What You Learned Before You Were Born

In Plato’s Meno, Socrates makes the somewhat odd claim that the ability of people to learn things without being directly told them proves that somehow they must have learned them or known them in advance. While we can reasonably assume this is wrong in a literal sense, there is some likeness of the truth here.

The whole of a human life is a continuous learning process generally speaking without any sudden jumps. We think of a baby’s learning as different from the learning of a child in school, and the learning of the child as rather different from the learning of an adult. But if you look at that process in itself, there may be sudden jumps in a person’s situation, such as when they graduate from school or when they get married, but there are no sudden jumps from not knowing anything about a topic or an object to suddenly knowing all about it. The learning itself happens gradually. It is the same with the manner in which it takes place; adults do indeed learn in a different manner from that in which children or infants learn. But if you ask how that manner got to be different, it certainly did so gradually, not suddenly.

But in addition to all this, there is a kind of “knowledge” that is not learned at all during one’s life, but is possessed from the beginning. From the beginning people have the ability to interact with the world in such a way that they will survive and go on to learn things. Thus from the beginning they must “know” how to do this. Now one might object that infants have no such knowledge, and that the only reason they survive is that their parents or others keep them alive. But the objection is mistaken: infants know to cry out when they hungry or in pain, and this is part of what keeps them alive. Similarly, an infant knows to drink the milk from its mother rather than refusing it, and this is part of what keeps it alive. Similarly in regard to learning, if an infant did not know the importance of paying close attention to speech sounds, it would never learn a language.

When was this “knowledge” learned? Not in the form of a separated soul, but through the historical process of natural selection.

Selection and Artificial Intelligence

This has significant bearing on our final points in the last post. Is the learning found in AI in its current forms more like the first kind of learning above, or like the kind found in the process of natural selection?

There may be a little of both, but the vast majority of learning in such systems is very much the second kind, and not the first kind. For example, AlphaGo is trained by self-play, where moves and methods of play that tend to lose are eliminated in much the way that in the process of natural selection, manners of life that do not promote survival are eliminated. Likewise a predictive model like GPT-3 is trained, through a vast number of examples, to avoid predictions that turn out to be less accurate and to make predictions that tend to be more accurate.

Now (whether or not this is done in individual cases) you might take a model of this kind and fine tune it based on incoming data, perhaps even in real time, which is a bit more like the first kind of learning. But in our actual situation, the majority of what is known by our AI systems is based on the second kind of learning.

This state of affairs should not be surprising, because the first kind of learning described above is impossible without being preceded by the second. The truth in Socrates’ claim is that if a system does not already “know” how to learn, of course it will not learn anything.

Intelligence and Universality

Elsewhere I have mentioned the argument, often made in great annoyance, that people who take some new accomplishment in AI or machine learning and proclaim that it is “not real intelligence” or that the algorithm is “still fundamentally stupid”, and other things of that kind, are “moving the goalposts,” especially since in many such cases, there really were people who said that something that could do such a thing would be intelligent.

As I said in the linked post, however, there is no problem of moving goalposts unless you originally had them in the wrong place. And attaching intelligence to any particular accomplishment, such as “playing chess well” or even “producing a sensible sounding text,” or anything else with that sort of particularity, is misplacing the goalposts. As we might remember, what excited Francis Bacon was the thought that there were no clear limits, at all, on what science (namely the working out of intelligence) might accomplish. In fact he seems to have believed that there were no limits at all, which is false. Nonetheless, he was correct that those limits are extremely vague, and that much that many assumed to be impossible would turn out to be possible. In other words, human intelligence does not have very meaningful limits on what it can accomplish, and artificial intelligence will be real intelligence (in the same sense that artificial diamonds can be real diamonds) when artificial intelligence has no meaningful limits on what it can accomplish.

I have no time for playing games with objections like, “but humans can’t multiply two 1000 digit numbers in one second, and no amount of thought will give them that ability.” If you have questions of this kind, please answer them for yourself, and if you can’t, sit still and think about it until you can. I have full confidence in your ability to find the answers, given sufficient thought.

What is needed for “real intelligence,” then, is universality. In a sense everyone knew all along that this was the right place for the goalposts. Even if someone said “if a machine can play chess, it will be intelligent,” they almost certainly meant that their expectation was that a machine that could play chess would have no clear limits on what it could accomplish. If you could have told them for a fact that the future would be different: that a machine would be able to play chess but that (that particular machine) would never be able to do anything else, they would have conceded that the machine would not be intelligent.

Training and Universality

Current AI systems are not universal, and clearly have no ability whatsoever to become universal, without first undergoing deep changes in those systems, changes that would have to be initiated by human beings. What is missing?

The problem is the training data. The process of evolution produced the general ability to learn by using the world itself as the training data. In contrast, our AI systems take a very small subset of the world (like a large set of Go games or a large set of internet text), and train a learning system on that subset. Why take a subset? Because the world is too large to fit into a computer, especially if that computer is a small part of the world.

This suggests that going from the current situation to “artificial but real” intelligence is not merely a question of making things better and better little by little. There is a more fundamental problem that would have to be overcome, and it won’t be overcome simply by larger training sets, by faster computing, and things of this kind. This does not mean that the problem is impossible, but it may turn out to be much more difficult than people expected. For example, if there is no direct solution, people might try to create Robin Hanson’s “ems”, where one would more or less copy the learning achieved by natural selection. Or even if that is not done directly, a better understanding of what it means to “know how to learn,” might lead to a solution, although probably one that would not depend on training a model on massive amounts of data.

What happens if there is no solution, or no solution is found? At times people will object to the possibility of such a situation along these times: “this situation is incoherent, since obviously people will be able to keep making better and better machine learning systems, so sooner or later they will be just as good as human intelligence.” But in fact the situation is not incoherent; if it happened, various types of AI system would approach various asymptotes, and this is entirely coherent. We can already see this in the case of GPT-3, where as I noted, there is an absolute bound on its future performance. In general such bounds in their realistic form are more restrictive than their in-principle form; I do not actually expect some successor to GPT-3 to write sensible full length books. Note however that even if this happened (as long as the content itself was not fundamentally better than what humans have done) I would not be “moving the goalposts”; I do not expect that to happen, but its happening would not imply any fundamental difference, since this is still within the “absolute” bounds that we have discussed. In contrast, if a successor to GPT-3 published a cure for cancer, this would prove that I had made some mistake on the level of principle.

Some Remarks on GPT-N

At the end of May, OpenAI published a paper on GPT-3, a language model which is a successor to their previous version, GPT-2. While quite impressive, the reaction from many people interested in artificial intelligence has been seriously exaggerated. Sam Altman, OpenAI’s CEO, has said as much himself:

The GPT-3 hype is way too much. It’s impressive (thanks for the nice compliments!) but it still has serious weaknesses and sometimes makes very silly mistakes. AI is going to change the world, but GPT-3 is just a very early glimpse. We have a lot still to figure out.

I used “GPT-N” in the title here because most of the comments I intend to make are almost completely general, and will apply to any future version that uses sufficiently similar methods.

What it does

GPT-3 is a predictive language model, that is, given an input text it tries to predict what would come next, much in the way that if you read the first few words of this sentence with the rest covered up, you might try to guess what would be likely to come next. To the degree that it does this well, it can be used to generate text from a “prompt,” that is, we give it something like a few words or a few sentences, and then add whatever it predicts should come next. For example, let’s take this very blog post and see what GPT-3 would like to say:

What it doesn’t do

While GPT-3 does seem to be able to generate some pretty interesting results, there are several limitations that need to be taken into account when using it.

First and foremost, and most importantly, it can’t do anything without a large amount of input data. If you want it to write like “a real human,” you need to give it a lot of real human writing. For most people, this means copying and pasting a lot. And while the program is able to read through that and get a feel for the way humans communicate, you can’t exactly use it to write essays or research papers. The best you could do is use it as a “fill in the blank” tool to write stories, and that’s not even very impressive.

While the program does learn from what it reads and is quite good at predicting words and phrases based on what has already been written, this method isn’t very effective at producing realistic prose. The best you could hope for is something like the “Deep Writing Machine” Twitter account, which spits out disconnected phrases in an ominous, but very bland voice.

In addition, the model is limited only to language. It does not understand context or human thought at all, so it has no way of tying anything together. You could use it to generate a massive amount of backstory and other material for a game, but that’s about it.

Finally, the limitations in writing are only reinforced by the limitations in reading. Even with a large library to draw on, the program is only as good as the parameters set for it. Even if you set it to the greatest writers mankind has ever known, without any special parameters, its writing would be just like anyone else’s.

The Model

GPT-3 consists of several layers. The first layer is a “memory network” that involves the program remembering previously entered data and using it when appropriate (i.e. it remembers commonly misspelled words and frequently used words). The next layer is the reasoning network, which involves common sense logic (i.e. if A, then B). The third is the repetition network, which involves pulling previously used material from memory and using it to create new combinations (i.e. using previously used words in new orders).

I added the bold formatting, the rest is as produced by the model. This was also done in one run, without repetitions. This is an important qualification, since many examples on the internet have been produced by deleting something produced by the model and forcing it to generate something new until something sensible resulted. Note that the model does not seem to have understood my line, “let’s take this very blog post and see what GPT-3 would like to say.” That is, rather than trying to “say” anything, it attempted to continue the blog post in the way I might have continued it without the block quote.

