Where Recursive Justification Hits Bottom

by Eliezer Yudkowsky9 min read8th Jul 200874 comments

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PhilosophyReflective ReasoningEpistemologyOccam's Razor
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Why do I believe that the Sun will rise tomorrow?

Because I've seen the Sun rise on thousands of previous days.

Ah... but why do I believe the future will be like the past?

Even if I go past the mere surface observation of the Sun rising, to the apparently universal and exceptionless laws of gravitation and nuclear physics, then I am still left with the question:  "Why do I believe this will also be true tomorrow?"

I could appeal to Occam's Razor, the principle of using the simplest theory that fits the facts... but why believe in Occam's Razor?  Because it's been successful on past problems?  But who says that this means Occam's Razor will work tomorrow?

And lo, the one said:

"Science also depends on unjustified assumptions.  Thus science is ultimately based on faith, so don't you criticize me for believing in [silly-belief-#238721]."

As I've previously observed:

It's a most peculiar psychology—this business of "Science is based on faith too, so there!"  Typically this is said by people who claim that faith is a good thing.  Then why do they say "Science is based on faith too!" in that angry-triumphal tone, rather than as a compliment? 

Arguing that you should be immune to criticism is rarely a good sign.

But this doesn't answer the legitimate philosophical dilemma:  If every belief must be justified, and those justifications in turn must be justified, then how is the infinite recursion terminated?

And if you're allowed to end in something assumed-without-justification, then why aren't you allowed to assume anything without justification?

A similar critique is sometimes leveled against Bayesianism—that it requires assuming some prior—by people who apparently think that the problem of induction is a particular problem of Bayesianism, which you can avoid by using classical statistics.  I will speak of this later, perhaps.

But first, let it be clearly admitted that the rules of Bayesian updating, do not of themselves solve the problem of induction.

Suppose you're drawing red and white balls from an urn.  You observe that, of the first 9 balls, 3 are red and 6 are white.  What is the probability that the next ball drawn will be red?

That depends on your prior beliefs about the urn.  If you think the urn-maker generated a uniform random number between 0 and 1, and used that number as the fixed probability of each ball being red, then the answer is 4/11 (by Laplace's Law of Succession).  If you think the urn originally contained 10 red balls and 10 white balls, then the answer is 7/11.

Which goes to say that, with the right prior—or rather the wrong prior—the chance of the Sun rising tomorrow, would seem to go down with each succeeding day... if you were absolutely certain, a priori, that there was a great barrel out there from which, on each day, there was drawn a little slip of paper that determined whether the Sun rose or not; and that the barrel contained only a limited number of slips saying "Yes", and the slips were drawn without replacement.

There are possible minds in mind design space who have anti-Occamian and anti-Laplacian priors; they believe that simpler theories are less likely to be correct, and that the more often something happens, the less likely it is to happen again.

And when you ask these strange beings why they keep using priors that never seem to work in real life... they reply, "Because it's never worked for us before!"

Now, one lesson you might derive from this, is "Don't be born with a stupid prior."  This is an amazingly helpful principle on many real-world problems, but I doubt it will satisfy philosophers.

Here's how I treat this problem myself:  I try to approach questions like "Should I trust my brain?" or "Should I trust Occam's Razor?" as though they were nothing special— or at least, nothing special as deep questions go.

Should I trust Occam's Razor?  Well, how well does (any particular version of) Occam's Razor seem to work in practice?  What kind of probability-theoretic justifications can I find for it?  When I look at the universe, does it seem like the kind of universe in which Occam's Razor would work well?

Should I trust my brain?  Obviously not; it doesn't always work.  But nonetheless, the human brain seems much more powerful than the most sophisticated computer programs I could consider trusting otherwise.  How well does my brain work in practice, on which sorts of problems?

When I examine the causal history of my brain—its origins in natural selection—I find, on the one hand, all sorts of specific reasons for doubt; my brain was optimized to run on the ancestral savanna, not to do math.  But on the other hand, it's also clear why, loosely speaking, it's possible that the brain really could work.  Natural selection would have quickly eliminated brains so completely unsuited to reasoning, so anti-helpful, as anti-Occamian or anti-Laplacian priors.

So what I did in practice, does not amount to declaring a sudden halt to questioning and justification.  I'm not halting the chain of examination at the point that I encounter Occam's Razor, or my brain, or some other unquestionable.  The chain of examination continues—but it continues, unavoidably, using my current brain and my current grasp on reasoning techniques.  What else could I possibly use?

