Newcomb’s paradox is a famous puzzle in decision theory that has provoked much discussion. It has been formulated in different ways, but a standard formulation runs as follows.
The Predictor is a person who is able to make a prediction about a future choice of yours with a very high degree of certainty. (In some versions, the Predictor is infallible — a point to which we will return.) The Predictor invites you to play a game involving two boxes: A and B. Box A is transparent and you can see that it contains $1,000. Box B is opaque. You’re now given a straight binary choice: you may pick either both boxes or only box B. But before you choose, the Predictor informs you that he has already predicted which choice you will make and has arranged the contents of box B accordingly. If he predicted that you will pick only box B then he placed $1,000,000 in that box; but if he predicted that you will pick both boxes then he left box B empty.
The million-dollar question is this: What choice should you make? (The thought experiment assumes, of course, that you want to maximize your winnings!)
Some argue that the rational decision is to pick both boxes. They reason thus: the prediction has already been made and nothing can change that now. The contents of the boxes are settled. At this point, either box B contains $1,000,000 or it does not. But either way, given that box A contains $1,000, the decision to pick both boxes must result in greater overall winnings than picking only box B.
Others argue that the rational decision is to pick box B. After all, the Predictor is extremely good at his predictions, which means that if you were to pick only box B then you’d be extremely likely to go home with $1,000,000, whereas if you were to pick both boxes the chances are very high that you’d go home empty-handed.
On the face of it, both lines of reasoning seem cogent — and therein lies the paradox.
My purpose in this post is not to try to resolve Newcomb’s paradox or to defend one particular answer to Newcomb’s question. (To those who ask, I’d say that how one should answer the question depends crucially on what assumptions one makes about foreknowledge and free choice; the paradox arises because commonplace intuitions give support to conflicting assumptions.) Instead I want to ask a very different question in order to develop a theological analogy. The question is this:
Does the Predictor make a sincere offer?
In other words, is the Predictor somehow deceptive or dishonest in the way he presents the offer? Is he as good as his word?
For the sake of simplicity (and for other reasons that will become clear shortly) let’s assume that the Predictor is infallible. What this means is that his predicting choice C logically entails that you make choice C. (Note that this entailment is a purely logical relationship and implies nothing about causation, explanation, metaphysical dependence, or any other ‘thicker’ relationship.)
Given this assumption there are only two scenarios to consider, one for each possible choice:
Scenario 1: The Predictor predicts that you will pick both boxes; he therefore leaves box B empty; he explains the game to you; you decide to pick both boxes; you take home $1,000.
Scenario 2: The Predictor predicts that you will pick only box B; he therefore puts $1,000,000 in box B; he explains the game to you; you decide to pick only box B; you take home $1,000,000.
Now consider what your reasonable response should be after playing the game and receiving your winnings. Start with Scenario 2. In this case you would hardly have cause for complaint. What the Predictor told you implied that if you picked only box B then there would be $1,000,000 in that box — and that’s precisely what happened. Only an ingrate would grumble about not also receiving the $1,000. The Predictor was true to his word and you’re one million bucks the richer for it.
But what about Scenario 1? It’s tempting to argue that here you could legitimately raise the following complaint. “Sure, I was free to choose only box B. But the fact is that there never was $1,000,000 in that box. You implied that I had the chance to win a million bucks, but given that fact about the past, I never really had that chance. So your offer wasn’t sincere.”
It shouldn’t take much reflection to see that this complaint is quite misguided, for two reasons. First, it’s true that there never was $1,000,000 in box B; but it’s equally true (given the way things were set up) that had you chosen only box B then that box would have contained $1,000,000. The reason you didn’t get that money is straightforward: you chose, in effect, not to get it.
Secondly, the complaint is misguided because the veracity of the Predictor’s claims and his willingness to fulfill his promises in Scenario 1 are no different than they are in Scenario 2. He didn’t say that there would be $1,000,000 in box B and he didn’t promise that you would take home more than $1,000. Rather, what he told you was that things were arranged such that you would get a million dollars if and only if you were to choose box B alone.
So the complaint that the Predictor’s offer was insincere is quite unfounded. Whatever the outcome, you made your choice based on what was offered to you, an offer that involved neither dishonesty nor any promise that would not be fulfilled. If you end up disappointed with the outcome of your choice, you have no one to blame but yourself.
Now what does this have to do with theology?
I propose that if the argument above is sound then it serves to refute one popular objection to the Calvinist doctrine of particular redemption (or “limited atonement” as it is more commonly, and infelicitously, labeled). According this doctrine, Christ died in an atoning sense only for the elect, that is, for those who put their faith in Christ and receive eternal life. (This is not to say that Christ’s death doesn’t bring any benefits to the non-elect, but only that it was not intended to make atonement for their sins.)
It has often been argued that if the atonement really was particular rather than universal then the gospel offer can’t be sincere, because salvation is offered indiscriminately to everyone yet provision for salvation has been made only for the elect. So forgiveness is offered to some people whose sins have not been paid for by Christ. If this is the case, so the argument goes, not only can the evangelist be fairly charged with insincerity — perhaps even duplicity — but so can God, from whom the evangelist receives his commission.
But this objection is as misguided as the complaint against the Predictor, for the two ‘offers’ are parallel in every relevant respect. (Note: in every relevant respect.) For on the Calvinist view, the gospel offer doesn’t amount to “Jesus died to atone for all your sins, but you must believe in him in order to receive the benefits of that atonement” (where ‘you’ could be just anyone). That would be misleading if not outright dishonest. (It’s worth noting, incidentally, that none of the evangelistic appeals recorded in Acts sound like that.)
A far better rendering of the gospel offer would be this:
Jesus came to save his people from their sins (Matt. 1:21), to give his life as a ransom for many (Mark 10:45), to lay down his life for his friends (John 15:13). If you will only repent of your sins, put your trust in him, and confess him as Lord and Savior, then all your sins will be forgiven, you will be reconciled to God, and you will inherit eternal life.
It should be clear that this wonderful free offer of salvation is neither dishonest nor duplicitous. It makes no false claims. It makes no promises that would not be fulfilled without reservation.
On what basis then could the unbeliever on the Day of Judgment have cause for complaint? “Sure, I had the opportunity to repent and trust in Christ. But the fact is that Christ never actually made atonement for my sins. So the gospel offer wasn’t sincere.” He would be quite correct about the atonement, given the doctrine of particular redemption. Nevertheless, his complaint is without foundation precisely because of this pivotal truth: had he repented and trusted in Christ then atonement would have been made for his sins.
The reason he didn’t receive forgiveness and eternal life is straightforward: he chose not to receive them. So if he ends up disappointed with the final outcome, he has no one to blame but himself. The offer of salvation was absolutely sincere, the particularity of the atonement notwithstanding.
It should be noted, by the way, that the argument above doesn’t beg any questions by taking for granted a compatibilist view of human freedom, or unconditional election, or any other distinctively Calvinist doctrines. Even if it did, however, that wouldn’t be problematic, since the objection in question concerns the internal consistency of Calvinism.
None of this provides any positive support for the doctrine of particular redemption; that must come from elsewhere. But it does successfully defuse, I think, one popular objection to it.