Truth vs Probability of Text

If we interpret the above text from GPT-3 “charitably”, much of it is true or close to true. But I use scare quotes here because when we speak of interpreting human speech charitably, we are assuming that someone was trying to speak the truth, and so we think, “What would they have meant if they were trying to say something true?” The situation is different here, because GPT-3 has no intention of producing truth, nor of avoiding it. Insofar as there is any intention, the intention is to produce the text which would be likely to come after the input text; in this case, as the input text was the beginning of this blog post, the intention was to produce the text that would likely follow in such a post. Note that there is an indirect relationship with truth, which explains why there is any truth at all in GPT-3’s remarks. If the input text is true, it is at least somewhat likely that what would follow would also be true, so if the model is good at guessing what would be likely to follow, it will be likely to produce something true in such cases. But it is just as easy to convince it to produce something false, simply by providing an input text that would be likely to be followed by something false.

This results in an absolute upper limit on the quality of the output of a model of this kind, including any successor version, as long as the model works by predicting the probability of the following text. Namely, its best output cannot be substantially better than the best content in its training data, which is in this version is a large quantity of texts from the internet. The reason for this limitation is clear; to the degree that the model has any intention at all, the intention is to reflect the training data, not to surpass it. As an example, consider the difference between Deep Mind’s AlphaGo and AlphaGo Zero. AlphaGo Zero is a better Go player than the original AlphaGo, and this is largely because the original is trained on human play, while AlphaGo Zero is trained from scratch on self play. In other words, the original version is to some extent predicting “what would a Go player play in this situation,” which is not the same as predicting “what move would win in this situation.”

Now I will predict (and perhaps even GPT-3 could predict) that many people will want to jump in and say, “Great. That shows you are wrong. Even the original AlphaGo plays Go much better than a human. So there is no reason that an advanced version of GPT-3 could not be better than humans at saying things that are true.”

The difference, of course, is that AlphaGo was trained in two ways, first on predicting what move would be likely in a human game, and second on what would be likely to win, based on its experience during self play. If you had trained the model only on predicting what would follow in human games, without the second aspect, the model would not have resulted in play that substantially improved upon human performance. But in the case of GPT-3 or any model trained in the same way, there is no selection whatsoever for truth as such; it is trained only to predict what would follow in a human text. So no successor to GPT-3, in the sense of a model of this particular kind, however large, will ever be able to produce output better than human, or in its own words, “its writing would be just like anyone else’s.”

Self Knowledge and Goals

OpenAI originally claimed that GPT-2 was too dangerous to release; ironically, they now intend to sell access to GPT-3. Nonetheless, many people, in large part those influenced by the opinions of Nick Bostrom and Eliezer Yudkowsky, continue to worry that an advanced version might turn out to be a personal agent with nefarious goals, or at least goals that would conflict with the human good. Thus Alexander Kruel:

GPT-2: *writes poems*
Skeptics: Meh
GPT-3: *writes code for a simple but functioning app*
Skeptics: Gimmick.
GPT-4: *proves simple but novel math theorems*
Skeptics: Interesting but not useful.
GPT-5: *creates GPT-6*
Skeptics: Wait! What?
GPT-6: *FOOM*
Skeptics: *dead*

In a sense the argument is moot, since I have explained above why no future version of GPT will ever be able to produce anything better than people can produce themselves. But even if we ignore that fact, GPT-3 is not a personal agent of any kind, and seeks goals in no meaningful sense, and the same will apply to any future version that works in substantially the same way.

The basic reason for this is that GPT-3 is disembodied, in the sense of this earlier post on Nick Bostrom’s orthogonality thesis. The only thing it “knows” is texts, and the only “experience” it can have is receiving an input text. So it does not know that it exists, it cannot learn that it can affect the world, and consequently it cannot engage in goal seeking behavior.

You might object that it can in fact affect the world, since it is in fact in the world. Its predictions cause an output, and that output is in the world. And that output and be reintroduced as input (which is how “conversations” with GPT-3 are produced). Thus it seems it can experience the results of its own activities, and thus should be able to acquire self knowledge and goals. This objection is not ultimately correct, but it is not so far from the truth. You would not need extremely large modifications in order to make something that in principle could acquire self knowledge and seek goals. The main reason that this cannot happen is the “P in “GPT,” that is, the fact that the model is “pre-trained.” The only learning that can happen is the learning that happens while it is reading an input text, and the purpose of that learning is to guess what is happening in the one specific text, for the purpose of guessing what is coming next in this text. All of this learning vanishes upon finishing the prediction task and receiving another input. A secondary reason is that since the only experience it can have is receiving an input text, even if it were given a longer memory, it would probably not be possible for it to notice that its outputs were caused by its predictions, because it likely has no internal mechanism to reflect on the predictions themselves.

Nonetheless, if you “fixed” these two problems, by allowing it to continue to learn, and by allowing its internal representations to be part of its own input, there is nothing in principle that would prevent it from achieving self knowledge, and from seeking goals. Would this be dangerous? Not very likely. As indicated elsewhere, motivation produced in this way and without the biological history that produced human motivation is not likely to be very intense. In this context, if we are speaking of taking a text-predicting model and adding on an ability to learn and reflect on its predictions, it is likely to enjoy doing those things and not much else. For many this argument will seem “hand-wavy,” and very weak. I could go into this at more depth, but I will not do so at this time, and will simply invite the reader to spend more time thinking about it. Dangerous or not, would it be easy to make these modifications? Nothing in this description sounds difficult, but no, it would not be easy. Actually making an artificial intelligence is hard. But this is a story for another time.

Fire, Water, and Numbers

Fire vs. Water

All things are water,” says Thales.

“All things are fire,” says Heraclitus.

“Wait,” says David Hume’s Philo. “You both agree that all things are made up of one substance. Thales, you prefer to call it water, and Heraclitus, you prefer to call it fire. But isn’t that merely a verbal dispute? According to both of you, whatever you point at is fundamentally the same fundamental stuff. So whether you point at water or fire, or anything else, for that matter, you are always pointing at the same fundamental stuff. Where is the real disagreement?”

Philo has a somewhat valid point here, and I mentioned the same thing in the linked post referring to Thales. Nonetheless, as I also said in the same post, as well as in the discussion of the disagreement about God, while there is some common ground, there are also likely remaining points of disagreement. It might depend on context, and perhaps the disagreement is more about the best way of thinking about things than about the things themselves, somewhat like discussing whether the earth or the universe is the thing spinning, but Heraclitus could respond, for example, by saying that thinking of the fundamental stuff as fire is more valid because fire is constantly changing, while water often appears to be completely still, and (Heraclitus claims) everything is in fact constantly changing. This could represent a real disagreement, but it is not a large one, and Thales could simply respond: “Ok, everything is flowing water. Problem fixed.”

Numbers

It is said that Pythagoras and his followers held that “all things are numbers.” To what degree and in what sense this attribution is accurate is unclear, but in any case, some people hold this very position today, even if they would not call themselves Pythagoreans. Thus for example in a recent episode of Sean Carroll’s podcast, Carroll speaks with Max Tegmark, who seems to adopt this position:

0:23:37 MT: It’s squishy a little bit blue and moose like. [laughter] Those properties, I just described don’t sound very mathematical at all. But when we look at it, Sean through our physics eyes, we see that it’s actually a blob of quarks and electrons. And what properties does an electron have? It has the property, minus one, one half, one, and so on. We, physicists have made up these nerdy names for these properties like electric charge, spin, lepton number. But it’s just we humans who invented that language of calling them that, they are really just numbers. And you know as well as I do that the only difference between an electron and a top quark is what numbers its properties are. We have not discovered any other properties that they actually have. So that’s the stuff in space, all the different particles, in the Standard Model, you’ve written so much nice stuff about in your books are all described by just by sets of numbers. What about the space that they’re in? What property does the space have? I think I actually have your old nerdy non-popular, right?

0:24:50 SC: My unpopular book, yes.

0:24:52 MT: Space has, for example, the property three, that’s a number and we have a nerdy name for that too. We call it the dimensionality of space. It’s the maximum number of fingers I can put in space that are all perpendicular to each other. The name dimensionality is just the human language thing, the property is three. We also discovered that it has some other properties, like curvature and topology that Einstein was interested in. But those are all mathematical properties too. And as far as we know today in physics, we have never discovered any properties of either space or the stuff in space yet that are actually non-mathematical. And then it starts to feel a little bit less insane that maybe we are living in a mathematical object. It’s not so different from if you were a character living in a video game. And you started to analyze how your world worked. You would secretly be discovering just the mathematical workings of the code, right?

Tegmark presumably would believe that by saying that things “are really just numbers,” he would disagree with Thales and Heraclitus about the nature of things. But does he? Philo might well be skeptical that there is any meaningful disagreement here, just as between Thales and Heraclitus. As soon as you begin to say, “all things are this particular kind of thing,” the same issues will arise to hinder your disagreement with others who characterize things in a different way.

The discussion might be clearer if I put my cards on the table in advance:

First, there is some validity to the objection, just as there is to the objection concerning the difference between Thales and Heraclitus.

Second, there is nonetheless some residual disagreement, and on that basis it turns out that Tegmark and Pythagoras are more correct than Thales and Heraclitus.

Third, Tegmark most likely does not understand the sense in which he might be correct, rather supposing himself correct the way Thales might suppose himself correct in insisting, “No, things are really not fire, they are really water.”

Mathematical and non-mathematical properties

As an approach to these issues, consider the statement by Tegmark, “We have never discovered any properties of either space or the stuff in space yet that are actually non-mathematical.”

What would it look like if we found a property that was “actually non-mathematical?” Well, what about the property of being blue? As Tegmark remarks, that does not sound very mathematical. But it turns out that color is a certain property of a surface regarding how it reflects flight, and this is much more of a “mathematical” property, at least in the sense that we can give it a mathematical description, which we would have a hard time doing if we simply took the word “blue.”

