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No, Newcomb's paradox does not refute the possibility of an omniscient being (if it did, then assuming that such a being is possible, we would face a contradiction).
Let me remind you of the paradox condition:
“The predictor puts two boxes in front of the player — an open box and a closed box. The open box contains a thousand dollars, and the closed box contains either a million dollars or nothing. The player can take either only the closed box, or both boxes together. The contents of the box depend on the predictor:
• If it predicts that the player will choose both boxes, then the closed box will be empty
• If a player is predicted to choose a closed box, the box will contain a million dollars.
Which box should the player choose to get the highest amount?”
If the predictor is an omniscient being (i.e. predicts perfectly accurately), the player must always choose a closed box – the predictor will predict this and the player will receive the coveted million dollars. If the player decides to choose both boxes, the predictor will also predict this, and the player will receive only a thousand dollars. There is no contradiction here.