Indeed, no matter what I did with this dilemma, it would be me doing it.  Even if I trusted something else, like some computer program, it would be my own decision to trust it.

The technique of rejecting beliefs that have absolutely no justification, is in general an extremely important one.  I sometimes say that the fundamental question of rationality is "Why do you believe what you believe?"  I don't even want to say something that sounds like it might allow a single exception to the rule that everything needs justification.

Which is, itself, a dangerous sort of motivation; you can't always avoid everything that might be risky, and when someone annoys you by saying something silly, you can't reverse that stupidity to arrive at intelligence.

But I would nonetheless emphasize the difference between saying:

"Here is this assumption I cannot justify, which must be simply taken, and not further examined."

Versus saying:

"Here the inquiry continues to examine this assumption, with the full force of my present intelligence—as opposed to the full force of something else, like a random number generator or a magic 8-ball—even though my present intelligence happens to be founded on this assumption."

Still... wouldn't it be nice if we could examine the problem of how much to trust our brains without using our current intelligence?  Wouldn't it be nice if we could examine the problem of how to think, without using our current grasp of rationality?

When you phrase it that way, it starts looking like the answer might be "No".

E. T. Jaynes used to say that you must always use all the information available to you—he was a Bayesian probability theorist, and had to clean up the paradoxes other people generated when they used different information at different points in their calculations.  The principle of "Always put forth your true best effort" has at least as much appeal as "Never do anything that might look circular."  After all, the alternative to putting forth your best effort is presumably doing less than your best.

But still... wouldn't it be nice if there were some way to justify using Occam's Razor, or justify predicting that the future will resemble the past, without assuming that those methods of reasoning which have worked on previous occasions are better than those which have continually failed?

Wouldn't it be nice if there were some chain of justifications that neither ended in an unexaminable assumption, nor was forced to examine itself under its own rules, but, instead, could be explained starting from absolute scratch to an ideal philosophy student of perfect emptiness?

Well, I'd certainly be interested, but I don't expect to see it done any time soon.  I've argued elsewhere in several places against the idea that you can have a perfectly empty ghost-in-the-machine; there is no argument that you can explain to a rock.

Even if someone cracks the First Cause problem and comes up with the actual reason the universe is simple, which does not itself presume a simple universe... then I would still expect that the explanation could only be understood by a mindful listener, and not by, say, a rock.  A listener that didn't start out already implementing modus ponens might be out of luck.

So, at the end of the day, what happens when someone keeps asking me "Why do you believe what you believe?"

At present, I start going around in a loop at the point where I explain, "I predict the future as though it will resemble the past on the simplest and most stable level of organization I can identify, because previously, this rule has usually worked to generate good results; and using the simple assumption of a simple universe, I can see why it generates good results; and I can even see how my brain might have evolved to be able to observe the universe with some degree of accuracy, if my observations are correct."

But then... haven't I just licensed circular logic?

Actually, I've just licensed reflecting on your mind's degree of trustworthiness, using your current mind as opposed to something else.

Reflection of this sort is, indeed, the reason we reject most circular logic in the first place.  We want to have a coherent causal story about how our mind comes to know something, a story that explains how the process we used to arrive at our beliefs, is itself trustworthy.  This is the essential demand behind the rationalist's fundamental question, "Why do you believe what you believe?"

Now suppose you write on a sheet of paper:  "(1) Everything on this sheet of paper is true, (2) The mass of a helium atom is 20 grams."  If that trick actually worked in real life, you would be able to know the true mass of a helium atom just by believing some circular logic which asserted it.  Which would enable you to arrive at a true map of the universe sitting in your living room with the blinds drawn.  Which would violate the second law of thermodynamics by generating information from nowhere.  Which would not be a plausible story about how your mind could end up believing something true.

Even if you started out believing the sheet of paper, it would not seem that you had any reason for why the paper corresponded to reality.  It would just be a miraculous coincidence that (a) the mass of a helium atom was 20 grams, and (b) the paper happened to say so.

Believing, in general, self-validating statement sets, does not seem like it should work to map external reality—when we reflect on it as a causal story about minds—using, of course, our current minds to do so.

But what about evolving to give more credence to simpler beliefs, and to believe that algorithms which have worked in the past are more likely to work in the future?  Even when we reflect on this as a causal story of the origin of minds, it still seems like this could plausibly work to map reality.

And what about trusting reflective coherence in general?  Wouldn't most possible minds, randomly generated and allowed to settle into a state of reflective coherence, be incorrect?  Ah, but we evolved by natural selection; we were not generated randomly.

