Stuart Altmann on wed 23 jul 97
"...You can't prove a negative -- i.e. "global warming is *not* happening."
--Karl Platt
That you can't prove a negative is a common but unfounded belief. Of
course, empirical evidence never "proves" any statement, not in the sense
that, say, a mathematician proves a theorem. Empirical evidence can only
provide evidence that is consistent with (or contrary to) a statement or
hypothesis. Thus, the claim that negative statements can not be proved is a
claim that, unlike positive statements, one cannot obtain confirming evidence
for them.
Let me illustrate how, in fact, one can obtain evidence to confirm negative
statements, first with an all-or-none kind of negative hypothesis, "The moon
is made *not* made entirely of rocks." To test this, I go to the moon and
sample what is there. (If technology permits, I obtain a 'representative'
sample, and that usually means one in which the samples are random and
independent.) I examine the samples: most are indeed just rocks but a few
turn out to be porcelain clay and others are green cheese! I have confirmed
my negative hypothesis.
Next, consider hypotheses about likelihoods, about probabilities. If I say
that in all mammals the sex ratio at conception is 50:50 - a positive
statement - I am not claiming that, say, every family with 8 children will
have exactly 4 boys and 4 girls, only that at each conception, the chance
that the offspring will be of each sex is 1/2, and so in the long run (in
very large samples), the sex ratio would tend toward 50:50. (In humans, the
slight deviation from 50:50 *at birth* probably is due primarily to sex
differences in mortality before birth.)
Okay, now consider a negative statement. I study the golden lemur of
Madagascar and I claim that in these animals, the sex ratio is *not* 50:50.
Do I have any evidence for this negative claim? Sure: a sample of 100
golden lemur embryos consisted of 85 females, 15 males. Furthermore, I can
easily calculate the probability that a deviation from 50:50 this large could
have happened by chance.
Notice that my negative hypothesis, that the sex ratio is not 50:50, is
equivalent to a positive hypothesis, that the sex ratio is either greater
than 50:50 or less than 50:50. Similarly, the claim that the moon is *not*
made entirely of rocks is equivalent to the claim that the moon *is* composed
of some materials other than rocks. Most negative statements have such
equivalent positive versions.
Gathering evidence to confirm the claim that global warming is not happening
would be more difficult than the above illustrations, not just because of the
technical difficulties in making the relevant observations but because of
normal seasonal and other fluctuations in the earth's heat budget. Yet, the
basic principles of evidence are the same; the fact that the claim is
negative is irrelevant. Note also that this negative hypothesis, too, is
equivalent to a positive one: that all observed increases in atmospheric
temperature are consistent with the earth's normal fluctuations around a
constant mean value, and thus that all increases are, in the long run,
balanced by decreases of corresponding magnitude.
Stuart Altmann
| |
|