So presumably we would find a non-mathematical property by seeing some property of things, then investigating it, and then concluding, “We have fully investigated this property and there is no mathematical description of it.” This did not happen with the color blue, nor has it yet happened with any other property; either we can say that we have not yet fully investigated it, or we can give some sort of mathematical description.

Tegmark appears to take the above situation to be surprising. Wow, we might have found reality to be non-mathematical, but it actually turns out to be entirely mathematical! I suggest something different. As hinted by connection with the linked post, things could not have turned out differently. A sufficiently detailed analysis of anything will be a mathematical analysis or something very like it. But this is not because things “are actually just numbers,” as though this were some deep discovery about the essence of things, but because of what it is for people to engage in “a detailed analysis” of anything.

Suppose you want to investigate some thing or some property. The first thing you need to do is to distinguish it from other things or other properties. The color blue is not the color red, the color yellow, or the color green.

Numbers are involved right here at the very first step. There are at least three colors, namely red, yellow, and blue.

Of course we can find more colors, but what if it turns out there seems to be no definite number of them, but we can always find more? Even in this situation, in order to “analyze” them, we need some way of distinguishing and comparing them. We will put them in some sort of order: one color is brighter than another, or one length is greater than another, or one sound is higher pitched than another.

As soon as you find some ordering of that sort (brightness, or greatness of length, or pitch), it will become possible to give a mathematical analysis in terms of the real numbers, as we discussed in relation to “good” and “better.” Now someone defending Tegmark might respond: there was no guarantee we would find any such measure or any such method to compare them. Without such a measure, you could perhaps count your property along with other properties. But you could not give a mathematical analysis of the property itself. So it is surprising that it turned out this way.

But you distinguished your property from other properties, and that must have involved recognizing some things in common with other properties, at least that it was something rather than nothing and that it was a property, and some ways in which it was different from other properties. Thus for example blue, like red, can be seen, while a musical note can be heard but not seen (at least by most people.) Red and blue have in common that they are colors. But what is the difference between them? If we are to respond in any way to this question, except perhaps, “it looks different,” we must find some comparison. And if we find a comparison, we are well on the way to a mathematical account. If we don’t find a comparison, people might rightly complain that we have not yet done any detailed investigation.

But to make the point stronger, let’s assume the best we can do is “it looks different.” Even if this is the case, this very thing will allow us to construct a comparison that will ultimately allow us to construct a mathematical measure. For “it looks different” is itself something that comes in degrees. Blue looks different from red, but orange does so as well, just less different. Insofar as this judgment is somewhat subjective, it might be hard to get a great deal of accuracy with this method. But it would indeed begin to supply us with a kind of sliding scale of colors, and we would be able to number this scale with the real numbers.

From a historical point of view, it took a while for people to realize that this would always be possible. Thus for example Isidore of Seville said that “unless sounds are held by the memory of man, they perish, because they cannot be written down.” It was not, however, so much ignorance of sound that caused this, as ignorance of “detailed analysis.”

This is closely connected to what we said about names. A mathematical analysis is a detailed system of naming, where we name not only individual items, but also various groups, using names like “two,” “three,” and “four.” If we find that we cannot simply count the thing, but we can always find more examples, we look for comparative ways to name them. And when we find a comparison, we note that some things are more distant from one end of the scale and other things are less distant. This allows us to analyze the property using real numbers or some similar mathematical concept. This is also related to our discussion of technical terminology; in an advanced stage any science will begin to use somewhat mathematical methods. Unfortunately, this can also result in people adopting mathematical language in order to look like their understanding has reached an advanced stage, when it has not.

It should be sufficiently clear from this why I suggested that things could not have turned out otherwise. A “non-mathematical” property, in Tegmark’s sense, can only be a property you haven’t analyzed, or one that you haven’t succeeded in analyzing if you did attempt it.

The three consequences

Above, I made three claims about Tegmark’s position. The reasons for them may already be somewhat clarified by the above, but nonetheless I will look at this in a bit more detail.

First, I said there was some truth in the objection that “everything is numbers” is not much different from “everything is water,” or “everything is fire.” One notices some “hand-waving,” so to speak, in Tegmark’s claim that “We, physicists have made up these nerdy names for these properties like electric charge, spin, lepton number. But it’s just we humans who invented that language of calling them that, they are really just numbers.” A measure of charge or spin or whatever may be a number. But who is to say the thing being measured is a number? Nonetheless, there is a reasonable point there. If you are to give an account at all, it will in some way express the form of the thing, which implies explaining relationships, which depends on the distinction of various related things, which entails the possibility of counting the things that are related. In other words, someone could say, “You have a mathematical account of a thing. But the thing itself is non-mathematical.” But if you then ask them to explain that non-mathematical thing, the new explanation will be just as mathematical as the original explanation.

Given this fact, namely that the “mathematical” aspect is a question of how detailed explanations work, what is the difference between saying “we can give a mathematical explanation, but apart from explanations, the things are numbers,” and “we can give a mathematical explanation, but apart from explanations, the things are fires?”

Exactly. There isn’t much difference. Nonetheless, I made the second claim that there is some residual disagreement and that by this measure, the mathematical claim is better than the one about fire or water. Of course we don’t really know what Thales or Heraclitus thought in detail. But Aristotle, at any rate, claimed that Thales intended to assert that material causes alone exist. And this would be at least a reasonable understanding of the claim that all things are water, or fire. Just as Heraclitus could say that fire is a better term than water because fire is always changing, Thales, if he really wanted to exclude other causes, could say that water is a better term than “numbers” because water seems to be material and numbers do not. But since other causes do exist, the opposite is the case: the mathematical claim is better than the materialistic ones.

Many people say that Tegmark’s account is flawed in a similar way, but with respect to another cause; that is, that mathematical accounts exclude final causes. But this is a lot like Ed Feser’s claim that a mathematical account of color implies that colors don’t really exist; namely they are like in just being wrong. A mathematical account of color does not imply that things are not colored, and a mathematical account of the world does not imply that final causes do not exist. As I said early on, a final causes explains why an efficient cause does what it does, and there is nothing about a mathematical explanation that prevents you from saying why the efficient cause does what it does.

My third point, that Tegmark does not understand the sense in which he is right, should be plain enough. As I stated above, he takes it to be a somewhat surprising discovery that we consistently find it possible to give mathematical accounts of the world, and this only makes sense if we assume it would in theory have been possible to discover something else. But that could not have happened, not because the world couldn’t have been a certain way, but because of the nature of explanation.

The Power of a Name

Fairy tales and other stories occasionally suggest the idea that a name gives some kind of power over the thing named, or at least that one’s problems concerning a thing may be solved by knowing its name, as in the story of Rumpelstiltskin. There is perhaps a similar suggestion in Revelation 2:7, “Whoever has ears, let them hear what the Spirit says to the churches. To the one who is victorious, I will give some of the hidden manna. I will also give that person a white stone with a new name written on it, known only to the one who receives it.” The secrecy of the new name may indicate (among other things) that others will have no power over that person.

There is more truth in this idea than one might assume without much thought. For example, anonymous authors do not want to be “doxxed” because knowing the name of the author really does give some power in relation to them which is not had without the knowledge of their name. Likewise, as a blogger, occasionally I want to cite something, but cannot remember the name of the author or article where the statement is made. Even if I remember the content fairly clearly, lacking the memory of the name makes finding the content far more difficult, while on the other name, knowing the name gives me the power of finding the content much more easily.

But let us look a bit more deeply into this. Hilary Lawson, whose position was somewhat discussed here, has a discussion along these lines in Part II of his book, Closure: A Story of Everything. Since he denies that language truly refers to the world at all, as I mentioned in the linked post on his position, it is important to him that language has other effects, and in particular has practical goals. He says in chapter 4:

In order to understand the mechanism of practical linguistic closure consider an example where a proficient speaker of English comes across a new word. Suppose that we are visiting a zoo with a friend. We stand outside a cage and our friend says: ‘An aasvogel.” …

It might appear at first from this example that nothing has been added by the realisation of linguistic closure. The sound ‘aasvogel’ still sounds the same, the image of the bird still looks the same. So what has changed? The sensory closures on either side may not have changed, but a new closure has been realised. A new closure which is in addition to the prior available closures and which enables intervention which was not possible previously. For example, we now have a means of picking out this particular bird in the zoo because the meaning that has been realised will have identified a something in virtue of which this bird is an aasvogel and which thus enables us to distinguish it from others. As a result there will be many consequences for how we might be able to intervene.

The important point here is simply that naming something, even before taking any additional steps, immediately gives one the ability to do various practical things that one could not previously do. In a passage by Helen Keller, previously quoted here, she says:

Since I had no power of thought, I did not compare one mental state with another. So I was not conscious of any change or process going on in my brain when my teacher began to instruct me. I merely felt keen delight in obtaining more easily what I wanted by means of the finger motions she taught me.

We may have similar experiences as adults learning a foreign language while living abroad. At first one has very little ability to interact with the foreign world, but suddenly everything is possible.

Or consider the situation of a hunter gatherer who may not know how to count. It may be obvious to them that a bigger pile of fruit is better than a smaller one, but if two piles look similar, they may have no way to know which is better. But once they decide to give “one fruit and another” a name like “two,” and “two and one” a name like “three,” and so on, suddenly they obtain a great advantage that they previously did not possess. It is now possible to count piles and to discover that one pile has sixty-four while another has sixty-three. And it turns out that by treating the “sixty-four” as bigger than the other pile, although it does not look bigger, they end up better off.

