TFBW's Forum

I don't really have a specific math question. I guess it's just more of an observation that could use some clarification and also some elaboration on what 5-sigma actually means. I just wasn't sure where else to post this.

After seeing some overly enthusiastic science journalists initially reporting expectations that CERN would be making an announcement on Wednesday that the Higgs Boson (God Particle) had been discovered with a 5-sigma degree of certainty, a position they have since backed away from, it got me thinking about the nature of evidence and the militant atheist's usual demand for that same type of empirical evidence for the existence of God.

Carl Sagan once said something along the lines of extraordinary claims require extraordinary proof. For me, this gives rise to several questions. Are the claims that a person has committed crimes such that, if found guilty, the perpetrator would be deserving of imprisonment or even death, extraordinary claims? And, if so, do those claims require extraordinary evidence as proof?

The evidence that convicted Charles Manson and has kept him in prison for 40 years was entirely circumstantial and anecdotal in nature. It certainly wasn't derived from repeatable experiments who's data was amenable to statistical analysis.

I wonder if one of those militant atheists have ever sat on a jury and cast a vote to convict based on a preponderance of entirely circumstantial and anecdotal evidence that proved to them, beyond a reasonable doubt, the guilt of the defendant. There's no way to know for sure, but I would find it odd if that has never happened.

Of course, I expect the argument to be that I am comparing apples to oranges. That may be true and I suppose that is another area that could use some clarification and elaboration, but questions remain.

Are matters of life and death less important to the militant atheist than the existence of God? And is circumstantial evidence that happens to be amenable to statistical analysis of data points, by necessity, inherently superior to other types of circumstantial evidence that are perfectly acceptable for critical decision making in other areas of grave importance?

It seems to me there is a mountain of cross corroborating circumstantial evidence, when considered together, for the existence of God even if each piece of evidence, taken individually, could have an alternate plausible explanation constructed.

Am I way off base here?

To the extent that it's a mathematics question, it's pretty easy to answer. The "sigma" in question relates to a number of standard deviations away from the mean in a normal distribution. In this case, we have an experimental result, and the certainty that the result is not due to random variance in the experiment is five sigma. For those of us who don't naturally think in terms of standard deviations, that's about 99.999971335% certain. (This number is derived from the standard deviation to probability factor conversion table in my document entitled "More Monkey Business".)

According to this Wikipedia page, the field of particle physics has standardised on five sigma as its "accepted discovery" threshold. I'll quote the relevant bit here, because Wikipedia is prone to change.

Evidently the source of this information was some bullet points in a BBC article on the LHC in late 2011. Make of that what you will.

This is all well and good when you're making measurements with known error margins and a normal distribution. The BBC article has a useful analogy in relation to coin-tossing. If you have a theory that a coin is 100% biased, and always lands heads when tossed, a single toss that lands heads doesn't prove much: there was a 50/50 chance it was going to land "heads" even if it's perfectly fair. If you tossed it twenty times and got "heads" on all tosses, however, you'd have confirmed your theory to the five sigma level. While it's technically possible for that outcome to happen by chance, the odds against it are 1,048,576 to one, so it's 99.999904633% certain that the confirmation isn't a fluke. We can compute this because we're dealing with well-defined behaviours and their associated numbers.

Obviously things are considerably fuzzier when it comes to the existence of God. My "monkey math" essays are analyses of simple information-bearing systems, which show how even relatively simple systems can not feasibly arise by chance (with much higher than five sigma certainty). This is an argument against the possibility of life originating by natural processes. Evolutionary theory posits that Natural Selection directs the process once life exists, but there is no evidence-based explanation of how the complex functionality of the first living cell came to be. Pure random luck is ruled out with far more than five-sigma certainty, so there must be some other explanation. I say that explanation is a supernatural designer. Dawkins thinks that we will eventually discover some analogue of natural selection that works for chemical evolution -- but note that he has no actual evidence for that position, so it can hardly be called scientific.

