A Priori

My posts for the next two days will be on related topics.

Something feels off about this to me. Now I have to figure out if it's because fiction feels stranger than reality or because I am not confronting a weak point in my existing beliefs. How do we tell the difference between the two before figuring out which is happening? Obviously afterward it will be clear, but post-hoc isn't actually helpful. It may be enough that I get to the point where I consider the question.

On further reflection I think it may be that I identify a priori truths with propositions that any conceivable entity would assign a high plausibility value given enough thought. I think I'm saying "in the limit, experience-invariant" rather than "non-experiential". I believe that some things, like 2+2=4, are experience-invariant: in every universe I can imagine, an entity who knows enough about it should conclude that 2+2=4. Perhaps my imagination is deficient, though. :)

Generalizing from past observations to future expectations is often referred to in philosophy as the "problem of induction". It has the same problem is that you have to accept induction working in the past to expect it to work in the future, and if Bertrand Russell is right to argue that you were created five seconds ago with false memories you can't know it worked in the past either. Against that kind of skepticism I can only fall back on a David Stove type "common sense" position, but fortunately I am not interested in persuading others but understanding the world well enough to attain my goals.

You left the italics tag on.

Greedy, all you're doing is specifying properties into the definition of what you mean by "entity" or "knows enough". I can always build a tape recorder that plays back "Two and two make five!" forever.

TGGP, fixed the tag. And remember, it's not about persuading an ideal philosophy student of perfect emptiness, it's about understanding why the engine works.

I can rigorously model a universe with different contents, and even one with different laws of physics, but I can't think of how I could rigorously model (as opposed to vaguely imagine) one where 2+2=3. It just breaks everything. This suggests there's still some difference in epistemic status between math and everything else. Are "necessary" and "contingent" no more than semantic stopsigns? How about "logical possibility" as distinct from physical possibility?

I don't really understand what Eliezer is arguing against. Clearly he understands the value of mathematics, and clearly he understands the difference between induction and deduction. He seems to be arguing that deduction is a kind of induction, but that doesn't make much sense to me.

Nick: you can construct a model where there is a notion of 'natural number' and a notion of 'plus' except this plus happens to act 'oddly' when applied to 2 and 2. I don't think this model would be particularly interesting, but it could be made.

Nick, I'm honestly not sure if there's a difference between logical possibility and physical possibility - it involves questions I haven't answered yet, though I'm still diligently hitting Explain instead of Worship or Ignore. But I do know that everything we know about logic comes from "observing" neurons firing, and it shouldn't matter if those neurons fire inside or outside our own skulls.

Gray Area, what I'm arguing is that deduction, induction, and direct sensory experiences, should all be considered as equivalent-to-observation.

Eliezer: Good answer. I take the same view, although I think the "can you model it" question suggests there is a difference. Do you think a rigorous, consistent (or not provably inconsistent) model of arithmetic or physics is possible where 2+2=3? (or the 3rd decimal place of pi is 2, or Fermat's last theorem is false, or ...)

It seems like you could justify Occam's Razor by looking at the past history of discarded explanations. An explanation that is ridiculously complex, yet fits all the observations so far, will probably be broken by the next observation; a simple explanation is less likely to fail in the future. A hypothesis that says "Occam's Razor will work until October 8th, 2007" falls into the general category of "hypotheses with seemingly random exceptions", which should have a history of lesser accuracy than hypotheses with justified exceptions or no exceptions. To quote Virtues: "Simplicity is virtuous in belief, design, planning, and justification. When you profess a huge belief with many details, each additional detail is another chance for the belief to be wrong. Each specification adds to your burden; if you can lighten your burden you must do so. There is no straw that lacks the power to break your back. Of artifacts it is said: The most reliable gear is the one that is designed out of the machine. Of plans: A tangled web breaks. A chain of a thousand links will arrive at a correct conclusion if every step is correct, but if one step is wrong it may carry you anywhere."

But in this era of neurology, one ought to be aware that thoughts are existent in the universe; they are identical to the operation of brains.

Really? I'm aware that physical outputs are totally determined by physical inputs. Neurology can tell us what sorts of physical causes give rise to what sorts of physical effects. We even have reason to believe that thoughts can be infered from the physical state of the brain in a lawlike fashion but this surely doesn't let us infer that thoughts are IDENTICAL to the operation of brains. Merely that they always go together in the actual world.

In particular (as chalmers argues most convincingly) there is nothing contradictory about imagining we have the same physical state but totally different experiences, i.e., that it might feel like something totally different to be us. Worse we actually only know about the physical world through our experiences so you can't simplify the problem purely down to a physical one. It's actually the more complicated one of why the lawlike relationship between experiences and physical facts is set up right for us to have knowledge. It could have been that the physical world was all the same but we just had totally incoherent experiences.

"I'm aware that physical outputs are totally determined by physical inputs."

Even this is far from a settled matter, since I think this implies both determinism and causal closure.

logicnazi, if we can talk about our experiences, our experiences have a causal effect on the physical world. Assuming, as you do, causal closure (which is not known, but the most parsimonious hypothesis), this means that the idea of different experiences with the same physical state is indeed incoherent.

"We even have reason to believe that thoughts can be infered from the physical state of the brain in a lawlike fashion but this surely doesn't let us infer that thoughts are IDENTICAL to the operation of brains. Merely that they always go together in the actual world."

Look at airplanes: they all have a bunch of common characteristics like an engine, wings, rudders, etc. If you argued that an airplane was not really "identical" to the pile of parts, but that they just "always went together", people would look at you like you had three heads. Yet, when applied to brains, people think this argument makes sense. A brain is made up of the frontal cortex, visual cortex, auditory cortex, amygdala, pituitary gland, cerebellum, etc.; that's just what it is.

Tom: I agree with your analogy. Yudkowsy said: "Gray Area, what I'm arguing is that deduction, induction, and direct sensory experiences, should all be considered as equivalent-to-observation."

This is only convincing to someone who believes logic is only possible when their is some physical structure directly corresponds to logical output. Yet even the evidence indicating this is true uses logic.

I recently started (and then backed out of)a debate with a Christian presupositionalist.I had no idea how to show how logic itself works except by example. Naturally, there is no lesson on how logic works in the bible. So then, how does logic itself work and depend on physical structure? He would not answer my questions reguarding method of rationalists. Since we could not agree what rationality itself is, I did eventually learn that he doesn't believe in evolution or an old earth. He revealed this information only after realizing I no longer could take him seriously. This only occured after 25 emails between us! I wasted all that time to learn he didn't believe the results of modern science. I'll never make that mistake again. Anyone agree or disagree with the futility of debating someone who believes the universe is around 6,000 years old (and is also above age 25)?

I am not sure if my understanding of Occam’s Razor matches Eliezer Yudkowsky’s.

I understand it more as (to use a mechanical analogy) “don’t add any more parts to a machine than are needed to make it work properly.”

This seems to fit Occam’s Razor if I take it to be a guide, not a prediction or a law. It does not say that the theory with the fewest parts is more likely to be correct. It just reminds us to take out anything that is unnecessary.

If scientists have often found that theories with more parts are less often correct, that may further encourage us to look for and test the simpler theories first. But it does not tell us that they are more likely to be correct only because they are simpler.

As soon as I try an aesthetic analogy “strip the iPod down to its essential features” (and make them easy to use), I run into trouble. There is no agreement on what the essential features are or on what is easiest to use. (1)

Perhaps Occam works best with a certain type of simplicity. F=MA being much simpler than the Mac OS. Even if it did require a different genius to discover it.

John

(1) I realize that in order to make the mechanical analogy work we need to know what the machine is before we apply Occam’s Razor. Once we start improving the product (replacing the stick shift with automatic transmission, adding air conditioning) we are into feature wars. It is not possible to know in advance what customers will find essential.

But even then we would not want unnecessary parts in the transmission or the air conditioner.

