Absolute Authority

For all your talk about The One, I'm going to start to call you Morpheus.

I wonder what your life must be like. The way you write, it sounds as if you spend a lot of your time trying to convince crazy people (by which I mean most of humanity, of course) to be less crazy and more rational, like us. Why not just ignore them?

Then I looked at your Wikipedia entry and noticed how young you are. Ah! When I was your age, I was also trying to convert everybody. My endless arguments about software development methods, circa 1994, are still in Google's Usenet archive. So, who am I to talk?

(Note: Mostly I write comments that complain about something you say, but please understand that there's a selection bias here. Even though I often find myself thinking "What an interesting way to think about that. Great idea, Eliezer!" I would rather write comments that have some kind of content, and those tend to be the critical ones.)

I really enjoy your deep analysis of topics, but might I suggest writing shorter entries a bit more often?

Sam, if I write shorter entries, I'll never get everything said.

James: Snort. One of these days I'll do a post on "maturity bias".

Oh Eliezer, why'd you have to toss that parenthetical in about priors? The rest of the post is so wonderful. But the priors thing... hell, for my part, the objection isn't to priors that aren't imposed by some Authority, it's priors that are completely pulled out of one's arse. Demanding something beyond the whim of some metaphorical marble bouncing about in one's brain before one gets to make a probability statement is hardly the same as demanding capital-A-Authority.

The main reason people think a probability of 100% is necessary is that they assume that any other probability implies a subjective feeling of doubt, and they are aware that it is impossible to go through life in a continuous state of subjective doubt about whether or not food is necessary to sustain one's life and the like.

Once someone has separated the probability from this subjective feeling, a person can see that a subjective feeling of certainty can be justified in many cases, even though the probability is less than 100%. Once this has been admitted, I think most people would not have a problem with admitting that 100% probabilities are not possible.

Eliezer, every time you say "the one" you mean to say "one".

I once thought I had a fast, crushing argument against the existence of God. I would point to various objects around me and ask "What does that do?" e.g. point at a beach ball and they would say "bounce," point at a bird and they would say "sing." And I would triumphantly say, "See, God can't exist!" and they would look at me blankly.

In my mind, every object I had ever seen did it's own peculiar thing - that is, it didn't do "just anything." Therefore the idea of omnipotence - the ability to make objects do whatever you please is contradicted by all the evidence, and therefore God (a supposedly omnipotent being) is too.

What I didn't grasp, was that all the evidence of every object they had seen in their entire life wasn't convincing to them(!), as long as they could still imagine a counter-example. They gave their own imagination the same weight as real evidence. So it wasn't a quick argument after all, it would require explaining evidence vs. imagination and that would lead to another thing, and another, and before you know it, it's an entire website full of articles. So I have to agree with Eliezer, there's no simple way to convey an entire mental framework in short order.

Practically all words (eg "dead") actually cut across a continuum; maybe we should reclaim the word "certainty". We are certain that evolution is how life got to be what it is, because the level of doubt is so low you can pretty much forget about it. Any other meaning you could assign to the word "certain" makes it useless because everything falls on one side.

Denis, you will definitely enjoy this one.

Thinking of science in religious terms makes the whole thing fall over, for everyone. The only way you can have 100% certainty in something is if it's not falsifiable. The only way something can be unfalsifiable is if it is mysterious, ethereal and makes no testable predictions.

My withering rejoinder? "Yes, you may have god. But do you have any knowledge?"

'Any other meaning you could assign to the word "certain" makes it useless because everything falls on one side.'

Yes, exactly. The concept of "certainty" as colloquially used has no referents. It is such a strict standard, the only things that could possibly be referents for it are statements made by an omniscient entity. A statement by any lesser entity could be wrong and therefore could not be a referent. We are beating ourselves up over a concept no more valid that "unicorn."

Ian, your God argument doesn't follow:

1) Objects behave in certain, predictable ways 2) God can make objects behave arbitrarily 4) No objects behave arbitrarily 5) There is no God

Hidden argumentation:

3) Therefore, God WILL make things behave arbitrarily

You can't assume that an omnipotent God will behave in any particular way.

You can't assume that an omnipotent God will behave in any particular way.

