way, given human beings with the psychological makeup that they actually have, and the physical abilities that they actually have, a detailed prediction of the future which is known to people will be at least in some respects anti-correlated with reality.
In this sense, the impossibility comes up because the predictions are made known to people. The argument does not prove that there could not be a book somewhere with the whole of the future laid out in detail; but such a book cannot be actually discovered by people without failing to predict the future correctly.