Still, taking out all unnecessary parts won’t guarantee that the machinery will work properly any more than removing unnecessary parts of a theory will guarantee the correctness of the theory.

I think a discussion of what people mean exactly when they invoke Occam's Razor would be great, though it's probably a large enough topic to deserve its own thread.

The notion of hypothesis parsimony is, I think, a very subtle one. For example, Nick Tarleton above claimed that 'causal closure' is 'the most parsimonious hypothesis.' At some other point, Eliezer claimed the multi-world interpretation of quantum mechanics as the most parsimonious. This isn't obvious! How is parsimony measured? Would some version of Chalmers' dualism really be less parsimonious? How will we agree on a procedure to compare 'hypothesis size?' How much should we value 'God' vs 'the anthropic landscape' favored at Stanford?

"Anyone agree or disagree with the futility of debating someone who believes the universe is around 6,000 years old (and is also above age 25)?"

Agree 100%. The Universe is slightly over 10,000 years old. The 6000-ers got their math badly wrong. Crackpots, the lot of them.

Constant, the obviousness felt by both disagreeing parties almost never changes. How many formal debates actually end with the other person changing their mind? I would take it further and say formal debate is usually worthless too.

In the meantime where are your error bars? I bet somewhere there is a fundy who includes error bars.

Error bars: give or take about 14 billion years. My calculations are quite precise. I am still working out the ramifications of the universe being 10,000 minus 14 billion years old.

I knew you would come through Constant simply by reading your name.

"But what is a "reasonable" distribution? Why not label "reasonable" a very complicated prior distribution, which makes Occam's Razor work in all observed tests so far, but generates exceptions in future cases?"

Occam's Razor is only relevant to model selection problems. A complicated prior distribution does not matter. What does matter is how much the prior distribution volume in parameter space decreases as the model becomes more complex (more parameters). Each additional parameter in the model spreads the prior distribution over an increased parameter space.

For a more complex model to have a higher posterior distribution, the evidence (likelihood) must increase the posterior volume more than the addition prior parameter(s) decrease it. Since it is possible to fit the model to noise (uncertainly) in the data, the likelihood for the model with more parameters will be greater or equal to the likelihood for a model with less parameters. When an increase in likelihood is due to fitting data instead of noise, the more complex model becomes more probable. Otherwise the decrease in the prior distribution volume reduces the probability for the model with more parameters.

A reasonable distribution is one that assigns a reasonable prior to all the parameters in the model. After that Bayes Theorem takes care of the rest.

Eliezer: It sure does seem to me that when you say that "a mind needs a certain amount of dynamic structure to be an argument acceptor" you are saying that it does in fact know certain things prior to any "learning" taking place, e.g. that there are "priors". I would argue that 2+2=4 is part of this set, but as the punchline argues, we have already established the basics, now we are just haggling.

William,

By considering models in the first place, one is already using Occam's razor. With no preference for simplicity in the priors at all, one would start with uniform priors for all possible data sequences, not finite-parameter models of data sequences. If you formalize models as being programs for Turing machines which have a separate tape for inputting the program, and your prior is a uniform distribution over possible inputs on that tape, you exactly recover the 2^-k Occam's razor law, where k is the number of program bits that the Turing machine reads during its execution (i.e. the Kolmogorov complexity).

Interestingly, the degree to which one can outperform this distribution is provably bounded. Suppose you are considering some distribution of priors and you want to see how much it outperforms the 2^-k distribution. It can do so if its prior for the true model is higher than 2^-k. So you compute the ratio of this prior to 2^-k for every model. If I remember correctly, there is a theorem which says that this set of ratios will have a finite supremum for any computable prior distribution (which is not obvious since the set of models is infinite). Of course, in some respects, this is an unfair comparison since the 2^-k distribution is itself uncomputable. Hopefully I am not misstating the theorem. I think it is stated and proved in the book by Li and Vitanyi.

To see why ignoring Occam's razor is unthinkable (and to be amused), consider the following joke.

An astronaut visits a planet with intelligent aliens. These aliens believe in the reverse induction principle. That is, whatever has happened in the past is unlikely to be what will happen in the future. That the sun has risen every previous day is to them not evidence that it will rise tomorrow, but the contrary. Unsurprisingly, this causes all sorts of problems for the aliens, and they are starving and miserable. The astronaut asks them, "Why are you clinging to this belief, given that it obviously causes you so much suffering?" The aliens respond, "Well...it's never worked well for us in the past!"

You could argue that Occam's Razor is a reasonable distribution on prior probabilities. But what is a "reasonable" distribution?

If you make the assumption that what you observe is the result of a computational process, the prior probability of a lossless description/explanation/theory of length l becomes inversely proportional to the size of the space of halting programs of length l. You're free to dismiss the assumption, of course.

"But," you cry, "why is the universe itself orderly?"

One reason among many may be the KAM-Theorem.

Occam's Razor has two aspects. One is model fitting. If the model with more free parameters fits better that could merely be because it has more free parameters. It would take a thorough Bayesian analysis to work out if it was really better. A model that fits just as well but with fewer parameters is obviously better.

Occam's Razor goes blunt when you already know that the situation is complicated and messy. In neurology, in sociology, in economics, you can observe the underlying mechanisms. It is obvious enough that there are not going to be simple laws. If two models fit equally well, you just don't know, even if one is simpler than the other.

The "quant" trying to make money on the financial markets can take a modelling approach and may find the Razor sharp, but the scientist, trying to get to the bottom of things, has little reason to go for an explanation simpler than the known complexity of the underlying mechanisms.

Alan: Does a scientist likewise have no reason to pay attention to any model of the universe but fundamental physics? High level descriptions of the world very frequently can account for most of the variance in high level phenomena without containing the known complexity of the substrate.

Do high level descriptions of the world frequently account for most of the variance in high level phenomena without containing the known complexity of the substrate?

I think you can constrast thermodynamics and sociology by noticing that there is no Princess Diana molecule. All the molecules are on the same footing. None of them get to spoil the statistics by setting a trend and getting in all the newspapers papers. So perhaps Occam's Razor grabs credit not due to it, as researchers favour simple theories when they have specific reasons to do so.

An example of the mis-use of Occam's Razor arises in discussion of the question of whether minimum wage laws cause unemployment. Many people think they do and it is reasonable to imagine a politician finding an increase in the minimum wage to be politically necessary even as he wonders how to dodge blame for the subsequent rise in unemployment that he believes will follow. He will likely look to timing, seeking to delay the increase until there is a good chance of a tightening labour market raising wages.

How can you do empirical research on the effect of minimum wage laws on employment when practical men are scheming to conceal the very effect that you are looking for? One way is to appeal to Occam's Razor. Let us prefer the simpler hypothesis that increases to the minimum wage are random. That is bogus. We already know of the politicing and scheming that goes on. If our research methods cannot accommodate it, they leave us in the dark and Occam's Razor does not light our way.

"I am not sure if my understanding of Occam’s Razor matches Eliezer Yudkowsky’s.

I understand it more as (to use a mechanical analogy) “don’t add any more parts to a machine than are needed to make it work properly.”

Think of Kolmogorov complexity: the most parsimonious hypothesis is the one that can generate the data using the least number of bits when fed into a Turing machine.

"One way is to appeal to Occam's Razor. Let us prefer the simpler hypothesis that increases to the minimum wage are random. That is bogus."

Why it is bogus? An ideal stock market, operating over a fixed resource base, must necessarily be random (or at least pseudorandom). If it had any patterns distinguishable by investors, people would exploit those patterns to make money, and in the process eliminate them. The same principle could apply here: the minute a politician discovers a pattern in the economy, he begins exploiting it to get votes, and so erases the pattern by selectively hacking off the parts of it the voters consider bad.

Let's see. What else would I have to believe in order to accept a statement like "~(p&~p) is not a theorem in propositional logic?"