If trusting this argument seems worrisome to you, then forget about the problem of philosophical justifications, and ask yourself whether it's really truly true.

(You will, of course, use your own mind to do so.)

Is this the same as the one who says, "I believe that the Bible is the word of God, because the Bible says so"?

Couldn't they argue that their blind faith must also have been placed in them by God, and is therefore trustworthy?

In point of fact, when religious people finally come to reject the Bible, they do not do so by magically jumping to a non-religious state of pure emptiness, and then evaluating their religious beliefs in that non-religious state of mind, and then jumping back to a new state with their religious beliefs removed.

People go from being religious, to being non-religious, because even in a religious state of mind, doubt seeps in.  They notice their prayers (and worse, the prayers of seemingly much worthier people) are not being answered.  They notice that God, who speaks to them in their heart in order to provide seemingly consoling answers about the universe, is not able to tell them the hundredth digit of pi (which would be a lot more reassuring, if God's purpose were reassurance).  They examine the story of God's creation of the world and damnation of unbelievers, and it doesn't seem to make sense even under their own religious premises.

Being religious doesn't make you less than human.  Your brain still has the abilities of a human brain.  The dangerous part is that being religious might stop you from applying those native abilities to your religion—stop you from reflecting fully on yourself.  People don't heal their errors by resetting themselves to an ideal philosopher of pure emptiness and reconsidering all their sensory experiences from scratch.  They heal themselves by becoming more willing to question their current beliefs, using more of the power of their current mind.

This is why it's important to distinguish between reflecting on your mind using your mind (it's not like you can use anything else) and having an unquestionable assumption that you can't reflect on.

"I believe that the Bible is the word of God, because the Bible says so."  Well, if the Bible were an astoundingly reliable source of information about all other matters, if it had not said that grasshoppers had four legs or that the universe was created in six days, but had instead contained the Periodic Table of Elements centuries before chemistry—if the Bible had served us only well and told us only truth—then we might, in fact, be inclined to take seriously the additional statement in the Bible, that the Bible had been generated by God.  We might not trust it entirely, because it could also be aliens or the Dark Lords of the Matrix, but it would at least be worth taking seriously.

Likewise, if everything else that priests had told us, turned out to be true, we might take more seriously their statement that faith had been placed in us by God and was a systematically trustworthy source—especially if people could divine the hundredth digit of pi by faith as well.

So the important part of appreciating the circularity of "I believe that the Bible is the word of God, because the Bible says so," is not so much that you are going to reject the idea of reflecting on your mind using your current mind.  But, rather, that you realize that anything which calls into question the Bible's trustworthiness, also calls into question the Bible's assurance of its trustworthiness.

This applies to rationality too: if the future should cease to resemble the past—even on its lowest and simplest and most stable observed levels of organization—well, mostly, I'd be dead, because my brain's processes require a lawful universe where chemistry goes on working.  But if somehow I survived, then I would have to start questioning the principle that the future should be predicted to be like the past.

But for now... what's the alternative to saying, "I'm going to believe that the future will be like the past on the most stable level of organization I can identify, because that's previously worked better for me than any other algorithm I've tried"?

Is it saying, "I'm going to believe that the future will not be like the past, because that algorithm has always failed before"?

At this point I feel obliged to drag up the point that rationalists are not out to win arguments with ideal philosophers of perfect emptiness; we are simply out to win.  For which purpose we want to get as close to the truth as we can possibly manage.  So at the end of the day, I embrace the principle:  "Question your brain, question your intuitions, question your principles of rationality, using the full current force of your mind, and doing the best you can do at every point."

If one of your current principles does come up wanting—according to your own mind's examination, since you can't step outside yourself—then change it!  And then go back and look at things again, using your new improved principles.

The point is not to be reflectively consistent.  The point is to win.  But if you look at yourself and play to win, you are making yourself more reflectively consistent—that's what it means to "play to win" while "looking at yourself".

Everything, without exception, needs justification.  Sometimes—unavoidably, as far as I can tell—those justifications will go around in reflective loops.  I do think that reflective loops have a meta-character which should enable one to distinguish them, by common sense, from circular logics.  But anyone seriously considering a circular logic in the first place, is probably out to lunch in matters of rationality; and will simply insist that their circular logic is a "reflective loop" even if it consists of a single scrap of paper saying "Trust me".  Well, you can't always optimize your rationality techniques according to the sole consideration of preventing those bent on self-destruction from abusing them.

The important thing is to hold nothing back in your criticisms of how to criticize; nor should you regard the unavoidability of loopy justifications as a warrant of immunity from questioning.