In this sense one could look at the scientific enterprise of looking for mathematical laws of nature as one long process of looking for better names. We can see that some things are faster and some things are slower, but the vague names “fast” and “slow” cannot accomplish much. Once we can name different speeds more precisely, we can put them all in order and accomplish much more, just as the hunter gatherer can accomplish more after learning to count. And this extends to the full power of technology: the men who landed on the moon, did so ultimately due to the power of names.

If you take Lawson’s view, that language does not refer to the world at all, all of this is basically casting magic spells. In fact, he spells this out himself, in so many words, in chapter 3:

All material is in this sense magical. It enables intervention that cannot be understood. Ancient magicians were those who had access to closures that others did not know, in the same way that the Pharaohs had access to closures not available to their subjects. This gave them a supernatural character. It is now that thought that their magic has been explained, as the knowledge of herbs, metals or the weather. No such thing has taken place. More powerful closures have been realised, more powerful magic that can subsume the feeble closures of those magicians. We have simply lost sight of its magical character. Anthropology has many accounts of tribes who on being observed by a Western scientist believe that the observer has access to some very powerful magic. Magic that produces sound and images from boxes, and makes travel swift. We are inclined to smile patronisingly believing that we merely have knowledge — the technology behind radio and television, and motor vehicles — and not magic. The closures behind the technology do indeed provide us with knowledge and understanding and enable us to handle activity, but they do not explain how the closures enable intervention. How the closures are successful remains incomprehensible and in this sense is our magic.

I don’t think we should dismiss this point of view entirely, but I do think it is more mistaken than otherwise, basically because of the original mistake of thinking that language cannot refer to the world. But the point that names are extremely powerful is correct and important, to the point where even the analogy of technology as “magic that works” does make a certain amount of sense.

Anticipations of Darwin

I noted here that long before Darwin, there was fairly decent evidence for some sort of theory of evolution, even evidence available from the general human experience of plant and animal life, without deep scientific study.

As said in the earlier post, Aristotle notes that Empedocles hypothesized something along the lines of natural selection:

Wherever then all the parts came about just what they would have been if they had come to be for an end, such things survived, being organized spontaneously in a fitting way; whereas those which grew otherwise perished and continue to perish, as Empedocles says his ‘man-faced ox-progeny’ did.

Since Aristotle is arguing against Empedocles, we should be cautious in assuming that the characterization of his position is entirely accurate. But as presented by Aristotle, the position is an argument against the existence of final causes: since things can be “organized spontaneously” in the way “they would have been if they had come to be for an end,” there is no reason to think they in fact came to be for an end.

This particular conclusion, namely that in such a process nothing comes to be for an end, is a mistake, based on the assumption that different kinds of causes are mutually exclusive, rather than recognizing that different kinds of causes are different ways of explaining one and the same thing. But the general idea regarding what happened historically is correct: good conditions are more capable of persisting, bad conditions less so, and thus over time good conditions tend to predominate.

Other interesting anticipations may be found in Ibn Khaldun‘s book, The Muqaddimah, published in 1377. For example we find this passage:

It should be known that we — may God guide you and us — notice that this world with all the created things in it has a certain order and solid construction. It shows nexuses between causes and things caused, combinations of some parts of creation with others, and transformations of some existent things into others, in a pattern that is both remarkable and endless. Beginning with the world of the body and sensual perception, and therein first with the world of the visible elements, (one notices) how these elements are arranged gradually and continually in an ascending order, from earth to water, (from water) to air, and (from air) to fire. Each one of the elements is prepared to be transformed into the next higher or lower one, and sometimes is transformed. The higher one is always finer than the one preceding it. Eventually, the world of the spheres is reached. They are finer than anything else. They are in layers which are inter­connected, in a shape which the senses are able to perceive only through the existence of motions. These motions provide some people with knowledge of the measurements and positions of the spheres, and also with knowledge of the existence of the essences beyond, the influence of which is noticeable in the spheres through the fact (that they have motion).

One should then look at the world of creation. It started out from the minerals and progressed, in an ingenious, gradual manner, to plants and animals. The last stage of minerals is connected with the first stage of plants, such as herbs and seedless plants. The last stage of plants, such as palms and vines, is connected with the first stage of animals, such as snails and shellfish which have only the power of touch. The word “connection” with regard to these created things means that the last stage of each group is fully prepared to become the first stage of the next group.

The animal world then widens, its species become numerous, and, in a gradual process of creation, it finally leads to man, who is able to think and to reflect. The higher stage of man is reached from the world of the monkeys, in which both sagacity and perception are found, but which has not reached the stage of actual reflection and thinking. At this point we come to the first stage of man after (the world of monkeys). This is as far as our (physical) observation extends.

It is possible that he makes his position clearer elsewhere (I have not read the entire work.) The passage here does not explicitly assert that humans arose from lower animals, but does suggest it, correctly associating human beings with monkeys in particular, even if some of his other connections are somewhat strange. In other words, both here and elsewhere, he speaks of one stage of things being “prepared to become” another stage, and says that this transition sometimes happens: “Each one of the elements is prepared to be transformed into the next higher or lower one, and sometimes is transformed.”

While Ibn Khaldun is at least suggesting that we notice a biological order that corresponds to some degree to an actual historical order, we do not see in this text any indication of what the mechanism is supposed to be. In contrast, Empedocles gives us a mechanism but no clarity regarding historical order. Admittedly, this may be an artifact of the fact that I have not read more of Ibn Khaldun and the fact that we have only fragments from Empedocles.

One of the strongest anticipations of all, although put in very general terms, can be found in David Hume’s Dialogues Concerning Natural Religion, in the following passage:

Besides, why may not motion have been propagated by impulse through all eternity, and the same stock of it, or nearly the same, be still upheld in the universe? As much is lost by the composition of motion, as much is gained by its resolution. And whatever the causes are, the fact is certain, that matter is, and always has been, in continual agitation, as far as human experience or tradition reaches. There is not probably, at present, in the whole universe, one particle of matter at absolute rest.

And this very consideration too, continued PHILO, which we have stumbled on in the course of the argument, suggests a new hypothesis of cosmogony, that is not absolutely absurd and improbable. Is there a system, an order, an economy of things, by which matter can preserve that perpetual agitation which seems essential to it, and yet maintain a constancy in the forms which it produces? There certainly is such an economy; for this is actually the case with the present world. The continual motion of matter, therefore, in less than infinite transpositions, must produce this economy or order; and by its very nature, that order, when once established, supports itself, for many ages, if not to eternity. But wherever matter is so poised, arranged, and adjusted, as to continue in perpetual motion, and yet preserve a constancy in the forms, its situation must, of necessity, have all the same appearance of art and contrivance which we observe at present. All the parts of each form must have a relation to each other, and to the whole; and the whole itself must have a relation to the other parts of the universe; to the element in which the form subsists; to the materials with which it repairs its waste and decay; and to every other form which is hostile or friendly. A defect in any of these particulars destroys the form; and the matter of which it is composed is again set loose, and is thrown into irregular motions and fermentations, till it unite itself to some other regular form. If no such form be prepared to receive it, and if there be a great quantity of this corrupted matter in the universe, the universe itself is entirely disordered; whether it be the feeble embryo of a world in its first beginnings that is thus destroyed, or the rotten carcass of one languishing in old age and infirmity. In either case, a chaos ensues; till finite, though innumerable revolutions produce at last some forms, whose parts and organs are so adjusted as to support the forms amidst a continued succession of matter.

Suppose (for we shall endeavour to vary the expression), that matter were thrown into any position, by a blind, unguided force; it is evident that this first position must, in all probability, be the most confused and most disorderly imaginable, without any resemblance to those works of human contrivance, which, along with a symmetry of parts, discover an adjustment of means to ends, and a tendency to self-preservation. If the actuating force cease after this operation, matter must remain for ever in disorder, and continue an immense chaos, without any proportion or activity. But suppose that the actuating force, whatever it be, still continues in matter, this first position will immediately give place to a second, which will likewise in all probability be as disorderly as the first, and so on through many successions of changes and revolutions. No particular order or position ever continues a moment unaltered. The original force, still remaining in activity, gives a perpetual restlessness to matter. Every possible situation is produced, and instantly destroyed. If a glimpse or dawn of order appears for a moment, it is instantly hurried away, and confounded, by that never-ceasing force which actuates every part of matter.

Thus the universe goes on for many ages in a continued succession of chaos and disorder. But is it not possible that it may settle at last, so as not to lose its motion and active force (for that we have supposed inherent in it), yet so as to preserve an uniformity of appearance, amidst the continual motion and fluctuation of its parts? This we find to be the case with the universe at present. Every individual is perpetually changing, and every part of every individual; and yet the whole remains, in appearance, the same. May we not hope for such a position, or rather be assured of it, from the eternal revolutions of unguided matter; and may not this account for all the appearing wisdom and contrivance which is in the universe? Let us contemplate the subject a little, and we shall find, that this adjustment, if attained by matter of a seeming stability in the forms, with a real and perpetual revolution or motion of parts, affords a plausible, if not a true solution of the difficulty.

It is in vain, therefore, to insist upon the uses of the parts in animals or vegetables, and their curious adjustment to each other. I would fain know, how an animal could subsist, unless its parts were so adjusted? Do we not find, that it immediately perishes whenever this adjustment ceases, and that its matter corrupting tries some new form? It happens indeed, that the parts of the world are so well adjusted, that some regular form immediately lays claim to this corrupted matter: and if it were not so, could the world subsist? Must it not dissolve as well as the animal, and pass through new positions and situations, till in great, but finite succession, it falls at last into the present or some such order?

Although extremely general, Hume is suggesting both a history and a mechanism. Hume posits conservation of motion or other similar laws of nature, presumably mathematical, and describes what will happen when you apply such laws to a world. Most situations are unstable, and precisely because they are unstable, they will not last, and other situations will come to be. But some situations are stable, and when such situations occur, they will last.

