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Conformity and Rationality, Part 2

In part one, we toyed with the idea that a disagreement with someone over something would give you evidence that you were mistaken, and that the rational response would therefore be agnosticism. So, for example, if you think God exists and I say He doesn't, you thereby acquire evidence that you're mistaken and the rational response consists in your dropping the belief that He exists.

We also saw that, taking the views of foreign cultures, wild-eyed philosophers, non-conformists and the like into consideration, you hold very few beliefs that are completely untainted by disagreement. (Undoubtedly, somebody somewhere holds some view that is incompatible with your belief that you're sitting at a computer right now.) So, if disagreement about some subject gives you reason to be agnostic about that subject, then it seems that we should be agnostic about almost everything.

Well, this conclusion is obviously too strong. I'll explain why below, but in the course of doing so, it will become apparent that disagreements might still give us significant evidence against our beliefs.

Disagreement and Reliability

Suppose you invent an instrument that picks winners for sporting events, and suppose that you use this instrument (we'll call it a "Winometer") to predict the winner of every NCAA football game. Now consider the following possibilities:

Winometer 1:
The Winometer proves to be considerably less reliable than you are. While you're able to pick the winner about 80 percent of the time, say, the Winometer's less than 50 percent accurate.

Winometer 2:
The Winometer proves to be considerably more reliable than you are. While you're able to pick the winner about half the time (as if you're just flipping a coin), the Winometer picks the winner almost 95 percent of the time.

Winometer 3:
You and the Winometer turn out to be equally reliable. You don't always agree — sometimes you're right while it's wrong, and vice versa — but on average, you're both about 75 percent accurate.

Suppose, then, that Northern Illinois University will play Ohio State on opening day, and suppose that you disagree with the Winometer's pick. You think the Buckeyes are going to win, and the Winometer picks NIU. In terms of your confidence that the Buckeyes will win, how should you respond to the Winometer's prediction? What does rationality require of you?

Let's start with the scenario outlined in Winometer 2.

In this scenario, it seems obvious that you'd be irrational if you remained confident that the Buckeyes would win. The Winometer is considerably better at predicting winners than you are, the Winometer says the Buckeyes will lose, and you know this. You therefore possess unambiguous evidence that you're mistaken, and you thereby acquire an obligation to become less confident that the Buckeyes will win. In fact, given the fact that the Winometer is almost always right and it says NIU will win, rationality probably requires you to become fully confident that the Buckeyes will lose.¹

How about Winometer 3, then?

Here, it seems pretty obvious that you also have a rational obligation to become less confident that the Buckeyes will win. Since you and the Winometer are both 75 percent reliable, your being mistaken about the winner is just as probable as the Winometer's being mistaken about the winner.

But note a difference here between Winometer 2 and Winometer 3. In Winometer 2, you ought to become confident that NIU will win, and this is due to the fact that the Winometer is considerably more reliable than you are. In Winometer 3, however, you are just as reliable as the Winometer is. So, the fact that you picked the Buckeyes gives you reason to doubt that the Winometer is right. Given the fact that the Winometer is just as likely to be wrong as you are, it seems that you ought to withhold judgment on the winner.

But now consider Winometer 1.

In this scenario, there's no positive correlation at all between the winner and the Winometer's predictions. (In fact, given the fact that the Winometer is less than 50 percent accurate, the Winometer's predicting that NIU will win is actually evidence that NIU will lose.) Since you know this about the Winometer, it seems clear that you can rationally dismiss the Winometer's prediction and maintain your confidence that the Buckeyes will win. Given the Winometer's unreliability, its picking NIU gives you no evidence at all that the Buckeyes will lose.

Abstracting from these scenarios, we can say the following:

The rational response to disagreement with an instrument (such as Winometer, or a thermometer, or a scale, or a watch, or the light meter in a camera) depends on the reliability of the instrument in question. If an instrument is just as reliable as or more reliable than you are, you seem rationally obligated to make your beliefs conform to its readings. But if you have reason to believe the instrument is less reliable than you are (e.g., the sign at a Phoenix bank tells you it's 24 degrees Fahrenheit at 3 p.m. in the middle of July), you seem rationally justified in dismissing its readings. You seem to have no rational obligation, then, to make your beliefs conform to the readings of unreliable instruments.

Reliable Instruments Versus Reliable People

The same principles apply to disagreements between people.

