Chances are

This week I want to critically examine this idea that, while we can’t establish any certainty regarding God’s existence, we can still reasonably believe/disbelieve on the grounds of probability. This is a line we often associate with atheists, who in the spirit of scientism, are careful to state they can’t disprove God’s existence, but then add that establishing His existence is very, very unlikely is sufficient cause for their disbelief. And, apologies for repeating this point, it is. To establish something is likely to be true is a good reason to believe in it. It’s how we figure our way through an uncertain world. To cling only to those things we can be certain of would get us nowhere.

There are also a few theist arguments that appeal to probability to make their point, and again, if they could be made credible, I’d be swayed by them. What I would like to suggest in this post, is that the types of issues at the heart of the God/no-God debate are such that probabilistic thinking is of little, if any, help.

So, to begin at the beginning, what do we even mean by something being likely, or probable? That’s by no means a simple question. Indeed, a long time ago when I was training to be a maths teacher, I was told that a good rule of thumb regarding how difficult a student would find a new topic is to ask, ‘how long did it take humans to come up with this idea?’ Given that mathematical treatments of probability arose comparatively recently (17th century) it’s fair to assume that we don’t necessarily carry a particularly strong instinct for this sort of thinking. Certainly that’s been my experience in the classroom.

Probability, or likelihood, is the study of what constitutes a reasonable expectation, given what we currently know about a situation. In real life, it’s often a proxy for missing information. I get in my car and drive to work, fully expecting to arrive safely. I base this upon my driving history, and the history of accidents in the area. The crucial information I lack, is whether or not a particular tired, drunk, distressed or distracted driver’s journey is going to coincide with my own. In the absence of such information, I go with the average, and mostly the average is right (safe driving builds in a degree of just-in-case prudence, it’s why we keep our hands on the wheel, look out for hazards and stick to the speed limit).

The first thing a student trying to come to terms with probability will notice is the difficulty of meshing the known average with the individual case. Yes, it’s highly unlikely you will the lottery, and hence buying a ticket is on some level a bad idea – unless you’re the person who wins, in which case the mathematician’s advice was nonsense. Probability deals very well with long run averages, and slightly less well with individual risk assessments.

Another thing to notice is that probability works best in an unchanging environment. It generates, ‘all other things being equal…’ statements very well, yet most often in the real world, it’s the unknown variables that we’re trying to deal with.
‘Is this ocean safe to swim in?’
‘Sure, there’s only been one shark attack here in the last hundred years.’
‘When was that?’
‘About half an hour ago.’
The long run average isn’t always the whole story.

Another trap for the unwary is the tendency to be overly impressed by rare occurrences. Or, as the old aphorism goes: ‘one in a million events happen every day.’ To use the common example, shuffle a pack of cards thoroughly, then examine their order. The prior probability that that particular order should come out is astronomically small, teetering just this side of the impossible, and yet in this case a highly unlikely event is also inevitable.

We know too, from the history of the courtroom, that we common folk can be easily suckered by the way the numbers are presented. A man is charged with murdering his wife. The prosecution point out he is known to have been violent to his partner in the past. The defence come back with, yes, but of all the women murdered in this country, only a tiny percentage were murdered by a partner that was previously violent toward them (any similarity to well known cases purely coincidental, you understand). And, sometimes the jury buy this. The more relevant statistic asks, of those women who are murdered, and have previously been subjected to violence by their partner, in what percentage of cases what that same partner the murderer (answer, most of them.)

So, probability is tricky to get our heads around, and is tremendously easy to get wrong. And yet, most of the time, likelihood is all we have to go on. Ideally, in making ‘how likely is it?’ calls, we are taking the best available data into account, and combining it with those other factors we are also convinced are relevant (this, in a very simplified version, is what Bayesian probability is about, seeking a greater degree of corroboration for those claims we already have reason to believe are unlikely).

The problem is, we don’t live in the ideal world, and as every courtroom lawyer understands, often when people judge something to be unlikely, they’re not talking about probability at all. Rather they’re talking about plausibility, how likely something feels to them, given their current set of beliefs and understandings. So lawyers play not just to the evidence, but also to the emotions and prejudices of those weighing it.

And, to arrive belatedly at something resembling a point, when it comes to discussions of God, my sense is that almost overwhelmingly it is the second type of ‘probability’ that is being invoked. People understand full well that saying they believe something because they judge it to be probable, sounds much more respectable than saying they believe it because it feels right to them.

So, my question to the atheist who wishes to claim ‘probably there is no God’ is how did they do that particular calculation? What were the factors they weighed, measured and computed in order to reach this conclusion? Is it only twenty percent likely there is a God, three percent, one in twelve thousand? It feels like a rhetorical device is being employed, rather than some means of calculation. Although I’ve often seen the atheistic claim of improbability, I’ve never seen anybody try to establish the grounds for the calculation (if you do know how it works, please do let us know).

