May 21, 2009
The truth about errors
By Gary Hayden
In 1902, the German mathematician Gottlob Frege had every reason to feel pleased with himself. The second volume of his life's work, The Fundamentals Of Arithmetic, was about to be published. It was an important book, which he believed would provide the long-awaited logical foundation for mathematics. An enormous accomplishment, by any standards.
Then, a letter arrived on his desk. It was from the British philosopher Bertrand Russell. The letter pointed to a fatal flaw in Frege's logical system: one which undermined his entire work.
The Fundamentals Of Arithmetic was already at the printers. So Frege had just enough time to add the following appendix: 'A scientist can hardly encounter anything more undesirable than to have the foundation collapse just as the work is finished. I was put into this position by Mr Bertrand Russell."
The words were calm and measured. However, I often wonder how Frege felt as he wrote them. Depressed? Disappointed? Humiliated? Perhaps even angry? After all, it cannot be easy to see the foundations of your life's work collapse around you.
I like to think that he accepted the disappointment stoically. In any case, he took it on the chin. All credit to him for that.
The fact is that everybody gets it wrong sometimes. Actually, not just sometimes. Often. Any reasonable person must surely admit that lots of his opinions might, on close inspection, turn out to be incorrect. Being fallible is, after all, part of being human.
The trouble is that we do not know which of our opinions are the wrong ones. Individually, they all seem very reasonable. So although we may be willing to admit our fallibility in some abstract sense, it can be very difficult to face up to the possibility of being mistaken in any particular instance.
So what is the secret of avoiding error? Sadly, there isn't one. One thing that will certainly help is cultivating an attitude of openness to other people's viewpoints - especially those that contradict our own.
In this respect, scientists and mathematicians have a great advantage over the rest of us as they constantly have to defend their theories against criticism. Engaging with others' ideas is, for them, all in a day's work.
The rest of us can, if we wish, sail through life without ever subjecting our views - be they moral, political, metaphysical or religious - to sustained criticism. Indeed, most of us avoid alternative viewpoints like the plague and tend to gravitate towards those who hold similar opinions.
Even when we do enter into debate with others, we often do so with closed minds. We are so intent on justifying our own ideas that we do not really engage with what the other person is saying at all. Their opinions simply bounce off us.
Getting closer to the truth
We all have a natural inclination to think that the truth about something is the way it seems to us. Equally, we have a strong aversion to changing our views and admitting to being wrong.
In view of the fact that we are fallible, it behoves us all to examine alternative viewpoints as fairly and as vigorously as we can. In doing so, we may find valid reasons to modify our existing opinions. On the other hand, we may find that our opinions survive criticism, in which case we get to hold them in a richer, deeper and more fulfilling sense.
They say that everyone has a right to their opinion, but I sometimes wonder if an opinion that has never been challenged really qualifies as an opinion at all.
Far from resenting those who challenge our views, I believe we ought to be grateful to them. After all, they may present us with the possibility of replacing our current beliefs with new and better ones and perhaps moving just that little bit closer to the truth.
As author Jonathan Swift put it: 'A man should never be ashamed to own that he has been in the wrong, which is but saying... that he is wiser today than yesterday.'
Gary Hayden is a freelance writer who specialises in education, science, philosophy, health, well-being, travel and short fiction.