Always apply full force, whether it loops or not—do the best you can possibly do, whether it loops or not—and play, ultimately, to win.

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"There are possible minds in mind design space who have anti-Occamian and anti-Laplacian priors; they believe that simpler theories are less likely to be correct, and that the more often something happens, the less likely it is to happen again."

You've been making this point a lot lately. But I don't see any reason for "mind design space" to have that kind of symmetry. Why do you believe this? Could you elaborate on it at some point?

7Strange79yMind design space is very large and comprehensive. It's like how the set of all possible theories contains both A and ~A.

That something is included in "mind design space" does not imply that it actually exists. Think of it instead as everything that we might label "mind" if it did exist.

9rkyeun8yImagine a mind as already exists. Now I install a small frog trained to kick its leg when you try to perform Occamian or Laplacian thinking, and its kicking leg hits a button that inverts your output so your conclusion is exactly backwards from the one you should/would have made but for the frog. And thus symmetry.
5wafflepudding4yThough, the anti-Laplacian mind, in this case, is inherently more complicated. Maybe it's not a moot point that Laplacian minds are on average simpler than their anti-Laplacian counterparts? There are infinite Laplacian and anti-Laplacian minds, but of the two infinities, might one be proportionately larger? None of this is to detract from Eliezer's original point, of course. I only find it interesting to think about.
5rkyeun4yThey must be of exactly the same magnitude, as the odds and even integers are, because either can be given a frog. From any Laplacian mind, I can install a frog and get an anti-Laplacian. And vice versa. This even applies to ones I've installed a frog in already. Adding a second frog gets you a new mind that is just like the one two steps back, except lags behind it in computation power by two kicks. There is a 1:1 mapping between Laplacian and non-Laplacian minds, and I have demonstrated the constructor function of adding a frog.
4CCC8yA question. The possible mind, that assumes that things are more likely to work if they have never worked before, can in all honesty continue to use this prior if it has never worked before. But this is only a self-sustaining method if it continues not to work. Let us introduce our hypothetical poor-prior, rationalist observer to a rigged game of chance; let us say, a roulette wheel. (For simplicity, let's call him Jim). We allow Jim to inspect an (unrigged) roulette wheel beforehand. We ask him to place a bet, on any number of his choice; once he places his bet, we use our rigged roulette wheel to ensure that he wins and continues to win, for any number of future guesses. Now, from Jim's point of view, whatever line of reasoning he is using to find the correct number to bet on, it is working. He'll presumably select a different number every time; it continues to work. Thus, the idea that a theory that work now is less likely to work in the future is working... and thus is less likely to work in the future. Wouldn't this success cause him to eventually reject his prior?

Hrm... can't one at least go one step down past Occam's razor? ie, doesn't that more or less directly follow from P(A&B)<=P(A)?

6Quarkster11yNo, because you can't say anything about the relationship of P(A) in comparison to P(C|D)
3Psy-Kosh11yNot sure why you were silently voted down into negatives here, but if I understand your meaning correctly, then you're basically saying this: P(A)*P(B|A) vs P(C) aren't automatically comparable because C, well, isn't A? I'd then say "if C and A are in "similar terms"/level of complexity... ie, if the principle of indifference or whatever would lead you to assign equivalent probabilities to P(C) and P(A) (suppose, say, C = ~A and C and both have similar complexity), then you could apply it. (or did I miss your meaning?)
4Quarkster11yYou got my meaning. I have a bad habit of under-explaining things. As far as the second part goes, I'm wary of the math. While I would imagine that your argument would tend to work out much of the time, it certainly isn't a proof, and Bayes' Theorem doesn't deal with the respective complexity of the canonical events A and B except to say that they are each more probable individually than separately. Issues of what is meant by the complexity of the events also arise. I suspect that if your assertion was easy to prove, then it would have been proven by now and mentioned in the main entry. Thus, while Occam's razor may follow from Bayes' theorem in certain cases, I am far from satisfied that it does for all cases.
3DanielLC9yHow do you know that? Why must P(A) be a function of the complexity of A? Also, this is only sufficient to yield a bound on Occam's razor. How do you know that the universe doesn't favor a given complexity?
3Psy-Kosh9yNot a sole function of its complexity, but if A and B have the same complexity, and you have no further initial reason to place more belief in one or the other, then would you agree that you should assign P(A) = P(B)?
3DanielLC9yComplexity is a function of the hypothesis. Other functions can be made. In fact, complexity isn't even a specific function. What language are we using?

