Yep. That's why predicting the future of a system you're a part of is sometimes literally impossible; it boils, fundamentally, to the fact that logical negation doesn't have a fixed point.

If your prediction is a probability distribution, rather than a discrete outcome label, then, assuming the distribution over the future depends continuously on your action, there should be a fixed point, I think?

Like, if you output a probability distribution among n options, and then there is a continuous map from the probability distribution you describe in your output, to another probability distribution over those options…

Err, hm, maybe you need a stronger hypothesis on the continuous map? If it is contractive then it will definitely have a fixed point. I don’t remember the hypothesis needed.

That's a beautifully simple characterization. I've never heard of of that. What keywords do I need to find more on this topic?