I've noted many flaws and points of confusion in Sean Carroll's new book, The Big Picture: On the Origins of Life, Meaning, and the Universe Itself (Dutton, 2016), but one of the strongest sections is its explanation of Bayes' Theorem. The Theorem is a quantitive way to express confidence in certain beliefs. It requires assigning credences (or probabilities) to events or statements, and then tweaking them based on new information.

For example, suppose you're wondering whether a randomly flipped coin will turn up heads. Your prior credence (or initial probability) is 0.5, since it has a 50% chance of landing on heads. But then suppose you learn that the coin is rigged, and there's extra weight added to one side. That new information would naturally cause you to adjust your credence, either up or down depending on the information.

This all should be pretty familiar. Whether we realize it or not, we all use this process, sometimes called induction, to make decisions every day. We start with beliefs, take in new information, and (ideally) adjust those beliefs to better correspond with reality. Bayes' Theorem simply adds a more quantitative dimension to that calculation. Instead of using mere intuition to adjust our credences up or down in light of new information, Bayes uses hard statistics.

According to Carroll, we can learn three lessons from Bayes' Theorem:

1. Never assign perfect certainty to any belief (i.e., no belief can have a credence of 1.0)
2. Always be prepared to update our credences when new evidence comes along
3. Trust mathematics to show how new evidence alters our existing beliefs

Carroll especially shines when explaining how a piece of new information can either boost our confidence up, or bring it down—but it can't do both. For instance, many atheists claim the problem of evil should reduce the probability of whether God exists. But many theists suggest that the problem of evil is actually evidence for God, since an objective moral standard depends on a divine lawgiver. We may be tempted to accept both proposals: the problem of evil brings the probability of God down a little, and it also raises the probability back up. But as Carroll explains, the Theorem doesn't allow that. Each new piece of information can either raise or lower our prior credences. It can't do both.

(Another example is the huge size of the universe. Atheists often point to that in arguments against God, or at least against the idea that humans occupy a special place in the cosmos. Typically, theists respond that God designed a vast universe because (1) it was the only physical way to provide a space hospitable for human life, (2) God is not limited in any way so efficiency is not a concern, and (3) since almost all people marvel at the scale of the cosmos, and wonder is good, God created a large universe as a gift for us to experience and explore—the same reason we prefer a wondrous mountain over a plain pebble. But in light of Bayes' Theorem, the theist can only use those arguments to support their belief in God if they can show they are more likely true than not, that God would do those things if he existed. If the theist cannot or will not make that case, then the best they can hope for is mitigating how much the "large universe" argument bends the probability of God toward atheism.)

On paper, Bayes' Theorem is very helpful, and Carroll admirably shows why. But my one complaint with his presentation in the book is that he skirts around some of its main criticisms. For example, the Bayes calculation depends entirely on the accuracy of the credences. Assigning credences is easy for things like rolling idealized dice, flipping idealized coins, or dealing an idealized deck of cards. But what about more complex things? What's the prior probability of the existence of God? How probable is evil given God's existence? What's the statistical probability of a miracle given certain background information?

In non-idealized scenarios, which pretty much means all of everyday life, it's extremely difficult to assign accurate credences. It's often just a subjective shot in the dark. Carroll admits this, writing, "Some people don't like Bayesian emphasis on priors, because they seem subjective rather than objective. And that's right—they are. It can't be helped; we have to start somewhere" (80). His hope, however, is that Bayes offers a sort of course correction because new credences—what Bayes followers call "consequent probabilities"—will make up for imprecise prior credences. However, this leads to a major problem. If the prior credences are subjective and imprecise, then introducing new subjective, imprecise credences will not solve the problem—it will only compound it.

Throughout the rest of his book, Carroll regularly suggests that Bayesian reasoning supports his poetic naturalism, or components of it. But he almost never shows us the actual Bayesian calculations, with specific credences than can be examined and challenged.

