"Cigarette smoking has not been scientifically established as a cause
of lung cancer. The cause or causes of lung cancer are unknown."
Imperial Tobacco legal documents, as
reported in the Observer, 5 October 2003.

"Prove it" looks like a fair challenge to issue to anyone making
a claim you suspect to be false. And properly understood, that’s just what it
is. The problem is that an adequate "proof" almost always leaves a
space for the shadow of unreasonable doubt.

If proof demands absolute certainty, then arguably nothing can ever be proven.
Descartes,
for example, whittled down his beliefs until he was left only with those he
thought to be absolutely certain. All that remained was the fact that he existed.
Worse, subsequent critics have maintained that, if he were to be truly consistent,
not even that could be certain.

Descartes was continuing a quest for certainty which was probably launched
by Plato. In his famous simile
of the divided line in The Republic, Plato makes it clear that the highest
form of knowledge is of certain, immutable truths. Absolute certainty has been
the goal of many philosophers ever since.

However, running parallel to this "rationalist" tradition, more pragmatic
minds have had other ideas. Aristotle, for example, wrote, "it
is the mark of an educated man to look for precision in each class of things
just so far as the nature of the subject admits." Strict proof is not
possible in some subjects and the wise person thus accepts only as much proof
as is possible.

David Hume agreed, distinguishing
between matters of fact and relations of ideas. The latter include mathematics,
logic and statements which are true by definition. The former include all truths
about the actual world. Hume pointed out that we cannot establish these truths
according to the strict methods of deduction which we use with, say, mathematics.
Rather, past experience provides evidence for their truth; evidence which is
never logically watertight, but which we can judge to be sufficient.

Take as a simple example the boiling point of water. Logically, it does not
follow from the fact that all water to date has boiled at 100 degrees Celsius
(adjusting for impurities and air pressure, of course) that all future water
will do the same. But that doesn’t matter, because facts about the world aren’t
established by strict logical deduction. Rather, they are determined by a process
of generalisation from past experience.

Perhaps most importantly for present purposes, it is usually (if not always)
impossible to rule out on logical grounds alternative explanations. For instance,
armed with a bluffers guide version of quantum theory, you might point out that
is possible that the act of measuring temperature changes the substance measured,
and that in nature, water actually boils at something other than 100 degrees.
This is logically possible. But we have no reason to believe it to be true.
Nevertheless, if you want to insist on a higher standard of proof than we normally
do, you could say that the existence of this possibility shows we haven’t shown
beyond all doubt that all water boils at 100 degrees.

It should be obvious that on this understanding of what proof requires, no
facts about the world can ever be proved. Matters become murkier, however, when
we get to facts for which there is overwhelming evidence, but not quite as much
as our most well-established truths. Here is where we come across cases such
as smoking and cancer. (The issue here is complicated further by the difficulties
of establishing causal relations and differentiating causal factors and causes
simpliciter.)

Imperial tobacco seems to be exploiting both the complications of causality
and proof. What unites them, though, is the simple fact that, although there
is overwhelming evidence that smoking is a major contributor to increased incidence
of lung cancer, there is wiggle-room available for the sceptic to demand a higher
standard of proof and claim that science has not yet met it. Not all alternative
explanations have been ruled out and it remains at least possible that smoking
is not a major causal factor at all.

We should not be fooled by such sophistry. The fact that other explanations
are logically possible is a red herring, for such is also the case for the boiling
point of water. The fact that it is possible science has got it wrong is also
uninteresting: science is by its nature fallible and to demand infallibility
from it is to disobey Aristotle’s wise injunction.

Like the connoisseur of good vodka, the truth seeker should not demand 100%
proof. We have to live with a small measure of uncertainty. Proof only requires
us to move beyond reasonable doubt. It cannot require us to remove all possibility
of doubt whatsoever.

See also Absence
and Evidence