One obvious source for this pattern of thought is religion, where the scriptures are alleged to come from God; therefore to confess any flaw in them would destroy their authority utterly; so any trace of doubt is a sin, and claiming certainty is mandatory whether you’re certain or not.
But I suspect that the traditional school regimen also has something to do with it. The teacher tells you certain things, and you have to believe them, and you have to recite them back on the test. But when a student makes a suggestion in class, you don’t have to go along with it—you’re free to agree or disagree (it seems) and no one will punish you.
This experience, I fear, maps the domain of belief onto the social domains of authority, of command, of law. In the social domain, there is a qualitative difference between absolute laws and nonabsolute laws, between commands and suggestions, between authorities and unauthorities. There seems to be strict knowledge and unstrict knowledge, like a strict regulation and an unstrict regulation. Strict authorities must be yielded to, while unstrict suggestions can be obeyed or discarded as a matter of personal preference. And Science, since it confesses itself to have a possibility of error, must belong in the second class.
(I note in passing that I see a certain similarity to they who think that if you don’t get an Authoritative probability written on a piece of paper from the teacher in class, or handed down from some similar Unarguable Source, then your uncertainty is not a matter for Bayesian probability theory. Someone might—gasp!—argue with your estimate of the prior probability. It thus seems to the not-fully-enlightened ones that Bayesian priors belong to the class of beliefs proposed by students, and not the class of beliefs commanded you by teachers—it is not proper knowledge.)
The abyssal cultural gap between the Authoritative Way and the Quantitative Way is rather annoying to those of us staring across it from the rationalist side. Here is someone who believes they have knowledge more reliable than science’s mere probabilistic guesses—such as the guess that the Moon will rise in its appointed place and phase tomorrow, just like it has every observed night since the invention of astronomical record-keeping, and just as predicted by physical theories whose previous predictions have been successfully confirmed to fourteen decimal places. And what is this knowledge that the unenlightened ones set above ours, and why? It’s probably some musty old scroll that has been contradicted eleventeen ways from Sunday, and from Monday, and from every day of the week. Yet this is more reliable than Science (they say) because it never admits to error, never changes its mind, no matter how often it is contradicted. They toss around the word “certainty” like a tennis ball, using it as lightly as a feather—while scientists are weighed down by dutiful doubt, struggling to achieve even a modicum of probability. “I’m perfect,” they say without a care in the world, “I must be so far above you, who must still struggle to improve yourselves.”
There is nothing simple you can say to them—no fast crushing rebuttal. By thinking carefully, you may be able to win over the audience, if this is a public debate. Unfortunately you cannot just blurt out, “Foolish mortal, the Quantitative Way is beyond your comprehension, and the beliefs you lightly name ‘certain’ are less assured than the least of our mighty hypotheses.” It’s a difference of life-gestalt that isn’t easy to describe in words at all, let alone quickly.
What might you try, rhetorically, in front of an audience? Hard to say . . . maybe:
“The power of science comes from having the ability to change our minds and admit we’re wrong. If you’ve never admitted you’re wrong, it doesn’t mean you’ve made fewer mistakes.”
“Anyone can say they’re absolutely certain. It’s a bit harder to never, ever make any mistakes. Scientists understand the difference, so they don’t say they’re absolutely certain. That’s all. It doesn’t mean that they have any specific reason to doubt a theory—absolutely every scrap of evidence can be going the same way, all the stars and planets lined up like dominos in support of a single hypothesis, and the scientists still won’t say they’re absolutely sure, because they’ve just got higher standards. It doesn’t mean scientists are less entitled to certainty than, say, the politicians who always seem so sure of everything.”
“Scientists don’t use the phrase ‘not absolutely certain’ the way you’re used to from regular conversation. I mean, suppose you went to the doctor, and got a blood test, and the doctor came back and said, ‘We ran some tests, and it’s not absolutely certain that you’re not made out of cheese, and there’s a non-zero chance that twenty fairies made out of sentient chocolate are singing the “I love you” song from Barney inside your lower intestine.’ Run for the hills, your doctor needs a doctor. When a scientist says the same thing, it means that they think the probability is so tiny that you couldn’t see it with an electron microscope, but the scientist is willing to see the evidence in the extremely unlikely event that you have it.”
“Would you be willing to change your mind about the things you call ‘certain’ if you saw enough evidence? I mean, suppose that God himself descended from the clouds and told you that your whole religion was true except for the Virgin Birth. If that would change your mind, you can’t say you’re absolutely certain of the Virgin Birth. For technical reasons of probability theory, if it’s theoretically possible for you to change your mind about something, it can’t have a probability exactly equal to one. The uncertainty might be smaller than a dust speck, but it has to be there. And if you wouldn’t change your mind even if God told you otherwise, then you have a problem with refusing to admit you’re wrong that transcends anything a mortal like me can say to you, I guess.”
But, in a way, the more interesting question is what you say to someone not in front of an audience. How do you begin the long process of teaching someone to live in a universe without certainty?
I think the first, beginning step should be understanding that you can live without certainty—that if, hypothetically speaking, you couldn’t be certain of anything, it would not deprive you of the ability to make moral or factual distinctions. To paraphrase Lois Bujold, “Don’t push harder, lower the resistance.”