A statement of the form "X is a theorem in this particular formal mathematical system" means that I can use the operations allowed within that system to construct a "proof" of the sentence X. In theory, I can make a machine that takes a "proof" as input and returns "true" if the proof is indeed a correct proof and "false" if there is a step in the proof that is not allowed by the formal system. If the machine works as intended, then if the machine says that a proof is a correct one, it really is a correct proof and that statement really is a theorem in that system.

My brain is like such a machine. I can look at a mathematical proof in a formal system and check if the proof really is a correct proof within that system. In order to believe that 2+2=3, I would have to believe that the "theorem checker" module in my brain - that part responsible for deductive reasoning - is not operating properly. What I perceive as a correct step in a proof is, in actuality, an incorrect step, and my brain is hardwired to make that particular kind of mistake without realizing it. In other words, in order to believe that "2+2=4" is false, I would have to believe that the proof of "2+2=4" in my head does not mean what I think it means.

I would have to believe that I am not capable of correct deductive reasoning. A person not capable of correct deductive reasoning is insane.

If "2+2=4" is false, then I am insane.

All of my beliefs have to come with the background assumption that I am not insane. If I am, in fact, insane, then all my internal models of the universe have to be replaced with the black hole of maximum entropy. I can no more trust my probability estimates than I could trust the probability estimates of a rock.

I choose to act as though I am sane because if I am sane, I gain maximum benefits from that belief, and if I am not sane, it doesn't matter anyway. I can be convinced I am mistaken about something, but I cannot be convinced that I am insane.

A person not capable of correct deductive reasoning is insane. The people usually deemed insane are those with deviant behavior, or what Caplan calls "the extreme tails of a preference distribution with high variance".

And as the symbol of your treaty, your white flag, you use the phrase "a priori truth".

I should note that the most famous paper in 20th Century analytic philosophy, Quine's "Two Dogmas of Empiricism", is an attack on the idea of the a priori. The paper was written in 1951 and built on papers written in the previous two decades. A large proportion of contemporary philosophers agree with Quine's basic position. This doesn't stop them from doing theoretical work, just as Eliezer's disavowal of the a priori need not prevent him theorizing about rationality, philosophy of science, or epistemology.

In "Two Dogmas", Quine talks mainly about a certain view of a priori knowledge that was held by logical empiricists such as Carnap, Ayer, etc. This view, that all a priori statements are analytic, already gives a significantly smaller role to a priori justification than did previous philosophers. Roughly, the empiricists didn't think that there were synthetic statements that could be known a priori.

Quine's paper is quite hard to read without some of the philosophical background. A more recent discussion of his view can be found in Harman's essay "Death of Meaning" in his book "Reasoning, Meaning, and Mind". This is available online (if you have subscription) at Oxford Scholarship.

Eliezer - It's just fundamentally mistaken to conflate reasoning with "observing your own brain as evidence". For one thing, no amount of mere observation will suffice to bring us to a conclusion, as Lewis Carroll's tortoise taught us. Further, it mistakes content and vehicle. When I judge that p, and subsequently infer q, the basis for my inference is simply p - the proposition itself - and not the psychological fact that I judge that p. I could infer some things from the latter fact too, of course, but that's a very different matter. (And in turn distinct from inferring things from the second-order judgment that I judge that p!)

Anyway, here's a simple argument for the inescapability of a priori justification:

For any instance of empirical justification, it seems like we can construct a parallel instance of a priori justification simply through conditionalization. Suppose that empirical evidence E would justify your drawing conclusion C. Then presumably you could justifiably believe the conditional "if E then C" prior to experiencing E. We can repeat this procedure to conditionalize out all empirical grounds for belief, and the result will be a conditional statement that is justifiable a priori -- i.e. not dependent on any particular experiences or empirical evidence at all.

Tom McCabe wrote: "If you argued that an airplane was not really "identical" to the pile of parts, but that they just "always went together", people would look at you like you had three heads. Yet, when applied to brains, people think this argument makes sense."

This is because there is nothing more to our concept of being an airplane than the reduction basis. Any possible world with all the parts arranged in the right way is immediately recognizable, under that description, as a world containing an airplane. Indeed, that's just what it is to be an airplane. Minds are a rather different matter. They are not conceptually reducible to neurons firing. It is conceptually possible for the two to come apart (if we imagine a world with different laws of nature, perhaps), so they are not simply one and the same thing.

(Philosophers have written books on this argument, so I don't pretend that the above is incontrovertible. But it is certainly not so easily dismissed as Tom and others - including my past self - might assume. More detail here.)

It's just fundamentally mistaken to conflate reasoning with "observing your own brain as evidence".

If you view it as an argument, yes. The engines yield the same outputs.

Minds are a rather different matter. They are not conceptually reducible to neurons firing.

Just because you do not know how the trick works, does not mean the trick is powered by magic pixie dust.

Eliezer Yudkowsky said: "Just because you do not know how the trick works, does not mean the trick is powered by magic pixie dust."

I agree yet this won't convinve a sophisticated right-wing Christian (or Jew, or Muslim, etc).

Who said anything about 'magic pixie dust'? I agree that the brain gives rise to (or 'powers') the mind, thanks to the laws of nature that happen to govern our universe. I may even agree with all the causal claims you want to make. But if you're going to start talking about identity, then you need to do some real philosophy.

"If you view it as an argument, yes. The engines yield the same outputs."

What does the latter have to do with rationality?

Does Eliezer really need to do some "real philosophy"? If he does not, will he miss out on the Singularity? Will A.I be insufficiently friendly? I don't see any reason to think so. I say be content in utter philosophical wrongness. Shout to the heavens that our actual world is a zombie world with XYZ rather than H20 flowing in the creeks that tastes grue, all provided it has no impact on your expectations.

But if you're going to start talking about identity, then you need to do some real philosophy.

What's the difference between the brain giving rise to a mind by the laws of nature and the brain giving rise to a mind without identity by the laws of nature?

But if you're going to start talking about identity, then you need to do some real philosophy.

"Identity" is not magic. There is no abiding personal essence, just continuity of memory. A real philosopher said that, by the way.

I do think there are important unanswered questions in the philosophy of mind, but this isn't one of them. (Although one of them is "where is our thinking still contaminated by the idea of magic personal identity?", which I suspect is at the root of several apparent paradoxes.)

Tom, I think we are actually agreeing. I'm arguing that if you already know the situation is complicated you cannot just appeal to Occam's Razor, you need some reason specific to the situation about why the simple hypothesis should win.

You are proposing a reason, specific to economics, about why the complications might be washed away, making it reasonable to prefer the simpler hypothesis. My claim is that those extra reasons are essential. Occam's Razor, on its own, is useless in situations known to be complicated.

Tom McCabe, Thank you for the comment. You have started me thinking about the differences between Occam's Razor and Einstein's "Everything should be made as simple as possible, but not simpler." John

"--" should have been "Shakespeare's Fool" John

TGGP - You seem to have missed the conditional nature of my claim. I'm not forcing philosophy on anyone; just saying if you're going to do it at all, best do it well.

Nick - I never suggested there was an "abiding personal essence". (Contemporary philosophers like Derek Parfit and David Velleman have done a stellar job in revealing the conceptual confusions underlying such an idea.) In any case, it's hardly relevant. The issue here is individuation (how to count the distinct things in the world), not personal identity and persistence through time.

James - if you're asking what difference identity makes, that's a good question. To answer literally, if "two" things are really identical, i.e. really one, then there is no possible world (however distant or "unrealistic") where they come apart -- where there is one without the other. That's arguably the criterion for what it is to be one rather than two. Now you may ask why we should care about this difference. Here's an answer: we care about the fundamental constituents of reality, or "what it takes" to create a world like ours. Imagine a god were to create all the physical stuff of our universe. Does that suffice, or does he have more work to do before he can rest? My earlier arguments suggest that there is more work to do here. He also needs to add some extra, 'bridging' psycho-physical laws of nature, to ensure that brainy matter gives rise to conscious minds. If they were truly one and the same thing, this extra step would not be required. (Cf. airplanes.) That's an interesting result, no?

