How Free Will and Omniscience Works

[Angrboda]

"Uuuhh, whatever happened here, sir, I think we missed it"
— Aliens

I primarily came to throw a spanner in the works, but I'll engage in a bit of clean-up first.

MysticKnight, excellent analysis. So you aren't a worthless blob of protoplasm after all.

I must say that I disagree that foreknowledge and predictive ability are equivalent. It's not settled in epistemology exactly what knowledge is, but I think the fact that prediction is both fallible and not based on perception of the actual fact itself precludes it being considered knowledge. In Rhythm's words, you've replaced knowing with guessing.

Other minor points, indeterminacy, quantum or otherwise, does not rescue free will. If I encounter a basket of apples, and each time I reach for one, my arm swims and picks a different one, the apple eventually chosen wasn't the result of free will. Randomness and indeterminacy do not lead to meaningful free will. What the free will proponent wishes for is not things that are not determined, but rather choices that are determined in a specific way, that being determined by a free will. (And IATIA, I have for some time postulated that our concept of free will arose as a consequence of problems in predicting the behavior of prey; we can't efficiently predict which way the prey will zig or zag, but if we model it as being able to freely choose either, we can assert a productive response to its potential behaviors that result in our getting fed.)

I think the most significant error in idunno's presentation was likely to attempt to assert the independence of omniscience from free will without demonstrating anything about free will itself. I can readily assert that God's omniscience does not preclude the existence of square circles, but, even if I'm correct, I haven't really said anything. In order to say anything meaningful about God's omniscience and free will requires three parts: the God part, the free will part, and the relationship part. Attempting to only demonstrate the relationship part, beyond being rather vacuous, is likely the cause of the sort of semantic tail chasing that occurred here.

As to the PAP, which I confess I haven't spent much time thinking about (at all), it suffers from a common flaw that many compatibilist and libertarian views have. This is easiest to demonstrate by showing the flaw in this analogy. While the chooser in this scenario might have ephemerally selected Democrat or Republican, and might have had two possibilities, the system as a whole did not. The system as a whole was determined to vote Democrat by the nature and design of the system. Compatibilists appeal to this frequently by suggesting that their internal choices are free if they are not coerced by an external agent. This arbitrary line drawing serves nothing more than to create illusions of independence and freedom when the freedom itself is a direct result of choosing to draw the line this or that specific way. The system as a whole has no such freedom, and "this far and no farther" doesn't work to keep determinism at bay.



Anyway, on to the spanner! (This was introduced at a recent philosophy discussion, so I confess it's quite new to me, too.)

A person is playing a game operated by the Predictor, an entity somehow presented as being exceptionally skilled at predicting people's actions. The exact nature of the Predictor varies between retellings of the paradox. Some assume that the character always has a reputation for being completely infallible and incapable of error; others assume that the predictor has a very low error rate. The Predictor can be presented as a psychic, as a superintelligent alien, as a deity, as a brain-scanning computer, etc. However, the original discussion by Nozick says only that the Predictor's predictions are "almost certainly" correct, and also specifies that "what you actually decide to do is not part of the explanation of why he made the prediction he made". With this original version of the problem, some of the discussion below is inapplicable.

The player of the game is presented with two boxes, one transparent (labeled A) and the other opaque (labeled B). The player is permitted to take the contents of both boxes, or just the opaque box B. Box A contains a visible $1,000. The contents of box B, however, are determined as follows: At some point before the start of the game, the Predictor makes a prediction as to whether the player of the game will take just box B, or both boxes. If the Predictor predicts that both boxes will be taken, then box B will contain nothing. If the Predictor predicts that only box B will be taken, then box B will contain $1,000,000.

By the time the game begins, and the player is called upon to choose which boxes to take, the prediction has already been made, and the contents of box B have already been determined. That is, box B contains either $0 or $1,000,000 before the game begins, and once the game begins even the Predictor is powerless to change the contents of the boxes. Before the game begins, the player is aware of all the rules of the game, including the two possible contents of box B, the fact that its contents are based on the Predictor's prediction, and knowledge of the Predictor's infallibility. The only information withheld from the player is what prediction the Predictor made, and thus what the contents of box B are.



The problem is called a paradox because two strategies that both sound intuitively logical give conflicting answers to the question of what choice maximizes the player's payout. The first strategy argues that, regardless of what prediction the Predictor has made, taking both boxes yields more money. That is, if the prediction is for both A and B to be taken, then the player's decision becomes a matter of choosing between $1,000 (by taking A and B) and $0 (by taking just B), in which case taking both boxes is obviously preferable. But, even if the prediction is for the player to take only B, then taking both boxes yields $1,001,000, and taking only B yields only $1,000,000—taking both boxes is still better, regardless of which prediction has been made.

The second strategy suggests taking only B. By this strategy, we can ignore the possibilities that return $0 and $1,001,000, as they both require that the Predictor has made an incorrect prediction, and the problem states that the Predictor is almost never wrong. Thus, the choice becomes whether to receive $1,000 (both boxes) or to receive $1,000,000 (only box B)—so taking only box B is better.

In his 1969 article, Nozick noted that "To almost everyone, it is perfectly clear and obvious what should be done. The difficulty is that these people seem to divide almost evenly on the problem, with large numbers thinking that the opposing half is just being silly."