One of the common defenses of Absolute Authority is something I call “The Argument From The Argument From Gray,” which runs like this:
Moral relativists say: The world isn’t black and white, therefore:
Everything is gray, therefore:
No one is better than anyone else, therefore:
I can do whatever I want and you can’t stop me bwahahaha.
But we’ve got to be able to stop people from committing murder.
Therefore there has to be some way of being absolutely certain, or the moral relativists win.
Reversed stupidity is not intelligence. You can’t arrive at a correct answer by reversing every single line of an argument that ends with a bad conclusion—it gives the fool too much detailed control over you. Every single line must be correct for a mathematical argument to carry. And it doesn’t follow, from the fact that moral relativists say “The world isn’t black and white,” that this is false, any more than it follows, from Stalin’s belief that 2 + 2 = 4, that “2 + 2 = 4” is false. The error (and it only takes one) is in the leap from the two-color view to the single-color view, that all grays are the same shade.
It would concede far too much (indeed, concede the whole argument) to agree with the premise that you need absolute knowledge of absolutely good options and absolutely evil options in order to be moral. You can have uncertain knowledge of relatively better and relatively worse options, and still choose. It should be routine, in fact, not something to get all dramatic about.
I mean, yes, if you have to choose between two alternatives A and B, and you somehow succeed in establishing knowably certain well-calibrated 100% confidence that A is absolutely and entirely desirable and that B is the sum of everything evil and disgusting, then this is a sufficient condition for choosing A over B. It is not a necessary condition.
Oh, and: Logical fallacy: Appeal
to consequences of belief.
Let’s see, what else do they need to know? Well, there’s the entire rationalist culture which says that doubt, questioning, and confession of error are not terrible shameful things.
There’s the whole notion of gaining information by looking at things, rather than being proselytized. When you look at things harder, sometimes you find out that they’re different from what you thought they were at first glance; but it doesn’t mean that Nature lied to you, or that you should give up on seeing.
Then there’s the concept of a calibrated confidence—that “probability” isn’t the same concept as the little progress bar in your head that measures your emotional commitment to an idea. It’s more like a measure of how often, pragmatically, in real life, people in a certain state of belief say things that are actually true. If you take one hundred people and ask them each to make a statement of which they are “absolutely certain,” how many of these statements will be correct? Not one hundred.
If anything, the statements that people are really fanatic about are far less likely to be correct than statements like “the Sun is larger than the Moon” that seem too obvious to get excited about. For every statement you can find of which someone is “absolutely certain,” you can probably find someone “absolutely certain” of its opposite, because such fanatic professions of belief do not arise in the absence of opposition. So the little progress bar in people’s heads that measures their emotional commitment to a belief does not translate well into a calibrated confidence—it doesn’t even behave monotonically.
As for “absolute certainty”—well, if you say that something is 99.9999% probable, it means you think you could make one million equally strong independent statements, one after the other, over the course of a solid year or so, and be wrong, on average, around once. This is incredible enough. (It’s amazing to realize we can actually get that level of confidence for “Thou shalt not win the lottery.”) So let us say nothing of probability 1.0. Once you realize you don’t need probabilities of 1.0 to get along in life, you’ll realize how absolutely ridiculous it is to think you could ever get to 1.0 with a human brain. A probability of 1.0 isn’t just certainty, it’s infinite certainty.
In fact, it seems to me that to prevent public misunderstanding, maybe scientists should go around saying “We are not INFINITELY certain” rather than “We are not certain.” For the latter case, in ordinary discourse, suggests you know some specific reason for doubt.
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53
How to Convince Me That 2 + 2 = 3
In What is Evidence? I wrote:
This is why rationalists put such a heavy premium on the paradoxical-seeming claim that a belief is only really worthwhile if you could, in principle, be persuaded to believe otherwise. If your retina ended up in the same state regardless of what light entered it, you would be blind . . . Hence the phrase, “blind faith.” If what you believe doesn’t depend on what you see, you’ve been blinded as effectively as by poking out your eyeballs.
Cihan Baran replied:
I can not conceive of a situation that would make 2 + 2 = 4 false. Perhaps for that reason, my belief in 2 + 2 = 4 is unconditional.
I admit, I cannot conceive of a “situation” that would make 2 + 2 = 4 false. (There are redefinitions, but those are not “situations,” and then you’re no longer talking about 2, 4, =, or +.) But that doesn’t make my belief unconditional. I find it quite easy to imagine a situation which would convince me that 2 + 2 = 3.
Suppose I got up one morning, and took out two earplugs, and set them down next to two other earplugs on my nighttable, and noticed that there were now three earplugs, without any earplugs having appeared or disappeared—in contrast to my stored memory that 2 + 2 was supposed to equal 4. Moreover, when I visualized the process in my own mind, it seemed that making XX and XX come out to XXXX required an extra X to appear from nowhere, and was, moreover, inconsistent with other arithmetic I visualized, since subtracting XX from XXX left XX, but subtracting XX from XXXX left XXX. This would conflict with my stored memory that 3 - 2 = 1, but memory would be absurd in the face of physical and mental confirmation that XXX - XX = XX.