The need for conservation of motion or similar natural laws is not accidental here. This is why I included the first paragraph above, rather than beginning the quotation where Hume begins to describe his “new hypothesis of cosmogony.” Without motion, the situation could not change, so a new situation could not come to be, and the very ideas of stable and unstable situations would not make sense. Likewise, if motion existed but did not follow any law, all situations should be unstable, so no amount of change could lead to a stable situation. Thus since things always fall downwards instead of in random directions, things stabilize near a center, while merely random motion could not be expected to have this effect. Thus a critic might argue that Hume seems to be positing randomness as the origin of things, but is cheating, so to speak, by positing original stabilities like natural laws, which are not random at all. Whatever might be said of this, it is an important point, and I will be returning to it later.

Since his description is more general than a description of living things in particular, Hume does not mention anything like the theory of the common descent of living things. But there is no huge gulf here: this would simply be a particular application. In fact, some people have suggested that Hume may have had textual influence on Darwin.

While there are other anticipations (there is one in Immanuel Kant that I am not currently inclined to seek out), I will skip to Philip Gosse, who published two years before Darwin. As described in the linked post, while Gosse denies the historicity of evolution in a temporal sense, he posits that the geological evidence was deliberately constructed (by God) to be evidence of common descent.

What was Darwin’s own role, then, if all the elements of his theory were known to various people years, centuries, or even millennia in advance? If we look at this in terms of Thomas Kuhn’s account of scientific progress, it is not so much that Darwin invented new ideas, as that he brought the evidence and arguments together in such a way as to produce — extremely quickly after the publication of his work — a newly formed consensus on those ideas.

Infinity

I discussed this topic previously, but without coming to a definite conclusion. Here I will give what I think is the correct explanation.

In his book Infinity, Causation, and Paradox, Alexander Pruss argues for what he calls “causal finitism,” or the principle that nothing can be affected by infinitely many causes:

In this volume, I will present a number of paradoxes of infinity, some old like Thomson’s Lamp and some new, and offer a unified metaphysical response to all of them by means of the hypothesis of causal finitism, which roughly says that nothing can be affected by infinitely many causes. In particular, Thomson’s Lamp story is ruled out since the final state of the lamp would be affected by infinitely many switch togglings. And in addition to arguing for the hypothesis as the best unified resolution to the paradoxes I shall offer some direct arguments against infinite regresses.

Thomson’s Lamp, if the reader is not familiar with it, is the question of what happens to a lamp if you switch it on and off an infinite number of times in a finite interval, doubling your velocity after each switch. At the end of the interval, is it on or off?

I think Pruss’s account is roughly speaking correct. I say “roughly speaking” because I would be hesitant to claim that nothing can be “affected” by infinitely many causes. Rather I would say that nothing is one effect simultaneously of infinitely many causes, and this is true for the same reason that there cannot be an infinite causal regress. That is, an infinite causal regress removes the notion of cause by removing the possibility of explanation, which is an intrinsic part of the idea of a cause. Similarly, it is impossible to explain anything using an infinite number of causes, because that infinity as such cannot be comprehended, and thus cannot be used to understand the thing which is the supposed effect. And since the infinity cannot explain the thing, neither can it be the cause of the thing.

What does this imply about the sorts of questions that were raised in my previous discussion, as for example about an infinite past or an infinite future, or a spatially infinite universe?

I presented an argument there, without necessarily claiming it to be correct, that such things are impossible precisely because they seem to imply an infinite causal regress. If there an infinite number of stars in the universe, for example, there seems to be an infinite regress of material causes: the universe seems to be composed of this local portion plus the rest, with the rest composed in a similar way, ad infinitum.

Unfortunately, there is an error in this argument against a spatially infinite world, and in similar arguments against a temporally infinite world, whether past or future. This can be seen in my response to Bertrand Russell when I discuss the material causes of water. Even if it is possible to break every portion of water down into smaller portions, it does not follow that this is an infinite sequence of material causes, or that it helps to explain water. In a similar way, even if the universe can be broken down into an infinite number of pieces in the above way, it does not follow that the universe has an infinite number of material causes: rather, this breakdown fails to explain, and fails to give causes at all.

St. Thomas gives a different argument against an infinite multitude, roughly speaking that it would lack a formal cause:

This, however, is impossible; since every kind of multitude must belong to a species of multitude. Now the species of multitude are to be reckoned by the species of numbers. But no species of number is infinite; for every number is multitude measured by one. Hence it is impossible for there to be an actually infinite multitude, either absolute or accidental.

By this argument, it would be impossible for there to be “an infinite number of stars” because the collection would lack “a species of multitude.” Unfortunately there is a problem with this argument as well, namely that it presupposes that the number is inherently fixed before it is considered by human beings. In reality, counting depends on someone who counts and a method they use for counting; to talk about the “number of stars” is a choice to break down the world in that particular way. There are other ways to think of it, as for example when we use the word “universe”, we count everything at once as a unit.

According to my account here, are some sorts of infinity actually impossible? Yes, namely those which demand an infinite sequence of explanation, or which demand an infinite number of things in order to explain something. Thus for example consider this story from Pruss about shuffling an infinite deck of cards:

Suppose I have an infinitely deep deck of cards, numbered with the positive integers. Can I shuffle it?

Given an infinite past, here is a procedure: n days ago, I perfectly fairly shuffle the top n cards in the deck.

This procedure is impossible because it makes the current state of the deck the direct effect of what I did n days ago, for all n. And the effect is a paradox: it is mathematically impossible for the integers to be randomly shuffled, because any series of integers will be biased towards lower numbers. Note that the existence of an infinite past is not the problem so much as assuming that one could have carried out such a procedure during an infinite past; in reality, if there was an infinite past, its contents are equally “infinite,” that is, they do not have such a definable, definite, “finite” relationship with the present.

Structure of Explanation

When we explain a thing, we give a cause; we assign the thing an origin that explains it.

We can go into a little more detail here. When we ask “why” something is the case, there is always an implication of possible alternatives. At the very least, the question implies, “Why is this the case rather than not being the case?” Thus “being the case” and “not being the case” are two possible alternatives.

The alternatives can be seen as possibilities in the sense explained in an earlier post. There may or may not be any actual matter involved, but again, the idea is that reality (or more specifically some part of reality) seems like something that would be open to being formed in one way or another, and we are asking why it is formed in one particular way rather than the other way. “Why is it raining?” In principle, the sky is open to being clear, or being filled with clouds and a thunderstorm, and to many other possibilities.

A successful explanation will be a complete explanation when it says “once you take the origin into account, the apparent alternatives were only apparent, and not really possible.” It will be a partial explanation when it says, “once you take the origin into account, the other alternatives were less sensible (i.e. made less sense as possibilities) than the actual thing.”

Let’s consider some examples in the form of “why” questions and answers.

Q1. Why do rocks fall? (e.g. instead of the alternatives of hovering in the air, going upwards, or anything else.)

A1. Gravity pulls things downwards, and rocks are heavier than air.

The answer gives an efficient cause, and once this cause is taken into account, it can be seen that hovering in the air or going upwards were not possibilities relative to that cause.

Obviously there is not meant to be a deep explanation here; the point here is to discuss the structure of explanation. The given answer is in fact basically Newton’s answer (although he provided more mathematical detail), while with general relativity Einstein provided a better explanation.

The explanation is incomplete in several ways. It is not a first cause; someone can now ask, “Why does gravity pull things downwards, instead of upwards or to the side?” Similarly, while it is in fact the cause of falling rocks, someone can still ask, “Why didn’t anything else prevent gravity from making the rocks fall?” This is a different question, and would require a different answer, but it seems to reopen the possibility of the rocks hovering or moving upwards, from a more general point of view. David Hume was in part appealing to the possibility of such additional questions when he said that we can see no necessary connection between cause and effect.

Q2. Why is 7 prime? (i.e. instead of the alternative of not being prime.)

A2. 7/2 = 3.5, so 7 is not divisible by 2. 7/3 = 2.333…, so 7 is not divisible by 3. In a similar way, it is not divisible by 4, 5, or 6. Thus in general it is not divisible by any number except 1 and itself, which is what it means to be prime.

If we assumed that the questioner did not know what being prime means, we could have given a purely formal response simply by noting that it is not divisible by numbers between 1 and itself, and explaining that this is what it is to be prime. As it is, the response gives a sufficient material disposition. Relative to this explanation, “not being prime,” was never a real possibility for 7 in the first place. The explanation is complete in that it completely excludes the apparent alternative.

Q3. Why did Peter go to the store? (e.g. instead of going to the park or the museum, or instead of staying home.)

A3. He went to the store in order to buy groceries.

The answer gives a final cause. In view of this cause the alternatives were merely apparent. Going to the park or the museum, or even staying home, were not possible since there were no groceries there.

As in the case of the rock, the explanation is partial in several ways. Someone can still ask, “Why did he want groceries?” And again someone can ask why he didn’t go to some other store, or why something didn’t hinder him, and so on. Such questions seem to reopen various possibilities, and thus the explanation is not an ultimately complete one.

Suppose, however, that someone brings up the possibility that instead of going to the store, he could have gone to his neighbor and offered money for groceries in his neighbor’s refrigerator. This possibility is not excluded simply by the purpose of buying groceries. Nonetheless, the possibility seems less sensible than getting them from the store, for multiple reasons. Again, the implication is that our explanation is only partial: it does not completely exclude alternatives, but it makes them less sensible.

Let’s consider a weirder question: Why is there something rather than nothing?

Now the alternatives are explicit, namely there being something, and there being nothing.