Eliezer: "You could see someone else's engine operating materially, through material chains of cause and effect, to compute by "pure thought" that 1 + 1 = 2. How is observing this pattern in someone else's brain any different, as a way of knowing, from observing your own brain doing the same thing? When "pure thought" tells you that 1 + 1 = 2, "independently of any experience or observation", you are, in effect, observing your own brain as evidence."

Richard: "It's just fundamentally mistaken to conflate reasoning with "observing your own brain as evidence"."

Eliezer: "If you view it as an argument, yes. The engines yield the same outputs."

Richard: "What does the latter have to do with rationality?"

Pure thought is something your brain does. If you consider having successfully determined a conclusion from pure thought evidence that that thought is correct, then you must consider the output of your brain (i.e. its, that is your, internal representation of this conclusion) as valid evidence for the conclusion. Otherwise you have no reason to trust your conclusion is correct, because this conclusion is exactly the output of your brain after reasoning.

If you consider your own brain as evidence, and someone else's brain works in the same way, computing the same answers as yours, observing their brain is the same as observing your brain is the same as observing your own thoughts. You could know abstractly that "Bob, upon contempating X for 10 minutes, would consider it a priori true iff I would", perhaps from knowledge of both of your brains compute whether something is a priori true. If you then found out that "Bob thinks X a priori true" you could derive that X was a priori true without having to think about it: you know your output would be the same ("X is a priori true") without having to determine it.

Richard: oops, I thought you meant personal identity. Ach, homonyms.

Do you think that the human bodies in a physics-only zombie world would behave identically to ours? ( = Do you think physics is causally closed?)

Nick Hay: great explanation.

Richard: sure, minds and brains can "come apart" in possible worlds other than ours (or indeed in this one, if and when someone teaches a computer to think), but I have never understood why some people seem to think that this suggests that there's anything weird about the relationship between actual minds and actual brains in the actual world.

Consider those airplanes again, but let's use a more general term like "flying machine" that isn't so tightly tied to the details of their construction. You can imagine (yes?) a world in which a Boeing 747 takes off, then its wings fall away and it just continues flying; or in which there are flying machines having no apparent similarity to the ones we use in the actual world. In other words, you can conceptually separate flying from the actual aerodynamic phenomena that (here, in the actual world) enable it. None the less, flying (here, in the actual world) is a consequence of those aerodynamic phenomena, and if a god made a world physically just like ours then the Boeing 747s in it would be able to fly without any further "bridging" aviatiophysical laws of nature being added.

So why does the (uncontroversial) fact that one can imagine thinking without a brain, and that (in so far as there "are" possible worlds) there are possible worlds in which thinking happens without brains, give the slightest reason to suspect that psychophysical bridging laws are required to enable our brains to support our minds?

g - there's no possible world that's physically identical to ours but where the Boeing's don't fly. There is a possible world that's physically identical to ours that lacks consciousness. That's the difference. It shows that physics suffices for flight but not fully-fledged mentality. (N.B. the interesting case here is not minds without brains, but brains without minds.)

Nick Hay - Thanks for bringing this back to the key issue. In fact I do not "consider having successfully determined a conclusion from pure thought evidence that that thought is correct". I take my evidence to be something beyond myself: whatever premises guided my reasoning, not the mere psychological fact of my concluding as I did. (This is why I brought up the content/vehicle distinction in my original comment.) Granted, reasoning presupposes that one's thought processes are reliable, and a subjectively convincing line of thought may be undermined by showing that the thinker was rationally incapacitated at the time (due to a deceptive drug, say). But presuppositions are not premises.

Compare: (1) P, therefore Q (2) If I were to think about it, I would conclude that Q. Therefore Q.

These are different arguments! If I come to believe Q via #2, my evidence is the (hypothetical) brain process you talk about. But in the first case, my evidence is simply P, and not any fact about me at all.

P.S. Nobody denies that a priori justifiable claims may also be justified empirically, say by the testimony of a reliable thinker, or by observing a reliable brain or other computational engine. But it's a different kind of justification. And of course the mere fact that there is a second argument for a conclusion does nothing to show that the first one was flawed.

Sorry, my second sentence to NH is unclear. The psychological fact could be taken as a kind of indirect evidence, as noted in my postscript. But it is not what I take my evidence to be, when I am reasoning according to a #1-style argument. We could say the evidence of my thought [vehicle] is not the evidence in my thought [content].

Nick T. - yes, I accept the causal closure of the physical. (And thus epiphenomenalism. I discuss the epistemic consequences in my post 'Why do you think you're conscious?')

On the broader issue - to expand on my response to James above - see my post on the explanatory power of dualism.

Richard, are you saying that if in this world I attempted to move around some material to produce an artificial brain, it would not work unless I also did some psycho-manipulation of some sort? Or is the psycho-stuff bound so tightly with the material that the materially-sufficient is psycho-sufficient?

I neglected to link to this before when I mentioned anticipated experiences, which is one of my favorite posts here. I am so fond of linking to it I assumed I already had.

Richard, you have presented absolutely no evidence that there is a possible world physically identical to ours but in which we are not conscious, beyond saying that it's "conceptually possible" for minds and brains to "come apart", if we imagine a world with different laws of nature.

But it's equally conceptually possible for flying machines and aerofoils to come apart, if we imagine a world with different laws of nature, and (it appears) you don't see that as any reason to think that flying machines fly by aerofoils plus some extra bridging aviatiophysical laws.

Incidentally, I think you're misunderstanding what Eliezer is trying to do. He's saying (unless I'm misunderstanding him too) roughly "forget about justification; never mind what inference processes we can find the best arguments for; what matters is what actually works; if accepting the results of reasoning in your own brain works, then accepting the results of reasoning in an equally competent other brain works equally well".

I agree with Richard that we should respect the fact that philosophers have spilled a lot of ink on the consciousness question; we should read them and respond to their arguments. We should have at least one post devoted to this topic. But after doing so, I'm betting I'll still mainly agree with Eliezer.

Richard, I don't think Eliezer conflated reasoning with observing your own brain - he just suggested that simple Bayesian reasoning based on observing your own brain gets you pretty much all the conclusions you need from most other "reasoning."

Robin and Richard - I think it is possible that Eliezer did not word his statement as cleanly as he might. However if his wording conflated categories, I am confident that with some care the exact same point can be re-worded without such conflation. There is something real and significant here that he's pointing out, and it's not going to go away simply because he was (if he was) a bit to loose in his presentation.

I think this contains one of the main points:

If you clear your mind of justification, of argument, then it seems obvious why Occam's Razor works in practice: we live in a simple world, a low-entropy universe in which there are short explanations to be found. "But," you cry, "why is the universe itself orderly?" This I do not know, but it is what I see as the next mystery to be explained. This is not the same question as "How do I argue Occam's Razor to a hypothetical debater who has not already accepted it?"

The philosophers have been busy trying to answer the question which Eliezer has taken pains to distinguish from another question. A lot of the philosophical material on the question of Occam's razor either tries to justify it in a non-question-begging fashion, or else argues that it cannot be so justified. Either way, the focus is on the justification. But there is something else that can be focused on: the question of whether Occam's razor is in fact true, or valid. Of course, in itself it is a method rather than a claim, but we can roughly translate it into the claim that among the possible hypotheses to explain a phenomenon, the true hypothesis tends to be the simplest. This can be asserted as a conjecture about the world we live in. Occam's Razor can be thought of as a general hypothesis about the world, which may or may not be true. And if it is true, then it is true even though we have been unable to justify our acceptance of it in a non-question-begging way. The truth does not actually depend on the possibility of our one day finding a non-circular justification for it.

