Let's look at a thought experiment:
There is an oracle who has exact knowledge of the state of a deterministic universe, so her predictions about the universe's future have always turned out to be correct. One day, John approaches the oracle and asks, "Can you tell me whether I will raise my hand in 1 minute?" The oracle, with her uncanny vision, however, sees this: John's brain circuits are in such a state that when he hears "Yes" or anything that he understands as on the affirmative side (such as "Of course", "You will", "I think so", etc), they will react in a way that keeps his hands down, and vice versa. The oracle therefore replies that although she knows the answer, she can't tell him because his brain is in such and such a state. But she can secretly write down her prediction on a piece of paper for him to check that it conforms to his choice later.
At any point in time, the oracle surely knows the future perfectly. So intuitively we would expect her to be able to give us a definite answer to a naive question like whether certain things are going to happen in the future. But the above example indicates there's no way she could achieve that despite of what she knows. How should we understand this? In the following I give my thoughts on this. I'd like to hear your comments and critics. Any other thoughts and ideas are welcome.
The Yes/No answer (prediction) given by the oracle plays a dual role:
- As a physical influence on the deterministic world. For instance, a "Yes" travels as some particular vibration of the air and reaches John's brain, causing certain changes and reactions there accordingly.
- As a piece of information whose semantics stands as a testament to the oracle's prediction.
When the oracle is sufficiently autonomous, not exerting relevant physical influence on the part of the universe she's trying to predict, her prediction plays only role 2. But if she's going to answer John, role 1 becomes inevitable. In the above example, the prediction as a physical influence on the universe happens to cause it to evolve in a way that contradicts the semantics of the prediction. Notice that this reasoning has nothing to do with so called free will whatsoever. It is only the structure of the (deterministic) universe and semantics of language that make the prediction impossible.
But what's the implication? Can we conclude that we can't expect the oracle to answer arbitrary questions about the future, even though, or should we say, precisely because, she is omniscient? Or there always will be questions about the future that will remain unknowable to you, even with the help of the oracle? People have been written much about oracles and prophecies since ancient times. It is interesting to note that many of them work in mysterious ways, writing their prophecies only in the form of obscurely ambiguous poems or nearly inscrutable text. I'd like to think perhaps a real oracle will be just like that, bound to write down her knowledge in a strange way.