Omniscience: unlimited knowledge. Not to be confounded with infallibility, although it is usually construed as including the latter.

The Eye of God*

In theology, omniscience is the possession by a ►divine being of complete knowledge of all states of the world -- including the thoughts of human beings -- be they past, present, or future. God is said to exercise His omnipotence on the basis of this divine kind of knowledge.

The concept of omniscience, however, may give rise to various apparent paradoxes. One of them is known as Newcomb's paradox: Imagine that you are a candidate on a TV quiz show. Two boxes are placed in front of you. The first box (as you are told) contains either 1,000 $ or nothing at all -- you don't know which. The second contains 100 $, and this you know for certain. You are given a choice: you may take just what is in the first box, or take what is in both.

An easy choice, you think? There is a catch to it, though: Like the omniscient god, the quiz master knows in advance precisely how you will decide. Prior to the show, he thoroughly familiarized himself with the contestants and thus knows their characters and decision processes much better than they themselves do. Now, if (before the show) he anticipated that you would choose to take only the first box, he put a thousand-Dollar bill into it. If, however, he anticipated you would choose both boxes, he left the first box empty. You were informed of this prior to the start of the show.

Thus, at the time you eventually make your choice, the money has already been placed and both boxes are closed. Not even the quiz master can change the contents of the boxes at this point. Since you do not know what the quiz master predicted, it seems a smart move to choose both of their contents - after all, the sum of money in them is already fixed and this way, you can be sure to receive at least 100 $ from the second box. Then, however, you reflect that if you do choose this way, the quiz master will have predicted as much and will, accordingly, have left the first box empty. It seems it would be much better for you if you choose just the first box, for if you make that choice, the quiz master will have predicted it and will have put 1,000 $ into the box. But then again, you reflect further, if the quiz master predicted that you would choose only the first box (based on his knowledge of your character etc.), wouldn't it be better still to trick him by changing your mind, asking for both boxes after all, and thereby collecting the money that is in both boxes?

The Omniscient Quiz Master

This situation leads to a dilemma in the following sense: Either it is possible for you to falsify the quiz master's prediction by making the opposite choice from the one he anticipated, or it is not. If it is possible, then the quiz master lacks complete knowledge of your character and so is not omniscient after all. If it is not, the question is why not; what accounts for the infallibility of the quiz master's predictions? Only two answers seem to be available. The first is that when you make your choice, you retroactively cause the quiz master to make the prediction he makes -- to make the prediction he made. While the notion of backward causation is not entirely without defenders, it is fairly uncontroversial to rule it out as absurd and thus to reject this answer. That leaves us with the second answer, which is that the quiz master's prediction is based on awareness of circumstances present at the time of the prediction that render your eventually choosing as he now predicts inevitable. Your choosing as you do would have to be predetermined. Thus, the idea of omniscience implies a completely predetermined world (►Laplace's demon) and thereby rules out choices, including choices between good and evil, that are not determined by prior circumstances. Although this has long been a subject of considerable controversy, many take this to be equivalent to denying free choice or freedom of will (the controversy being over whether freedom is compatible with being causally determined). This is why some theologians do not include knowledge of the future in God's omniscience in the first place. According to this weaker definition of omniscience, even a god who knew every fact about the past and present may be taken by surprise by human decisions that he had not predicted.

This is not the only problem with omniscience, however. Even the present can be known to an omniscient being only to a limited extent, as Gödel and Turing proved in 1930 and 1936, respectively. Even if God tried really hard, he would not be able to decide the truth or falsity of the ►continuum hypothesis. And if you present to God a computer program, He will often not be able to tell whether it contains a ►bug.

* Kindly made available here by the US Federal Reserve Bank.

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