Reader GGDFan77 asked me for my thoughts on the exchange between Dr. Richard Carrier, who I respect and consider a friend, and Dr. Luke Barnes regarding fine-tuning arguments. I initially responded in a series of comments in the combox for my post about Hugh Ross’s estimates for the probability of life-permitting prebiotic conditions. But those turned out to be so lengthy that I think the topic deserves its own dedicated post.
Here’s some brief context for readers not familiar with the exchanges between Dr. Richard Carrier and Dr. Luke Barnes:
* Dr. Carrier wrote an essay, “Neither Life Nor the Universe Appear Intelligently Designed,” in The End of Christianity (ed. John Loftus, Buffalo: Prometheus Books, 2011), pp. 279-304.
* Dr. Barnes wrote a four part series on his blog critiquing that essay by Carrier.
* Dr. Carrier and Dr. Barnes had an extensive back-and-forth exchange in the combox on Carrier’s blog.
Let me preface my comments by saying that I have a lot of empathy for any writer, including Dr. Carrier, who is trying to use the formal apparatus of Bayes’ theorem in a way that is accessible to a beginning-to-intermediate audience, which I take to be the target audience of The End of Christianity. If you go for too much precision and formalism, you risk losing your audience. If you focus too much on accessibility, you risk misunderstandings, oversimplifications, and outright errors. Finding the right balance isn’t easy.

Part 1

With all due respect to Dr. Carrier, I find part 1 of Dr. Barnes’ critique to be very persuasive and, in fact, to be a prima facie devastating critique. (I quickly skimmed the combox on Dr. Carrier’s site to see if they debated anything relevant to part 1, but I didn’t find anything, so it appears that the points in part 1 of Dr. Barnes’ series have gone unchallenged by Dr. Carrier.)
In particular, I agree with the following points by Dr. Barnes.

• “Bayes’ theorem, as the name suggests, is a theorem, not an argument, and certainly not a definition.”
• “Also, Carrier seems to be saying that P(h|b), P(~h|b), P(e|h.b), and P(e|~h.b) are the premises from which one formally proves Bayes’ theorem. This fails to understand the difference between the derivation of a theorem and the terms in an equation.”
• “Crucial to this approach is the idea of a reference class – exactly what things should we group together as A-like? This is the Achilles heel of finite frequentism.”
• “It gets even worse if our reference class is too narrow.”
• “This is related to the ‘problem of the single case’. The restriction to known, actual events creates an obvious problem for the study of unique events.”
• “Carrier completely abandons finite frequentism when he comes to discuss the multiverse.”
• “Whatever interpretation of probability that Carrier is applying to the multiverse, it isn’t the same one that he applies to fine-tuning.”
• “If we are using Bayes’ theorem, the likelihood of each hypothesis is extremely relevant.”

In addition, I would add the following comment.

• In his essay, Carrier writes: “Probability measures frequency (whether of things happening or of things being true).” Not exactly. The frequentist interpretation of probability measures relative frequency, but the frequentist interpretation of probability isn’t the only interpretation of probability. There are “many other games in town” besides that one; there is also the epistemic interpretation of probability (aka “subjective” aka “personal” aka “Bayesian”), which measures degree of belief. Thus, to say that probability just is relative frequency is to beg the question against all the rival interpretations of probability. (And, for the record, I’m actually a pluralist when it comes to probability; following Gillies, I think different interpretations can be used in different situations.)

Part 2

Here are my thoughts on Part 2 of Dr. Barnes’ reply.

This simulation tells us nothing about how actual cars are produced.

I strongly agree.

The fact that we can imagine every possible arrangement of metal and plastic does not mean that every actual car is constructed merely at random.

I agree.

Note a few leaps that Carrier makes. He leaps from bits in a computer to actual universes that contain conscious observers. He leaps from simulating every possible universe to producing universes “merely at random”.

I agree.

 This is a textbook example of affirming the consequent, a “training wheels” level logical fallacy.”

I think this is an uncharitable interpretation of Carrier’s statements by Barnes.

False. Obviously False.

I disagree with Barnes. Here is the passage by Carrier which Barnes is referring to.

It simply follows that if we exist and the universe is entirely a product of random chance (and not NID), then the probability that we would observe the kind of universe we do is 100 percent expected.

Let’s abbreviate the statement “we exist” as B (for our background knowledge); the statement “the universe is entirely a product of random chance (and not NID)” as C (for chance); and the statement “we observe the kind of universe we do” as E (for evidence). Then we can abbreviate the paragraph just quoted as:

Pr-L(E | B & C) = 1, where Pr-L represents a logical probability.