It can be seen that in one sense, as I said in the linked post, the question cannot have an answer, since there cannot be a cause or origin for “there is something” which would itself not be something. Nonetheless, if we consider the idea of possible alternatives, it is possible to see that the question does not need an answer; one of the alternatives was only an apparent alternative all along.

In other words, the sky can be open to being clear or cloudy. But there cannot be something which is open both to “there is something” and “there is nothing”, since any possibility of that kind would be “something which is open…”, which would already be something rather than nothing. The “nothing” alternative was merely apparent. Nothing was ever open to there being nothing.

Let’s consider another weird question. Suppose we throw a ball, and in the middle of the path we ask, Why is the ball in the middle of the path instead of at the end of the path?

We could respond in terms of a sufficient material disposition: it is in the middle of the path because you are asking your question at the middle, instead of waiting until the end.

Suppose the questioner responds: Look, I asked my question at the middle of the path. But that was just chance. I could have asked at any moment, including at the end. So I want to know why it was in the middle without considering when I am asking the question.

If we look at the question in this way, it can be seen in one way that no cause or origin can be given. Asked in this way, being at the end cannot be excluded, since they could have asked their question at the end. But like the question about something rather than nothing, the question does not need an answer. In this case, this is not because the alternatives were merely apparent in the sense that one was possible and the other not. But they were merely apparent in the sense that they were not alternatives. The ball goes both goes through the middle, and reaches the end. With the stipulation that we not consider the time of the question, the two possibilities are not mutually exclusive.

Additional Considerations

The above considerations about the nature of “explanation” lead to various conclusions, but also to various new questions. For example, one commenter suggested that “explanation” is merely subjective. Now as I said there, all experience is subjective experience (what would “objective experience” even mean, except that someone truly had a subjective experience?), including the experience of having an explanation. Nonetheless, the thing experienced is not subjective: the origins that we call explanations objectively exclude the apparent possibilities, or objectively make them less intelligible. The explanation of explanation here, however, provides an answer to what was perhaps the implicit question. Namely, why are we so interested in explanations in the first place, so that the experience of understanding something becomes a particularly special type of experience? Why, as Aristotle puts it, do “all men desire to know,” and why is that desire particularly satisfied by explanations?

In one sense it is sufficient simply to say that understanding is good in itself. Nonetheless, there is something particular about the structure of a human being that makes knowledge good for us, and which makes explanation a particularly desirable form of knowledge. In my employer and employee model of human psychology, I said that “the whole company is functioning well overall when the CEO’s goal of accurate prediction is regularly being achieved.” This very obviously requires knowledge, and explanation is especially beneficial because it excludes alternatives, which reduces uncertainty and therefore tends to make prediction more accurate.

However, my account also raises new questions. If explanation eliminates alternatives, what would happen if everything was explained? We could respond that “explaining everything” is not possible in the first place, but this is probably an inadequate response, because (from the linked argument) we only know that we cannot explain everything all at once, the way the person in the room cannot draw everything at once; we do not know that there is any particular thing that cannot be explained, just as there is no particular aspect of the room that cannot be drawn. So there can still be a question about what would happen if every particular thing in fact has an explanation, even if we cannot know all the explanations at once. In particular, since explanation eliminates alternatives, does the existence of explanations imply that there are not really any alternatives? This would suggest something like Leibniz’s argument that the actual world is the best possible world. It is easy to see that such an idea implies that there was only one “possibility” in the first place: Leibniz’s “best possible world” would be rather “the only possible world,” since the apparent alternatives, given that they would have been worse, were not real alternatives in the first place.

On the other hand, if we suppose that this is not the case, and there are ultimately many possibilities, does this imply the existence of “brute facts,” things that could have been otherwise, but which simply have no explanation? Or at least things that have no complete explanation?

Let the reader understand. I have already implicitly answered these questions. However, I will not link here to the implicit answers because if one finds it unclear when and where this was done, one would probably also find those answers unclear and inconclusive. Of course it is also possible that the reader does see when this was done, but still believes those responses inadequate. In any case, it is possible to provide the answers in a form which is much clearer and more conclusive, but this will likely not be a short or simple project.

Rao’s Divergentism

The main point of this post is to encourage the reader who has not yet done so, to read Venkatesh Rao’s essay Can You Hear Me Now. I will not say too much about it. The purpose is potentially for future reference, and simply to point out a connection with some current topics here.

Rao begins:

The fundamental question of life, the universe and everything is the one popularized by the Verizon guy in the ad: Can you hear me now?

This conclusion grew out of a conversation I had about a year ago, with some friends, in which I proposed a modest-little philosophy I dubbed divergentism. Here is a picture.

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Divergentism is the idea that as individuals grow out into the universe, they diverge from each other in thought-space. This, I argued, is true even if in absolute terms, the sum of shared beliefs is steadily increasing. Because the sum of beliefs that are not shared increases even faster on average. Unfortunately, you are unique, just like everybody else.

If you are a divergentist, you believe that as you age, the average answer to the fundamental Verizon question slowly drifts, as you age, from yes, to no, to silenceIf you’re unlucky, you’re a hedgehog and get unhappier and unhappier about this as you age. If you are lucky, you’re a fox and you increasingly make your peace with this condition. If you’re really lucky, you die too early to notice the slowly descending silence, before it even becomes necessary to Google the phrase existential horror.

To me, this seemed like a completely obvious idea. Much to my delight, most people I ran it by immediately hated it.

The entire essay is worth reading.

I would question whether this is really the “fundamental question of life, the universe, and everything,” but Rao has a point. People do tend to think of their life as meaningful on account of social connections, and if those social connections grow increasingly weaker, they will tend to worry that their life is becoming less meaningful.

The point about the intellectual life of an individual is largely true. This is connected to what I said about the philosophical progress of an individual some days ago. There is also a connection with Kuhn’s idea of how the progress of the sciences causes a gulf to arise between them in such a way that it becomes more and more difficult for scientists in different fields to communicate with one another. If we look at the overall intellectual life of an individual as a sort of individual advancing science, the “sciences” of each individual will generally speaking tend to diverge from one another, allowing less and less communication. This is not about people making mistakes, although obviously making mistakes will contribute to this process. As Rao says, it may be that “the sum of shared beliefs is steadily increasing,” but this will not prevent their intellectual lives overall from diverging, just as the divergence of the sciences does not result from falsity, but from increasingly detailed focus on different truths.

Pseudoscience

James Chastek reflects on science, pseudoscience, and religion:

The demarcation problem is a name for our failure to identify criteria that can distinguish science from pseudo-science, in spite of there being two such things. In the absence of rational criteria, we get clarity on the difference from various institutional-cultural institutions, like the consensus produced by university gatekeepers though peer review (which generates, by definition, peer pressure), grants, prestige, and other stick-and-carrot means.  Like most institutions we expect it to do reasonably well (or at least better than an every-man-for-himself chaos) though it will come at a cost of group-think, elitism, the occasional witch hunt etc..

The demarcation problem generalizes to our failure to identify any meta-criterion for what counts as legitimate discourse or belief. Kant’s famous attempt to articulate meta-criteria for thought, which concluded to limiting it to an intuition of Euclidean space distinct from linear time turned out to be no limitation at all, and Davidson pointed out that the very idea of a conceptual scheme – a finite scope or limit to human thought that could be determined in advance – requires us to posit a language that is in-principle untranslatable, which is to speak of something that has to meaning. Heraclitus was right – you can’t come to the borders of thought, even if you travel down every road. We simply can’t articulate a domain of acceptable belief in general from which we can identify the auslanders.

This is true of religion as well. By our own resources we can know there are pseudo ones and truer ones, but the degree of clarity we want in this area is going to have to be borrowed from an intellect other than our own. The various religious institutions are attempts to make up for this deficiency in reason and provide us with clearer and more precise articulations of true religion in exactly the same way that we get it in the sciences. That a westerner tends to accept Christianity arises from the same sort of process that makes him tend to accept scientific consensus. He walks within the ambit of various institutions that are designed to help him toward truth, and they almost certainly succeed at this more than he would succeed if left solely to his own lights. Anyone who thinks he can easily identify true science while no one can identify true religion is right in a sense, but he doesn’t recognize how heavily his belief is resting on institutional power.

Like Sean Collins as quoted in this earlier post, Chastek seems to be unreasonably emphasizing the similarity between science and religion where in fact there is a greater dissimilarity. As discussed in the last post, a field is only considered scientific once it has completely dominated the area of thought among persistent students of that field. It is not exactly that “no one disagrees,” so much as that it becomes too complicated for anyone except those students. But those students, to an extremely high degree, have a unified view of the field. An actual equivalent in the area of religion would be if virtually all theologians accepted the same religion. Even here, it might be a bit strange to find whole countries that accepted another religion, the way it would be strange to find a whole country believing in a flat earth. But perhaps not so strange; occasionally you do get a poll indicating a fairly large percentage of some nation believing some claim entirely opposed to the paradigm of some field of science. Nonetheless, if virtually all theologians accepted the same religion, the comparison between science and religion would be pretty apt. Since that is not the case in the slightest, religion looks more like a field where knowledge remains “undeveloped,” in the way I suggested in reference to some areas of philosophy.

Chastek is right to note that one cannot set down some absolute list of rules setting apart reasonable thought from unreasonable thought, or science from pseudoscience. Nonetheless, reflecting on the comments to the previous post, it occurs to me that we have a pretty good idea of what pseudoscience is. The term itself, of course, means something like “fake science,” so the idea would be something purporting to be scientific which is not scientific.