What happens when an immovable object meets an irresistible force?

I think you've mischaracterized Ian's argument. He seems to be arguing that because everything in his empirical experience behaves in particular ways and appears incapable of behaving arbitrarily, that this is strong evidence to suggest that no other being could exist which is capable of behaving arbitrarily.

I think the real weakness of this argument is that the characterization of things as behaving in particular ways is way too simplistic. Balls may roll as well as bounce. They can deflate or inflate, or crumple or explode, or any of a thousand other things. As you get more complex than balls, the range of options get wider and wider. For semi-intelligent animals the range is already spectacularly wide, and for sentient creatures, the array of possibility is literally terrifying to behold.

We see this vast range in our experience of things, and the range of behaviors and powers that they have, that it seems doubtful we can circumscribe too closely what some unknown being would be able to do. Now, complete omnipotence poses huge philosophical and mathematical problems not unlike infinite sets or probabilities of 1. Intuitively I can see that the same arguments rendering probabilities of 1 impossible (or at least impossible to prove) would seem to work equally well against total ominipotence.

But what if omnipotence, like the normal use of "certainty", doesn't have to mean the absolute ability to do anything at all, but merely so much power and range of use of power that it can do anything we could practically conceive for it to do. This is probably the sense in which early writers mean to claim that God is all-powerful, but the lack of precision in language tripped them up.

I suggest we don't have any strong evidence to suggest that such a being could never exist. In fact, anyone who doesn't consider interest in a potential singularity a complete load of horse manure must agree with me that it's entirely possible that some of us will either become create such beings.

In my mind, either this is no argument against religions with omnipotent gods or it's a damning argument against the singularity. Which is it?

LG - Your objection is only valid if you assume I am starting with the idea of omnipotence and trying to use the evidence to disprove it. In fact, I am starting with the evidence and showing that the idea of omnipotence can't be arrived at without contradiction.

1) Objects behave in certain, predictable ways 2) Therefore the suggestion that someone could make an object behave arbitrarily contradicts the evidence 3) Therefore the idea of "omnipotence" contradicts the evidence 4) Therefore the idea of God contradicts the evidence

It's a different style of reasoning: starting with reality vs. starting with imagination and then using reality only as a test.

Ian, are you arguing that the concept of omnipotence is incoherent, or merely (as Michael seems to have interpreted you:) that we have no reason to believe that any omnipotent entity actually exists?

If you really mean the latter, then I suspect most people here will agree with you: if one does not observe any evidence for omnipotence, and one accepts Occam's razor (as reasonable people do), then one concludes that no omnipotent entity exists, unless and until strong evidence to the contrary comes up.

But it remains the case that the idea of omnipotence is compatible with the evidence. The religious can, without logical self-contradiction, claim that God-in-Her-Infinite-Wisdom chooses to make created objects behave in predictable ways. It's true that one would be silly to believe this story: that would be violating Occam's razor, "starting with imagination, and then using reality only as a test"--however you want to phrase it--but it's not contradictory.

If you want to show that an omnipotent entity cannot exist (that P(God-exists) is closer to, say, P(1+1=9) than P(there's-an-invisible-unicorn-following-you)), you have to do a little more work. Fortunately, it's already been done (see Caledonian's comment).

Here's an example: some time ago I was discussing evolution with a creationist, and was asked "Can you prove it?" I responded that "prove" isn't the appropriate word, but rather scientists gather and evaluate evidence to see what position the evidence most clearly supports. He crowed in jubilation. "Then you don't have any proof!" he exclaimed.

So my response in that situation has changed. I now respond, "Yes, we have the same level of proof that sends people to death row: We've got the DNA!" That's adapted from Sean B. Carroll, author of Making of the Fittest.

With respect to the first potential response you identify,

"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."

RBH

Ian, your argument fails not merely because premise 1 isn't established apodictically. (Which is the flaw of inductive reasoning generally, but which, as Eliezer tries to point out to the religious, doesn't mean we don't have good reason to believe it.)

It also fails because we have counterexamples up the wazoo. Michael's point about sentient creatures is one of them. But we can generate a lot of others just by diddling around the space in which we define "objects." Balls bounce and roll, bowling balls just roll, spherical objects generally do all sorts of crazy things. So the "spherical things" case is a counterexample too, just so far as you define the class of objects in such a way that spherical things count as objects.

