# Higher-Order Evidence and Pascal’s Wager

I’ve been thinking a bit about the ways in which Higher-Order Evidence cases might be like Pascal’s Wager. In each case, an agent is presented with a reason for changing their doxastic state that isn’t in the form of evidence for or against the propositions in question.

Since most philosophers don’t think that highly of Pascal’s Wager, this isn’t the most flattering comparison. Indeed, some will think that if the cases are analogous, then the discussion of higher-order evidence isn’t really part of epistemology at all. Even if Pascal had given us a prudential reason to believe in God, he wouldn’t have given us an epistemic reason. I suspect, though, that this is a touch too quick. There are a variety of Pascal like cases where it isn’t so clear we have left epistemology behind.

Melati and Cinta are offered epistemic deals by demons. Here is the deal that Melati is offered.

There is this proposition p that you know to be true. I have a method M1 that will yield great knowledge about subjects of great interest. It is perfectly reliable. The only catch is that to use the method, you first have to firmly believe that p is false. If you do, you’ll get lots of knowledge about other things, indeed you’ll learn over 100 things that are of similar interest and importance to p.

And here is the deal that Cinta is offered.

Here are 100 propositions that you believe to be true. As you know, most people are not that reliable about the subject matters of those propositions. I can’t say whether you’re better or worse than average, though your accuracy rate is comfortably above 50%. Here’s what I can say. I have a method M2 that will yield very reliable beliefs about these subjects. People who have used it are 99% reliable when they use it. And given the subject matter, that’s a very high success rate. The only catch is that to use M2, you have to start by doubting every one of those propositions, and then only believe them if M2 says to do so.

There are two big parallels between Melati’s and Cinta’s deals. Both of them are asked to change their attitudes because that is necessary for commencing to use a method. At some level, they are asked to change their beliefs on prudential grounds. But note the payoff is not Pascalian salvation; it is knowledge. And the payoff is pretty similar in the two cases; probably around 100 pieces of new knowledge, and 1 false belief.

Yet despite those parallels, the cases feel very very different. Melati has no epistemic reason to believe that p is false. Indeed, it isn’t clear that she has all things considered reason to believe that p is false. And if she’s anything like me, she wouldn’t be capable of accepting the deal. (Carrie Jenkins, Selim Berker, Hillary Greaves and several others have discussed versions of what I’m calling Melati’s case, and the intuition that Melati has no epistemic reason to accept the deal seems incredibly widespread.)

Cinta’s situation is quite different. After all, the deal that the demon offers Cinta is very similar to the deal that Descartes offered his readers. Doubt a lot of things, including some things that you surely know, apply my method, and you’ll end up in a better position than where you started. In Descartes’s case, it wasn’t clear he was able to keep up his end of the bargain. That is, it wasn’t clear that he really had the magic method he claimed to have. But if he did have such a method, it wouldn’t be clear he was offering a bad deal. Moreover, we teach Descartes inside epistemology. If Cinta is being offered a version of Descartes’s deal, then it is arguable that she really has an epistemic reason to accept the deal.

What interests me about the cases of Melati and Cinta is that they suggest a way to capture the asymmetry in intuitions about higher-order evidence. Many people think that higher-order evidence can be good grounds to lose a belief. But I’ve never seen a case where the natural intuition is that higher-order evidence gives the agent grounds to adopt a belief where the first-order evidence is insufficient. Here’s a hypothesis that explains that. Higher-order evidence should be grouped in with things like Descartes’s motivation for doubting all one’s prior beliefs, if not with Pascal’s motivation for belief in God. And it is plausible that these kind of considerations in terms of epistemic consequences can provide reasons, perhaps even epistemic reasons, to lose a prior belief, without providing reasons to adopt a previously unheld belief.