A recurring element in Kuhn’s book, as in the title itself, is the idea of change in scientific paradigms. Kuhn remarks:

Probably the single most prevalent claim advanced by the proponents of a new paradigm is that they can solve the problems that have led the old one to a crisis. When it can legitimately be made, this claim is often the most effective one possible. In the area for which it is advanced the paradigm is known to be in trouble. That trouble has repeatedly been explored, and attempts to remove it have again and again proved vain. “Crucial experiments”—those able to discriminate particularly sharply between the two paradigms—have been recognized and attested before the new paradigm was even invented. Copernicus thus claimed that he had solved the long-vexing problem of the length of the calendar year, Newton that he had reconciled terrestrial and celestial mechanics, Lavoisier that he had solved the problems of gas-identity and of weight relations, and Einstein that he had made electrodynamics compatible with a revised science of motion.

Some pages later, considering why paradigm change is considered progress, he continues:

Because the unit of scientific achievement is the solved problem and because the group knows well which problems have already been solved, few scientists will easily be persuaded to adopt a viewpoint that again opens to question many problems that had previously been solved. Nature itself must first undermine professional security by making prior achievements seem problematic. Furthermore, even when that has occurred and a new candidate for paradigm has been evoked, scientists will be reluctant to embrace it unless convinced that two all-important conditions are being met. First, the new candidate must seem to resolve some outstanding and generally recognized problem that can be met in no other way. Second, the new paradigm must promise to preserve a relatively large part of the concrete problem-solving ability that has accrued to science through its predecessors. Novelty for its own sake is not a desideratum in the sciences as it is in so many other creative fields. As a result, though new paradigms seldom or never possess all the capabilities of their predecessors, they usually preserve a great deal of the most concrete parts of past achievement and they always permit additional concrete problem-solutions besides.

It is not automatically unscientific to suggest that the current paradigm is somehow mistaken and needs to be replaced: in fact the whole idea of paradigm change depends on scientists doing this on a fairly frequent basis. But Kuhn suggests that this mainly happens when there are well known problems with the current paradigm. Additionally, when a new one is proposed, it should be in order to solve new problems. This suggests one particular form of pseudoscientific behavior: to propose new paradigms when there are no special problems with the current ones. Or at any rate, to propose that they be taken just as seriously as the current ones; there is not necessarily anything unreasonable about saying, “Although we currently view things according to paradigm A, someday we might need to adopt something somewhat like paradigm B,” even if one is not yet aware of any great problems with paradigm A.

A particularly anti-scientific form of this would be to propose that the current paradigm be abandoned in favor of an earlier one. It is easy to see why scientists would be especially opposed to such a proposal: since the earlier one was abandoned in order to solve new problems and to resolve more and more serious discrepancies between the paradigm and experience, going back to an earlier paradigm would suddenly create all sorts of new problems.

On the other hand, why do we have the “science” part of “pseudoscience”? This is related to Chastek’s point about institutions as a force creating conformity of opinion. The pseudoscientist is a sort of predator in relation to these institutions. While the goal of science is truth, at least to a first approximation, the pseudoscientist has something different in mind: this is clear from the fact that he does not care whether his theory solves any new problems, and it is even more clear in the case of a retrogressive proposal. But the pseudoscientist will attempt to use the institutions of science to advance his cause. This will tend in reality to be highly unsuccessful in relation to ordinary scientists, for the same reason that Kuhn remarks that scientists who refuse to adopt a new paradigm after its general acceptance “are simply read out of the profession, which thereafter ignores their work.” In a similar way, if someone proposes an unnecessary paradigm change, scientists will simply ignore the proposal. But if the pseudoscientist manages to get beyond certain barriers, e.g. peer review, it may be more difficult for ordinary people to distinguish between ordinary science and pseudoscience, since they are not in fact using their own understanding of the matter, but simply possess a general trust that the scientists know the general truth about the field.

One of the most common usages of the term “pseudoscience” is in relation to young earth creationism, and rightly so. This is in fact a case of attempting to return to an earlier paradigm which was abandoned precisely because of the kind of tensions that are typical of paradigm change. Thus one of their favorite methods is to attempt to get things published in peer reviewed journals. Very occasionally this is successful, but obviously it has very little effect on the field itself: just as with late adopters or people who never change their mind, the rest of the field, as Kuhn says, “ignores their work.” But to the degree that they manage to lead ordinary people to adopt their views, this is to act in a sort of predator relationship with the institutions of science: to take advantage of these institutions for the sake of falsehood rather than truth.

That’s kind of blunt, someone will say. If paradigm change is frequently necessary, surely it could happen at least once that a former paradigm was better than a later one, such that it would be necessary to return to it, and for the sake of truth. People are not infallible, so surely this is possible.

Indeed, it is possible. But very unlikely, for all the reasons that Kuhn mentions. And in order for such a proposal to be truth oriented, it would have to be motivated by the perception of problems with the current paradigm, even if they were problems that had not been foreseen when the original paradigm was abandoned. In practice such proposals are normally not motivated by problems at all,  and thus there is very little orientation towards truth in them.

Naturally, all of this has some bearing on the comments to the last post, but I will leave most of that to the reader’s consideration. I will remark, however, that things like “he is simply ignorant of basic physics because he is a computer scientist, not a physicist,” or “Your last question tells me that you do not know much physics,” or that it is important not to “ignore the verdict of the reviewers and editors of a respected physics journal,” might be important clues for the ordinary fellow.

Technical Discussion and Philosophical Progress

In The Structure of Scientific Revolutions (p. 19-21), Thomas Kuhn remarks on the tendency of sciences to acquire a technical vocabulary and manner of discussion:

We shall be examining the nature of this highly directed or paradigm-based research in the next section, but must first note briefly how the emergence of a paradigm affects the structure of the group that practices the field. When, in the development of a natural science, an individual or group first produces a synthesis able to attract most of the next generation’s practitioners, the older schools gradually disappear. In part their disappearance is caused by their members’ conversion to the new paradigm. But there are always some men who cling to one or another of the older views, and they are simply read out of the profession, which thereafter ignores their work. The new paradigm implies a new and more rigid definition of the field. Those unwilling or unable to accommodate their work to it must proceed in isolation or attach themselves to some other group. Historically, they have often simply stayed in the departments of philosophy from which so many of the special sciences have been spawned. As these indications hint, it is sometimes just its reception of a paradigm that transforms a group previously interested merely in the study of nature into a profession or, at least, a discipline. In the sciences (though not in fields like medicine, technology, and law, of which the principal raison d’être is an external social need), the formation of specialized journals, the foundation of specialists’ societies, and the claim for a special place in the curriculum have usually been associated with a group’s first reception of a single paradigm. At least this was the case between the time, a century and a half ago, when the institutional pattern of scientific specialization first developed and the very recent time when the paraphernalia of specialization acquired a prestige of their own.

The more rigid definition of the scientific group has other consequences. When the individual scientist can take a paradigm for granted, he need no longer, in his major works, attempt to build his field anew, starting from first principles and justifying the use of each concept introduced. That can be left to the writer of textbooks. Given a textbook, however, the creative scientist can begin his research where it leaves off and thus concentrate exclusively upon the subtlest and most esoteric aspects of the natural phenomena that concern his group. And as he does this, his research communiqués will begin to change in ways whose evolution has been too little studied but whose modern end products are obvious to all and oppressive to many. No longer will his researches usually be embodied in books addressed, like Franklin’s Experiments . . . on Electricity or Darwin’s Origin of Species, to anyone who might be interested in the subject matter of the field. Instead they will usually appear as brief articles addressed only to professional colleagues, the men whose knowledge of a shared paradigm can be assumed and who prove to be the only ones able to read the papers addressed to them.

Today in the sciences, books are usually either texts or retrospective reflections upon one aspect or another of the scientific life. The scientist who writes one is more likely to find his professional reputation impaired than enhanced. Only in the earlier, pre-paradigm, stages of the development of the various sciences did the book ordinarily possess the same relation to professional achievement that it still retains in other creative fields. And only in those fields that still retain the book, with or without the article, as a vehicle for research communication are the lines of professionalization still so loosely drawn that the layman may hope to follow progress by reading the practitioners’ original reports. Both in mathematics and astronomy, research reports had ceased already in antiquity to be intelligible to a generally educated audience. In dynamics, research became similarly esoteric in the later Middle Ages, and it recaptured general intelligibility only briefly during the early seventeenth century when a new paradigm replaced the one that had guided medieval research. Electrical research began to require translation for the layman before the end of the eighteenth century, and most other fields of physical science ceased to be generally accessible in the nineteenth. During the same two centuries similar transitions can be isolated in the various parts of the biological sciences. In parts of the social sciences they may well be occurring today. Although it has become customary, and is surely proper, to deplore the widening gulf that separates the professional scientist from his colleagues in other fields, too little attention is paid to the essential relationship between that gulf and the mechanisms intrinsic to scientific advance.

As Kuhn says, this tendency has very well known results. Consider the papers constantly being published at arxiv.org, for example. If you are not familiar with the science in question, you will likely not be able to understand even the title, let alone the summary or the content. Many or most of the words will be meaningless to you, and even if they are not, their combinations will be.

It is also not difficult to see why this happens, and why it must happen. Everything we understand, we understand through form, which is a network of relationships. Thus if particular investigators wish to go into something in greater detail, these relationships will become more and more remote from the ordinary knowledge accessible to everyone. “Just say it in simple words” will become literally impossible, in the sense that explaining the “simple” statement will involve explaining a huge number of relationships that by default a person would have no knowledge of. That is the purpose, as Kuhn notes, of textbooks, namely to form connections between everyday knowledge and the more complex relationships studied in particular fields.

