4 2 4C H A P T E R 2 0 ■ S c i e n t i f i c R e a s o n i n gScientists often seek deeper explanations by asking why certain general
principles themselves are true. The principle that a sphere floats in water only
when it is less dense than water can be explained as an instance of the more
general principle that anything floats only when it displaces more than its
own weight in water. This broader principle not only explains why a wooden
sphere floats in water but also why a piece of gold will float when molded
into the form of a boat. This broader principle is in turn explained by deriv-
ing it from even more basic principles about gravity and the mutual repul-
sion of molecules. A larger scientific theory is thus used to explain not only
why particular things happen but also why certain general principles hold.
Of course, scientists often put forward conflicting theories, so we need
some way to test which theory is correct. One simple method is to use the
theory to make predictions. Since an explanation depends on principles that
are general, these principles have implications beyond the particular phe-
nomenon that they were originally intended to explain. The theory thus
predicts what will happen in circumstances that the scientist has not yet ob-
served. We can then test the theory by seeing whether these predictions hold
true. For example, we can make spheres out of a wide variety of materials,
calculate their densities, and then see which ones float. If any sphere that is
denser than water floats, then we have to give up our principle that a sphere
floats in water only if it is less dense than water. (This is an application of the
necessary condition test, discussed in Chapter 10.) If we find a sphere that is
less dense than water but does not float, then we have to give up the princi-
ple that a sphere floats if it is less dense than water. (This is an application of
the sufficient condition test, discussed in Chapter 10.)
These methods help us rule out certain scientific principles, but the fact
that a principle implies true predictions does not, by itself, prove that the
principle is true. That argument would commit something like the fallacy
of affirming the consequent (see Exercise XXI in Chapter 6). Nonetheless,
we can still say that a theory is confirmed if it yields true predictions, and it
is confirmed more strongly if it yields more, more varied, and more unex-
pected true predictions.
Scientific method is actually much more complex than this simple exam-
ple suggests. This becomes apparent when we encounter anomalies. Sup-
pose we have confirmed and explained the principle that a sphere floats in
water if and only if it is less dense than water. Suppose also that another
principle is well confirmed: A substance gets smaller and denser as it gets
colder. Taken together, these principles predict that a sphere of ice should
sink in water. Ice is colder than water, so, according to the second principle,
ice should be denser than water, and that, given the first principle, means
that it should not float in water. Of course, our prediction is wrong, since
spheres of ice do float in water. What do we do now? The obvious solution
is to modify the principle that a substance gets smaller and denser as it gets
colder. This holds for most substances, but not for water. Water expands and
thus gets less dense as it freezes.97364_ch20_ptg01_423-448.indd 424 15/11/13 12:09 3M
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