I would also check a pocket calculator, Google, and perhaps my copy of 1984 where Winston writes that “Freedom is the freedom to say two plus two equals three.” All of these would naturally show that the rest of the world agreed with my current visualization, and disagreed with my memory, that 2 + 2 = 3.
How could I possibly have ever been so deluded as to believe that 2 + 2 = 4? Two explanations would come to mind: First, a neurological fault (possibly caused by a sneeze) had made all the additive sums in my stored memory go up by one. Second, someone was messing with me, by hypnosis or by my being a computer simulation. In the second case, I would think it more likely that they had messed with my arithmetic recall than that 2 + 2 actually equalled 4. Neither of these plausible-sounding explanations would prevent me from noticing that I was very, very, very confused.
What would convince me that 2 + 2 = 3, in other words, is exactly the same kind of evidence that currently convinces me that 2 + 2 = 4: The evidential crossfire of physical observation, mental visualization, and social agreement.
There was a time when I had no idea that 2 + 2 = 4. I did not arrive at this new belief by random processes—then there would have been no particular reason for my brain to end up storing “2 + 2 = 4” instead of “2 + 2 = 7.” The fact that my brain stores an answer surprisingly similar to what happens when I lay down two earplugs alongside two earplugs, calls forth an explanation of what entanglement produces this strange mirroring of mind and reality.
There’s really only two possibilities, for a belief of fact—either the belief got there via a mind-reality entangling process, or not. If not, the belief can’t be correct except by coincidence. For beliefs with the slightest shred of internal complexity (requiring a computer program of more than 10 bits to simulate), the space of possibilities is large enough that coincidence vanishes.
Unconditional facts are not the same as unconditional beliefs. If entangled evidence convinces me that a fact is unconditional, this doesn’t mean I always believed in the fact without need of entangled evidence.
I believe that 2 + 2 = 4, and I find it quite easy to conceive of a situation which would convince me that 2 + 2 = 3. Namely, the same sort of situation that currently convinces me that 2 + 2 = 4. Thus I do not fear that I am a victim of blind faith.
If there are any Christians in the audience who know Bayes’s Theorem (no numerophobes, please), might I inquire of you what situation would convince you of the truth of Islam? Presumably it would be the same sort of situation causally responsible for producing your current belief in Christianity: We would push you screaming out of the uterus of a Muslim woman, and have you raised by Muslim parents who continually told you that it is good to believe unconditionally in Islam. Or is there more to it than that? If so, what situation would convince you of Islam, or at least, non-Christianity?
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54
Infinite Certainty
In Absolute Authority, I argued that you don’t need infinite certainty:
If you have to choose between two alternatives A and B, and you somehow succeed in establishing knowably certain well-calibrated 100% confidence that A is absolutely and entirely desirable and that B is the sum of everything evil and disgusting, then this is a sufficient condition for choosing A over B. It is not a necessary condition . . . You can have uncertain knowledge of relatively better and relatively worse options, and still choose. It should be routine, in fact.
Concerning the proposition that 2 + 2 = 4, we must distinguish between the map and the territory. Given the seeming absolute stability and universality of physical laws, it’s possible that never, in the whole history of the universe, has any particle exceeded the local lightspeed limit. That is, the lightspeed limit may be, not just true 99% of the time, or 99.9999% of the time, or (1 - 1/googolplex) of the time, but simply al
ways and absolutely true.
But whether we can ever have absolute confidence in the lightspeed limit is a whole ’nother question. The map is not the territory.
It may be entirely and wholly true that a student plagiarized their assignment, but whether you have any knowledge of this fact at all—let alone absolute confidence in the belief—is a separate issue. If you flip a coin and then don’t look at it, it may be completely true that the coin is showing heads, and you may be completely unsure of whether the coin is showing heads or tails. A degree of uncertainty is not the same as a degree of truth or a frequency of occurrence.
The same holds for mathematical truths. It’s questionable whether the statement “2 + 2 = 4” or “In Peano arithmetic, SS0 + SS0 = SSSS0” can be said to be true in any purely abstract sense, apart from physical systems that seem to behave in ways similar to the Peano axioms. Having said this, I will charge right ahead and guess that, in whatever sense “2 + 2 = 4” is true at all, it is always and precisely true, not just roughly true (“2 + 2 actually equals 4.0000004”) or true 999,999,999,999 times out of 1,000,000,000,000.
I’m not totally sure what “true” should mean in this case, but I stand by my guess. The credibility of “2 + 2 = 4 is always true” far exceeds the credibility of any particular philosophical position on what “true,” “always,” or “is” means in the statement above.
This doesn’t mean, though, that I have absolute confidence that 2 + 2 = 4. See the previous discussion on how to convince me that 2 + 2 = 3, which could be done using much the same sort of evidence that convinced me that 2 + 2 = 4 in the first place. I could have hallucinated all that previous evidence, or I could be misremembering it. In the annals of neurology there are stranger brain dysfunctions than this.
Rationality- From AI to Zombies Page 23