"The important thing is to hold nothing back in your criticisms of how to criticize; nor should you regard the unavoidability of loopy justifications as a warrant of immunity from questioning."

This doctrine still leaves me wondering why this meta-level hermeneutic of suspicion should be exempt from its own rule. Or, if it is somehow not exempt, how is it a superior basis for knowledge as it obfuscates its own suspect status even as it discounts other modes of knowing. At least the blind faith camp is transparent about its assumptions ("you... (read more)

3Kenny8yi think you're underestimating the importance of "winning all the small early battles"; I don't think there'd be anyone left to win "the pivotal battle" had we systematically exposed ourselves to probable defeat.

And if you're allowed to end in something assumed-without-justification, then why aren't you allowed to assume anything without justification?

I address this question in Incremental Doubt. Briefly, the answer is that we use a background of assumptions in order to inspect a foreground belief that is the current focus of our attention. The foreground is justified (if possible) by referring to the background (and doing some experiments, using background tools to design and execute the experiments). There is a risk that incorrect background beliefs will "lock in" an incorrect foreground belief, but this process of "incremental doubt" will make progress if we can chop our beliefs up into relatively independent chunks and continuously expose various beliefs to focused doubt (one (or a few) belief(s) at a time).

This is exactly like biological evolution, which mutates a few genes at a time. There is a risk that genes will get "locked in" to a local optimum, and indeed this happens occasionally, but evolution usually finds a way to get over the hump.

Should I trust Occam's Razor? Well, how well does (any particular version of) Occam's Razor seem to work in pract... (read more)

5SecondWind8yBy examining our cognitive pieces (techniques, beliefs, etc.) one at a time in light of the others, we check not for adherence of our map to the territory but rather for the map's self-consistency. This would appear to be the best an algorithm can do from the inside. Self-consistent may not mean true, but it does mean it can't find anything wrong with itself. (Of course, if your algorithm relies on observational inputs, there should be a theoretical set of observations which would break its self-consistency and thus force further reflection.)

"So at the end of the day, I embrace the principle: 'Question your brain, question your intuitions, question your principles of rationality, using the full current force of your mind, and doing the best you can do at every point.'"

. . . to the extent that doing so increases your power, as illustrated by the principle you embrace to a greater extent:

"The point is to win."

That's the faith position.

"Everything, without exception, needs justification."

. . . except that toward which justification is aimed: power.

"The important... (read more)

I think the best way to display the sheer mind-boggling absurdity of the "problem of induction" is to consider that we have two laws: the first law is the law science gives us for the evolution of a system and the second law simply states that the first law holds until time t and then "something else" happens. The first law is a product of the scientific method and the second law conforms to our intuition of what could happen. What the problem of induction is actually saying is that imagination trumps science. That's ridiculous. It's ap... (read more)

4Peterdjones8yYou seem to have a picture of science that consists of data-gathering. Once you bring in theories, you then have a situation where there a multuple theories, and some groups of scientists are exploring theory A rather than B..and that might as well be called belief.
0[anonymous]8yI think justification is important, especially in matters like AI design, as an uFAI could destroy the world. In the case of AI design in general, consider the question "Why should we program an AI with a prior biased towards simpler theories?" I don't think anyone would argue that a more detailed answer than "It's our best guess right now." would be desirable.
4[anonymous]8yI think justification is important, especially in matters like AI design, as an uFAI could destroy the world. In the case of AI design in general, consider the question "Why should we program an AI with a prior biased towards simpler theories?" I don't think anyone would just walk away from a more detailed answer than "It's our best guess right now.", if they were certain such an answer existed.

Hurrah! Eliezer says that Bayesian reasoning bottoms out in Pan-Critical Rationalism.

re: "Why do you believe what you believe?"

I've always said that Epistemology isn't "the Science of Knowledge" as it's often called, instead it's the answer to the problem of "How do you decide what to believe?" I think the emphasis on process is more useful than your phrasing's focus on justification.

BTW, I don't disagree with your stress on Bayesian reasoning as the process for figuring out what's true in the world. But Bartley really did ... (read more)

To understand the problem of induction simply think of organism X. Organism X is snatched from the wild and put in a new environment. On the first day in the new environment some strange compound is put in a small dish in the corner. Organism X eats it, simply because organism X is hungry. The second day, to organism X's surprise, the dish is refilled. The dish is refilled for the next 100 days. Organism X's confidence that tomorrow it will be fed is at an all time high by the 102nd day, but the very next day is November 18th. At the height of organism X's confidence that their single variable model is infallible is the exact moment organism X is slaughtered so that I can have an enjoyable turkey dinner for Thanksgiving.

