Photo: James Blachowicz |
Kepler’s illustration to explain his discovery of the elliptical orbit of Mars, circa 1754. Credit Universal History Archive/Getty Images |
In
1970, I had the chance to attend a lecture by Stephen Spender. He
described in some detail the stages through which he would pass in
crafting a poem. He jotted on a blackboard some lines of verse from
successive drafts of one of his poems, asking whether these lines (a)
expressed what he wanted to express and (b) did so in the desired form.
He then amended the lines to bring them closer either to the meaning he
wanted to communicate or to the poetic form of that communication.
I
was immediately struck by the similarities between his editing process
and those associated with scientific investigation and began to wonder
whether there was such a thing as a scientific method. Maybe the method
on which science relies exists wherever we find systematic
investigation. In saying there is no scientific method, what I mean,
more precisely, is that there is no distinctly scientific method.
There
is meaning, which we can grasp and anchor in a short phrase, and then
there is the expression of that meaning that accounts for it, whether in
a literal explanation or in poetry or in some other way. Our knowledge
separates into layers: Experience provides a base for a higher layer of
more conceptual understanding. This is as true for poetry as for
science.
Let’s
look at an example that is a little less complex than poetry. Consider
how Socrates guided his students to a definition – of justice or
knowledge or courage.
When Socrates asked “What is justice?” there was never any doubt that his listeners knew what the word “justice” meant. This is confirmed by the fact that Socrates and his listeners could agree on examples of justice. Defining justice, on the other hand — that is, being able to explain what it was conceptually that all these examples had in common — was something else altogether.
Suppose you and I try to define courage. We would begin with the meaning that is familiar to both of us. This shared meaning will be used to check proposed definitions and provide typical examples of it. Commonly, we may not be able to explain what something is, but we know it when we see it.
When Socrates asked “What is justice?” there was never any doubt that his listeners knew what the word “justice” meant. This is confirmed by the fact that Socrates and his listeners could agree on examples of justice. Defining justice, on the other hand — that is, being able to explain what it was conceptually that all these examples had in common — was something else altogether.
Suppose you and I try to define courage. We would begin with the meaning that is familiar to both of us. This shared meaning will be used to check proposed definitions and provide typical examples of it. Commonly, we may not be able to explain what something is, but we know it when we see it.
So
what do we mean by courage? Let’s try, “Courage is the ability to act
in the face of great fear.” This is an attempt to articulate (define)
what we mean by courage. What we do next is to compare the actual
meaning of courage we both possess with the literal meaning of the
expression “the ability to act in the face of great fear.”
In
comparing this literal meaning with the actual meaning of courage in
our minds, we come to realize that the literal meaning of our working
definition won’t work because, for example, “to act in the face of great
fear” could include tying one’s shoelace, yelling profanities, even
running away.
So
we must alter our definition to exclude these typically non-courageous
actions. One way of doing this is to produce a definition such as,
“Courage is the ability to act in the face of great fear, except for
tying one’s shoelace, yelling profanities and running away.” This does
produce a literal meaning closer to the actual meaning we want to
express or define.
Yet
we wouldn’t accept such a definition even if it itemized every possible
exception. Why? Because, from a different point of view, this
definition is inadequate: not because it fails to bring the meaning of
the definition closer to the actual meaning of courage, but because all
it does is try to save the original definition by tacking on ad hoc
exceptions. That is, we reject it because it fails to be a good,
well-formed definition. A good definition is simple and provides a
principle that would exclude all possible exceptions without having to
enumerate them one by one.
What
do we do? We come up with a new definition that once again is simple
(without adding exceptions). We could try, “Courage is the ability to
act while confronting a great fear.” Adding “confronting” would seem to
disqualify tying one’s shoelaces and even shouting profanities since one
could shout profanities while running away.
Yet
adding an ad hoc exception may sometimes be just what is called for.
Suppose I define courage as “the ability to act while confronting a
danger to oneself.” “Confronting” is retained, so this would (normally)
exclude running away. Yet one could also act out of anger, so that
courage may not be the principal trait exhibited. We could add the ad
hoc hypothesis “except when motivated principally by anger.” This would
be desirable in this case, for the phenomenon turned out to be composite
— actions that may arise from separate causes (courage and anger).
It’s
important to see that this process — like that whereby a poem is
written — rests on two requirements that have to be met. A good
definition or poem must be one (a) whose expressed meaning matches the
actual meaning that was grasped in a pre-articulated way and (b) which
satisfies some criterion of form (embodies an explanatory principle or
satisfies poetic form).
Now compare this with a scientific example: Johannes Kepler’s discovery that the orbit of Mars is an ellipse.
Now compare this with a scientific example: Johannes Kepler’s discovery that the orbit of Mars is an ellipse.
In
this case, the actual meaning of courage (what a definition is designed
to define) corresponds with the actual observations that Kepler sought
to explain — that is, the data regarding the orbit of Mars. In the case
of definition, we compare the literal meaning of a proposed definition
with the actual meaning we want to define. In Kepler’s case, he needed
to compare the predicted observations from a proposed explanatory
hypothesis with the actual observations he wanted to explain.
Early
on, Kepler determined that the orbit of Mars was not a circle (the
default perfect shape of the planetary spheres, an idea inherited from
the Greeks). There is a very simple equation for a circle, but the first
noncircular shape Kepler entertained as a replacement was an oval.
Despite our use of the word “oval” as sometimes synonymous with ellipse,
Kepler understood it as egg-shaped (in the asymmetrical chicken-egg
way). Maybe he thought the orbit had to be lopsided (rather than
symmetrical) because he knew the Sun was not at the center of the oval.
Unfortunately, there is no simple equation for such an oval (although
there is one for an ellipse).
When
a scientist tests a hypothesis and finds that its predictions do not
quite match available observations, there is always the option of
forcing the hypothesis to fit the data. One can resort to curve-fitting,
in which a hypothesis is patched together from different independent
pieces, each piece more or less fitting a different part of the data. A
tailor for whom fit is everything and style is nothing can make me a
suit that will fit like a glove — but as a patchwork with odd random
seams everywhere, it will also not look very much like a suit.
The
lesson is that it is not just the observed facts that drive a
scientist’s theorizing. A scientist would, presumably, no more be caught
in a patchwork hypothesis than in a patchwork suit. Science education,
however, has persistently relied more on empirical fit as its trump
card, perhaps partly to separate science from those dangerous
seat-of-the-pants theorizings (including philosophy) that pretend to
find their way apart from such evidence.
Kepler
could have hammered out a patchwork equation that would have
represented the oval orbit of Mars. It would have fit the facts better
than the earlier circle hypothesis. But it would have failed to meet the
second criterion that all such explanation requires: that it be simple,
with a single explanatory principle devoid of tacked-on ad hoc
exceptions, analogous to the case of courage as acting in the face of
great fear, except for running away, tying one’s shoelace and yelling
profanities.
Yet
in science, just as in defining a concept like courage, ad hoc
exceptions are sometimes exactly what are needed. While Galileo’s law
prescribes that the trajectory of a projectile like a cannonball follows
a parabolic path, the true path deviates from a parabola, mostly
because of air resistance. That is, a second, separate causal element
must be accounted for. And so we add the ad hoc exception “except when
resisted by air.”
This is enough. There is much more to a theory of inquiry, of course, that could cover forms as disparate as poetry and science.
Source: New York Times