The Elusive Notion of Proof
Wednesday, 6 April 2011
| Murray Hogg
One of my more interesting experiences was to serve as a jury member in a court-case where the aim was to determine “beyond reasonable doubt” whether the accused was guilty or not. This seemingly simple task was complicated by the fact that none of the seven witnesses told the same story! On the surface, it would seem that there would be no way to reach a decision but by the end of the trial all twelve jurors had decided that the accused was, indeed, guilty “beyond a reasonable doubt.”
Two lessons from that experience have remained with me. The first is that many of our speculations regarding proof are fairly abstract and not particularly helpful when it comes to making decisions on the basis of limited or conflicting evidence. When faced with such difficulties we often suspend judgement, but that’s not an option in some circumstances.
The second lesson concerned the way people go about processing information and arriving at decisions. Basically, the jury found that the best way to reach a decision was to construct a narrative of events which made sense of the evidence. As a process it all seems very subjective, until you realise that all twelve of us ended up in agreement – beyond, of course, what we regarded as reasonable to doubt.
It’s tempting to contrast this sort of thing with areas where we think we can reach a decision unsullied by any subjective opinion. Perhaps the best instance of this is in mathematics where “proof” is a very robust notion. What, after all, can be more certain than 2 + 2 = 4? But even here the situation is really more complex. As Scottish philosopher Thomas Reid pointed out the first thing a mathematician does after developing a complex proof is double-check it with other mathematicians. Should they disagree with the proof, then it’s back to the drawing-board. It turns out that even in the most rigorous of disciplines we find that the opinions of other people matter very much indeed.
Now, most of life falls somewhere between these two extremes. Sometimes, as in the court-cast I mention, we have a great deal of data, some of it contradictory and uncertain. Other times, as in mathematics, things seem rather more clear-cut. Most of the time, however, we find ourselves somewhere in the middle. I want to suggest that our decision making always involves some degree of personal judgement. We need to decide which data is important, how to structure it, and, importantly, just how much certainty we are going to ascribe to the results.
In my view, both religion and science lie somewhere in this middle region. In respects of the former, who can deny that Christian faith is based on less than absolute proof? Personally, I think Christians have good evidence from a range of sources, but ultimately it’s a personal judgement as to whether the Christian narrative makes the most sense of that evidence or not.
Why this lack of absolute proof? Well, while it’s a bit clichéd to say, I think that God gives enough evidence for those with eyes to see. The problem isn’t with the amount or quality of evidence, the problem lies with human nature. We do, after all, have a tendency to see what we want to see, to make the evidence conform to our opinions rather than our opinions to the evidence. That being the case, add as much evidence as you like, even to the point of absolute proof, and you won’t overcome the self-deceptive tendencies of the human heart—tendencies which become particularly acute when faced with the deeply personal choices called for in matters of religion.
But what of science? Is there more hope for objectivity and certainty here? After all, science is often touted as the best, the most certain, way of knowing we have. Well, in my university days as an engineering student, we used to bait science students with the claim that engineering was “real” science whereas physics, chemistry, biology, and so on were “just theoretical.” It was an untruth, as inter-disciplinary rivalries often are, but the logic by which we justified it had some merit. Engineers, we figured, always know when they get it wrong because the bridge falls down.
Unfortunately the sciences often lack this sort of inbuilt error checking mechanism and so scientists have to find other ways of confirming their speculations. The most powerful of these is the process of peer-review—a fancy way of referring to the practice of getting people whose opinion you trust to run an eye over your work. Another powerful technique is experimental confirmation—basically you devise ways to put your work to the test in order to make or break your theory. Yet another is to construct a narrative which makes sense of the data you’re trying to explain—evidence the power of Charles Darwin’s theory of evolution which, whether you love it or hate it, works precisely because it tells a story which makes sense of an overwhelming mass of otherwise confusing facts.
Whether in religion, in science, or in the court-room, however, it turns out that there is rarely, if ever, such a thing as “absolute proof.” Basically, we have the evidence we have, and we have to do the best we can with it. Should the question be too important to leave undecided the need for making the best possible decision becomes even more acute. There are no definite rules we can apply to ensure our decisions are correct “beyond a reasonable doubt”—this is the reality of the finite human situation. Who we marry, whether we take that job, whether we chose faith over unbelief, whether we accept a scientific theory, whether we send somebody to jail, in all of these we can do no more than weigh the evidence, listen to other opinions, and then exercise our best judgement in making a decision for which we ourselves take full responsibility.
Murray Hogg has degrees in Engineering and Theology and is currently completing a post-graduate thesis in epistemology (theory of knowledge). He is a Fellow of ISCAST, an Australian science-faith organization.