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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.



Steve Bradbury
April 8, 2011, 9:20AM
Thank you Murray for providing such a helpful reflection. I am currently facilitating a Master's level unit - "Sustainability, Climate Change and Justice" - in which the students and I are examining the causes and consequences of changing climate on some of the world's poorest and most vulnerable communities. A very common experience of nearly all of my students, when they have shared what they have been learning with folk in their churches, is anger and hostility. Inevitably, it seems, those that have expressed this anger very quickly move on to protestations regarding the scientific proof of Climate Change. Your reflections will, therefore, be helpful to my students. Thank you.
Angus McLeay
April 8, 2011, 12:05PM
Thanks Murray. It's been observed that a problem besetting the climate change debate (and evolution / creation) is the assumption that both sides deserve equal consideration. This approach ignores the fact that evidence and logic can differ dramatically. It is open to the charge of being radically postmodern in its approach to truth, ie. all views must allegedly have equal time because each is the 'equally valid truth' of a particular group / narrative.
Open debate is critical but climate change skeptics do not deserve equal respect merely because they have an alternative viewpoint. Likewise advocates for intelligent design should not qualify for a place in science curricula merely because students should be exposed to other views. The prior question is whether there is credible, significant evidence and reasoning behind opposing views. That seems to be more respectful of truth.
Alasdair Livingston
April 8, 2011, 12:08PM
Let's get our terminology right. In his intro, Murray Hogg speaks of "proving the truth of our beliefs". That makes no sense. If a belief could be proved true, we would call it knowledge, not belief. Doubt is an essential component of belief. Post-modern thought, so far as I understand it, abandons any adherence to public truth. What is true for you may not be true for me. Someone's truth is "a way of looking at the universe", one of many, all of equal validity. As for 2+2 =4, it can be said that it is just a tautology: four is the name we give to the sum of two and two. Is all mathematics tautologous, then, like a proof that all black things are black? Mathematics, once held up as the epitome of incontrovertible truth, has been dethroned by Kurt Godel's demonstration (I hesitate to say "proof") that, if I understand it correctly, a complete mathematical system cannot be certain, nor a certain one complete.
Ten years ago I was a firm believer in man-made climate change. Though I still hold it to be highly probable, I have grave doubts about the future disasters ascribed to it. They depend upon computer modelling. Remember that it was computer modelling, applied to financial risk analysis, that led to the Greed-Fuelled Catastrophe, otherwise known as the GFC.
Ian Packer
April 8, 2011, 12:23PM
Alasdair said: "Let's get our terminology right. In his intro, Murray Hogg speaks of "proving the truth of our beliefs". That makes no sense. If a belief could be proved true, we would call it knowledge, not belief."

That's mere semantics. All we are saying when claim something is knowledge is the degree of confidence we have or that we are agreed in our beliefs.

In addition, there is no such thing as 'post-modern thought'. There are a whole variety of ways of thinking that lay claim to the name 'postmodern'. Some are relativistic; some are not. Most accentuate the context-dependent and person-specific nature of our convictions. But that is quite different from the pop 'pomo' where "That's truth for you, but this is true for me."
Murray Hogg
April 8, 2011, 1:02PM
Alasdair and Ian:

Regarding Alisdair's comment that "if a belief could be proved true, we would call it knowledge, not belief" my response would be that the real issue here is that I was given 1000 words to make comment on the notion of "absolute proof." Give me an unlimited space to make a distinction between "belief" and "knowledge" and you'd get a considerably more nuanced discussion.

To rough out what that discussion might look like, I'd begin by offering the classical definition of knowledge as "justified true belief" - in which view, all items of our knowledge ARE beliefs - beliefs which are true, and which we are justified in holding. Note that this is a widely accepted technical definition of knowledge in epistemology and it is simply untrue, at a technical level, to say a belief stops being a belief just because it is true and justified (and therefore an item of knowledge).

Beyond this, suffice to say the literature on the questions of the truth and justification criteria is vast and I won't enter into either question here. Nor, I hasten to add, the widely acknowledged problem with the notion of knowledge as justified true belief - another enormously complex field.

The take home point from all of this, I would suggest, is that even on the simplest account of knowledge, the idea that we ever have "absolute proof" or, what would seem to follow, "absolutely certain knowledge," is problematic in the extreme.