Dawkins tries to turn the probability argument around the other way in chapter four of The God Delusion, by claiming that God is the Most Improbable Thing Imaginable. Specifically, he says, "however statistically improbable the entity you seek to explain by invoking a designer, the designer himself has to be at least as improbable." This misses the point, as Dawkins is so often wont to do. As the current analysis should make clear, high improbabilities rule out the possibility that something happened by chance, not that it exists at all. It's not immediately obvious that Dawkins' assertion about the relative probability of things is true, but even if we grant it, it does not reach the conclusion he suggests it does (i.e. the non-existence of God). To see this, consider the probability argument as it relates to life. We know that life exists, and that even the simplest form of life is far too complex to spontaneously assemble by pure chance. That doesn't mean that life does not exist (duh!): it simply means there must be some explanation other than pure chance for its existence. Similarly, if we grant the bizarre assertion that the probability of God arising by chance is even less likely, we conclude only that if God exists, he does not exist by chance. If Dawkins wants us to conclude that God doesn't exist at all, the argument requires an additional premise in order to be valid: specifically, "if God exists at all, he exists purely by chance." I can see no good reason to accept that premise.

An interesting ramble on the subject of probability that was, but it's not really what you asked about in the bulk of your post. What you really asked about was the nature of evidence, and that's a tricky subject that I'll post on later. Before I go, however, I'd like to look briefly at the "extraordinary claims require extraordinary evidence" maxim. Presumably it stands in contrast to ordinary claims, which only require ordinary evidence. Note, however, that the statement is, itself, a claim. It's a claim about claims. Is it an extraordinary claim, or an ordinary one? Was it accompanied by evidence of some sort, either ordinary or extraordinary, or were we expected to agree with it on the basis that it sounded clever?

People who make epistemological assertions rarely live up to their own standards.

"Evidence" is a notoriously tricky subject. I think that the best thing to do with any scientific rationalist who makes strong claims about how "evidence" is the only proper basis for belief is to give them an interrogation on the subject worthy of Socrates. If they're so sure about the nature of evidence, they'd better be pretty damn clear on the details.

You cite the issue of circumstantial evidence, and wonder whether a scientific rationalist would accept such evidence. Let's start there as a subject of inquiry. First up, what is "circumstantial evidence"? According to The Wiki, the difference between "circumstantial" and "direct" evidence is the need for inference in the former case. In the latter case, the deed itself is seen; in the former case, the evidence can be explained by the deed, but other explanations are also possible. The philosopher in me immediately suspects that this isn't always going to give us a clear-cut distinction between the cases, but even if it's a matter of degree, at least we have some sort of dimension along which to attempt our measurements. In law, testimony can provide either direct or circumstantial evidence: a witness to a crime provides direct evidence; a witness who merely saw the accused at the scene of the crime provides circumstantial evidence. The criminal was certainly at the scene of the crime, but being at the scene of the crime does not necessarily imply that one is the criminal.

Given this clarification, it's pretty obvious that scientific rationalists have no problem at all with circumstantial evidence. The conspicuous example which springs immediately to mind is the evolutionary doctrine of common ancestry. Mainstream evolutionary theory declares that all life on earth is related, having descended from a single original basic organism. The amount of actual ancestry for which we have any direct evidence is miniscule, especially in the context of the claim being made (i.e. all life in the entire history of the planet). Some of the circumstantial evidence is only considered supportive of common ancestry because the alternative explanations are distasteful. The fossil record, for example, is just as compatible (if not more so) with the theory that species were artificially introduced to Earth at different points in history. This explanation is "better" than the evolutionary one in the sense that it does not require us to infer the (unobserved) existence of intermediate forms between organisms with large structural differences. It's obviously unacceptable, however, because it's not a naturalistic explanation.

This suggests some lines of inquiry. First, does the scientific rationalist recognise how much of his evidence is circumstantial? Second, does the scientific rationalist realise that his a priori commitment to naturalistic explanations is playing a leading role in the interpretation of evidence? Third, if I have a commitment to scientific evidence but not to naturalistic explanations (and why should I commit to naturalistic explanations, given that I am literally surrounded by things which are quite properly explained by intelligent intervention), why am I acting improperly in saying that the fossil record is prima facie evidence of Progressive Creation, not Evolution?