In one of the rare places where he does provide actual credences, the chapter titled "Abducting God," Carroll applies Bayes' Theorem to God's existence. He assigns a prior credence of 50%. In other words, without considering any background evidence, we can initially assume that God's existence is as equally likely as not. That's not a bad starting point. But the rest of the chapter is filled with Carroll's wild presumptions about what the world would or would not like, given God's existence, and how the Bayes calculation should be updated. For example, he argues that the existence of evil, the massive size of the universe, and the lack of consensus about God all bring that 50% confidence level way down. Why? And by how much? It's tough to discern from his book since he provides no specific credences for his views, nor does he defend his belief that certain events would be more likely, given God, than not. He just throws around terms like "more likely" and "less likely" as if they were consensus views we all accept.

The chapter in question offers a perfect case study of how Bayes' Theorem can be both powerful and dangerous. Like a table saw, it can be very useful in certain tasks, but wildly destructive in the hands of a sloppy worker (note: I'm not necessarily suggesting Carroll is sloppy; this is just a general remark about Bayes' Theorem.)

The Theorem's effectiveness depends completely on the accuracy of the credences you put into it. And if we can't agree on the credences—or if, like Carroll, you refuse to even identify specific credences, much less defend them—then the output is irrelevant at best, and dangerously misleading at worst. On paper, Bayes' Theorem is a fantastic way to apprehend truth; in practice, it often has the opposite effect.

In the next post, we'll explore Carroll's answer to another fundamental question: why does the universe exist?

In the comment section to an earlier piece of mine on Strange Notions, Richard Carrier invited me to “interact” with him through his article “Neither Life nor the Universe Appears Intelligently Designed”, found in The End of Christianity, edited by John W. Loftus. This article is the “interaction” Carrier requested. I apologize for its delay.

Introduction

 
Richard Carrier’s argument to show that God probably didn’t create the universe, and therefore He probably doesn’t exist, in Carrier’s “Neither Life nor the Universe Appears Intelligently Designed”, like many attempts to use probability in defense of atheism or theism, is invalid and unsound, and based on fundamental misunderstandings of who God is and of the proper role of probability.

It is also a maddening, rambling screed, little more than bluff, bluster, and bullying, as well as an endless source of egotistical phrases, pace “critics know (and when honest, admit)”, “what any rational person would conclude”, “everyone else who’s rational and sane”, and “no rational person can honestly believe”. Nevertheless, let us “set aside ignoramuses who don’t know what they’re talking about and don’t even try to know” and analyze his main errors (it would take a monograph to examine every mistake).

His argument, repeated in different contexts, is essentially this. If God did not exist, life, the universe, and everything in it (including our minds) would look just the way they do. But if God exists, He could have created life, the universe, and everything in innumerable ways and, Carrier conjectures, surely not in the fractured, imperfect, pain-guaranteeing way we see. Therefore, because “the probability that a ‘designing’ god exists but never intelligently designed anything is likewise virtually zero, since by definition that’s also not how such a god behaves” and for other reasons Carrier creates, it is likely God does not exist.

The first and last parts are pure bluff. We have no idea what a “designing god” would do for a living, nor what the universe would look like had God not created it. To say we do assumes we have (absent God) an explanation of why there is something rather than nothing, which we do not have. Note carefully that “something” includes quantum fields, the “laws” of the universe, mathematics, anything you can think of. To say we know what the universe would look like had God not created it, is to claim one knows precisely why whatever physical, mathematical, mental, and philosophical foundations exist, exist the way they do, without circularly drawing on those foundations for their explanation. And that is impossible.

The second part is bluster. Call it the Carrier-as-God thesis, which essentially reads like this: “If I, Carrier the god, were to design the universe, it would be pink and happy with ‘bodies free of needless imperfections’. Since the Christian God obviously did not create this delightful world, he must not exist.” But how can Carrier presume to know why God did what He did? Carrier never explains.