You get a one-to-one mapping of object to function only by defining the objects on the functions, by picking as your object a uni-function (or few-function) idea like "ball." So your argument is actually circular in a sense.

Eliezer's use of "the one" is not an error or a Matrix reference, it's a deliberate echo of an ancient rabbinical trope. (Right, Eliezer?)

I think Ian makes an important point: people give their ability to imagine something the same weight as evidence. The most gratuitous example of this, relevant here because it's the impetus for inductive probabilism, is the so-called "problem of induction." Say we have two laws concerning the future evolution of some system, call them L1 and L2, such that at some future time t L2(t) gives a result that is defined only as being NOT the result given by L1(t). L1 is based on observation. L2 represents my ability to imagine that my observations will fail to hold at some future time t. The problem of induction is a result of giving MORE weight to L2 than L1.

Actually, I didn't realize "the one comes to us and says" was a rabbinical borrowing until it was pointed out to me. But it seems to have the right tone, and it's syntactical; I care not whether it is grammatical.

Poke, that's a really unhelpful way of thinking about the problem of induction. The problem of induction is a problem of logic in the first instance -- a description of the fact that we do have absolute knowledge of the truth of deductive arguments (conditional on the premises being true) but we don't have absolute knowledge of the truth of inductive arguments. And that's just because the conclusion of a deductive argument is (in some sense) contained in the premises, whereas the conclusion of a generalization isn't contained in the individual observations. What's contained in the individual observations (putting on social scientist hat here) is a probability, given one's underlying distribution, of finding data like what you found if the world is a certain way.

That's a real distinction -- it doesn't come from somehow giving weight to imaginary possibilities, it reflects the difference between logical truth (which IS absolute) and empirical truth (which is not).

Michael: "Balls may roll as well as bounce. They can deflate or inflate, or crumple or explode, or any of a thousand other things." Paul: "It also fails because we have counterexamples up the wazoo."

But even if an object behaves thousands of ways, it is still behaving in those ways and only those ways. If we want to work with it, we must follow cause and effect, we can't simply will it to do what we want. That is the case for all objects I know of, there are no counter-examples.

Z. M. Davis: "are you arguing that the concept of omnipotence is incoherent, or merely [...] that we have no reason to believe that any omnipotent entity actually exists?"

I am arguing that observation proves that omnipotence is impossible. If object behavior is determined by the kind of thing it is (which appears to be the case, since the same kinds of things act the same), then it is not determined by anything else, such as the will of an external agent.

"The religious can, without logical self-contradiction, claim that God-in-Her-Infinite-Wisdom chooses to make created objects behave in predictable ways."

Their claim that object behavior is determined by God contradicts the observation that it is determined by what kind of thing an object is.

p.s. I think this discussion has gotten a little OT (sorry Eliezer)

Paul Gowder,

I think your response is too general. How does the problem of induction being an deductive argument make the conclusion any less absurd? It's a deductive argument that takes as its premise my ability to imagine something being otherwise. That makes sense if you're an Empiricist philosopher, since you accept an Empiricist psychology a priori, but not a lot of sense if you're a scientist or committed to naturalism. Further, the difference you cite between deductive and inductive arguments (that the former is certain and the latter not), is the conclusion of the problem of induction; you can't use it to argue for the problem of induction.

Really like your article. Thanks

Poke: let's attack the problem a different way. You seem to want to cast doubt on the difference along the dimension of certainty between induction and deduction. ("the difference you cite between deductive and inductive arguments (that the former is certain and the latter not), is the conclusion of the problem of induction; you can't use it to argue for the problem of induction")

Either deduction and induction are different along the dimension of certainty, or they're not. So there are four possibilities. induction = certain, deduction = certain (IC, DC); InC, DnC; IC, DnC; and InC, DC.

