My point was that vampires were by definition not real - or at least, not understandable - because any time we found something real and understandable that met the definition of a vampire, we would change the definition to exclude it.

But the same exchange might have occurred with something entirely real. We are not in the habit of giving fully adequate definitions, so it is often possible to find counterexamples to the definitions we give, which might prompt the other person to add to the definition to exclude the counterexample. For example:

A: What is a dog?

B: A dog is a four-footed animal that is a popular pet.

A: So a cat is a dog.

B: Dogs bark.

A: So if I teach a cat to bark, it will become a dog.

etc.

I had a similar, shorter conversation with a theologian. He had hired me to critique a book he was writing, which claimed that reductionist science had reached its limits, and that it was time to turn to non-reductionist science.

The examples he gave were all phenomena which science had difficulty explaining, and which he claimed to explain as being irreducibly complex. For instance, because people had difficulty explaining how cells migrate in a developing fetus, he suggested (as Aristotle might have) that the cells had an innate fate or desire that led them to the right location.

What he really meant by non-reductionist science, was that as a "non-reductionist scientist", one is allowed to throw up one's hands, and say that there is no explanation for something. A claim that a phenomenon is supernatural is always the assertion that something has no explanation. (I don't know that it needs to be presented as a mental phenomenon, as Eliezer says.) So to "do" non-reductionist science is simply to not do science.

It should be possible, then, for a religious person to rightly claim that their point of view is outside the realm of science. If they said, for instance, that lightning is a spirit, that is not a testable hypothesis.

In practice, religions build up webs of claims, and of connections to the non-spiritual world, that can be tested for consistency. If someone claims not just that lightning is a spirit, but that an anthropomorphic God casts lightning bolts at sinners, that is a testable hypothesis. Once, when I was a Christian, lightning struck the cross behind my church. This struck me as strong empirical evidence against the idea that God directed every bolt. (I suppose one could interpret it as divine criticism of the church. The church elders did not, however, pursue that angle.)

Once, in a LARP, I played Isaac Asimov on a panel which was arguing whether vampires were real. It went something like this (modulo my memory): I asked the audience to define "vampire", and they said that vampires were creatures that lived by drinking blood.

I said that mosquitoes were vampires. So they said that vampires were humanoids who lived by drinking blood.

I said that Masai who drank the blood of their cattle were vampires. So they said that vampires were humanoids who lived by drinking blood, and were burned by sunlight.

I (may have) said that a Masai with xeroderma pigmentosum was a vampire. And so on.

My point was that vampires were by definition not real - or at least, not understandable - because any time we found something real and understandable that met the definition of a vampire, we would change the definition to exclude it.

(Strangely, some mythical creatures, such as vampires and unicorns, seem to be defined in a spiritual way; whereas others, such as mermaids and centaurs, do not. A horse genetically engineered to grow a horn would probably not be thought of as a "real" unicorn; a genenged mermaid probably would be admitted to be a "real" mermaid.)

Okay, so here's a dryad. You cut her open, and see white stuff. You take a sample, put it under a microscope, and still see white stuff. You use a scanning tunneling microscope, and still see white stuff. You build an AI and tell it to analyze the sample. The AI converts galaxies into computronium and microscopium, conducts every experiment it can think of, and after a trillion years reports: "The dryad is made of white stuff, and that's all I know. Screw this runaround, what's for dinner?"

But using an outside view of sorts (observed behavior), you can still predict what the dryad will do next. Just like with quarks and with Occam's razor and with prime numbers. And things you haven't reduced yet, but think you can, like people or the LHC.

So, what would you call this dryad?

I still seem to be able to envision what things would look like if a form of Cartesian dualism were true. Our ordinary laws of physics would govern all matter except one or more places deep in the brain, where the laws of physics would be violated where the soul is "pulling the strings" of the body, as it were. These deviations from physics would not happen unlawfully, but rather would be governed by special, complicated laws of psychology, rather than physics. In principle, this should be testable.

Unlawfulness and nonreductionism are distinct concepts; I can see how the former is incoherent, but the latter still seems logically possible, if false.