On the other side, there was once a very powerful probability argument employed in favour of a designer. It was the argument that looked around the world, observed the exquisite interlocking design of nature, and concluded that the chances of this simply shaking together by chance were immeasurably small, and hence must be discounted. The argument from design. Darwin provided us with a mechanism (natural selection) by which the probabilities could be re-imagined, and the argument lost its sting. It stands as an excellent reminder of just how hard it is to employ probability arguments to novel and complex situations.

We still often hear the fine tuning argument, which is sometimes an attempt to use probability to make a case for God’s existence. The argument goes that in principle the universe could have turned out vastly many ways, and almost all of them would have led to either a universe that couldn’t sustain itself, or one that couldn’t sustain life. Hence the fact that we are here at all is extremely unlikely, if chance were the driving force. The reason I’m not moved by this is that it seems to me to be too much like the pack of cards argument. Given there was a universe at all (and let us leave the bigger questions beneath this for later) then its parameters had to be unlikely, by definition. So why be particularly impressed by this particular unlikelihood? There’s an emotional reason, I grant you, but I can’t see the logical one.

And so, to conclude, too often putative arguments about likelihood are actually arguments about gut instincts. Things just feel unlikely, and so we dismiss them, and then dress them up in the language of probability. Which leads on to the related question, when is it reasonable to trust our gut instincts? And that’s a point I promise to come back to.

11 thoughts on “Chances are

  1. Another way to approach this would be divide everything into ‘the known’ and ‘the unknown’. If god(s) exist then it (they) obviously exist in the unknown.

    We might think of religions as ‘having a stab in the dark’ as to what might exist in the unknown. Yet they’ve all stick to supernatural beings (based on human beings) capable of creating everything that we find in (what is to us) ‘the known’.

    Why is there no speculation as to *what else* might exist in ‘the unknown’ besides these religious deities?

    And what are the chances (what is the probability) that any of these religions have got it right, despite having made only one guess?

    To make an earth-bound analogy…… a tribe growing up on an isolated island in the Pacific with no outside contact might intuit or logically deduce that there must be more stuff happening on this planet than their small island and the surrounding ocean. We would expect that. But what is the probability of them being able to accurately deduce or intuit the existence of North America…… or New York….. or Manhattan …. or the Empire State Building…. or Broadway….or the current mayor of New York?

    It is far more likely that they will just imagine other islands ‘out there’ …. islands which are quite similar to their own….. perhaps bigger, perhaps more exaggerated and so on.

    And isn’t that what most religions’ gods are in essence? … exaggerated projections of our experiences in the known directed at the unknown?

  2. Information content is the negative base-2 logarithm of probability. If, as theists tell us, God is eternal and omniscient, then he must have infinite information content, which makes the probability of his existing precisely 0.

  3. Hi Spinning

    Another point I should have made, and your example raises it nicely, is that probability works best when we can agree on the baseline assumptions. We think of the chance of rolling a six with a die as one in six precisely because we assume the die is fair, for example. So, if we do indeed assume that religious belief is, as you say, the process of projecting knowns onto the unknown, then it absolutely follows that the chance of that projection hitting the target is very low.

    However, given that it is this very assumption that we are trying to assess (what if it’s the process of opening oneself to information regarding the true nature of the universe, for example?) we can’t reasonably apply probability to assess the assumption that is needed to get the probability calculation off the ground. This is what I mean when I say that what appear to be calculations are very often the repackaging of prior beliefs.

    Now I don’t personally carry the model of a God who is communicating his nature to us and through us, so your description feels highly plausible to me. But that’s my intuition at work. And intuition does not a probability make, I don’t think.


  4. Hi Daniel

    Should we, strictly speaking, say the probability of us discovering his true and infinite nature through a process of guessing is zero? On this I suspect you and the theist would be in agreement. The probability of picking a correct raffle ticket does indeed vary inversely with the information content (say number of tickets) of the lottery, but the probability of a winning ticket existing (given they are all sold) does not.

    And, as with my previous comment, this neat trick works only if we assume in advance that the situation does not involve a God who both exists, and actively leads us to discover that existence. In this case, as with the rigged lottery where you are slipped the winning ticket in advance, the usual rules of probability do not apply.

    So, I shall stick to my assertion that it is very difficult to get a probability calculation off the ground that isn’t, at heart, question begging.

    That said, I may well have been dense and misread your intent here. I trust you’ll correct me if I have.


  5. Burk says:


    “So, my question to the atheist who wishes to claim ‘probably there is no God’ is how did they do that particular calculation? What were the factors they weighed, measured and computed in order to reach this conclusion?”

    1- The (lack of) necessity of the god explanation for anything that we have actually explained.

    2- The evidence for god on its own terms- the signs and wonders of the olden days, which on current observation and on minimally skeptical reading seem absent.

    3- The conflicting nature of the various gods people have believed in.