The evolutionary formation of the mind is, as Eliezer points out, based on the truth, and not on justification. Mutation throws one brain after another at the problems of life, and the brains that generate true beliefs are the ones that tend to survive. No justification is involved at this stage. For example, suppose that Occam's razor is true (to understand this, translate the method called "Occam's razor" into the appropriate assertion about the world so that it can be assigned a truth value). Then brains that apply Occam's razor will tend to survive. Notice what is happening here: the truth of Occam's razor is causing the evolution of brains that apply it. What this means is that the recognition is not mere accident. We apply Occam's razor because it is true. Generally speaking, if the truth of X causes the belief that X, then that belief is not mere arbitrary belief but can arguably be called knowledge. So, if Occam's razor is true and if we evolved to apply it, then our application of Occam's razor constitutes knowledge about the world. It does not, however, constitute knowledge from the more narrow point of view of "justified true belief".

This suggests that we have knowledge about the world which we are unable to justify but which is nevertheless knowledge and not mere arbitrary belief.

Constant - Sure, there's something to be said for epistemic externalism. But I thought Eliezer had higher ambitions than merely distinguishing rationality and reliability? He seems to be attacking the very notion of the a priori, claiming that philosophers lazily treat it as a semantic stopsign or 'truce' (a curious claim, since many philosophers take themselves to be more or less exclusively concerned with the a priori domain, and yet have been known to disagree with one other on occasion), and dismissively joking "it makes you wonder why a thirsty hunter-gatherer can't use the "a priori truth factory" to locate drinkable water." (The answer isn't that hard to see if one honestly wonders about it for a moment or two.) But maybe you're right, and these cheap shots are just part of the local attire, not intended for cognitive consumption.

g - I already answered this. Change the extra-physical laws of nature as you will, it is not conceptually possible for a world physically identical to ours to lack flying airplanes. What else are we to call the boeing-arranged atoms at 10000ft? The zombie (physically identical but non-conscious) world, by contrast, does seem conceptually possible. So there's no analogy here.

TGGP - Yes, I think that, thanks to the bridging laws, "the materially-sufficient is psycho-sufficient". This dualism is empirically indistinguishable from materialism. Anticipating experience may be a useful constraint for science, but that is not all there is to know. (See also my responses to James above.)

Richard, I would like to know what you mean by "conceptually possible" and why you think conceptual possibility has anything to do with actual possibility. I think you mean something like "I can/can't imagine X without any obvious inconsistencies". So, e.g., you can imagine, or think you can imagine, a world physically identical to ours in which people have no experiences; but you can't imagine, or think you can't imagine, a world physically identical to ours in which jumbo jets don't fly.

But whether something is "conceptually possible" in this sort of sense obviously has as much to do with the limits of our understanding as with what's actually possible, no?

1. Consider some notorious open problem in pure mathematics; the Riemann hypothesis, say. I can, in some sense, "imagine" a world in which RH is true and a world in which RH is false; I can tell you about some of the consequences in each case; but, despite that, one of those worlds is logically impossible; we just don't know which. (I'm ignoring, because I'm too lazy to think it through now, the possibility that RH might be undecidable.) So something can be "conceptually possible" despite being logically impossible and hence (if you believe in possible worlds) false in all possible worlds.

2. I cannot, so far as I can tell, imagine what it would be like if the world had two "timelike" dimensions and two "spacelike" ones rather than 1 and 3. (Perhaps if I sat down and concentrated for a while I could; in which case, make it twenty of each, or something.) I can calculate some of the consequences, I suppose, but I can form no coherent mental picture. None the less, it seems clear that such a world is possible in principle. So something can be (for a given person, at least) "conceptually impossible" despite being possible in other senses.

Examples like these make it seem obvious to me that "conceptual possibility" tells us much more about the limits of our imagination and reasoning than it does about the nature of reality.

You can't imagine a world physically like ours in which jumbo jets don't fly; that would be because flying is simple enough that we have some a pretty good understanding of how it works, and what mechanisms underlie it. Of course we don't have any similarly good understanding of how minds work. It seems to me that that's the only difference here. Lack of understanding is not evidence of magic.

(Suppose I claim that I can so imagine a world physically identical to ours in which boeing-arranged atoms at 10k feet aren't flying airplanes; they're, er, zairplanes; they are doing something physically indistinguishable from flying, but of course it isn't really flying. Those who fail to see the difference just lack sufficient subtlety of thought. Ridiculous, no?)

Anyway, let's suppose it's "conceptually possible" that the world should be exactly as it is, physically, but with no consciousness anywhere to be found. So what? All that means is that someone can form some sort of mental picture of what such a world might be like. I don't see how to eliminate the possibility that filling in the details might ultimately lead to a contradiction (as with either RH or not-RH). Or that digging further into the notion of "phenomenal consciousness" being used might reveal that it has no real content and serves only to obfuscate. (I strongly suspect that this is in fact the case. Of course that doesn't mean that those who appeal such notions have any intention to obfuscate.)

For what it's worth, I'm pretty sure that a zombie world is not conceptually possible to me: I can only "imagine" such a world by deliberately not thinking too hard about the details.

Oh, gosh, that was rather long. Sorry.

I liked it. I really don't get Robin's desire for short comments. This is the only blog where I've seen that restriction. Is he worried about the high cost of bandwidth? For text?

I think I can forgive it this once.

Zombies and similar creatures are "conceptually possible" when someone doesn't understand the connection between lower and higher levels of organization, so that the stored propositions about the lower and higher levels of organization are mentally unconnected and can be switched on or off independently. This is a fact about the person's state of mind, not a fact about the phenomenon in question.

g, beautifully said.

Hopefully Anonymous had a post about zombies here, in which I made fun of him.

Anticipating experience may be a useful constraint for science, but that is not all there is to know.
If I was going to dispute this I would have to specify what it means to "know" and get into one of those goofy epistemology discussions I derided here. Philosophy is the required method to argue against philosophy, oh bother. Good thing reality doesn't revolve around dispute.

g - No, by 'conceptually possible' I mean ideally conceptually possible, i.e. a priori coherent, or free of internal contradiction. (Feel free to substitute 'logical possibility' if you are more familiar with that term.) Contingent failures of imagination on our part don't count. So it's open to you to argue that zombies aren't conceptually possible after all, i.e. that further reflection would reveal a hidden contradiction in the concept. But there seems little reason, besides a dogmatic prior commitment to materialism, to think such a thing. Most (but admittedly not all) materialist philosophers grant the logical possibility of zombies, and instead dispute the inference to metaphysical possibility. This seems no less ad hoc. Anyway:

"I would like to know... why you think conceptual possibility has anything to do with actual possibility."

I actually wrote a whole thesis on this very question, so rather than further clogging the comments here, allow me to simply provide the link. If you're interested enough to read all that, and still have any objections to my view afterwards, I'd be very interested to hear them - my comments are open. For this page, though, I think I should bow out, unless Eliezer sees fit to address the concerns I raised about the original topic, and especially his treatment of the a priori.

I have future posts planned that will shed light on this topic, but not today.

Richard, I'm unconvinced that you have any way of telling whether the existence of zombies is ideally conceptually possible; the fact that you seem to be able to imagine a zombie world certainly isn't good evidence that it's "free of internal contradiction". (Consider, again, the Riemann hypothesis.)

I don't have anything like a proof that the idea of zombies is in fact incoherent. But if you're right that its coherence would entail the existence of these mysterious psychophysical bridging laws and all the rest of your epiphenomenal apparatus, then it seems to me that that's at least as much evidence against as your alleged ability to imagine it is evidence for. I don't think pointing this out constitutes "dogmatic prior commitment to materialism".

Whether "most materialist philosophers" are right in saying that furthermore the ideal conceptual possibility doesn't suffice to demonstrate that conscious minds don't simply supervene physically on brains, depends on the details of what you mean by ideal conceptual possibility. I suspect that the notion isn't in fact clear enough for such questions to have answers.

Anyway, I'll take a look at your thesis, and shall now also desist from clogging up the comments here.

No, by 'conceptually possible' I mean ideally conceptually possible, i.e. a priori coherent, or free of internal contradiction. (Feel free to substitute 'logical possibility' if you are more familiar with that term.)