Phil: Vampires ARE real. Both humans and animals can become vampires after being bitten by another vampire (very often a bat or racoon). After being bitten, they will go crazy and attempt to bite others. They also are unable to cross running water.

The virus has been discovered, and a vaccine exists.

http://en.wikipedia.org/wiki/Rabies

Yeah, I know, those aren't "real" vampires, even though that is very likely the source of the vampire mythology.

Eliezer, I think I agree with most of what you say in this post, but unless I misunderstand what you mean by "Bayesian confirmation," I think you're wrong about this bit:

If the "boring view" of reality is correct, then you can never predict anything irreducible because you are reducible. You can never get Bayesian confirmation for a hypothesis of irreducibility, because any prediction you can make is, therefore, something that could also be predicted by a reducible thing, namely your brain.

I think that while you can in this case never devise an empirical test whose outcome could logically prove irreducibility, there is no clear reason to believe that you cannot devise a test whose counterfactual outcome in an irreducible world would make irreducibility subjectively much more probable (given an Occamian prior).

Without getting into reducibility/irreducibility, consider the scenario that the physical universe makes it possible to build a hypercomputer -- that performs operations on arbitrary real numbers, for example -- but that our brains do not actually make use of this: they can be simulated perfectly well by an ordinary Turing machine, thank you very much. If this scenario were true, would it follow that we cannot possibly obtain "Bayesian confirmation" of its truth? I don't think that is the case: Of course, it is true that any empirical test our brains could devise in this scenario could also be passed by a Turing machine that simulated our brains to decide what its answer should be. In fact, every test "does the universe do X if we do Y at time T" we may devise to test whether the universe allows for infinite computations can be met by a Turing machine universe whose code simply includes the instruction to do X at time T. But, such a Turing machine may be complex enough that we start taking "the universe allows for hypercomputation" to be the simpler (and thus, more probable) alternative -- unless we are willing to completely exclude that possibility a priori, which I'm not willing to do and I expect you aren't, either.

Thus, I think that either your argument doesn't support your conclusion, or I don't understand your argument yet :-)

I would ask the same question as Nominull and Tiiba: Why is a fundamentally mental thing different from a fundamentally physical thing like quarks? If we discovered a spirit in a tree that wasn't composed of quarks and leptons, is there a reason we couldn't take that spirit to be a new fundamental particle that behaves in such-and-such a way, just as a down quark is a fundamental particle that behaves in such-and-such a way?

Eliezer: If, on the other hand, a supernatural hypothesis turns out to be true, then presumably you will also discover that it is not inconceivable.

Right. So apart from Occam's razor, what's the reason for excluding things that aren't quarks and leptons from your set of fundamental particles?

Of course water flows downhill because it wants to be lower. It just is not in its nature to be able to want anything else, which distinguishes it from more flexible want-systems like ourselves.

As to the supernatural, I suggest a useful analogy is mathematical objects, like 5, pi, the complex plane, or the Pythagorean theorem. These objects are not physical; they are not made of quarks nor reducible to them, even though any concrete instantiation of them (or instantiation of a thought about them) must involve some physical process; they are non-natural even though they pervade nature. Nobody here would deny the right of mathematicians to be pragmatic Platonists who treat mathematical objects as real things that they can think about and perform mental manipulations on. By analogy, I would at least consider the possibility that theologians have a similar right to make statements about their non-physical, non-natural object of study.

Tim, see The Argument from Common Usage and 37 Ways that Words can be Wrong.

This is why I claim that atheism is an established scientific result. One of the strongest lines of evidence is, indeed, that we have successfully reduced minds and shown the notion of an irreducible mind to be incoherent. Mind as an irreducible simple is basic to all monotheistic religions. Demonstrating something once thought coherent to be incoherent is, of course, one of the strongest lines of evidence in science. Other avenues through which atheism has been established by science include conservation in physics, chemistry and biology (which led directly to materialism), evolution, and the development of plausible sociological accounts of religion. I would argue that atheism is as well established as Plate Tectonics and Natural Selection. What I think is telling is that most contemporary approaches to religious apologetics implicitly recognize that science has established atheism.