It's clear even from this brief analysis that the interpretation of the evidence is more important than the evidence itself. Without the a priori commitment to naturalism, does the evidence lead to naturalistic conclusions? I think it's pretty clear that it does not. Richard Dawkins is always ready and willing to point out that living things have the appearance of design. The appearance of design is good circumstantial evidence for actual design and a designer, but this conclusion is utterly unacceptable to him because of the overriding priority of naturalism.

If you have an a priori commitment to naturalism of this sort, you're not going to view anything as evidence for the existence of God. The only possible avenue via which one might come to entertain the possibility of an intervening God that I can see, under those circumstances, is if one's naturalistic premises drive one to a logical conclusion which is patently absurd, prompting one to question the naturalistic premise.

I think that answers your question.

Thanks. Nicely done, but is it even a rational position to hold an a priori commitment to naturalistic explanations for everything, for now, given that the totality of information presently available is incomplete at best? Hasn't the term, supernatural, throughout history, always been definitially mutable from one discovery to the next?

First, sorry for the delay in replying. I was off the grid most of last week. Fortunately, however, this has given me the chance to finish re-reading a book called C. S. Lewis's Dangerous Idea, by Victor Reppert. The final chapter of this book deals more or less with the question you have asked. The title is a play on Dennett's book, Darwin's Dangerous Idea, which will also factor into this response.

Before going any further, I'd like to draw your attention to the fact that there's a lot of sleight-of-hand that goes on in this area. When trying to analyse an atheist's argument, it's important to keep track of what is presented as a premise, and what is presented as a conclusion. These things can easily trade places, giving the argument the appearance of coherence, but at the expense of circularity.

As a rough example, a common attitude among atheists is that science has removed (or is progressively removing) the need for God, and therefore atheism is justified. If you press for details on how science has deposed God in this manner, you will find that "science" is defined in a manner which entails some kind of naturalism (e.g. methodological naturalism). If naturalism is embraced at this level, then all science will exclude "God" as a matter of procedure. It should be pointed out that this kind of science does not (and can not) provide evidence against the existence of God, because it never admitted the possibility that God exists in the first place.

Scientific atheists apply atheistic assumptions to their science, but they are not satisfied with giving atheism the status of a premise or assumption: they want it to be a conclusion reached by means of evidence. For this reason, there is usually some effort to define "science" in such a way that it produces the appropriate sort of evidence, without making it too obvious that the game is being rigged.

One popular approach to the issue is to deny that explanations involving the supernatural have any actual explanatory value. Dawkins does this in The God Delusion, and provides us with a textbook example of smuggling one's conclusions into one's premises in so doing. The "explanatory value" material is in the last paragraph of chapter two. The paragraph takes the narrative through a couple of sharp turns: it starts by seeking a distinction between super-advanced aliens and a supernatural God, but suddenly deflects into a discussion of explanatory value. I'll quote the relevant part here.


There's a lot to be said about this passage. For one, it never explicitly answers the original question. Reading between the lines, I infer that the "provenance" issue relates to the question of ultimate origins: a superhuman alien is a product of evolution, whereas God is not. The immediately following sentence asserts that all intelligent entities are products of evolution. This assertion entails the denial of the existence of a non-evolved, intelligent God. Dawkins could thus prove his case by supporting his assertion with evidence or argument. Assuming that the material which follows is supposed to provide such support, we see that he chooses to talk about the explanatory value of "cranes" versus "skyhooks" (Dennett's terminology). A supernatural (non-evolved) God is a "skyhook" which explains nothing, he says, whereas a "crane" is a legitimate explanatory device.

This argument should leave the reader feeling as though something important has been left out. The issue being addressed is "the God Hypothesis": the hypothesis that, "there exists a superhuman, supernatural intelligence who deliberately designed and created the universe and everything in it, including us." This is a proposition which is either true or false, and Dawkins is arguing for the negative. The basis of his argument, however, is that proposing a creator God lacks explanatory value. There is an important question as to what constitutes "explanatory value", exactly, but in this case the only kind of value we are really interested in is truth. Is the God Hypothesis true or false? To argue that it lacks explanatory value is to change the subject: our immediate interest is its truth value.

