SCIENTIFIC INFERENCE AND GOODMAN'S PARADOX
by Mark Hodes
Everyone knows that scientists are impartial, disinterested observers
who examine raw data, notice regularities, and formulate general laws by
a well-understood process called inductive reasoning. Certainly, this
naive picture is one taught in our schools. During the first half of
this century, even some philosophers of science, whom one would not
ordinarily regard as simple-minded, were seduced by this scenario.
Inductive reasoning was imagined to proceed something like this: You
notice several crows, all of whom are black, and you tentatively
conclude that all crows are black. Then, each new crow you encounter
becomes a confirming instance of your generalization, which
consequently, in the absence of counter-examples, acquires greater
certainty. Our strongly held belief that the sun will rise tomorrow is a
result of induction. Even without a knowledge of Newtonian mechanics, we
believe that well-established regularities will persist.
In 1933, Rudolf Carnap, in his "Logische Syntax der Sprache" (The
Logical Syntax of Language) attempted to give a general account of the
mathematics by which general statements are confirmed. His work was in
deliberate analogy to DEDUCTIVE systems, which by then were well
developed. Carnap's and similar programs are now regarded as failures.
One nail in their coffin was "Fact, Fiction, and Forecast" by Nelson
Goodman, from whom our discussion derives.
Suppose that tomorrow an Alpha Centaurian scientist, Welcus Marby, visits
Earth and conducts a study of grass (as in lawns). His language contains
the color words "grue", which in English means "green until January
1, 1986, and blue afterward", and "bleen", which means "blue until
January 1, 1986, and green afterward." Over a few months, Marby
carefully examines many samples of grass from Oregon, Mexico, Hawaii,
etc., and finds them invariably grue. He concludes by inductive
reasoning that grass very probably will continue to be grue. Marby's
expectation is founded on the same basis as our belief in the coming
But wait. If grue has the meaning described, then in our terms Marby
expects the color of grass to change abruptly from green to blue on
January 1, 1986. Surely, this belief cannot be well-founded. We confront
Marby with his irrationality:
US: How can you expect the color of grass to change?
Marby: I don't. I expect it to remain grue.
US: But you expect it to change to blue.
Marby: What does "blue" mean?
US: In your terms, it means "bleen until January 1, 1986, and grue
Marby: "Blue" is a very strange word. Why should there be reference to
an arbitrary time? Surely, the properties of Terrene flora do not depend
upon a particular date on a calendar of historical origins. Your word
"green" is just as strange. I see now that it must mean "grue until
January 1, 1986, and bleen afterward." How can you possibly do science
well if you employ such ill-chosen predicates?
US: Our color predicates are time-independent. "Blue" means always blue.
"Green" means always green.
Marby: What you mean, speaking more precisely, is "green" always means
US: Well, yes. But your grue means changing from green to blue, and your
bleen means changing from blue to green.
Marby: My color predicates are time-independent in exactly the same
sense and to the same degree that yours are. Grue always means grue.
Bleen always means bleen. Your blue means changing from bleen to grue,
and your green means changing from grue to bleen. Surely, my inferences
about grass are at least as well-founded as yours, and considering that
you are a member of a pre-interstellar civilization, I would tend (on
purely objective grounds) to trust my inferences over yours. What is
grue, in the absence of identifiable causative agents of change, will
remain grue. Surely, even a marginally civilized autochthon of a
backwater planet can understand that much.
Since Marby is losing his cool and beginning to turn grue, perhaps we
should resolve this discussion. The physics-minded (not a redundancy)
among you have surely seen a way out of our dilemma. We need only define
color predicates by reference to wavelengths of light. (Do you smell a
garden path? If so, what color is it?)
Let green mean "differentially reflecting light predominantly in the
wavelengths 5000-6000 Angstroms." Let blue mean "differentially
... 4000-5000 Angstroms." Then grue would mean "reflecting
4000-5000 Angstroms before January 1, 1986, and 5000-6000 Angstroms
afterward." Now let us continue our dialogue with Marby:
US: By redefining our color predicates in terms of real physical
qualities, I've shown that your language inhibits sound inductive
inference, while mine promotes it.
Marby: I am afraid you have missed the point by using a time-dependent
unit of measurement, the Angstrom. Our Centaurian units are much more
sensible. Your Angstrom corresponds to an Angstgork before January 1,
1986, and a Maelstrom afterward. You have selected a unit of measurement
tailor-made to moot the very question we are discussing. I expect grass
to remain grue on sound physical grounds (properly fertilized),
specifically that grass should continue to reflect light in the
4000-5000 Angstgork region of the spectrum. In expecting grass to
"remain" green, you are irrationally expecting that the wavelength
distribution of reflected light will shift from the 5000-6000 Angstgork
range to the 5000-6000 Maelstrom range.
I've intended this grue-some little exercise to suggest a few points
about science and scientific thinking. First, simple-minded accounts of
the process of generalization as it occurs in science have not been
successful. Second, scientific reasoning is not independent of the
language in which it is expressed. Third, there is no such thing as raw
data. Every observation involves interpretation at some level, e.g., in
selecting a technical vocabulary with which to record the data. In
current philosophical jargon, scientific work is "theory-laden"
at all levels.
In a later issue, I will discuss some implications of this for
distinguishing science from pseudo-science. Meanwhile, as 1986
approaches, keep a close watch on your lawn.
If you wish to refute Welcus Marby, please send your brief reply to:
Welcus Marby, FRS (Alpha Centauri)
c/o Mark Hodes
701 Welch Road, Suite 1119
Palo Alto, CA 94304