A well-known problem, noticed by Meirav, is that it is difficult to distinguish hope from despair. Both the hoper and the despairer are unsure about an outcome and they both have a positive attitude towards it. So what's the difference? Meirav has a story involving a special factor, but I want to try something else.
If I predict an outcome, and the outcome happens, there is the pleasure of correct prediction. When I despair and predict a negative outcome, that pleasure takes the distinctive more intense "I told you so" form of vindicated despair. And if the good outcome happens, despite my despair, then I should be glad about the outcome, but there is a perverse kind of sadness at the frustration of the despair.
The opposite happens when I hope. When the better outcome happens, then even though I may not have predicted the better outcome, and hence I may not have the pleasure of correct prediction, I do have the pleasure of hope's vindication. And when the bad outcome happens, I forego the small comfort of the vindication of despair.
The pleasures of correct prediction and the pains of incorrect prediction are doxastic in nature: they are pleasures and pains of right and wrong opinion. But hope and despair can, of course, exist without prediction. But when I hope for a good outcome, then I dispose myself for pleasures and pains of this doxastic sort much as if I were predicting the good outcome. When I despair of the good outcome, then I dispose myself for these pleasures and pains much as if I were predicting the bad outcome.
We can think of hoping and despairing as moves in a game. If you hope for p, then you win if and only if p is true. If you despair of p, then you win if and only if p is false. In this game of hoping and despairing, you are respectively banking on the good and the bad outcomes.
But this banking is restricted. It is in general false that when I hope for a good outcome, I act as if it were to come true. I can hope for the best while preparing for the worst. But nonetheless, by hoping I align myself with the best.
This gives us an interesting emotional utility story about hope and despair. When I hope for a good outcome, I stack a second good outcome--a victory in the hope and despair game, and the pleasure of that victory--on top of the hoped-for good outcome, and I stack a second bad outcome--a sad loss in the game--on top of the hoped-against bad outcome. And when I despair of the good outcome, I moderate my goods and bads: when the bad outcome happens, the badness is moderated by the joy of victory in the game, but when the good outcome happens, the goodness is tempered by the pain of loss. Despair, thus, functions very much like an insurance policy, spreading some utility from worlds where things go well into worlds where things go badly.
If the four goods and bads that the hope/despair game super-adds (goods: vindicated hope and vindicated despair; bads: frustrated hope and needless despair) are equal in magnitude, and if we have additive expected utilities with expected utility maximization, then as far this super-addition goes, you are better off hoping when the probability of the good outcome is greater than 1/2 and are better off despairing when the probability of the bad outcome is is less than 1/2. And I suspect (without doing the calculations) that realistic risk-averseness will shift the rationality cut-off higher up, so that with credences slightly above 1/2, despair will still be reasonable. Hope, on the other hand, intensifies risks: the person who hoped whose hope was in vain is worse off than the person who despaired and was right. A particularly risk-averse person, by the above considerations, may have reason to despair even when the probability is fairly high. These considerations might give us a nice evolutionary explanation of why we developed the mechanisms of hope and despair as part of our emotional repertoire.
However, these considerations are crude. For there can be something qualitatively bad about despair: it makes one not be as single-minded. It aligns one's will with the bad outcome in such a way that one rejoices in it, and one is saddened by the good outcome. To engage in despair on the above utility grounds is like taking out life-insurance on someone one loves in order to be comforted should the person die, rather than for the normal reasons of fiscal prudence.
This suggests a reason why the New Testament calls Christians to hope. Hope in Christ is part and parcel of a single-minded betting of everything on Christ, rather than the hedging of despair or holding back from wagering in neither hoping nor despairing. We should not take out insurance policies against Christianity's truth. But when the hope is vindicated, the fact that we hoped will intensify the joy.
I am making no claim that the above is all there is to hope and despair.
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