In arguing that the God Hypothesis lacks explanatory value, Dawkins is making a case that the job of science is to explain, and therefore scientific hypotheses must have explanatory value, and thus the God Hypothesis is not a scientific hypothesis due to its (alleged) lack of explanatory value. On the other hand, evolutionary hypotheses (allegedly) have explanatory value, and are properly scientific. Thus, science gives evidence against the existence of God -- if you're not paying close attention to the fact that this formulation of "science" decouples it from "truth", making it instead the set of explanations favoured by philosophical naturalists.

This is but one of many contortions that have been performed to disguise the atheistic a priori commitment to naturalism in respectable scientific garb. There are probably other cases worth studying, but this one will do for now.

Reading my explanations above, you might suppose that I think of atheists as deliberately deceptive: that they have an a priori commitment to naturalism and understand it as such, but use sophistry to disguise that premise as a conclusion.

This is not actually the case. I don't think that atheists, generally, (or people, generally, for that matter) are entirely clear about the logical relations between premises and conclusions. Aristotle went out of fashion quite some time ago as a subject for teaching in school, and they threw out the good stuff with the bad, sadly. The trouble with atheists, such as Richard Dawkins, who claim science as their grounds, is that they believe themselves to be particularly rational people, and thus disinclined to doubt the rigorousness of their own arguments. Further, they often think that science itself is the heart and soul of reason, such that being a scientist makes one a member of the class of people most in touch with truth. The upshot of this is that Richard Dawkins frequently talks about the virtues of "critical thinking", and considers himself an expert in the subject because he's a scientist, without realising that he desperately needs some training in the subject himself. He's never likely to obtain it, however, because the teachers are in the philosophy department, which is considered "arts", not "science".

For a slight change of pace, then, without going off-topic, I'd like to explain how naturalistic thinking can come to permeate scientific thought, with the effect that most scientists treat naturalism as a strict requirement of science. This argument is meant to sound reasonable without being rigorously logical, and it's that kind of argument which is most seductive to those who relish in reason without understanding the full difficulties of producing a coherent argument.

Let's start with the idea that supernatural explanations do not explain, which was seen in the quotation from The God Delusion that I cited earlier. Without being too rigorous about the analysis (as rigour would expose flaws), what is the basis of this claim?

One of the key ideas behind this claim is what we might call the "supernatural lameness principle": the idea that supernatural explanations are the sort that simply says, "because God wills it". Clearly, if you can answer every scientific question with "because God wills it", you will have a fairly useless kind of science: all the questions have answers, but none of the answers are useful. A cursory analysis suggests that the problem lies in the fact that "because God wills it" is a teleological explanation: one which explains in terms of purpose and intention. What would be preferable is a mechanistic explanation: one which explains how things are happening, which is an aspect of the problem not addressed by "God wills it". Thus, useful science is necessarily mechanistic in its outlook. It won't do to ascribe God as the mechanism, either, because that would just be allowing the lame explanations back in through a semantic loophole.

With this idea elucidated, one can then see the appeal of another popular doctrine, which we might call the "replacement principle". This is the idea that because mechanistic explanations are better than supernatural ones, the former naturally supersede the latter, and thus science forever encroaches on the territory of religion, always replacing it and never yielding any territory back. Taking a long-term view of this, we see science perpetually on the rise, producing ever-more useful explanations of a broader range of things, and religion on the decline as its lame explanations are superseded.

So, let me now answer your earlier question, while playing Devil's Advocate. "Hasn't the term, supernatural, throughout history, always been definitially mutable from one discovery to the next?" No. The history of (useful) science has been to replace supernatural explanations with natural ones. "Supernatural" is merely a synonym for "not understood". As we come to understand the mechanisms behind the behaviour that we study, we replace lame supernatural explanations with superior mechanistic ones. Granted, it's often the case that the first such explanation is lacking in some regards, but it is still superior to the lame explanation that it displaced, and it may in turn be displaced by a better mechanistic explanation. The only sense in which "supernatural" is mutable is in the sense that our increased understanding of a subject (through mechanistic explanations, i.e. science) typically brings to our attention "new" areas of ignorance. They aren't really new, given that we have always been ignorant of them, but scientific progress makes us newly aware of this ignorance.