    4- The obvious psychological origins of the god concept, from our deepest archetypes and longings. Now! With the added high-tech feature of everlasting life in heaven!

    5- The typical mind-set of believer and their scriptural supports, which are intellectually hermetic and mono-maniacal. The Koran is an excellent example. All truth is in the Koran, etc… It is very telling that deism has such low repute among religious believers. But this is a consistent belief, coherent with what we (don’t) know about the origin of the cosmos and its rather clockwork evolution since then. But since religious belief has so many important psycological elements, (morals! hope!), deism is badly insufficient, adn thus is not “believed”.

    6- The nature of current “sophisticated” cases for god, such as that is the explanation for “everything”. Which sounds very much like an explanation for nothing.

    7- The inverse employed by intelligent design-ists, saying that the “probability” of the cosmological constants being what they are, or of life emerging or evolution happening are vanishingly small. Compared to what? As you say, we have zero comparison in the cosmic case, so citing probability is not relevant. In the case of the origin of life, we at least have a going theory, in terms of chemistry, etc., but still, employing probabilities is difficult. And evolution more generally.. that is not a problem at all for those knowledgeable in the field, whether one disparages the probabilities thereof or not.

    So, I am not offering probabilities based on any quantitative basis, but on various psychological bases, which are the mechanism one turns to when exposing a con game that deals in studiously unprovable claims. Conversely, if religionists cared to make even one disprovable claim (like the recent end-of-the world claims, for instance), our ability to diagnose their probabilities would be greatly enhanced!

  6. Hi Burk

    Yes, I think the psychological case for likelihood, the plausibility model, if you like, is the thing that drives much disbelief.

    Next time I want to look more closely at the link between evidence and belief, and specifically the principle that we reserve judgement, or perhaps actively disbelieve, when we can’t establish any solid shared evidence. That said, I’m not sure exactly where I stand on this, rather hoping it might become clear as I write!


  7. JP says:

    Hi Bernard,

    The way I see this is not so much about evidence as simply about having reasons to adopt a particular belief. This is somewhat in the spirit of Bertrand Russell’s “… it is undesirable to believe a proposition when there is no ground whatever for supposing it true.”

    In the case of God, or gods, the task is to determine what reasons (of any kind) we have to believe they exist (leaving aside the question of what exactly it means for God to exist at all). If every reason anybody can come up with is found wanting, then, at the end of the day, the case for God reduces to… nothing at all. If so, why then consider the “God hypothesis” to be credible?

  8. Hi JP

    I think that’s fair. The question then becomes, presumably, what does or doesn’t constitute a reason? Theists may well choose to jump in here, but my presumption is that reasons offered may include pragmatism (and rejecting this requires us to show that beliefs regarding the physical world aren’t themselves founded on pragmatism, which I always find to be irksomely difficult) consistency with accepted beliefs (particularly moral beliefs), consistency with personal experience, or perhaps offer the alternative principle, that so long as there is no defeating evidence, one is warranted to believe.

    I’m going to have a crack at addressing all three of these, and suspect the first of them will be the most difficult to deal with, particularly because principle’s like the one you mention form Russell themselves have a whiff of pragmatism about them (undesirable on what pragmatic terms?)


  9. JP says:

    Hi Bernard,

    Yes, there are very intriguing questions around this topic. I’m looking forward to see how you handle all these.

    As for BR, presumably he was aiming at finding true beliefs and he would define desirability in this sense. However, I agree that other pragmatic considerations can be at play, for example leading one to adopt beliefs because they somehow “fit” better.

    Opinions will no doubt differ as to what constitutes a good reason. Nevertheless, I think it’s possible to compare the merits of different approaches. For example, a psi proponent (PP) may find anecdotal, non reproducible results good enough while a skeptical observer will think otherwise. However, both should be able to agree that the evidence put forward by PP is non reproducible.

  10. Darrell says:


    I agree with you that the whole probability argument is inconclusive and each side can make a decent case in that regard. But it ultimately fails because it still involves an interpretation of the shared evidence.

    What happens then is the theist (or fundamentalist religious person) then turns and makes the same calculation as Burk does and says, “So, I am not offering probabilities based on any quantitative basis, but on various psychological bases, which are the mechanism one turns to when exposing a con game that deals in studiously unprovable claims.”

    And they would simply say that the assertion “God does not exist” is an unprovable claim. In other words, we get nowhere.

    Putting that aside, when you write, “…and specifically the principle that we reserve judgement, or perhaps actively disbelieve, when we can’t establish any solid shared evidence…” do you see that you are, by default, privileging empiricism? Additionally, you are appealing to a “principle” or an underlying part of a greater narrative–a meta-belief.

  11. Hi Darrell

    I agree, if one could establish such a principle, it would be a claim to give empiricism, or some reduced form of it perhaps, a privileged position. So, is such a principle defensible? I’m not sure it is, but I’ll try to expand on that next time.


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