The theist has three avenues of response. The first is to attack specific parts of science. This is what Fundamentalist Christians do. The second, by far the most popular, is to attack the very possibility of scientific knowledge. This is what nearly all "liberal" religious believers who claim there is no conflict between science and religion do. They generally adopt a skeptical epistemology, holding that no knowledge claim can be true, or instrumentalism about science, holding that scientific claims are nonfactual, or a quasi-Kantian constructivist metaphysics wherein "true" reality is forever out of reach. The weird thing is that this position, which essentially rejects all of science, is considered more "sophisticated" and acceptable than the Fundamentalist position which rejects only select parts of science but remains realist about the rest. The third approach is to adopt some sort of nonfactualism about religious claims; essentially to hold that your religious practice is merely tradition. I think this nearly exhausts contemporary positions on religious apologetics and is therefore evidence that people implicitly accept that science has established atheism.

Ennui: "In that special Cartesian theater, I can picture an even smaller Homunculus pulling the strings of the larger."

But what if the homunculus were ontologically fundamental?--of course the notion is silly and of course it's false, but I'm not yet convinced that it's literally nonsense on the order of square circles or A-and-not-A. It could be that I just need some intuition-reshaping, but in the meantime I can do nothing else but call it as I see it.

Constant: with dogs, you can point to examples and say "these animals, and animals closely related to these are dogs".

If the "boring view" of reality is correct, then you can never predict anything irreducible because you are reducible. You can never get Bayesian confirmation for a hypothesis of irreducibility, because any prediction you can make is, therefore, something that could also be predicted by a reducible thing, namely your brain.

Some boxes you really can't think outside. If our universe really is Turing computable, we will never be able to concretely envision anything that isn't Turing-computable—no matter how many levels of halting oracle hierarchy our mathematicians can talk about, we won't be able to predict what a halting oracle would actually say, in such fashion as to experimentally discriminate it from merely computable reasoning.

I don't quite understand this one. How does "you are reducible" imply "you cannot conceive anything nonreducible"? Human beings with their merely Turing-complete brains can understand the concept of a non-Turing-computable problems. If our universe turns out to be more than Turing computable, and aliens give us a box that can map an integer to an integer by a non-computable function together with a verbal description of the function (say, "N -> busy-beaver(N)"), we will be able to use it, and understand what it does and why it is useful. Even though we will not be able to predict the exact outputs without a similar box, we could conceive what would the output look like ("like an integer bigger than X and smaller than Y"). Correspondingly, I see no impossibility in that a reducible brain can imagine what a non-reducible universe would look like.

Say, suppose there is a universe made of three types of things: ghosts, transistors and billiard balls. Transistors and billiard balls can form structures that compute functions up to primitive recursive. Billiard balls can interact with ghosts and transistors, acting as an interface between two. Ghosts can directly interact only with billiard balls. Every ghost observes the state of billiard balls around itself every five seconds and outputs one of actions: haunt, spook or wail, that affect the billiard balls in some way. The computation performed by a ghost is Turing-complete, but not primitive recursive. Thus, ghosts can never be reduced to transistors and billiard balls. Creatures made of transistors can observe billiard balls and infer the existence of ghosts. They will obviously not be able to form a complete model of a ghost, but they could make statistical observations about them. They could form primitive recursive statements, such as "a ghost spooks 50% of the time regardless of billiard balls around, except if it was surrounded by four balls in pyramidal pattern 5 seconds ago, in which case it always haunts". These statements will not describe the entire behavior of a ghost, but they will be conceivable, imaginable and detectable by transistor-creatures. And it, I suppose, is a probable thought that can occur to a transistor-creature - "what if ghosts are not computable?" (in their definition of computability that is merely primitive recursive).

In the same way, I see no trouble in visualizing a world which is just like ours, but contains a non-reducible-to-quarks, non-computable (by my definition of computability that is merely Turing computable) ghost that reads the state of quarks and produces a behavior that is outside of the box I'm thinking in. It will be my problem, not Universe's.

I have to wonder if your characterization of people who deny reductionism is really correct. I agree most of them are probably confused and do not have a coherent model in the first place - certainly actual non-reductionism is a confusion - but I'm not certain all of them are confused in the way you say.