Suppose you and I and 37 of our closest friends go to White Castle to binge on square microwaved hamburgers. We order different kinds of burgers, different side-dishes, different drinks, and different numbers of each of these items. I put the order on my credit card, and we all agree that it would be easiest to split the bill 39 ways, not bothering to worry about who ordered extra onions, who got a large Mr. Pib instead of a medium, and so on.²

Now consider the following scenarios, which parallel Winometer's 1 through 3, above.³

White Castle 1:
You're extraordinary at math and I'm absolutely terrible at it. You've won competitions across the country and I have a difficult time dividing dollars into quarters. You and I both divide the bill by 39 in our heads. You get $11.42 and I get $13.94.

White Castle 2:
I'm extraordinary at math and you're absolutely terrible at it. I haven't missed a single problem on a single test or homework assignment since the second grade, and you can't keep the difference between addition and subtraction straight. You and I both divide the bill by 39 in our heads. You get $11.42 and I get $13.94.

White Castle 3:
You and I are equally good at math. We've received all the same grades on all the same tests, and we've never once come to different conclusions on the same question. You and I divide the bill by 39 in our heads. Expecting us to get the same answer, you get $11.42 and I get $13.94.

Given what you know about our relative math skills, in White Castle 3 the probability that you are mistaken is just as high as the probability that I am mistaken, and in White Castle 2 the probability that you are mistaken is even higher than the probability that I am mistaken. It seems clear, then, that in both of these scenarios you'd be irrational if you continued believing we each owed $11.42. In White Castle 1, however, things are different. Since I'm terrible at math, it would be perfectly rational for you to dismiss my answer and continue believing that we each owe $11.42.

The rational response to disagreement with another person, then, seems to be more or less identical to the rational response to disagreement with an instrument. If the person with whom you disagree is just as reliable or more reliable than you are, you seem rationally obligated to make your beliefs conform to his or hers. But if you have reason to believe that he or she is less reliable than you are, you seem rationally justified in discounting his or her opinion. You seem to have little or no rational obligation, then, to make your beliefs conform to the opinions of people you know to be unreliable.

Trickier Cases

Things get a little trickier, however, when we move away from math and start talking science, history, politics, philosophy, morality, religion, and so on.

Suppose you and I are in an intro philosophy class and we're both writing papers on the existence of God. Suppose we take exactly the same evidence into consideration, and suppose we're equally intelligent, equally motivated, equally free of external distractions, and so on. In short, suppose that, so far as each of us can tell, we are equally likely to arrive at the truth.

But now suppose that we come to different conclusions. You think God exists, and I think He doesn't.

Or suppose we're writing papers on the abortion debate. Again, so far as we can tell, we're equally likely to arrive at the truth. As it turns out, however, we disagree. You think abortion is morally justified and I think that it's not.

How are we rationally obligated to respond in these scenarios? Where you and I were equally likely to get the right solution to a math problem and came to different conclusions, it seemed pretty obvious that we were rationally obligated to make our beliefs conform. As far as you and I could tell, we were equally likely to arrive at the truth regarding the existence of God and the morality of abortion. Are we not rationally required to make our beliefs conform here as well? Given the fact that my being mistaken is no more and no less likely than your being mistaken, shouldn't we both become agnostic?

Or suppose the disagreement isn't between you and me but between you and your professor, who you recognize as much smarter, considerably better educated, and so on, than you are. What if your professor tells you God doesn't exist, that abortion is morally permissible, and so on?

In White Castle 2, you had a clear obligation to give up on your conclusion that each of us owed $11.42, and this was because you were considerably worse at math than I was, and I calculated that each of us owed $13.94. If your prof — who's much better at philosophy than you are — tells you that God doesn't exist or that abortion is morally permissible, don't you have the same obligation? If not, what makes the difference? How could it be possible for you to see that your prof is much better at philosophy than you are, yet rationally remain confident in some philosophical position that your prof rejects?

C O F F E E  S H O P

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Why shouldn't we believe the "expert" opinions of our professors when it comes to belief about God?

Join the discussion!

Well, I'm inclined to think that there are important differences between these cases, and that the relative reliability of the person with whom you're disagreeing isn't the whole story. In my next article I'll say why and spell out the conditions for rationally rejecting the opinion of somebody you recognize as not only equally reliable, but more reliable than you.