It seems to me that Carrier is correct. Contrary to what Barnes writes, however, it doesn’t follow that we can’t conclude it is highly probable someone was cheating in a game of poker. It just means that the correct way to show that cheating took place is not to use an argument analogous to the argument Carrier is refuting.
Aside: Reading the exchange between Carrier and Barnes reminds me of one of my wishes for people who use Bayes’ Theorem in this way: I really wish people would explicitly state the propositions they are including in their background knowledge. It avoids misunderstandings and misinterpretations.

Carrier says that “if the evidence looks exactly the same on either hypothesis, there is no logical sense in which we can say the evidence is more likely on either hypothesis”. Nope. Repeat after me: the probability of what is observed varies as a function of the hypothesis. That’s the whole point of Bayes theorem.”

I think Barnes is being uncharitable to Carrier. When Carrier writes, “the evidence looks the same,” I interpret him to mean “when the evidence is equally likely on either hypothesis.”

All that follows from the anthropic principle…

I need to study this section in detail, but I think agree with Barnes.
I would add the following. In his essay, Carrier writes this:

Would any of those conscious observers be right in concluding that their universe was intelligently designed to produce them? No. Not even one of them would be.

It would be most helpful if Carrier would explicitly defend this statement: “No. Not even one of them would be.” Unless I’ve misunderstood his argument, I think this is false. If we include in our background knowledge the fact that Carrier’s hypothetical conscious observers exist in a universe we know is the result of a random simulation, then we already know their universe is the result of a random simulation. Facts about the relative frequency aren’t even needed: we know the universe is the result of a random simulation.
If, however, we exclude that from our background knowledge, so that we are in the same epistemic situation as the hypothetical observers, then things are not so easy. Again, it would be helpful if Carrier could spell out his reasoning here.

Part 3

Let’s move onto Part 3 of Barnes’s reply.

“Refuted by scientists again and again”. What, in the peer-reviewed scientific literature? I’ve published a review of the scientific literature, 200+ papers, and I can only think of a handful that oppose this conclusion, and piles and piles that support it.

I think Dr. Carrier absolutely has to respond to this point by Dr. Barnes or publicly issue a retraction.

With regards to the claim that “the fundamental constants and quantities of nature must fall into an incomprehensibly narrow life-permitting range”, the weight of the peer-reviewed scientific literature is overwhelmingly with Craig. (If you disagree, start citing papers).

This strikes me as a devastating reply. Like the last point, I think Dr. Carrier absolutely has to respond or else issue a retraction.

He can only get his “narrow range” by varying one single constant”. Wrong. The very thing that got this field started was physicists noting coincidences between a number of constants and the requirements of life. Only a handful of the 200+ scientific papers in this field vary only one variable. Read this.

Ouch. Same as the last two points.

“1 in 8 and 1 in 4: see Victor Stenger”. If Carrier is referring to Stenger’s program MonkeyGod, then he’s kidding himself.

I haven’t studied MonkeyGod enough to have an opinion, so I have no comment on this one.

In all the possible universes we have explored, we have found that a tiny fraction would permit the existence of intelligent life. There are other possible universes,that we haven’t explored. This is only relevant if we have some reason to believe that the trend we have observed until now will be miraculously reversed just beyond the horizon of what we have explored.

If I understand Dr. Barnes’ point correctly here, then I think he is making a simple appeal to induction by enumeration and I think his argument is logically correct.

In fact, by beginning in our universe, known to be life-permitting, we have biased our search in favour of finding life-permitting universes.

I find this point very interesting. I hadn’t even thought of it that way, but I think he’s right.

Nope. For a given possible universe, we specify the physics. So we know that there are no other constants and variables. A universe with other constants would be a different universe.

I think I agree with this.

How does a historian come to think that he can crown a theory “the most popular going theory in cosmological physics today” without giving a reference? He has no authority on cosmology – no training, to expertise, no publications, and a growing pile of physics blunders.

Ouch.

In any case, the claim is wrong…

I don’t have the physics expertise to evaluate this paragraph.

By what criteria is that the simplest entity imaginable? If the point is lawless, why does it evolve into something else? How does it evolve? What evolves? What defines the state space? If it is a singular point, how are there now many spacetime points? Why are they arranged in a smooth manifold? Why spacetime? What if space and time aren’t fundamental? It’s not clear that a lawless physical state makes any sense. Even if it does, if it’s lawless, why do we observe a law-like universe?

Good questions.

Fine-tuning doesn’t claim that this universe has the maximum amount of life per unit volume (or baryon, or whatever). So this argument is irrelevant.

Dr. Barnes is, of course, correct that fine-tuning doesn’t logically entail that this universe has the maximum amount of life per unit volume, in the sense that “fine-tuning” is logically compatible with “the universe NOT having the maximum amount of life per unit volume.” But I disagree with Dr. Barnes that the hostility of life is irrelevant. In fact, as I’ve argued before, focusing only on facts about “fine-tuning” while ignoring facts about “course-tuning” (i.e., the hostility of the universe to life) commits the logical fallacy of understated evidence.

