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.