A deep-seated human desire is for certainty, for sure foundations, for guarantees in every area of life. Everyone wants to be sure that the vaccines are guaranteed to provide protection and that, for certain, they are safe. We look to science for this assurance. But sometimes the scientists differ among themselves, and the history of science has many discarded theories and predictions.
A jury must be convinced that the evidence points to a conviction 'beyond reasonable doubt'. But, as we know, there are wrongful convictions. And, as the Jerome Kern song tells us, you know your true love is true because something there inside cannot be denied, but alas, later we smile and say,
Smoke gets in your eyes.
Years ago, I was on a hospital committee which sent me to arbitrate between a junior doctor and an irate patient who had complained about her. When I inquired what had happened, the patient said that he had asked the doctor whether the proposed treatment could be guaranteed to be successful. The doctor had apparently snapped back: 'If you want a guarantee buy a toaster'. I had some difficulty in keeping my face straight! Fortunately, I was able to say a few soothing words to the patient and asked him to excuse the doctor, who hadn't been to bed for 48 hours and was not likely to be at her sunniest. She certainly didn't require any lectures from me. Perhaps she should have made the point in a more tactful way, but doctors, patients, all of us, must live with uncertainty.
The quest for certainty goes back to the world of the ancient Greek philosophers. They had to meet the challenge of sceptics who cast doubt on the existence of real knowledge, of what we could be certain of. One sceptical argument drew attention to the many ways in which our senses can deceive us: mountains in the distance seem a different colour from the way they look close at hand; water can seem cold to one hand but warm to another; optical illusions and hallucinations occur. How can we be sure that we are not being deceived all the time? Other sceptical arguments drew attention to the way in which natural language can deceive us – language singles out certain phenomena as salient, but there will be other truths, other ways of looking at a problem.
How do we know which is the correct way, or indeed if there
is a correct way? One Greek sceptic – Diogenes of Sinope – was so impressed with sceptical arguments that he lived in a barrel and when asked a question he simply wagged his finger.
Politicians frequently claim that their policies are 'absolutely clear' and they seem immune from scepticism. They can move seamlessly from one position of absolute certainty to another. I cannot envisage Boris Johnson living in a barrel and wagging his finger.
Plato was convinced by sceptical arguments about the reliability of the senses. But he did think that certainty about the world could be found via mathematics. He imagined the world as created in structures (the Forms) that could be understood through the language of mathematics; even if the senses could not provide certain knowledge, mathematics could. This view became hugely influential at the start of distinctively modern science at the beginning of the 17th century.
There used to be a popular belief that bad Catholics refused to look through Galileo's telescope and so did not accept the Copernican view that the Earth is moving round the Sun while spinning on its axis. But is wasn't just bad Catholics who disagreed. The best observational astronomers of the time, such as Tycho Brahe, disagreed with Galileo and produced overwhelming empirical arguments against his view. For example, if the Earth is spinning on its axis, why is there no strong centrifugal force throwing us off its surface? Why are we not able to observe changes in the apparent position of the stars due to the Earth's orbit (stellar parallax)?
Granted these and many other scientific arguments of observational science, why did Galileo persist in this heliocentric view? The answer is that, unusually for the time, some of the
Dialogues of Plato were being taught in a corner of North Italy. Galileo became familiar with them and became convinced of Plato's claim that, no matter what the empirical observations of the senses indicated, the Copernican system worked better mathematically and it was therefore bound to be true. It was mathematics rather than empirical observation which gave the impetus to present-day science.
There is no doubt that mathematics, and the kind of certainty it provides, is the basis for present-day physical science, and it has been unbelievably successful. The astrophysics community expressed anxiety that their probe to Mars – millions upon millions of miles away – had landed four minutes earlier or perhaps later than predicted. Try a train from Glasgow to Edinburgh.
There is, however, a downside to this. The impression has been created that unless there are numbers there can't be satisfactory science. Lord Kelvin expressed that view in so many words. In 1907, he wrote: 'When you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind'. But anatomy, for example, seems to me a perfectly respectable science but it is hardly a mathematical science, and the same is true of many areas in the biological sciences.
The main problem with numbers is that they can be used to give the impression of certainty for what is just guesswork. For example, I read in the newspapers that as a result of lockdown some children will earn £40,000 less than others. Really? How can that be known? It is just guesswork, and adorning guesswork with numbers suggests a totally misleading precision.
The general point is that if you are going to count something, there must obviously be factors that you can count. But are they the correct factors? I once read a journal paper about 'measuring' the doctor/patient relationship. The aim of the study was to discover whether a doctor was conducting a consultation in an optimum way. The factors selected for 'counting' included the making of eye contact, the angle of the doctor's chair, and how far the doctor was silent and allowed the patient to speak. But are these the right factors? They may just reflect the views of the researchers on what they think are the right factors for a successful doctor/patient consultation. Indeed, there may not be
any right factors of general applicability.
Some patients might feel embarrassed at being looked at; some might prefer that the doctor made suggestions for them to agree or disagree with; some might wonder why the doctor doesn't sit behind his desk. The investigator must choose certain factors if numbers are to be used, but they might not be appropriate for either a given doctor or a given patient. Doctors and patients have their own personalities and the attempt to standardise a consultation by using numbers is pseudo-science and very unfortunate.
Aristotle writes that it is the mark of an educated person not to look for certainty anymore than the nature of the subject permits. In some areas of knowledge, numbers may be false friends – probability is the guide of life, even when buying a toaster.
Robin Downie is Emeritus Professor of Moral Philosophy at the University of Glasgow