Surely, you don't agree that induction gives us certain knowledge. The "imagination-based" story: the fact that the coin came up heads the last three million times gives us very high probability for the proposition that the coin is loaded, but not certain. But you've rejected the "imagination-based" story. I'm fine with that. Because there are real stories. Countless real stories. Every time one scientist repeats another scientist's experiment and gets a different result, it's a demonstration of the fact that inductive knowledge isn't certain: the first scientist validly drew a conclusion from induction as a result of his/her experiments (do you disagree with that??), and the second scientist showed that the conclusion was wrong or at least incomplete. Ergo, induction doesn't give us certain knowledge.

That eliminates two possibilities, leaving us with InC, DnC and InC, DC. The following is a deductive argument. "1. A. 2. A-->B. 3. B." Assume 1 and 2 are true. Do you think we thereby have certain knowledge that B? If so, you seem to be committed to DC, and thereby to a difference between induction and deduction on the domain of certainty.

(Heavens... the things I do rather than sleep.)

Ian C: What about an universal Turing machine?

Maybe you should try telling some parables about people who thought they had certain knowledge. Maybe some of them should include other people who did not think their knowledge was certain.

I cannot accept that Probability must be applied to everything. Which of course indirectly states that there are no absolutes, since probability has no 0 or 1.

If you discard absolutes, you must be willing to accept mysticism and contradictions.

I can create a long list of false or contradictory statements, and anyone who lives by probabilities must obediently tell me that every one of them is possible.

• "Does God exist?" "Probably not, but it's possible."

• "Can he create a boulder that he cannot lift?" "Probably not, but it's possible."

• "If God dropped that boulder on me, would I survive?" "Probably not, but it's possible."

• "Can he lift that boulder that he created to be unliftable by him?" "I dunno. It's possible."

• "Do I exist?" "Probably, but you might not."

• "Does existence exist?" "It probably does, but it might not."

• "Can probability really have 0% or 100%?" "Probably not, but it might be possible..."

Besides, "There are no absolutes" is a statement that invokes an absolute to claim that there are none. It contradicts itself. It is an example of the fallacy of the stolen concept.

In the world of the unenlightened ones, there is authority and un-authority. What can be trusted, can be trusted; what cannot be trusted, you may as well throw away. There are good sources of information and bad sources of information.

This is pretty much the standard argument against Wikipedia. It fails to address the question of "what's it for?"

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.

I think that latter statement is equivalent to this:

V = Virgin Birth
G = God appears and proclaims ~V

P(V|G) < 1
∴​P(V) < 1

But that argument is predicated on P(G) > 0. It is internally consistent to believe P(V|G) < 1 and yet P(V) = 1, as long as one also believes P(G) = 0, i.e. one is certain that God will not appear and proclaim ~V.

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.

This is supposed to be an argument against giving anything an 100% probability. I do agree with the concept, but this particular argument seems wrong. It's based on Conservation of Expected Evidence (if the "technical reasons of probability theory" refer to something else, let me know). However, the Bayes rule doesn't just imply that "having a chance of changing your mind" -> "you are not 100% certain", it also gives us bounds on what posteriors we can have. If we evaluate a 5% chance to changing our minds on something, that would seem to imply that we cannot put a >95% in our original claim.

So, the reason I reject this is as follows:

EY lays out possible evidence for 2+2=3 here. Imagine you believe at 50% level that someone will cause you to view that evidence tomorrow. Hypnosis, or some other method. Applying Bayes rule like EY seems to be applying it here, you should evaluate right now at most a 50% chance that 2+2=4. I think the rational thing to do in that situation (where putting the earplugs together does in fact show 2+2 equaling 4), is to believe that 2+2=4, with around the same much confidence as you do now. Therefore, there is something wrong with this line of reasoning.

If anyone can point to what I'm doing wrong, or thinks that in the situation I outlined, the rational thing to do is to evaluate a 50% or lower chance of 2+2=4, I'd like to hear about it.

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.

Have you considered selling merch? I'm infinitely certain I'd buy a T-shirt with that quote.

The Dalai Lama stated that "If science proves some belief of Buddhism wrong, then Buddhism will have to change."

I like the guy :)

Another problem with some people is that they don’t consciously believe (or won’t openly admit) they have absolute certainty. In their speech, they say that they doubt this and that, that they "cannot know everything" but I guess that’s mostly a trick for them to say "and neither do you." With them, one first needs to convince them that they are lying to themselves before having a talk about certainty vs uncertainty.