The last part is bullying, probabilistic persiflage. Carrier thinks that by thumping the reader with (unnecessary, as it turns out) mathematics that science is happening, and thus nothing else need be said.

Carrier’s Main Argument

 
Carrier first defines “nonterrestrial intelligent design”:

“By ‘intelligent design,’ I mean design that is not the product of blind natural processes (such as some combination of chance and necessity), and by ‘nonterrestrial,’ I mean neither made by man (or woman) nor any other known life-form.”

Anything that happens by necessity must happen; necessary events are determined, i.e. caused, to happen in the way they did.

But nothing happens because of chance: chance is measure of knowledge and not a cause; it is not an ontological force and thus cannot direct events. Chance cannot be creative, though necessity, which implies design, is creative by definition. “Natural processes” cannot therefore be “blind.”

God is not a “life-form”. He nowhere takes up physical residence, nor does He live amorphously in some outer reach of the universe. God is not a creature, nor is He the same as the universe. In his inadequately described “designing god”, it’s clear Carrier doesn’t understand he is rejecting a god classical theologians also reject. Carrier’s god is not the ground of being, He whose name is I Am, existence itself, a necessary being who sustains all creation in each and every moment. Carrier’s god is instead a smart, long-lived creature possessed of fancy toys, perhaps made of pasta, who occasionally likes to tinker with bits and pieces of the universe but who is subject to the wiles and rules of the universe like other beings, though perhaps not to the same extent, an extent which Carrier always left vague.

Bayes' Theorem

 
Carrier then introduces Bayes' probability theorem, but only as a club to frighten his enemies and not as a legitimate tool to understand uncertainty. Bayes’ theorem is a simple means to update the probability of a hypothesis when considering new information. If the information comes all at once, the theorem isn’t especially needed, because there is no updating to be done. Nowhere does Carrier actually need Bayes and, anyway, probabilistic arguments are never as convincing as definitive proof, which is what we seek when asking whether God exists.

Here's a simple illustration. Suppose we accept the prior evidence (a proposition) "A standard deck of 52-playing cards, from which only one card will be pulled, and only one of which is labeled eight-of-clubs" and we later learn that "Jack removed the Jack-of-hearts from the deck." Conditional on these facts, we want the probability of the proposition, "I pull out an eight-of-clubs." This probability is obviously 1/51 whether we start with the first proposition and update with the second using Bayes, or just take both propositions simultaneously. Incidentally, this example highlights the crucial distinction that all probability is conditional on evidence which is specifically stated (there is no such thing as unconditional probability).

The problem is that Carrier artificially invents for himself various sets of “prior” information which he later tries to update using Bayes. Just like in the cards example, nowhere did he actually need Bayes for any of his arguments. Carrier further shows he misunderstands his subject when he says, “Probability measures frequency”. This is false: probability measures information, though information is sometimes in the form of frequencies, as in our card example. Suppose our proposition is, “Just two-thirds of Martians wear hats, and George is a Martian.” Given that specific evidence, the probability “George wears a hat” is 2/3, but there can be no frequency because, of course, there are no hat-wearing Martians.

Probability Errors

 
There is more than ample evidence Carrier is confused about the difference between probabilistic and philosophical argument. Here are some examples.

In order to form his priors, Carrier says the frequency of observed designed universes “is exactly zero.” A statement which, of course, assumes what he wants to prove, a classic error in logic, an error he duplicates when he insists he knows “full well” that intelligent extraterrestrials must, somewhere or at some time, exist. In both places, Carrier has substituted his desire for proof.

Again, “Yet any alien civilization selected at random will statistically be millions or billions of years more advanced [at designing life than we are].” Which alien civilizations are we selecting “at random”? What proof beyond conjecture and desire is there that (a) any other alien civilization exists and (b) that if any does exist it will be technologically and “statistically” more advanced than we, and that (c) even if they are more advanced, they would want to use their technological prowess to build lifeforms? This statement is nothing but an unproven science-fiction argument from desire. There is no set of premises which all can agree on that would allow us to deduce a probability here.