So there you have it: an attempt at playing Devil's Advocate. As I've said, I think that this line of reasoning is full of holes due to its lack of rigour, but I hope that I've managed to make the point of view look somewhat reasonable, and say the kind of things that Richard Dawkins would approve of. Nowhere in the argument do I profess an a priori commitment to naturalism -- but you can probably see that the banishment of the supernatural and the dedication to mechanistic explanations (which I have tried to present as necessary) entails a commitment to naturalism.

Not everyone will notice this relationship without it being pointed out to them, and attitudes towards the entailment can vary. That said, many people subscribe to the idea that "science disproves God" without realising that it is the definition of science (as I have presented it), not the products of science, that exclude God. When God is excluded at the root (the definition), it is quite simply inevitable that He will not be found in the fruit (the products). The fact that an inherently Godless science produces no evidence for God should come as a surprise to nobody.

There is one additional comment that I want to add at this point. It may seem harsh to describe the attitude to science that I have described above, which entails a de facto rather than premeditated commitment to naturalism, as "godless". After all, there are many theists who share this attitude to science, and it doesn't prevent them from being theists. I was discussing evolution and the nature of science with just such a theist over dinner only two weeks ago. I'm sure he would take exception to his model of science being called "godless". He sees plenty of room for God to cause the "random" events that drive evolution.

There's a lot that could be said about this "God of the gaps" model, but for now I'd like to swing our perspective around in the opposite direction, to those who explicitly embrace naturalism as a foundation of science, and see it as necessarily godless. The most candid and explicit example of this attitude that I know of can be found in Richard Lewontin's review of Carl Sagan's book, The Demon-Haunted World: Science as a Candle in the Dark. In it, we find some extraordinarily robust claims about the nature of knowledge. For one, Science is "the only begetter of truth".


Immediately following this, we see our first glimpse of how this ties in to philosophical materialism, and how the supernatural is thus considered synonymous with ignorance, as I have argued earlier.


It's not too surprising that philosophical materialism leads to "Science as the only begetter of truth" (or, in this case, that the latter is justified in terms of the former). Science is the study of the material world, and if you consider the material world to be the whole of reality, then science is the study of the whole of reality. This is a thoroughly naive view, of course: what of mathematics and logic, which are not material, yet without which there can be no science? Lewontin simply takes them for granted as truths, without conceding any ground to the supremacy of Science. Surely this is a problem, though? If mathematics and logic are truths which are not discovered through science, then they are exceptions to "Science as the only begetter of truth", and why should we think that they are the only exceptions? No doubt Lewontin would want to pick and choose -- mathematics is in, religion is out -- but this starts to look like a case of picking favourites rather than rational argument.

But let's not dwell too much on the difficulties which appear under analysis. Philosophical materialism is superficially supportive of Scientism, and this is the marriage we see here. But am I reading too much into this? Perhaps Lewontin has been exaggerating for effect? Not at all: he continues to drive the point home emphatically.


Science and the supernatural are presented as a dichotomy: a mutually exclusive and exhaustive set of alternatives. Sagan's message, says Lewontin, is simple: reject the "demons" and embrace naturalistic science. The dichotomy, however, is a shoddy one, philosophically speaking. Naturalism and supernaturalism are a dichotomy, by definition alone. The idea that science necessarily entails naturalism is the unstated premise which takes us to a dichotomy of science and supernaturalism. Lewontin does not use the language of logic, however: he says that supernaturalism has failed on some implied empirical basis, because it "rests on a set of beliefs and behaviors that fail every reasonable test." He also points out a widespread belief among scientists in the sufficiency of naturalism, as follows.


Again, this is superficially supportive of his position -- that is, until you remember that he presented a logical dichotomy, and the validity of that dichotomy rests on the idea that science necessarily entails naturalism. It's probably true that the bulk of scientists (most of whom haven't thought in any depth about the issue) consider mechanistic explanations to provide a fully sufficient account of observed phenomena, but even if that is so, it falls far short of establishing that science necessarily entails naturalism. Appealing to the intuitions of scientists on this matter seems like an unreliable method -- unless the idea was to present an argument from authority (in which case, "bravo, well played.")