Before we discovered that water was H2O, our concept of water did not include that it was H2O. Since our concept did not include that, then surely it would not have been incoherent, at the time, to say that water is not H2O (imagine that this occurs during the period after the discovery of H and O and before the discovery of the composition of water - imagine that there was such a period), since there was nothing in our concept of water at the time that logically contradicted that statement. However, today it is incoherent to say that water is not H2O, because our concept of water includes that it is H2O - water is regularly defined as H2O.

Let us think about the period when, because the concept did not include that it was H2O, it was free of internal contradiction to say that water is not H2O, and therefore logically possible, ideally conceptually possible, and a priori coherent, to say that water is not H2O. Given their concept of water and perhaps even given everything they knew at the time about water, it was logically possible - that is, not in logical contradiction to any fact or concept they possessed at the time - that water is not H2O. Looking back, I find myself reluctant to draw any deep lessons from this about a possible dual nature of water in which, say, H2O takes the role of the material substance and water takes the role of the epiphenomenon. I find myself moved not at all to contemplate the possibility of zombie H2O - H2O which is not water. The only lesson I find myself wanting to draw from this is that they did not know then what we know now.

Now we turn to the present moment, when some claim that a zombie world is logically possible. They may be right to claim that their own concept of consciousness does not logically contradict the denial of consciousness to a physical creature. It is not at all obvious that I should draw any deep lesson from this, any more than in the case of water.

Well said, Constant.

The logic for why zombies can't exist, very briefly, goes like this:

You see a bright red light.

The mysterious redness-quality of the red light seems inexplicable in merely material terms.

You think, within your stream of consciousness, "The redness of this light seems inexplicable in merely material terms."

You say out loud, "The redness of this light seems inexplicable in merely material terms."

Your lips moved.

Whatever caused your lips to move must lie within the realm of physics because it had a physical effect.

If we sum up all the forces acting on your lips - gravity, electromagnetism, etc. - we will necessarily include the proximal cause of your lips moving. This is because when we sum up the forces acting on your lips, we can tell where your lips will go. In particular, we can tell that they'll move. So if we delete anything that isn't on the force list, your lips go to exactly the same place.

As it so happens, the proximal cause of your lips moving is nervous instructions sent from your motor cortex and cerebellum. It is not possible to imagine a world in which your lips move and all the laws of physics are the same, but there are no nervous impulses from the motor cortex, because the laws of physics include the nervous impulses from the motor cortex, which is why your lips move. Everything that actually causes your lips to move is not epiphenomenal - it has a direct and material effect - meaning that it shows up within low-level physics.

If something makes an atom go from one place to another that isn't within our known physics, then we'll see, when we examine the atom, that the sum of forces says the atom should go one way, but the atom goes another way instead. This would mean that our list of laws of physics, on that low level of organization, was incomplete; we would not be able to account for why an atom goes to one place instead of another without postulating additional physical laws. Not "psychophysical bridging laws", physical laws that directly cause the atom to be in one place rather than another, given its initial conditions.

Exactly the same logic applies as we work our way backward along the causal chain. Whatever caused you to think, "The redness of this light seems inexplicable in merely material terms," must exist within the web of material cause and effect in order to have the final result of your lips moving.

Whatever causes the mysterious redness of red to seem inexplicable in material terms, must exist in the web of material cause and effect, because a thought to this effect appears within your stream of consciousness, and you are capable of speaking your stream of consciousness out loud, which makes your lips move.

This may seem really odd. But just because something seems really odd, doesn't mean it isn't true. Your sense of "really odd" does not give you direct, veridical information about the universe. Even when something seems really, really odd, it's still a fact about you, not a fact about the universe.

Penrose's theory that consciousness involves magical physics is wrong, but coherent. The theory that consciousness involves no physics is not. Admittedly, realizing this requires logic and human beings are not logically omniscient, so in that sense zombie-believers may be "coherent" relative to their own failure to realize that philosophical discussions are themselves material phenomena. Which is of course the point of this post.

The causes of all material effects are also material in the sense that any correct physical prediction will include them by identity, and any predictive method which fails to include them in any way will deliver incorrect predictions. Philosophical discussions and philosophical intuitions are material phenomena and all their causes are within the laws of physics; on pain of our physical predictions being incorrect if the known laws of physics fail to capture-by-identity the causes of all philosophical intuitions.

All this is true a priori.

(Let me just add that the first chapter of my thesis addresses Constant's concerns, and my previously linked post 'why do you think you're conscious?' speaks to Eliezer's worries about epiphenomenalism -- what is sometimes called 'the paradox of phenomenal judgment.' Some general advice: philosophers aren't idiots, so it's rarely warranted to attribute their disagreement to a mere "failure to realize" some obvious fact.)

Richard,

I don't know what you mean about "idiots". My arguments are not intended as insults. In fact I fully expect you to have already dealt with them. However, I have little choice but to answer the particular point you raised at a particular time, because if I try to jump ahead and anticipate all your answers and then your answers to my answers to your answers, the result will probably be an incredibly confusing monologue that is more likely than not to simply have mis-anticipated your actual responses. Aside from that there is the matter of comment length to consider.

Richard, I don't actually believe philosophers are idiots because I've seen their standardized test scores. I do think they could more productively use their intellects though. If I were to ignore IQ/general intelligence and simply try to judge whether one philosopher does better philosophizing than another, would I be able to do it without becoming a philosopher myself and judging their arguments? I can determine that rocket physicists are good at what they do because they successfully send rockets in the air, I know brain surgeons are because the brains they operate on end up with the behavior they promise. I can't think of anything I would hire a philosopher for, other than teaching a philosophy course. So is the merit of philosophy an entirely circular thing or is there a heuristic the non-philosopher layman can use that will let him know he should pay more attention to philosophers than palm-readers?

Occam's razor states- the explaination of any phenomenon should make use of as few assumptions as possible, eliminating those that make no difference in the observable predictions of the explainatory hypothesis.
That does not say the universe is simple or explainable by material means or any such thing.
In fact those assumptions violate Occam's razor! Saying the universe is simple or explainable by material means are unneeded assumptions.
In order to explain the phenomena of physics we need material, material forces, chance, and freedom. The chance comes from the inherent unpredictablity of certain phenomena (where will the particle land?) and the freedom comes from the experimenters ability to choose what aspect (particle or wave) of the phenomena to view. Currently there is no known material mechanical explaination for chance or freedom. The claim there will someday be one is an unneeded assumption based on faith.
If philosophy is going to be of value, it should agree with the basic facts of science. The mechanistic, material universe was tossed out almost 100 years ago.
Read Max Born's Nobel prize acceptance speech and update your thinking.

Richard is quite right to point out that philosophers of mind are well aware of the counter arguments that Constant and Eliezer offer. And he is right to insist this is a subtle question to which a few quick comments do not do justice. There are however many philosophers who agree with Constant and Eliezer. See for example the October Philosophical Quarterly article on Anti-Zombies.

Not to be too uncharitable, but I'd say the arguments of us material monists are simple, and it's only the flaws in the complex dualist arguments that are subtle.

PS: I've got some back copies of the Journal of Consciousness Studies on my bookshelf, so don't necessarily assume that I'm unaware of the big philosophical mess here.

TGGP, your question illustrates nicely my explanation for why more history than futurism.

This book review claims that the majority position in philosophy rejects the dualism Constant and Eliezer object to - this is most certainly not a dispute between philosophers and scientists.

Sorry, have you argued someplace else for either reduction or eliminative materialism?

I have a series of posts planned on that in due time.

In a comment on "How to convince we that 2+2=3", I pointed out that the study of neccessary truths is not the same as the possession of neccessary truths (credit to David Deutsch for that important insight). Unfortunately, the discussion here seems to have gotten hung up on a philosophical formulation that blurs that important distinction, a priori. Eliezer's quotative paragraph illustrates the problem:

The Internet Encyclopedia of Philosophy defines "a priori" propositions as those knowable independently of experience. Wikipedia quotes Hume: Relations of ideas are "discoverable by the mere operation of thought, without dependence on what is anywhere existent in the universe." You can see that 1 + 1 = 2 just by thinking about it, without looking at apples.