Part 4

Let’s move onto part 4 of Dr. Barnes’ reply. Barnes writes:

What is Carrier’s main argument in response to fine-tuning, in his article “Neither Life nor the Universe Appear Intelligently Designed”? He kept accusing me of misrepresenting him, but never clarified his argument.

I agree.

Bayes’ theorem follows from Cox’s theorem, which assumes only some reasonable desiderata of reasoning.

I haven’t studied Cox’s theorem, so I can’t comment on that directly. Instead, I want to point out that Bayes’s theorem also follows from the Kolmogorov axioms of the probability calculus plus the definition of conditional probability.

A given proposition K_i can play the role of “background” or “evidence”, depending on the term.

I agree.

Talking about “the prior” or “the likelihood” in such a context is ambiguous. Better to use notation.

I strongly agree.

Look closely at p(o | ~NID.b’). This is the probability that a universe with intelligent observers exists, given that there is no intelligent cause of their universe, and given background information b’ that does not imply o. This is exactly the probability that Carrier is afraid of, the one that could equal an “ungodly percentage” (pg. 293). It is the probability that “the universe we observe would exist by chance” (pg. 293). Carrier argues that this term is irrelevant because ignores o. It does, but rightly so. The posterior does not ignore o. Look at Bayes’ theorem: p(H|EB) = p(E|HB) p(H|B) /p(E|B).  Both E and B are known, and yet the likelihood p(E|HB) just ignores the fact that we know E! Rightly so! This is the whole point of Bayes’ theorem.

1. Here I think Dr. Barnes is being just a tad snarky (“This is exactly the probability that Carrier is afraid of”).
2. This may be a nitpick, but I wouldn’t word things the way Dr. Barnes does, when he writes that p(o | ~NID.b’) is “the probability that ‘the universe we observe would exist by chance.'” Instead, I would define that probability in plain English as “the probability that intelligent observers exist conditional upon our background knowledge conjoined with the hypothesis that a non-terrestrial intelligent designer did NOT design the universe.” The key difference here is that the latter phrasing keeps the distinction between “the universe we observe” and “intelligent observers exist.”
3. I strongly agree with this: “Carrier argues that this term is irrelevant because ignores o. It does, but rightly so. The posterior does not ignore o. Look at Bayes’ theorem: p(H|EB) = p(E|HB) p(H|B) /p(E|B).  Both E and B are known, and yet the likelihood p(E|HB) just ignores the fact that we know E! Rightly so! “
4. Again, this may be another nitpick but I agree and disagree with this statement: “This is the whole point of Bayes’ theorem.” Not exactly; here I think Dr. Barnes is unwittingly presupposing the epistemic interpretation of Bayes’s theorem. Based on that interpretation, he’s correct. On rival interpretations–such as the frequency interpretation–we wouldn’t talk about knowledge at all, but the relative frequency among some reference class.

Here’s the problem with the argument above. What (3) shows is that, since f follows from o, I need not condition the posterior on f. There is a redundancy in our description of what we know. But that does not mean that the posterior p(NID|f.b) is independent of the “ungodly percentage” p(o | ~NID.b’). The surprising fact on ~NID, that a life-permitting universe universe exists at all, cannot hide in the background. We can draw it out. It’s right there in equation (7).

I agree. Dr. Barnes is making a very similar point to the one I make below, where I talk about pushing the problem back a step.

There a couple of different versions of NID floating around Carrier’s essay….

I agree with pretty much this entire section of Dr. Barnes’s essay.

Question 5: What mathematician should I read to learn about reference classes and why probabilities measure frequencies? Is Carrier a frequentist or a Bayesian?

Actually, this is a question not best suited for a mathematician, but a philosopher. In my opinion, the “go-to” reference books for this question are (1) Choice & Chance by Brian Skyrms and (2) Philosophical Interpretations of Probability by Gillies.

Question 9: Moving on to Carrier’s scientific claims, there’s some explaining to do.

I think Dr. Carrier must directly answer the questions in the bulleted list that follows.

This time could have been spent showing that I am wrong. More time is spent attacking me than defending, or even explaining, his case. Take the comment on January 7, 2014 at 8:43 am. Of 14 sentences: 1 clarification of a previous comment, 2 repetitions of points from his article that I agreed with, 2 claims contrary to mine (hurray! interaction!), and 9 that merely accuse of error and incompetence.

I strongly agree. I hope that Dr. Carrier will directly respond to Dr. Barnes without the personal attacks.