Incidentally, thanks to Alisdair for pointing to Gödel's Incompleteness Theorem - had I been a little more on my toes at the time of writing the article it would have admirably served the purpose of demonstrating the tenuous nature of proof even in mathematics, arguably the most rigorous of disciplines.
Philip MacKinnon
May 2, 2011, 1:47PM
I find this article and the conclusions drawn by some of the correspondents troubling.
I fail to see how any comfort can be drawn from Murray Hog's arguments by those who support the theory of anthropogenic warming. He seems to be placing reliance in the "safety in numbers" argument; be that through jurors who arrive at the same conclusion, or the review of new scientific knowledge by peers.

It is not the cases where safety in numbers works that should be of concern to us, but those where it does not. There is not always safety in numbers; it is quite possible for the majority to be wrong. Within science there are many examples of this. Indeed it is the basis of Kuhn's theory of scientific development; a revolution displaces the current orthodoxy.

Which brings me to my second concern: the dangers of narratives. Whilst I agree that we construct narratives to make sense of the world (be that historical or scientific), narratives can also blind us to reality. We simply do not look at the world in the right way, ask the right questions. We may have a lot vested in our narrative and not wish it to be wrong. In consequence, far from the ideal of trying to falsify our narrative (as Murry suggest we do) we look for evidence to support it. There is evidence of this occurring in medical research, where reviews of clinical trials suggest there is an overestimation in favour of the clinician's hypothesisthat where a trial is not properly blinded or randomised.

Significant progress in knowledge can occur where a minority adopt and test a different narrative: they are able to think outside the prevailing orthodoxy. (this could be one juror challenging the assumptions of the majority) This point is important, it is unlikely the majority opinion will identify this new way of looking at the world, and the majority may actively oppose it.

This brings me to my main point: the importance controversy. An important mechanism in the progress of knowledge is to allow debate, not silence it. If those who contest a viewpoint are wrong, it is likely that sooner or later they will be shown to be so.

Shutting down debate, for example on global warming as some correspondents are suggesting, is absolutely wrong. It is an act of considerable arrogance and smacks of Marxist historicism. On a complex issue such as the mechanisms of climate change--given our current knowledge--there is room for an ongoing debate.

In summary I am troubled by the activities of Ethos which seems to be linking a belief in anthropogenic global warming with Christianity. It is not starting where I suspect many Christians and other members of the community are; and that is the debate about climate change itself.

I challenge Steve Bradbury to run a creative controversy activity in his unit which asks the fundamental question of climate change "is human activity resulting in global climate change" Let his students have the fun of doing that!
Murray Hogg
July 16, 2011, 7:43AM
Dear Phillip MacKinnon,

My apologies for taking so long to respond to your comments above.

Let me be very clear that nowhere did I argue that the decisions of jurors, or of scientific peer-review, are beyond question. Indeed, the point of the article is precisely to point out that our speculations, scientific or otherwise, are _never_ absolutely certain.

I argued that, in the absence of any means of arriving at absolute certainty, methods such as the juror system or scientific peer-review are, essentially, the best we've got.

Is this advocating "safety in numbers"? To some extent, yes. But that "safety" is only as secure as the process in question: whether that be the juror process, the scientific peer-review process, or whatever. Such "safety" is, in other words, far from absolute. If one wanted "absolute safety" one would need "absolute proof," and, as the article clearly states, such proof is rarely forthcoming.

Let me point out that I specifically mentioned scientific knowledge in order to waylay any charge that I was somehow privledging scientific claims above any other. I regard no scientific claim as absolutely proven and I consider that the article makes this point quite clear.

I simply reiterate the point of the article: in almost no instance do we have anything like "absolute proof" and in its absence we have to find strategies which enable us to do the best with what we've got.

I do not regard anthropogenic global warming as an exception to this general comment.

Kindest Regards,
Murray Hogg
Ian Robinson
September 6, 2011, 12:22PM
ON a slightly different tack, I support the notion that there is a risk inherent in the task of deciding upon evidence, looking for coherence (is it consistent?), congruence (does it work?) and elegance (a favourite criterion in science, albeit entirely value laden).

Switch to the arena of aplication. Anyone who seeks to make a difference in anything that is pressing upon human wellbeing will know that same risk. While we can sit back and see both sides, something I love to do, people's actual lives require actual action, maybe wrong or incomplete but at least better than a spectator's level of concern.

In Christianity, the action that arises from compassion is primary, not the action that arises from certainty. Note that I have just reversed the compass of the argument there. I am not privileging certainty based on axiom. So if we have no 'proof' in faith, it is of one piece with the level of risk that calls faith into action ina broken world.

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