All of these definitions seem to assume there is no distinction between the existence of neccessary truths and knowing neccessary truths (more correctly, justifiably assigning extremely high probability to them). But there are neccessary truths that are not knowable by any means we have or expect to have. Eg, the digits of Gregory Chaitin's Omega constant, beyond the first few. Omega is the probability that a random Turing machine will halt. Whatever value it has, it neccessarily has.

(One might say more charitably that these definitions are only categorizing knowledge and say nothing about non-knowledge. If so, they mislead, and also make a subtler mistake. Neccessary truths are not a special type of knowledge, they are topic of knowledge)

One can understand why the mistake is made. Epistemology, the branch of philosophy about how we know what we know, is not looking for a way to assign untouchable status to what seems its most certain knowledge.

We use Occam's Razor because it has tended to work better than Occam's Butterknife.

What's so complicated about that?

I read no comments

"You could argue that Occam's Razor has worked in the past, and is therefore likely to continue to work in the future. But this, itself, appeals to a prediction from Occam's Razor."

It seems to me like it is more of an appeal to induction. (Granted the problem Hume raised about induction, but also granted Hume's [and my own] defection to practicality.)

To distinguish the word "arbitrary" from "random", I think of an arbitrator—i.e., an outside judge chooses something. (Maybe this results in a uniform prior for me, if'n I don't know what she'll do. Or maybe I'm a mathematician and I choose to be ready for any choice that arbitrator might make.)

When I'm teaching linear algebra and explain arbitrary parameters to my students, I use exactly this metaphor. How many times does someone else have to come in and arbitrate the value of other variables, before you can tell the questioner what the answer is?

Could you not argue Occam's Razor from the conjunction fallacy? The more components that are required to be true, the less likely they are all simultaneously true. Propositions with less components are therefore more likely, or does that not follow?

2+2=4 is part of the definition of +. The question isn't why we think 2+2=4. The question is why we're so obsessed with addition. 2 << 2 = 8, but you don't hear people talking about how 2 and 2 makes eight.

You simply can't do anything without something being a priori. Is the universe orderly? Maybe it looks orderly by coincidence. The probability that it looks this way given that it's random is simple enough, but we also need to know the probability that it looks this way and it's not orderly. We need some a priori probability that it isn't orderly, or we simply can't work it out. Occam's Razor isn't just there to tell you that A is more likely than B. It's there to tell you how likely A and B are, which you'll need if you want to know how likely they are given C.

A statement can be true a priori in the sense that no sensory evidence is needed to infer it- the principle of non-contradiction, for example.

A priori, translated very roughly but with respect to the spirit of the phrase, means "before experience". It is used with a posteriori which means "after experience". Something known a priori is equivalent to your prior probability; something known a posteriori is equivalent to the posterior probability. That is, when you are concerned with an event, before any experience of the event, your knowledge is a priori.

This is, of course, a slippery slope: that prior is simply the posterior of something else.

Some philosophers have tried to use a radical a priori to avoid this slope: an ideal a priori before any experience at all, a la Descartes' "cogito, ergo sum". This is the equivalent of the universal prior problem: what is your first prior? Unsurprisingly, their answers aren't convincing.

However, a priori / a posteriori is still a useful distinction. The first uses some reasoning as the prior for the probability calculation; the second uses statistics as the prior. Something like existential risk requires a priori reasoning (in this limited sense) about the risks, since we can't have an a posteriori experience about existential catastrophes.

(More necromancy!)

I thought Occam's Razor was justified by the fact that every new proposition involved necessarily increased the number of ways in which the entire explanation could fail. Then you require evidence for yet another belief, and since you cannot be 100% accurate in any of your propositions, your accuracy continually decreases as well.

A Priori has always just seemed to me like another way to describe what we call "assumption" in classical logic. You can't deduce anything in classical logic without starting from certain assumptions and seeing what you can deduce from them, and one of the strengths of classical logic is that it forces you to actually list your assumptions up front, so someone else can say "I agree with your reasoning, but I think your assumption "B" is invalid".

Trying to take assumptions apart, see if they are valid, see if they can either be proven inductively from evidence or deductively from other assumptions, and trying to figure out where that specific assumption comes from, is a very valid thing to do (hitting the "explain" button), but on some level, I think you are always going to have to have some assumptions in order to use any logical system (either classic logic, or Bayesian reasoning).

How is observing this pattern in someone else's brain any different, as a way of knowing, from observing your own brain doing the same thing? When "pure thought" tells you that 1 + 1 = 2, "independently of any experience or observation", you are, in effect, observing your own brain as evidence.

No no no. The difference between a priori and a posteriori is where the justification lies. You may be counting your fingers when you count 1 + 1. It may be that you won't be able to figure out the answer if someone cut off your fingers. In fact, it may be you won't be able to understand what 1 means if you didn't have your fingers. But the justification for 1 + 1 being 2 is not in your fingers.

So it may be that you are able to observe how your brain operates when you're counting 1 + 1. But even if your brain operated in a different way, 1 + 1 is still 2. If B is taller than A, and C is taller than B, C is taller than A. It may be that you're not able to understand this without three pencils. But C being taller than A is a priori knowledge.

If you are a philosopher whose daily work is to write papers, criticize other people's papers, and respond to others' criticisms of your own papers, then you may look at Occam's Razor and shrug. Here is an end to justifying, arguing and convincing. You decide to call a truce on writing papers; if your fellow philosophers do not demand justification for your un-arguable beliefs, you will not demand justification for theirs. And as the symbol of your treaty, your white flag, you use the phrase "a priori truth".

Or the word "intuition".

But to a Bayesian, in this era of cognitive science and evolutionary biology and Artificial Intelligence, saying "a priori" doesn't explain why the brain-engine runs. If the brain has an amazing "a priori truth factory" that works to produce accurate beliefs, it makes you wonder why a thirsty hunter-gatherer can't use the "a priori truth factory" to locate drinkable water. It makes you wonder why eyes evolved in the first place, if there are ways to produce accurate beliefs without looking at things.

The claim that there is some non-infernetial apriori truth, or accurate intuition, is not equivalent to the claim that apriori truth is available about everything. Moreever, non-inferential, soundness-style, apriori truth has an evolutionary justification: we might believe X, despite not having seen it with our own eyes, because only those of our ancestors who believed X survived. Innate knowlede, the naturalistic apriori, must be sharply distinguished from the mystical apriori (and both must be distinguished from inference-from-premises).

James R. Newman said: "The fact that one apple added to one apple invariably gives two apples helps in the teaching of arithmetic, but has no bearing on the truth of the proposition that 1 + 1 = 2. The Internet Encyclopedia of Philosophy defines "a priori" propositions as those knowable independently of experience. Wikipedia quotes Hume: Relations of ideas are "discoverable by the mere operation of thought, without dependence on what is anywhere existent in the universe." You can see that 1 + 1 = 2 just by thinking about it, without looking at apples."

And that is quite uncontentious, providing that it applies to truth as validity (correct inference from possibly arbitrary premises), and not as soundness, or the non-inferential apriori (for instance, the question of whether ones chosen premises are really true).

"You could see someone else's engine operating materially, through material chains of cause and effect, to compute by "pure thought" that 1 + 1 = 2. How is observing this pattern in someone else's brain any different, as a way of knowing, from observing your own brain doing the same thing? When "pure thought" tells you that 1 + 1 = 2, "independently of any experience or observation", you are, in effect, observing your own brain as evidence."

And when your Pure Thought tell that the principal of non-contradiction is true (something you need in order to infer 1+1=2), you may be benefitting from your ancestor's hard won experience. The problem is that the apriori needs to be defined in terms of isolated systems, and no system is ultimately isolated.