Carrier then writes:

“You cannot deduce from ‘God exists’ that the only way he would ever make a universe is that way. There must surely be some probability that he might do it another way. Indeed, the probability must be quite high, simply because it’s weird for an intelligent agent of means to go the most inefficient and unnecessary route to obtain his goals, and ‘weird’ means by definition ‘rare,’ which means ‘infrequent.’ which means ‘improbable.'”

Carrier constantly assumes he knows not only what God would do, but what various lesser gods would do. His case would have been infinitely strengthened had he given the evidence for these beliefs, rather than merely stating them.

He continues:

“Conversely, the probability that a ‘designing’ god exists but never intelligently designed anything is likewise virtually zero, since by definition that’s also not how such a god behaves.”

Who says? Has Carrier conducted a survey among deistical gods and their designing proclivities? Or is he merely assuming, without proof, that the gods must need design (maybe it scratches some intergalactic itch)? Anyway, Carrier’s god can’t create a universe (defined as everything that exists). That level of heft requires the God of infinite ability, the only way to get something from nothing.

“Hence it’s precisely the fact that God never does things like that in our observation that makes positing God as a causal explanation of other things so implausible.”

So much for miracles, then; and a rather dogmatic dismissal at that.

Design and Intelligence

 
Carrier misunderstands other aspects of probability, too. He appears to believe, like many, that evolution occurs “randomly” and is a “product of chance”. That’s impossible. Nothing is caused by “chance” or occurs “randomly” because chance is not a cause and neither is randomness. Chance and randomness are measures of our ignorance of causes, and are not themselves ontological realities. It is always a bluff to say that “randomness” or “chance” caused some effect. You either know the cause or you do not. If you know it, state it. If you do not, then admit it (using probability).

Intelligent design enthusiasts make the same mistake, and when they do, Carrier is there to show us, to his credit: “Michael Behe’s claim that the flagellar propulsion system of the E. coli bacterium is irreducibly complex and thus cannot have evolved”. The system’s evolution, to Behe, was completely “improbable.” Yet improbability arguments don’t work for or against evolution. If a thing has happened—and the propulsion system happened—it was caused. That we don’t know of the cause is where probability enters, but only as a measure of our ignorance of the cause. Whether we know or don’t know of the cause, there is still a cause. Things don’t “just happen.” That’s why when we see that organisms have evolved, which is indisputable, we know there must be some thing or things causing those changes.

What about the start of all life, i.e. biogenesis? Carrier says, “by definition the origin of life must be a random accident.” Thus does hope replace reality. Life could not have sprung up “randomly”, for randomness isn’t a cause. As it is, there is no direct evidence of how life arose, a gap which Carrier replaces with bluster, a science-of-the-gaps theory. I have no idea how life got here. God might have done it directly, or merely designed the system so that it had to arise. But something caused it. To say “I don’t know what the cause was” is not proof that “God was not the cause”.

How about the start of the universe? Carrier says:

“Suppose in a thousand years we develop computers capable of simulating the outcome of every possible universe, with every possible arrangement of physical constants, and these simulations tell us which of those universes will produce arrangements that make conscious observers (as an inevitable undesigned by-product). It follows that in none of those universes are the conscious observers intelligently designed (they are merely inevitable by-products), and none of those universes are intelligently designed (they are all of them constructed purely at random)...
 
Our universe looks exactly like random chance would produce, but not exactly like intelligent design would produce.”

Unfortunately, this isn’t even wrong. It is impossible—as in not possible, no matter what—for “random chance” to create even a mote on the speck of a quark let alone an entire universe. Anyway, how would Carrier or anybody know what a designed universe looks like? Again, no guidebook exists. To say this one isn’t designed is stunningly bold, a belief without evidence of any kind—except the desire that it not be so.

