Is that a fact? by Keith Devlin
This is a copy of a web-page: Devlin’s Angle: Is that a fact? by Keith Devlin, from May 1998, originally published in the public domain by the Mathematical association of America, at times it is not available on that association’s website.
Facts about brain science don’t often crop up at cocktail parties. Indeed, there is only one that I know of, and that’s the well known tidbit that our brains do not grow any new cells after we reach adulthood. I’ll bet that, like me, you have known for years that, as far as the brain is concerned, it’s all down hill from the moment we get our driver’s license. Every day, another ten thousand cells die. Or is it a hundred thousand? A million? No matter, it’s a bunch, right?
Having this factoid at the ready provides a great line of escape when we find ourselves talking to someone whose name we can’t quite recall. We look sheepish and blurt out, with an embarrassed laugh, “Well, you know, my brain cells have been dying off by the millions for the past thirty years (or whatever), and the old memory isn’t what it used to be.”
Unfortunately, scientists have just discovered that this old stalwart piece of scientific knowledge isn’t true after all. In an article just published in the Proceedings of the National Academy of Sciences, Dr. Elizabeth Gould of Princeton University and her colleagues present evidence showing that our brains continue to generate new cells throughout our lives.
Well, actually, the crucial experiments were performed not on people but on marmoset monkeys, but if you’re a brain scientist, that’s close enough apparently.
The new discovery has enormous implications for future developments in medical science, raising the possibility of treatments for victims of stroke or Alzheimer’s disease, by finding ways to stimulate the brain into producing new cells to replace those killed or affected by the disease.
But what does it tell us about the nature of scientific knowledge when something that has been regarded as a scientific fact for decades, by expert and layperson alike, suddenly turns out to have been false all along? What else might follow? Will we wake up tomorrow to find that water can sometimes flow up hill, or that E is not, after all, equal to m-c-squared? Is scientific truth no more reliable than the word of a former White House aide in pursuit of a lucrative book deal?
Speaking as a scientist, the most honest answer I can give is that this kind of unexpected reversal probably won’t happen in the two cases I just cited. But I can’t be absolutely, 100 percent sure. No one can. Because science is not about determining the absolute truth. In science, there is no such thing. What the scientist does is make careful observations and take measurements as accurately as possible, and then look for an explanation that best fits those observations and measurements. If that explanation is sufficiently complete, and encompasses a variety of other observations and measurements, it is called a “scientific theory”. The theory of gravity and the theory of evolution are two of the best known examples.
Despite what you sometimes read, a scientific theory can never be proven. The best that the scientist hopes for is “confirmation” - that further experiments, observations, or measurements agree with predications made on the basis of the theory. Confirmation can make the scientist more confident that the theory is “right”. But there are no cast iron guarantees.
In contrast, just a single experiment or observation can be enough to overturn a scientific theory. Though you can never prove a theory is true, you can “easily” prove one is false. This understanding of how we obtain scientific knowledge was captured some years ago by the philosopher of science, the late Sir Karl Popper, who talked about the purpose of scientific experiment being to seek to “falsify” a theory. The more resistant a theory is to attempts to being proved wrong, the more reliable we can take it to be.
This is why, for all that scientists may occasionally find themselves with egg on their faces, as when it is discovered that human brains generate new cells just as do other parts of the body, the scientific method continues to provide us with the most reliable knowledge we can ever have. Unlike in other walks of life, “scientific truth” is not decided by an opinion poll, by a ballot, by persuasive rhetoric, by passing laws, or by force or violence. In science, “truth” is determined by the observed facts. Once Dr. Gould and her colleagues had made their crucial observations and others had confirmed their findings, the matter was regarded as settled. The old king - no new brain cells - was dead. Long live the new king. Far from diminishing our faith in science, such about face should make us more confident.
Of course, mathematics is quite different, isn’t it? In mathematics, once something has been proved, it remains true for all time. Well, yes, that’s true - up to a point. In axiomatic, pure mathematics, once a mathematician has established the truth of a statement A on the basis of the axioms, then, provided the proof is correct, A will still be true (on the basis of those axioms) a century from now, ten centuries from now, indeed for all time. But this nice, clean picture is misleading on at least two grounds.
First, except for the simples of cases, it is never an easy matter to be certain a given proof is correct. I examined this problem in a playful mood in a previous column in this series.
Second, though many mathematicians pursue their entire careers without any concern for the real-world origins of the systems they study or for the applications their work may lead to (and in my mind there is absolutely nothing wrong with adopting that approach), the fact is that mathematics is just one of a number of conceptual systems (or ways of thinking) that humankind has developed to help us to understand the world we live in and to improve our lives and increase our chance of survival (both our personal survival and the survival of our genes). As it happens, it is one of the most successful of those conceptual systems, and lies beneath many of the others, including all the sciences. But it is still just one among a number of conceptual frames. And when we think of mathematics as a conceptual framework to understand (or predict) the world, a result in pure mathematics, proved on the basis of certain axioms, is only as “true for the world” (and hence only as useful) as those axioms apply to - or match - the world.
One of the most obvious examples of a change in the way an axiom system was viewed occurred with geometry, of course. For two thousand years, Euclidean geometry was regarded as “the geometry of the world we live in.” When non Euclidean geometries were discovered in the nineteenth century, they were at first treated as mere curiosities invented by mathematicians. But when Einstein’s theory of relativity replaced Newton’s framework, we were forced to acknowledge that Euclidean geometry was not, after all, the geometry of the universe. It provides a good approximation that serves us well in most earthly circumstances, and several unearthly ones as well. But from a scientific standpoint, Euclid’s axioms do not provide a sound basis for proving mathematical results about the universe we inhabit. After Einstein, the old “mathematical truth” had to be discarded and replaced by a new one. The king is dead. Long live the king. I think such a change is just as good for mathematics as for other sciences.
Rationale: Every logical argument must be defined in some language, and every language has limitations. Attempting to construct a logical argument while ignoring how the limitations of language might affect that argument is a bizarre approach. The correct acknowledgment of the interactions of logic and language explains almost all of the paradoxes, and resolves almost all of the contradictions, conundrums, and contentious issues in modern philosophy and mathematics.
Please see the menu for numerous articles of interest. Please leave a comment or send an email if you are interested in the material on this site.
Interested in supporting this site?
You can help by sharing the site with others. You can also donate at where there are full details.