From my experience it seems that the claims of the people who deny "reductionism" could be coherently understood if we assume that they are actually confused about what reductionism actually consists of, and that they are not denying actual reductionism, just one particular version of it that they are imagining the term necessarily refers to.

E.g. if we assume that they are simply saying that in some cases, the irreducible components of the universe are complicated rather than simple, and that the lowest level is something that appears to be "high level", then this is, though almost certainly wrong, at least coherent. It is also technically reductionist, albeit possibly trivially so (worst case: entire universe is a giant lookup table). But they don't think of it as reductionism as it doesn't much resemble what they're used to seeing called by that name.

Indeed I would go so far as to say that the people who deny reductionism are very often the same people who are implicitly making the mistake of greedy reductionism! They fail to think in terms of interactions of components, of actual systems, and so make the mistake of inferring angry atoms. They do reduce things, it's just that they reduce everything to supernatural things that can only interact via some sort of superposition principle. This pretty much fails at predicting anything, but it is at least coherent.

I don't know, does this make sense?

I remember, when first reading this article, that it was really convincing and compelling. I looked it up again because I wanted to be able to make the argument myself, and now I find that I don't understand how you can get from "if the staid conventional normal boring understanding of physics and the brain is correct" to "there's no way in principle that a human being can concretely envision, and derive testable experimental predictions about, an alternate universe in which things are irreducibly mental." That seems like too large a jump for me. Any help?

God is a shapeshifting horror from the outer beyond that constantly adapts its properties to whatever is most convenient given the argument currently being considered.

@poke (i think you posted in the wrong thread) -- if you did a survey, limited to scientists, and asked questions like "is general relativity largely correct?', or 'Does DNA encode genes?', you would get near-100% agreement. If you asked 'is atheism true?', you would get a much lower number. Therefore, whatever opinions or arguments might seem convincing to you personally, atheism is not the strongest modern scientific result.

As ought to be obvious, statements about god are not scientific statements. You will not find peer-reviewed scientific literature proving or disproving the existence of god. God is a topic of endless of fascination on the fringes of science, which include philosophy, blogs like this one and popular books written by scientists, but is largely absent from the literature of actual science, for good reason.

If god is not a natural being, then science does not have the means to say whether it exists or not. It is not even clear what "exists" means for such entities. You can say that it makes no sense to talk about non-natural, non-material entities in any way, but as I pointed out before, we do it all the time for mathematical entities and I assume nobody here has a problem with that.

I find atheist fundamentalists amusing, because they are so certain that they know what "god" means, just like religious fundamentalists. Most sane and intelligent people with religious tendencies (and there are many, although they don't seem to get much press) understand that if "god" means anything, it is a pointer towards something unknown and perhaps unknowable, and arguing about whether it exists in the physical sense is missing the point completely.

Z. M. Davis: But if you think about the things that the homunculus tends to do, I think you would find yourself needing to move to levels below the homunculus to do it. To give it a coherent set of actions it is likely to take, and not to take, at any given time, you would have to populate it with wants, with likes, with beliefs, with structures for reasoning about beliefs.

I think eventually you would come to an algorithm of which the homunculus would have to be an instantiation, and you would have to assume that that algorithm was represented somewhere.

I just don't see how you can make sensible predictions about ontologically basic complicated things. And I know people will go on about how you can't make predictions about a person with free will, but that's a crock. You expect me to try to coherently answer your post. I expect a cop to arrest me if I drive too fast. More to the point, we don't expect neurologically intact humans to spend three years walking backwards, or talk to puddles, or remove their clothing and sing "I'm a little teapot" in Times Square.

And the same goes for gods, incidentally. Religious folk will say that their gods' ways are ineffable, that they can't be predicted. But they still expect their gods to answer prayers, and forgive sins, and torture people like me for millennia, and they don't expect them to transform mount everest into a roast beef sandwich, or thunder forth nursery rhymes from the heavens.

They have coherent expectations, and for those expectations to make sense you have to open the black box and put things in there. You have to postulate structure, and relationships between parts, and soon you haven't got something ontologically basic anymore.