Please clarify "I do think that reflective loops have a meta-character which should enable one to distinguish them, by common sense, from circular logics."

What physical configuration of the universe would refute this?

At the height of organism X's confidence that their single variable model is infallible is the exact moment organism X is slaughtered so that I can have an enjoyable turkey dinner for Thanksgiving.
Yes... so?

How might this organism deduce that it was going to be killed on that day from the data available to it?

"I don't see how such a mind could possibly do anything that we consider mind-like, in practice."

This is a fabulous way of putting it. "In practice" may even be too strong a caveat.

Cole: symmetry of problem space is implied by "no free lunch". So, an optimizer that works in problem volume X should have a dual pessimizer that works just as well in anti-X.

Minds are a subset of optimizers.

A good way of putting it, Julian. Anti-Occamian anti-Laplacian minds perform well in anti-Occamian anti-Laplacian universes!

...though, I'm not really sure what happens when they try to reflect on themselves, or for that matter, how you build a mind out of anti-Occamian materials. The notion of an anti-regular universe may be consistent to first order, but not to second order. Is it regularly anti-regular, or anti-regularly anti-regular?

I'd actually like to see one of these supposed anti-Occam or anti-regular priors described in full detail - I'm not sure the concept is coherent.

In fact, an anti-Occam prior is impossible. As I've mentioned before, as long as you're talking about anything that has any remote resemblance to something we might call simplicity, things can decrease in simplicity indefinitely, but there is a limit to increase. In other words, you can only get so simple, but you can always get more complicated. So if you assign a one-to-one correspondence between the natural numbers and potential claims, it follows of necessity that as the natural numbers go to infinity, the complexity of the corresponding claims goes to... (read more)

5aspera8yI think it would be possible to have an anti-Occam prior if the total complexity of the universe is bounded. Suppose we list integers according to an unknown rule, and we favor rules with high complexity. Given the problem statement, we should take an anti-Occam prior to determine the rule given the list of integers. It doesn't diverge because the list has finite length, so the complexity is bounded. Scaling up, the universe presumably has a finite number of possible configurations given any prior information. If we additionally had information that led us to take an Anti-Occam prior, it would not diverge.

Eliezer, I want to read more about design spaces. Is this a common term in computer science? Do you remember where you picked it up?

It seems to me that playing to win requires an implicit assumption that it is possible to win, and this assumes that there is structure out there, a very weak form of Occam's razor.

In fact, an anti-Occam prior is impossible.

Unknown, your argument amounts to this: Assume we have a countable set of hypotheses. Assume we have a complexity measure such that, for any given level of complexity, there are a finite number of hypotheses that are below the given level of complexity. Take any ordering of the set of hypotheses. As we go through the hypotheses according to the ordering, the complexity of the hypotheses must increase. This is true, but not very interesting, and not relevant to Occam's Razor.

In this framework, a natural way to stat... (read more)

I'd actually like to see one of these supposed anti-Occam or anti-regular priors described in full detail - I'm not sure the concept is coherent.

That's easy. Go to a casino and watch the average moron play roulette using a "strategy".

Also, Russell Kirk is a moron too. I love how his text is full of nothingness, or, as Eliezer says, "applause lights". Loved that expression, by the way.

Peter Turney: yes, I define Occam's Razor in such a way that all orderings of the hypotheses are Occamian.

The razor still cuts, because in real life, a person must choose some particular ordering of the hypotheses. And once he has done this, the true hypothesis must fall relatively early in the series, namely after a finite number of other hypotheses, and before an infinite number of other hypotheses. The razor cuts away this infinite number of hypotheses and leaves a finite number.

The razor still cuts, because in real life, a person must choose some particular ordering of the hypotheses.

Unknown, you have removed all meaning from Occam's Razor. The way you define it, it is impossible not to use Occam's Razor. When somebody says to you, "You should use Occam's Razor," you hear them saying "A is A".

An anti-Laplacian prior is defined in the obvious way; if you've observed R red balls and W white balls, assign probability (W + 1) / (R + W + 2) of seeing a red ball on the next round.

An anti-Occamian prior is more difficult, for essentially the reasons Unknown states; but let's not forget that, in real life, Occam priors are technically uncomputable because you can't consider all possible simple computations. So if you only consider a finite number of possibilities, you can have an improper prior that assigns greater probability to more complex explanations, and then normalize with whatever explanations you're actually considering.

