My original plan for Knowledge: A Human Interest Story was to concatenate my various writings on interest-relativity over the years. That plan failed, because it turned out I’d changed my mind on too many things. The result is, I hope, better than the original plan; the presentation of a coherent theory built out of the not always consistent ideas in those earlier papers.
Like many people, I started thinking about interest-relativity because of work by Jeremy Fantl and Matthew McGrath (2002). In that paper, and in the literature that followed, there were two big arguments for interest-relativity. One was an argument from cases. Those arguments made interest-relativity appear to be both similar to, and also a competitor to, contextualism. The cases that motivated it were similar, and a lot of the development of the argument was designed to show that interest-relative theories provided a better explanation of the intuitions about cases than contextualism.
I’ve long been sceptical of that line of argument, and instead more interested in a different line that, I think, was always present. That line starts with the clash between three principles and an intuition about rational action. The three principles are:
- We know a lot.
- What we know can be taken for granted in decision making.
- What we know is independent of which decision we are facing.
Then the intuition is that for some things we know, and some bets that win if the known thing is true, it is irrational to take the bet. The argument for interest-relativity is that something has to give, and the least costly thing to give up is the decision-invariance of knowledge. What we know depends on what decision we’re making.
This argument doesn’t rely on intuitions about what is or is not knowledge. It does rely on intuitions about rational action, but I think these are fairly widely shared. And it does rely on various principles, which arguably rest in turn on theoretical intuitions. But it doesn’t have a role for intuitions about cases of knowledge.
The book is structured around a version of this argument, focussing on the kind of bets involved in a game I call the Red-Blue game. Here’s how the game works. Two sentences are displayed to the player, one in red, the other in blue. The player has to pick a colour and a truth-value. They win iff the sentence with the colour they pick has the truth-value they pick. So if they say “Red-True”, they win iff the red sentence is true. ‘Winning’ here means getting a non-trivial but not huge reward; in the book I make it $50. The players know these rules of the game and don’t know anything else relevant about the game. Now consider an instance of the game with these sentences.
- Red
- Two plus two equals four.
- Blue
- The Battle of Agincourt was in 1415.
For people with normal levels of historical expertise, the only rational play here is Red-True. Or, at least, that’s the intuition I want to rest on, and it’s one that has been fairly widely shared by people I speak to. Now here’s a sceptical argument. If the player knew that the Battle of Agincourt was in 1415, they would know Blue-True is a winning move, while they’d only know that Red-True wins if two plus two equals four. So Blue-True would, in a sense, weakly dominate Red-True. So it’s at least permissible to play Blue-True. But it’s not permissible to play Blue-True, so the player does not know that the Battle of Agincourt was in 1415. By varying the blue sentence, we can similarly argue that the player knows very little, contradicting the claim ‘we know a lot’.
The solution I prefer is that once this game comes up, what the player knows changes. They may have known when the Battle of Agincourt was, and they may know it tomorrow, but they don’t know it now. That’s the canonical instance of interest-relativity in the book. This is still, I think, basically the same argument as in earlier arguments for interest-relativity, but focussing on this case has several distinctive features.
I’ve already mentioned one of these features. The book does not rest on an intuition that the player loses knowledge. To be honest, even after all these years, I still find that counter-intuitive. It rests on an argument that the player loses knowledge, which in turn rests on intuitions about rational play, and principles connecting knowledge and rational play.
Another obvious consequence is that the view has nothing to do with high stakes. I didn’t put more at stake than $50. I don’t think the intuitions change much if you lower the payouts a fair bit from that. I say, here agreeing with Schroeder (2012), that what matters are the odds the player faces, not the stakes.