" this engine works at all, then it should have the same output if it observes (with eyes and retina) a similar brain-engine carrying out a similar collision, and copies into itself the resulting pattern. In other words, for every form of a priori knowledge obtained by "pure thought", you are learning exactly the same thing you would learn if you saw an outside brain-engine carrying out the same pure flashes of neural activation. The engines are equivalent, the bottom-line outputs are equivalent, the belief-entanglements are the same."

If something can only learnt through empiricism, then offloading to another Engine that doesn't have the appropriate sensors doesn't help. On the other hand, the claim that any apriori inference can be offloaded to another Engine, an isolated external processor does not disprove the existence of the apriori. The aposteriori is that which cannot be learnt by an isolated (no sensors) system; the inferenital apriori is that which can -- but it doesn't matter which Engine is doing the processing.

"There is nothing you can know "a priori", which you could not know with equal validity by observing the chemical release of neurotransmitters within some outside brain. What do you think you are, dear reader?"

So long as you are talking about inference from premises. But observing their brain is not going to tell me that their premises are true.

"Are the sort of neural flashes that philosophers label "a priori beliefs", arbitrary? "

Those flashes are noninferential/soundness style apriori intuitions, and are not addressed by the forgoing.

You can't excuse calling a proposition "a priori" by pointing out that other philosophers are having trouble justifying their propositions. If a philosopher fails to explain something, this fact cannot supply electricity to a refrigerator, nor act as a magical factory for accurate beliefs. There's no truce, no white flag, until you understand why the engine works.

If the engine does nothing but infer conclusions from premises, however computationally or materialistiically, you still don't know some important things: whether the premises are true, and the conclusions sound.

If you clear your mind of justification, of argument, then it seems obvious why Occam's Razor works in practice: we live in a simple world, a low-entropy universe in which there are short explanations to be found.

We do, according to our explanations...which were selected for simplicity in the first place. You don't have an insight into the universe separate from explanations.

Perhaps you cannot argue anything to a hypothetical debater who has not accepted Occam's Razor, just as you cannot argue anything to a rock. A mind needs a certain amount of dynamic structure to be an argument-acceptor. If a mind doesn't implement Modus Ponens, it can accept "A" and "A->B" all day long without ever producing "B". How do you justify Modus Ponens to a mind that hasn't accepted it? How do you argue a rock into becoming a mind?

Then apriori truths of a non-inferential kind are preconditions of rationality. Which has nothing to do with materialism or computationalism

But of course there's such a thing as an a priori statement! Running a computation forwards without any uncertainty in it yields a result: this is "a priori" in the sense that, since it operates only on abstract mental data with no reference to empirical reality, it requires no experience to "get right" (rather, experience is required to locate a useful computation, out of all possible computations). 2+2 really does equal 4, every time, all the time, because any computation isomorphic to 2+2 must always yield an answer isomorphic to 4.

When you add 1 + 1 and get 2 by thinking, these thoughts are themselves embodied in flashes of neural patterns. In principle, we could observe, experientially, the exact same material events as they occurred within someone else's brain.

"the exact same material events"?

He has made a prediction of observable events that I predict is very very very wrong.

Your brain is not my brain. Not the exact same size, shape, or connectivity. Not performing the exact same ocean of processing at any one time that one might also be adding 1+1 to equal 2. For that matter, your brain 5 minutes ago adding 1+1 equal 2 will not exhibit "the exact same material events" as your brain doing it now, or ten minutes from now.

This is one of many times where I wish LessWrong had seen more influence from Korzybski.

I must respectfully disagree with your interpretation of Kant's use of the term "a priori knowledge." Kant says "While all knowledge beings with experience, it does not all arise out of experience." Hence, Kant never himself says that we can have knowledge without ever having had experience, that is to say, the shorthand explanation of Kant's philosophy, namely that "a priori truths are truths that can be attained without experience" does a poor job of representing the nuance of his epistemological system. Again, he says "While all knowledge beings with experience, it does not all arise out of experience" meaning that you have to exist in order to attain a priori knowledge (a harken back to Descartes' "I think therefore I am"); however, a priori truths are not going to be found within the physical laws of the world. Rather, a priori truths are found in the very nature of our mental reasoning process, as well as in the very nature of language itself. This is so regardless of the very real fact that language, alongside the accompanying mental capacity required to wield it, are a large part the result of the very laws of nature Kant has deemed irrelevant. This is because Kant is not concerning himself (in this part of the argument) with the distinction between phenomena (our experience) and noumena (the thing into itself, i.e., the external world outside of our perspective). Rather, Kant states that regardless of the nature of the reality outside of human experience, the nature of our experience itself (regardless of what shaped that experience) can be studied independently of its causes, and in doing so, illuminate many concepts that were until then unknown, e.g., the existence of a priori truths themselves; the categories; and the transcendental deduction.

I hope this insight from a Kantian scholar sheds some light on your very unique and interesting argument.

When "pure thought" tells you that 1 + 1 = 2, "independently of any experience or observation", you are, in effect, observing your own brain as evidence.

I mean, yeah? You can still do that in your armchair, without looking at anything outside of yourself. Mathematical facts are indeed "discoverable by the mere operation of thought, without dependence on what is anywhere existent in the universe," if you modify the statement a little to say "anywhere else existent" in order to acknowledge that the operation of thought indeed exists in the universe. Do mathematical facts exist independently of the universe? Maybe, maybe not, it probably depends what you mean by "exist" and it doesn't really matter to anyone since either way, you can't discover any mathematical facts without using your brain, which is in the universe. So there's no observable difference between whether Platonic math exists or not.

"free will" is a useful concept which should be kept, even though it has been used to refer to nonsensical things. Just because one can't will what he wills, doesn't mean we shouldn't be able to talk about willing what you do. Similarly, just because you can't get knowledge without thinking, doesn't mean we shouldn't be able to use "a priori knowledge" to talk about getting knowledge without looking.

Modus Ponens can be justified by truth tables. A is $\begin{array}{ccc}{}_B{}^A& T& F\\ T& T& F\\ F& T& F\end{array}$, and $A\to B$ is $\begin{array}{ccc}{}_B{}^A& T& F\\ T& T& T\\ F& F& T\end{array}$. By combining these to $A\wedge A\to B$ we get the truth table $\begin{array}{ccc}{}_B{}^A& T& T\\ T& T\wedge T=T& F\wedge T=F\\ F& T\wedge F=F& F\wedge T=T\end{array}$ which is only true if both A and B are true.

Of course, one can always reject the notion of truth tables and then we are back to square one...

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As for Occam's Razor - I used to think of it in terms of avoiding overfitting. More complex explanations have more degrees of freedom which makes it easier for them to explain all the datapoints by "twisting" instead of by uncovering some underlying rule.

Now that I've been exposed to Bayesianism though, and consider beliefs to be defined by the predictions you can get from them, I see Occam's Razor as a matter of pragmatism:

1. If two explanations yield the exact same predictions, then they are different representations of the same belief. We should choose the simpler one not because it is more true or more accurate - they are identically true and identically accurate - but because it is easier to work with.
2. If the two explanations yield some different predictions, then we don't even need Occam's Razor - we need to test these predictions and see which explanation is more accurate.
3. If for whatever reason we can't test these predictions (too expensive? unethical? cannot be done with current technology?) but we still need to pick one, picking the simpler one is still a good rule of thumb because it is bounded - we can always make the explanation more complex, but there is a limit to how much simpler we can make it before it no longer explains the observations. So we have a stopping condition - if the rule was to pick the more complex explanations we would be stuck forever in a race to make the explanation more and more complicated.

Indeed, it seems there is no way to justify Occam’s Razor except by appealing to Occam’s Razor, making this argument unlikely to convince any judge who does not already accept Occam’s Razor.

That's very much not proven. There are multiple arguments for Occams Razor ,(see the Wikipedia page) , most or all of which aren't circular.