Did anyone offer an argument against the possibility of a perfect and complete prediction about a system from within that system along the following lines:
Let's imagine a machine (like a desktop computer) that had access to all of the information about a system (a universe, for the sake of argument) and knew all the physical rules governing that universe. Suppose it could make a perfect and complete prediction about the future of the universe and print it out on its screen. Consider a person sitting at that computer. To make a perfect and complete prediction, the computer would have to predict what that person would do in the future. But to do that, to predict what the person would do the moment after the computer's own prediction were to flash on the screen, the computer would have to know the output of its own prediction. In other words, it could not finish its prediction until it knew its prediction, which is impossible. More generally, if the machine's prediction were to exist in the future of the system in any consequential way, the machine would have to take its prediction into account in the creation of its prediction (I'll assume that to exist inconsequentially is impossible). Therefore, by contradiction, such a machine is impossible; a perfect and complete prediction about a system cannot be made from within that system.
Another way to think about this intuitively: whatever the computer printed out, the person could do something different. If the computer said "person will not shift in her seat in the next 5 seconds," the person could easily just shift in her seat to spite the machine.
Could such an argument be a reflection of the unmeasurability of the universe, as explained in this post? It seems unlikely to me, since this argument does not deal with any quantum mechanical properties; it seems unlikely that the source of the logical impossibility of such a theoretical device comes from the quantum mechanical properties of our universe (this could theoretically be some different universe, with different properties... I'm assuming? I am no quantum physicist so I don't know).
Could this instead be a reflection of something like Godel's incompleteness theorems (I say 'something like' because I don't want to be accused of carrying out one of the uncountably many terrible arguments that cite these theorems): some limitation that made it impossible for a set of physical rules to exist such that everything in that universe could be predicted, even with perfect and complete information?
Is such an argument sound? If so, why is such a machine logically impossible and does this have any relation to known logical/mathematical/scientific theorems or does it have any significant implications?