Immediately following this, he makes an interesting distinction in relation to things believed for lack of evidence. This is interesting precisely because it is a distinction.


Note that the supernatural is not rejected for lack of evidence, but because of the alleged sufficiency of naturalistic explanations. Contrast this with little green men, whose existence would be an unequivocally material phenomenon. There, the lack of belief is justified by the lack of evidence. As I have said before, keep a close eye on this kind of thing: evidence against the existence of God can sometimes be presented as equivalent to evidence against the existence of little green men from Mars. Lewontin makes the distinction clear in this instance. The sufficiency of science is reiterated at the start of the following paragraph, for emphasis.


Lewontin goes on to talk about why he thinks Sagan's approach is not rhetorically effective. Much of what he says is interesting, but somewhat off topic given our analysis here. I recommend reading it, because it is quite candid about several things which those who take a position of scientism usually deny or downplay. I'll include one quotation, just to whet your appetite.


This is a refreshing change from most who present The Scientific Method as the One True Path to Objective Truth. Usually the argument is based on the purity of The Scientific Method to protect against irrational contaminants. But here we have a scientist who admits that scientists are not above rhetorical games and rationalisations. It's like a breath of fresh air. In any case, after Lewontin has discussed the social impediments which hinder acceptance of Science as the One True Path -- impediments such as the counter-intuitiveness of some scientific claims, the failure to deliver on extravagant promises (e.g. cure cancer), and the prevalence of "just so" storytelling -- he explains that an a priori commitment to naturalism is key to understanding why science is exalted above all else despite these foibles.


I don't think you'll find a more explicit statement of "materialism as premise, not conclusion" from a proponent of Scientism anywhere else. It does raise some questions, though. Is it reasonable to hold to this premise so dogmatically and rigidly? The basis for the position seems to be that it is necessary for proper science (the "science entails materialism" thing again), but this idea is the one that has gone begging for support throughout our analysis. Will Lewontin now provide the missing argument? Surprisingly, no: the next thing Lewontin says reveals that the dichotomy isn't a dichotomy at all.


There's got to be a "but" coming soon, right? Well no, actually. What follows is a socio-historical explanation of how one US demographic came to resent another US demographic, and how the introduction of evolution into the national school curriculum came to be viewed as another part of that social conflict, setting the stage for an ongoing battle of materialistic science versus fundamentalism. This flows into a brief discussion of the problem of democratic governance, particularly the dissociation of political rhetoric from actual expertise. It's not discussed in enough depth to warrant much comment, and it leads only to a conclusion that the problem is difficult, and we don't know how to solve it.


Obviously, this does not address the question we are asking here -- that of the relationship between science and naturalism -- so the problem remains. Reading between the lines, I can come up with no better justification than I already did in my previous post: the idea that "mechanistic explanations are better than supernatural ones", and thus an a priori commitment to naturalism is nothing more than a commitment to seeking the best explanations.

It sounds reasonable, when put that way, but there are obvious difficulties. For one, naturalism is an ontological commitment: it entails assertions about the existence (or not) of things, and puts those assertions beyond the possibility of scientific test, because it declares the naturalistic explanations better than the alternatives a priori, without the need for specific case-by-case analysis. In other words, the explanation that life evolved from non-life through natural processes would be "better than" the explanation that God created life from non-life through an explicit act of intervention even if the former were false and the latter were true. Surely any decent measure of "better explanation" is going to favour a true explanation over a false one?

At best, there seems to be a conflict here between Science as the "only begetter of truth", and the necessity of holding a naturalistic premise (or the use of naturalism to certify the science, which amounts to the same thing). The truth of the scientific conclusions will only be as good as the premises on which they rest, and the premises can't be verified by science.

In the final analysis, Lewontin's explicit premise of materialism seems either viciously dogmatic or detrimental to the idea that science is a reliable source of truth. I don't think he'd be happy with either choice in that dilemma, and I think that most proponents of Scientism shy away from giving materialism the status of "premise" precisely because they see this problem looming.