If we predict what theories others will accept, a), the forecast clearly needs to be kept secret from the people in question lest it influence them now (as Popper calls it, the 'Oedipus-effect'). If we keep the prediction secret, either it becomes a prediction from without—and therefore is not self-prediction—or it still requires us to predict that we will keep our results secret. Yet whether we decide to keep our results secret will depend on future circumstances, which in turn depend on the growth of our own knowledge—so to assume we can predict our own adherence to secrecy begs the question of whether self-prediction is possible.
Could we predict the creation of new theories without understanding what we predict? For example, we might describe the shapes of some letters that will be written down, and predict their historical consequences. Arguably this isn't possible either, because if we can predict those shapes, we can write them down now, and if we can write them down now, there is no reason they shouldn't have consequences now.
He also proves that it is impossible even for a Laplacean demon to predict its own future state, as this would involve both describing the initial conditions and describing the future state. To describe its own state 1 hour from now, it would have to describe (1) the inital conditions (required for any prediction task) and (2) all its actions up to that point. (1) takes some amount of time—so it would never be able to predict the future state before it comes to pass.
As for predicting the growth of knowledge in someone else's mind (prediction from without): To do this reliably you would need to know everything that might be relevant to their decision—in other words you would have to possess a significant chunk of all their knowledge. You would have to be superhuman.
So, predicting the growth of knowledge is either self-defeating or practically impossible. (For more, see Karl Popper, The Open Universe, Chapter III, particularly section 21.) Some implications are:
- Free will. If the growth of knowledge could be predicted in principle, so could our decisions, which would make them deterministic. In fact, knowledge creation is unpredictable, and free will is a better explanation for this than 'randomness'.
- When you try to teach or persuade someone of something, the result is unpredictable. If you could predict what ideas the person would have as a result of your teaching, it would not be new knowledge. Yet we know from the theory of conjecture and refutation that it is new: People only learn by creative conjecture and criticism. I'm not sure if this particular argument holds. It would be interesting to hear others' views on it. But there are also the other problems with predicting the growth of knowledge in other people's minds—the Oedipus-effect and the sheer complexity of the knowledge that would be required by such a predictor.