4Will_Sawin10yWRW has probability 1/2 2/3 1/2 = 1/6 WWR has probability 1/2 1/3 3/4 = 1/8 This is coherent if you require that the probability of different permutations of the same sequence be the same. An Anti-Laplacian urn must necessarily be finite. On the other hand, Laplace assigns both a probability of 1/12.

By "full detail" I meant a prior over all possible states, not just over the next observation. The most disturbing prior I think is one that makes all observations independent of each other. All other priors allow some predictions of the future from the past - and given any particular prior we naturally find a way to call its favored states "simpler." I doubt the word "simple" has a meaning pinned down independently of that.

Surely the ultimate grounding for any argument has to be the facts of reality? Every chain of reasoning must end not by looping back on itself but by a hand pointing at something in reality.

A. It should be mentioned that this "Induction Problem" ("Why would things work in the future as in the past, more probably than in some other way") (or actually the criticism of the Induction Hypothesis) is due to the Scottish Enlightenment philosopher and liberal David Hume. http://en.wikipedia.org/wiki/David_Hume#Problem_of_induction

B. Why do our brains trust in Occam's Razor or in induction (that things work in the future as in the past, ...)? Because the universe behaved that way in the past, so most brains working in another way w... (read more)

Lincoln Cannon: Aiming for power is just as arbitrary as aiming for having many descendants. Capability is important, because it's an objective measure. But power as an abstract? Power for what? Is a millionaire more powerful than a charismatic person? Each can do things the other can not. There are many capabilities that will help you with lots of goals, but even a super entity is going to have to make trade-offs, and it can't decide to simply go for more power because each possible investment will yield the most power in certain situations (and certain g... (read more)

I was wondering when someone would mention Hume. Instructive to note Hume's 'solution' to the Problem of Induction: behave as if there were no such problem. Practically speaking, in actual life, it is impossible to do otherwise. As relates to this discussion, it seems to foreguess Eliezer's point that there are no 'mysterious' answers to be found. Everything will be as it was, once we have found what we are looking for.

Hume also recommended billiards, backgammon, and dining with friends. Sound advice, indeed.

It's clear that there are some questions to which there are (and likely never will be) fully satisfactory answers, and it is also clear that there is nothing to be done about it but to soldier on and do the best you can (see http://www.overcomingbias.com/2007/05/doubting_thomas.html). However, there really are at least a few things that pretty much have to be assumed without further examination. I have in mind the basic moral axioms like the principle that the other guy's welfare is something that you should be at all concerned about in the first place.

""If I had not done among them the works which none other man did, they had not had sin: but now have they both seen and hated both me and my Father"

Even the Bible doesn't demand blind faith.

Huh. If you believe that the timespan of this Earth is finite, which you probably should if you are a Christian, then does that mean that, according to that prior, your confidence in the sun rising tomorrow should, in fact, be decreasing with each passing day? o.o And does this mean, that every time the sun rises ought to decrease your confidence in that prior, which should then lend itself less weight in your determination of the sun's likelihood of rising.....

Seems like a convergent series to me, but I'd like to see someone else better-versed in the math than me work it out.

5shminux9yNot necessarily, a memoryless process (e.g. same odds of the second coming happening today as yesterday) follows the Exponential distribution [http://en.wikipedia.org/wiki/Exponential_distribution]. It has a finite expected value, even though it has no memory. Radioactive decay is a standard example.
3Arandur9yOh, I see. :3 Thanks.

To me this is also greatly linked with the "belief in belief" theme : most people who do claim that Occam's Razor don't hold, who question using rationality on philosophical questions, do use them in daily life. When they see the cat entering a room, here a noise, see a broken glass, they assume it's the cat who broke the glass, not aliens or angels who teleported in the room, broke the glass, and then disappeared. When they feel hungry, they open the fridge, take out some food, and eat it, assuming the food will be in the fridge "like befor... (read more)

But for now... what's the alternative to saying, "I'm going to believe that the future will be like the past on the most stable level of organization I can identify, because that's previously worked better for me than any other algorithm I've tried"?

Is it saying, "I'm going to believe that the future will not be like the past, because that algorithm has always failed before"?

To me, this is the point: "what's my alternative?"

A principle I got from a Stephen Donaldson novel applies to "the future will be like the past". The guy needed to find a bit of sabotage in a computer system. He had no expertise in software - or hardware, for that matter. But he needed to find the problem, or he would be dead.