Motivations

 
Perhaps the following sentences reveal how Carrier so easily fooled himself: “Hence I have demonstrated with logical certainty that the truth of Christianity is very improbable on these facts. And what is very improbable should not be believed. When enough people realize this, Christianity will come to an end.” And, contradicting himself in the matter of certainty of Christianity, he later says, “Christianity is fully disconfirmed by the evidence of life and the universe.”

Carrier nowhere in the body of his argument spoke of Christianity, but only vaguely of ETs, gods, and some curious ideas of what God would act like if He were Richard Carrier. Strange, then, that he should be so confident he has destroyed all of Christianity.

And no other religion.

 
 
(Image credit: Daily Kos)

"No other formula in the alchemy of logic has exerted more astonishing powers. For it has established the existence of God from the premiss of total ignorance; and it has measured with numerical precision the probability the sun will rise tomorrow."

Probability carries with it “a smack of astrology, of alchemy.” Comte, Keynes reminds us, regarded the application of the mathematical calculus of probability as “purement chimérique et, par conséquent, tout à fait vicieuse" ("purely chimerical, and therefore, quite vicious".)

Note the last word, vicious, a word which was laughed off in the mad rush towards the utopia of Quantification an era which Comte, incidentally, and despite his intentions, helped usher in. We are very close to the moment when a number must by law be attached to every judgment of uncertainty.

Therefore, you may not be surprised to learn there is not one, but two books which argue that a fixed, firm number may be put on the proposition, "God exists." The first, by Stephen Unwin, is called The Probability of God: A Simple Calculation That Proves the Ultimate Truth, in which he uses Bayes’s theorem to demonstrate, with probability one minus epsilon, that the Christian God exists.

This is countered by Proving History: Bayes’s Theorem and the Quest for the Historical Jesus by Richard Carrier, who uses Bayes’s theorem to prove, with probability one minus epsilon, that the Christian God does not exist because Jesus himself never did.

So here we have probability proving two diametrically opposite conclusions. Comte was right: Alchemy, indeed.

Carrier of course has the harder task, and he attacks it with great gusto. He identifies as a mythicist, which he defines as someone who believes the historical Jesus was a myth. Carrier doesn’t just deny the divine Jesus, but asserts that the man called Jesus never existed.

He's convinced Jesus was a first-century creation, invented whole cloth, likely born of a conspiracy to create a new religion. I won’t dig into the details of Carrier’s points—I believe other contributors will be doing that at Strange Notions in the near future. But if you are interested, here is a link to a several-thousand-word essay in which Carrier “takes apart” a minor blog post written by a historian who claims Jesus lived.

On the other hand, an early review of Unwin’s work, which I have read and which is mercifully brief (and in large font with small pages), asks just the right question: “Can you imagine anyone arguing that the existence of evil in the world, given that God exists, is 23% as opposed to 24%, for instance?” Indeed. Too bad this kind of question is not asked in science.

The reviewer also recognized that probability questions have an order. That is, the probability that evil exists given God does is different from the probability that God exists given evil does. This crucial distinction Unwin minds attentively.

The real question is this: how can probability prove a thing and its opposite simultaneously? The answer is simple: the same way logic can prove a thing and its opposite. This does not prove that logic should be lumped with pseudoscience, however. You can’t blame the tool for its misuse.

All arguments of certainty and uncertainty are conditional. For example, is the proposition “Jesus was divine” true? Well, that depends on the evidence. If you say, “Given Jesus lived, died, and was resurrected as related in the Gospels” then the proposition has probability one (i.e., it is true.) But if you say, “Given Jesus was a myth, created as a conspiracy to flummox the Romans and garner tithes” then the proposition has probability zero (i.e., it is false.)

Given still other evidence, the probability the proposition is true may lie between these two extremes. In no case, however, is probability or logic broken. It does explain why focusing on probability is wrong, though.

These authors would help themselves better, and contribute to a more fruitful discussion about Jesus, by explicating the evidence and eschewing unnecessary quantification.
 
 
(Image credit: Witty Sparks)