Carrier’s Endnote 23

GGDFan777 also asked me to parse endnote 23 of Dr. Carrier’s essay. Unless otherwise indicated, the quotations are from that endnote.

This is undeniable: if only a finely tuned universe can produce life, then by defintion P(FINELY TUNED UNIVERSE | INTELLIGENT OBSERVERS EXIST) = 1, because of (a) the logical fact that “if and only if A, then B” entails “if B, then A” (hence (“if and only if a finely tuned universe, then intelligent observers” entails “if intelligent observers, then a finely tuned universe,” which is strict entailment, hence true regardless of how that fine-tuning came about; by analogy with “if and only if colors exist, then orange is a color” entails “if orange is a color, then colors exist”; note that this is not the fallacy of affirming the consequent because it properly derives from a biconditional), and because of (b) the fact in conditional probability that P(INTELLIGENT OBSERVERS EXIST)=1 (the probability that we are mistaken about intelligent observers existing is zero, a la Descartes, therefore the probability that they exist is 100 percent) and P(A and B) = P(A|B) x Pr(B), and 1 x 1 =1.

I agree.

Collins concedes that if we include in b “everything we know about the world, including our existence,” then P(L | ~God & A LIFE-BEARING UNIVERSE IS OBSERVED) = 100 percent (Collins, “The Teleological Argument,” 207).

I don’t have access to the material by Collins, but I don’t have any reason to doubt that what Carrier says here is correct.

He thus desperately needs to somehow “not count” such known facts. That’s irrational, and he ought to know it’s irrational.

Sigh. I think the statement “desperately needs” is snarky and off-putting. I think these two sentences are uncharitable to Collins, for reasons I will explain below.

He tries anyway (e.g., 241-44), by putting “a life-bearing universe is observed” (his LPU) in e instead of b. But then b still contains “observers exist,” which still entails “a life-bearing universe exists,” and anything entailed by a 100 percent probability has itself a probability of 100 percent (as proven above). In other words, since the probability of observing ~LPU if ~LPU is zero (since if ~LPU, observers won’t exist), it can never be the case that P(LPU|~God.b) < 100 percent as Collins claims (on 207), because if the probability of ~LPU is zero the probability of LPU is 1 (being the converse), and b contains “observers exist,” which entails the probability of ~LPU is zero.

I agree with his analysis, but — you knew there was a “but” coming — I think this misses the point, which seems to be a restatement of the anthropic principle dressed up in the formalism of probability notation. Yes, if we include “(embodied) intelligent observers exist” in our background knowledge (B), then it follows that a life-permitting universe (LPU) exists. But that isn’t very interesting. In one sense, this move simply pushes the problem back a step.
To see why, we can (in a sense) do a Bayesian analysis in reverse. Abstract away everything we know, including our own existence, and include in our background knowledge only the fact that our universe exists. Based on that fact alone, the prior (epistemic) probability of “(embodied) intelligent observers exist” is not 1 on naturalism and it is not 1 on theism.
In the jargon of academic philosophy of religion, the proponent of a fine-tuning argument for theism is asking us to compare the epistemic probability–not relative frequency–of a life-existing universe conditional upon theism to the epistemic probability of a life-existing universe conditional upon naturalism. To respond to that argument with “But we exist” misses the point.
The proponent of the fine-tuning argument can, should, and will respond, “No shit, Sherlock. Everyone agrees that we exist. The question is whether the life-permitting preconditions of our universe is evidence relevant to theism and naturalism.”

If (in even greater desperation) Collins tried putting “I think, therefore I am” in e, his conclusion would only be true for people who aren’t observers (since b then contains no observers), and since the probability of there being people who aren’t observers is zero, his calculation would be irrelevant

Again, I find the snark (“greater desperation”) off-putting, but let’s put that aside. At the risk of repeating myself, the fact that each of us knows that we exist doesn’t make fine-tuning arguments go away. Yes, we know that our universe is life-permitting because we know that we exist. But why is our universe life-permitting? Some philosophers (including both theists and atheists like Paul Draper) argue that that is evidence favoring theism over naturalism. If they are right, then so be it. But if they are wrong, they are NOT wrong because we exist. That objection just doesn’t work.

(it would be true only for people who don’t exist, i.e., any conclusion that is conditional on “there are no observers” is of no interest to observers).

Dr. Carrier doesn’t speak for all observers. I’m an observer and find the question of interest. So does Paul Draper. So do many atheist philosophers who don’t think fine-tuning arguments work, including Bradley Monton, Keith Parsons, Graham Oppy, Quentin Smith, and so forth. So do many (but not all) theist philosophers. So do many non-philosophers of all stripes. If he doesn’t find the question of interest, that’s fine. But, at risk of stating the obvious, his lack of interest in the argument isn’t a defeater for the argument.