The character got the principle he needed from bridge. In bridge, sometimes you're screwed unless your partner has the card you need him to have. So the play is to assume your partner has the card, and play accordingly, because if he doesn't, you're screwed anyway.

Assume you can win. Assume that everything necessary for you to win is true. If it isn't, you're screwed anyway.

If the future isn't like the past, how am I to know what ideas to rely ... (read more)

Well, if you wanted to actually test Occam's razor in a scientific way, you would have to test it against an alternate hypothesis and see which one gave better predictions, wouldn't you?

So how about this as an alternate hypothesis:

"Occam's Razor has no objective truth value; there is no fundamental reason that the truth is more likely to be a simpler explanation. It only SEEMS like Occam's Razor is true because it is exponentially harder to find a valid explanation in a larger truth-space, so usually when we do manage to find a valid explanation for ... (read more)

3TheOtherDave8yCan you summarize the articulation of Occam's Razor that this conflicts with? Because I don't normally think of OR as asserting anything about fundamental reasons, merely about reliable strategies... and your hypothesis agrees about reliable strategies.
4BerryPick68yDoes the alternate hypothesis even give us different results? How would a world in which the second hypothesis was true look like when compared to one in which Occam's Razor holds?
3Yosarian28yWell, let's see. If you take an unsolved scientific question, and create a hypothesis that is the simplest possible fit for that answer given the known facts, how often is that answer true, and how often is a more complex answer actually true? I'm sure we can all think of examples and counterexamples (Newton's theories are a lot simpler fit for the facts he knew then relativity, but they turned out to not be true), but you would probably have to take a large sample of scientific problems. I would think that Occam's razor would turn out to be correct most of the time in a statistical analysis, but it seems like a testable hypothesis, at least in the set of (problems human scientists have solved).
3TheOtherDave8ySorry, I still don't get it. Suppose we somehow do this study, and we find that N% of the time the "simplest possible fit given the known facts" is true, and (1-N)% of the time it isn't. For what range of Ns would you conclude that Occam's Razor is correct, and for what range of Ns would you conclude that your alternative hypothesis is instead correct?
3Yosarian28yI will admit that I'm struggling a bit here, because I'm having trouble coming up with a coherent mental picture of what a legitimate alternate hypothesis to Occam's razor would actually look like. In fact, if you take my hypothesis to be true, then Occam's razor would still fundamentally hold, at least in the simplest form of "a less complicated theory is more likely to be true then a more complicated", since if "theory-space A" is smaller then "theory-space B", then any given point in theory-space A is more likely to be true then any given point in theory-space B even if the answer has an equal chance of being in space A as it does of being in space B. So I think my original hypothesis actually itself reduces to Occam's Razor. I think this is where I just say oops [http://lesswrong.com/lw/i9/the_importance_of_saying_oops/] and drop this whole train of thought.
4Qiaochu_Yuan8yHere's one. The universe is a particularly perverse simulation, largely controlled by a sequence of pseudorandom number generators. This sequence of PRNGs gets steadily more and more Kolmogorov-complicated (the superbeings that run us love complicated forms of torture), so even if we figured out how a given one worked the next one would already be in play, and it is totally unrelated, so we'd have to start all over. Occam's razor fails badly in such a universe because the explanation for any particular thing happening gets more complicated over time. In other words, Quirrell-whistling writ large.
3BerryPick68yI guess we could test this one by looking at successful explanations over time and seeing whether their complexity increases at a steady rate? Then again, I can already find two or three holes in that test... Hmm. This is a tricky one.
3TheOtherDave8yYeah, that's what I think too. Presumably, what I'd expect to see if Occam's Razor is an unreliable guideline is that when I'm choosing between two explanations, one of which is more complex for a consistent and coherent definition of complexity, it turns out that simpler explanation is often incorrect.
[-][anonymous]7y 3

When philosopher Susan Haack wrote "Evidence and Inquiry" back in 1995, she really hit the nail on the head on this one. I'll share an extensive quotation from her, and then I'll make a couple remarks:

The obser­vation that people have many beliefs in which they are not, or not much, justified...hints, though it doesn't say explicitly, that people also have beliefs in which they are justified. And it is a legitimate question, certainly, what reasons there are for even this degree of optimism. On this issue, it may be feasible to appeal to evol

... (read more)
4TheAncientGeek4yWell, if his evidence for the existence of natural laws is not itself based on induction, he escapes circularity No one knows what a natural law is, and no one has detected one by direct inspection. The popular answer, that they are "just descriptions" fails particularly badly if one is trying to demonstrate how one has avoided circularity. PS thanks for the Kelley link.