SCIENTIFIC INFERENCE AND GOODMAN'S PARADOX by Mark Hodes Everyone knows that scientists ar

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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 day. 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 afterward." 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 "green." 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


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