What if the player did not in fact face this choice, but is idly planning about what to do should it come up? This might strike you as a little over the top, but I’ve spent quite a bit of time wondering about this in the course of the book. I say the argument that they don’t know when the Battle was still goes through. Just being interested in a question can change what one knows. That’s because knowing something requires being properly willing to treat it as well supported enough to use it, should it be relevant, in any inquiry you are engaged in.1
1 The ‘well supported enough to use’ locution does some work in the presentation in KAHIS; it’s meant to be compatible with not using a piece of knowledge for reasons other than it’s lack of evidential support. I now think it would be better to make the distinction I make in the Replies (later in this symposium) between finding out inquiries, and checking inquiries, and say that anything you know can, if relevant, be used in any finding out inquiry. But that’s not what I said in KAHIS.
In earlier work, I understood questions about what one should be willing to use as being settled by the outputs of the inquiry. The above argument inferred that one should not start inquiry with knowledge of the Battle’s date from the fact that this would lead to the wrong conclusion: Play Blue-True! I used to think that was what made it wrong to use the Battle’s date. This extra step is, I now think, a mistake. Knowledge is not a constraint on where one ends inquiry, but on where one starts it. The relevant constraint is that for someone inquiring into Q?, and p is relevant in the right way to that question, they know p only if the questions Q? and If p, Q? are in a deep sense the same question, and they are answered in the same way. If p is not something relevant to anything one is currently inquiring into, the constraint is that there is some possible inquiry where one would use p as the first step. This move avoids some very implausible consequences of what I’d previously said about knowledge of practically (and theoretically) irrelevant propositions.
I’ve spoken liberally about questions here, but the last few points that are distinctive to the book turn on being a bit more careful about what a question is. In earlier work I’d equated, sometimes explicitly, sometimes implicitly, the following two questions:
- Which live option maximises expected utility?
- What should I do?
But these are not the same question, and some of the challenges for an interest-relative view turn on getting clear on the difference between them. Here are four important differences.
First, if two options have the same expected utility, I still might have to decide which to do. I want a can of Coke, there are two on the shelf. It would do just as well to take either, but I have to actually take one. Knowing the answer to the utility question, they have the same utility, doesn’t settle what my arm should do.
Second, if two options have really similar expected utility, I shouldn’t always take the one with higher expected utility. It might be more trouble than it’s worth to calculate which has higher utility, and I might be (faultlessly) unreliable at choosing the higher expected utility without calculating. Maybe it would be less work by some miniscule amount to pick up the left can rather than the right can. It could, I say, still be practically rational to act like the cans are equally good, and choose arbitrarily. In chapter 6, I show that some objections to interest-relative accounts, which work as long as we equate these questions, no longer work if we separate them.
Third, it’s not obvious how to use the expected utility framework to model mathematical uncertainty. But mathematical uncertainty might be something we want the interest-relative story to capture. If I’m playing the red-blue game, and the blue sentence is 67 plus 58 equals 125, my intuition is that only Red-True is rational to choose. I’m just more likely to make an error about this calculation than about two plus two. But working this into an expected utility model raises extra complications.
Fourth, an expected utility comparison needs a probability function, and the usual picture is that the probability in question is evidential probability. This raises problems if there are propositions that, if known, are part of one’s evidence, and whether they are known is interest-relative. For instance, imagine that there is a Ford outside my window, in fact a Mustang with a distinctive shape, and I’m looking straight at it. I’m asked to play the red-blue game with the blue sentence being There is a Ford outside my window. I think in that context I don’t know there is a Ford outside, so it’s not part of my evidence there is a Ford outside. This makes the very notion of expected utility complicated. In chapter 8, I suggest a way of dealing with that complication.
The last new point in the book which I’ll mention here concerns double-checking. The argument from the red-blue game to interest-relativity requires some principles linking knowledge and action. It has been argued, quite plausibly, that these principles are inconsistent with the rationality of double checking something one already knows. After all, if one knows p, then checking p seems worse than just reasoning from one’s knowledge that p must be true. I argue, in chapter 5, this isn’t right. There are many goals to inquiry. One possible goal is forming a more sensitive belief about some subject. Even if one knows p, then an inquiry that aims to maximise sensitivity should not simply reason from p to the truth of p. This is, I hope, an independently interesting claim about inquiry, but the role it plays here is to defend principles connecting knowledge and action from counterexamples involving double-checking.