Sort of. An intelligent agent within a closed system will never be able to determine all information within that closed system because of recursive frustrators. Think a long the lines of "this sentence is a lie". It's knowledge influences what is true, so it can never perfectly predict itself.
A non interfering observer outside the system would have no problem determining all information within, given the adequate facilities to do so.
I suppose there's also fuzzy logic and quantum variation to consider, but I'm no expert in quantum mechanics, so I won't speak to that.
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So being able to predict your own actions is a paradox? I'm not sure I understand
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Your knowledge of what you are going to do effects what you do. In essence, there's no way to predict it. Let's I gave you a switch with two settings. On and off. Across is a lightbulb. You must predict whether the light will be on or off at a specified moment, and pull the corresponding lever. You have all information about this machine at your disposal. Your switch is connected to a lightbulb that will do the opposite of whatever the switch is set to. The other light is turned on when triggered by a light detector. So which way do you turn the switch? Obviously it's impossible to pick the correct outcome, because the outcome will always be the opposite of what you predict. Essentially, your knowledge changes outcomes. So in a sense, because of this, there is a sort of free will. The other argument is that there lies truly random probability behind events, at both the quantum and neurological levels, making our decisions nondeterministic. This requires more specified scientific knowledge, and I'd rather deal in pure logic.