In Chapter XIII, Kuhn relates this sort of development with the word “science” and progress:

The preceding pages have carried my schematic description of scientific development as far as it can go in this essay. Nevertheless, they cannot quite provide a conclusion. If this description has at all caught the essential structure of a science’s continuing evolution, it will simultaneously have posed a special problem: Why should the enterprise sketched above move steadily ahead in ways that, say, art, political theory, or philosophy does not? Why is progress a perquisite reserved almost exclusively for the activities we call science? The most usual answers to that question have been denied in the body of this essay. We must conclude it by asking whether substitutes can be found.

Notice immediately that part of the question is entirely semantic. To a very great extent the term ‘science’ is reserved for fields that do progress in obvious ways. Nowhere does this show more clearly than in the recurrent debates about whether one or another of the contemporary social sciences is really a science. These debates have parallels in the pre-paradigm periods of fields that are today unhesitatingly labeled science. Their ostensible issue throughout is a definition of that vexing term. Men argue that psychology, for example, is a science because it possesses such and such characteristics. Others counter that those characteristics are either unnecessary or not sufficient to make a field a science. Often great energy is invested, great passion aroused, and the outsider is at a loss to know why. Can very much depend upon a definition of ‘science’? Can a definition tell a man whether he is a scientist or not? If so, why do not natural scientists or artists worry about the definition of the term? Inevitably one suspects that the issue is more fundamental. Probably questions like the following are really being asked: Why does my field fail to move ahead in the way that, say, physics does? What changes in technique or method or ideology would enable it to do so? These are not, however, questions that could respond to an agreement on definition. Furthermore, if precedent from the natural sciences serves, they will cease to be a source of concern not when a definition is found, but when the groups that now doubt their own status achieve consensus about their past and present accomplishments. It may, for example, be significant that economists argue less about whether their field is a science than do practitioners of some other fields of social science. Is that because economists know what science is? Or is it rather economics about which they agree?

The last point is telling. There is significantly more consensus among economists than among other sorts of social science, and consequently less worry about whether their field is scientific or not. The difference, then, is a difference of how much agreement is found. There is not necessarily any difference with respect to the kind of increasingly detailed thought that results in increasingly technical discussion. Kuhn remarks:

The theologian who articulates dogma or the philosopher who refines the Kantian imperatives contributes to progress, if only to that of the group that shares his premises. No creative school recognizes a category of work that is, on the one hand, a creative success, but is not, on the other, an addition to the collective achievement of the group. If we doubt, as many do, that nonscientific fields make progress, that cannot be because individual schools make none. Rather, it must be because there are always competing schools, each of which constantly questions the very foundations of the others. The man who argues that philosophy, for example, has made no progress emphasizes that there are still Aristotelians, not that Aristotelianism has failed to progress.

In this sense, if a particular school believes they possess the general truth about some matter (here theology or philosophy), they will quite naturally begin to discuss it in greater detail and in ways which are mainly intelligible to students of that school, just as happens in other technical fields. The field is only failing to progress in the sense that there are other large communities making contrasting claims, while we begin to use the term “science” and to speak of progress when one school completely dominates the field, and to a first approximation even people who know nothing about it assume that the particular school has things basically right.

What does this imply about progress in philosophy?

1. There is progress in the knowledge of topics that were once considered “philosophy,” but when we get to this point, we usually begin to use the name of a particular science, and with good reason, since technical specialization arises in the manner discussed above. Tyler Cowen discusses this sort of thing here.

2. Areas in which there doesn’t seem to be such progress, are probably most often areas where human knowledge remains at an early stage of development; it is precisely at such early stages that discussion does not have a technical character and when it can generally be understood by ordinary people without a specialized education. I pointed out that Aristotle was mistaken to assume that the sciences in general were fully developed. We would be equally mistaken to make such an assumption at the present times. As Kuhn notes, astronomy and mathematics achieved a “scientific” stage centuries before geology and biology did the same, and these long before economics and the like. The conclusion that one should draw is that metaphysics is hard, not that it is impossible or meaningless.

3. Even now, particular philosophical schools or individuals can make progress even without such consensus. This is evidently true if their overall position is correct or more correct than that of others, but it remains true even if their overall position is more wrong than that of other schools. Naturally, in the latter situation, they will not advance beyond the better position of other schools, but they will advance.

4. One who wishes to progress philosophically cannot avoid the tendency to technical specialization, even as an individual. This can be rather problematic for bloggers and people engaging in similar projects. John Nerst describes this problem:

The more I think about this issue the more unsolvable it seems to become. Loyal readers of a publication won’t be satisfied by having the same points reiterated again and again. News media get around this by focusing on, well, news. News are events, you can describe them and react to them for a while until they’re no longer news. Publications that aim to be more analytical and focus on discussing ideas, frameworks, slow processes and large-scale narratives instead of events have a more difficult task because their subject matter doesn’t change quickly enough for it to be possible to churn out new material every day without repeating yourself[2].

Unless you start building upwards. Instead of laying out stone after stone on the ground you put one on top of another, and then one on top of two others laying next to each other, and then one on top of all that, making a single three-level structure. In practice this means writing new material that builds on what came before, taking ideas further and further towards greater complexity, nuance and sophistication. This is what academia does when working correctly.

Mass media (including the more analytical outlets) do it very little and it’s obvious why: it’s too demanding[3]. If an article references six other things you need to have read to fully understand it you’re going to have a lot of difficulty attracting new readers.

Some of his conclusions:

I think that’s the real reason I don’t try to pitch more writing to various online publications. In my summary of 2018 I said it was because I thought my writing was to “too idiosyncratic, abstract and personal to fit in anywhere but my own blog”. Now I think the main reason is that I don’t so much want to take part in public debate or make myself a career. I want to explore ideas that lie at the edge of my own thinking. To do that I must assume that a reader knows broadly the same things I know and I’m just not that interested in writing about things where I can’t do that[9]. I want to follow my thoughts to for me new and unknown places — and import whatever packages I need to do it. This style isn’t compatible with the expectation that a piece will be able to stand on its own and deliver a single recognizable (and defensible) point[10].

The downside is of course obscurity. To achieve both relevance in the wider world and to build on other ideas enough to reach for the sky you need extraordinary success — so extraordinary that you’re essentially pulling the rest of the world along with you.

Obscurity is certainly one result. Another (relevant at least from the VP’s point of view) is disrespect. Scientists are generally respected despite the general incomprehensibility of their writing, on account of the absence of opposing schools. This lack leads people to assume that their arguments must be mostly right, even though they cannot understand them themselves. This can actually lead to an “Emperor has No Clothes” situation, where a scientist publishes something basically crazy, but others, even in his field, are reluctant to say so because they might appear to be the ones who are ignorant. As an example, consider Joy Christian’s “Disproof of Bell’s Theorem.” After reading this text, Scott Aaronson comments:

In response to my post criticizing his “disproof” of Bell’s Theorem, Joy Christian taunted me that “all I knew was words.”  By this, he meant that my criticisms were entirely based on circumstantial evidence, for example that (1) Joy clearly didn’t understand what the word “theorem” even meant, (2) every other sentence he uttered contained howling misconceptions, (3) his papers were written in an obscure, “crackpot” way, and (4) several people had written very clear papers pointing out mathematical errors in his work, to which Joy had responded only with bluster.  But I hadn’t actually studied Joy’s “work” at a technical level.  Well, yesterday I finally did, and I confess that I was astonished by what I found.  Before, I’d actually given Joy some tiny benefit of the doubt—possibly misled by the length and semi-respectful tone of the papers refuting his claims.  I had assumed that Joy’s errors, though ultimately trivial (how could they not be, when he’s claiming to contradict such a well-understood fact provable with a few lines of arithmetic?), would nevertheless be artfully concealed, and would require some expertise in geometric algebra to spot.  I’d also assumed that of course Joy would have some well-defined hidden-variable model that reproduced the quantum-mechanical predictions for the Bell/CHSH experiment (how could he not?), and that the “only” problem would be that, due to cleverly-hidden mistakes, his model would be subtly nonlocal.

What I actually found was a thousand times worse: closer to the stuff freshmen scrawl on an exam when they have no clue what they’re talking about but are hoping for a few pity points.  It’s so bad that I don’t understand how even Joy’s fellow crackpots haven’t laughed this off the stage.  Look, Joy has a hidden variable λ, which is either 1 or -1 uniformly at random.  He also has a measurement choice a of Alice, and a measurement choice b of Bob.  He then defines Alice and Bob’s measurement outcomes A and B via the following functions:

A(a,λ) = something complicated = (as Joy correctly observes) λ

B(b,λ) = something complicated = (as Joy correctly observes) -λ

I shit you not.  A(a,λ) = λ, and B(b,λ) = -λ.  Neither A nor B has any dependence on the choices of measurement a and b, and the complicated definitions that he gives for them turn out to be completely superfluous.  No matter what measurements are made, A and B are always perfectly anticorrelated with each other.

You might wonder: what could lead anyone—no matter how deluded—even to think such a thing could violate the Bell/CHSH inequalities?

“Give opposite answers in all cases” is in fact entirely irrelevant to Bell’s inequality. Thus the rest of Joy’s paper has no bearing whatsoever on the issue: it is essentially meaningless nonsense. Aaronson says he was possibly “misled by the length and semi-respectful tone of the papers refuting his claims.” But it is not difficult to see why people would be cautious in this way: the fear that they would turn out to be the ones missing something important.

The individual blogger in philosophy, however, is in a different position. If they wish to develop their thought it must become more technical, and there is no similar community backing that would cause others to assume that the writing basically makes sense. Thus, one’s writing is not only likely to become more and more obscure, but others will become more and more likely to assume that it is more or less meaningless word salad. This will happen even more to the degree that there is cultural opposition to one’s vocabulary, concepts, and topics.