Labyrinths of Reason (8 page)

The requirement of total evidence is the key to unlocking the puzzle. Were our knowledge of the universe so poor that black ravens, nonblack ravens, black nonravens, and nonblack nonravens were nothing but data points, then it would be proper to confirm as the paradox suggests.

We know too much about ravens to confirm that way. Someone finds an albino crow (a counterpart of the 99-foot man). It’s a nonblack
thing and a nonraven. Far from confirming the “ravens are black” theory, it would cast strong doubt on it. Crows are in the same genus as ravens. If crows are prone to albinism, then possibly ravens are too. This background information negates the confirmation.

More generally, we know that ravens bear many, many more similarities to related birds than they do to red herrings or blue lawn elves. When this totality of evidence is taken into perspective, we realize it is a waste of time to examine nonblack nonravens. Whether all ravens are black is an issue best decided by observations of ravens and their relatives and by studies of biological variability.

Arguments from number of ravens vs. nonblack things are perhaps misleading. Consider again the case where the universe consists of seven sealed boxes, a case where most agree it is proper to count nonblack nonravens as confirming instances. Is the deciding difference between this and the real world truly one of number?

Picture a universe containing, say, 10
⁸⁰
sealed boxes. Most of the boxes contain black ravens; a few contain green crab apples; and maybe there is a white raven or two somewhere. You have opened a great number of boxes and thus far found only black ravens and green crab apples. Opening a new box and finding yet another black raven confirms “All ravens are black”—to a slight degree, for you have already opened a lot of boxes and there are trillions yet unopened.

Would not opening a box and finding a green crab apple slightly confirm the hypothesis as well? For one thing, it means one less possible refutation to worry about. For another, it increases your confidence that the objects you find in the boxes have certain fixed colors. You might even explain your faith in the hypothesis like this: “Every raven I’ve seen has been black. In fact, whenever I’ve seen something that wasn’t black, it was always a crab apple, never a raven. The crab apples are ‘the exception that proves the rule.’”

In this universe of sealed boxes, there is no ornithology, no albinism, no biological variation. In short, there is no background information about the way the world works. Instead of containing real ravens or crab apples, the boxes might as well contain slips of paper bearing the words “black raven,” “white raven,” etc. Now it is completely reduced to a formal game. If you open a box and find it to contain a slip of paper saying “white crow,” there is no way of seeing that it has any different bearing on the hypothesis than “green crab apple.”

We all know instinctively that it is wrong to ignore background evidence, but (before Hempel) this important fact went unrecognized in discussions of scientific method. It is unnecessary (logicians say impossible!) to deny the equivalence of the contrapositive. Hempel concluded simply that one must be wary of logical transformations of hypotheses. Yes, a contrapositive is equivalent, but confirmation does not always “recognize” logical transformations. The sundry ways in which consequences of inductive beliefs can mislead are the source of many paradoxes. A more troublesome paradox of induction is to come.

I
N HIS ESSAY “The Analytical Language of John Wilkins,” Jorge Luis Borges mentions a Chinese encyclopedia, the
Celestial Emporium of Benevolent Knowledge:
“On those remote pages it is written that animals are divided into (a) those that belong to the Emperor, (b) embalmed ones, (c) those that are trained, (d) suckling pigs, (e) mermaids, (f) fabulous ones, (g) stray dogs, (h) those that are included in this classification, (i) those that tremble as if they were mad, (j) innumerable ones, (k) those drawn with a very fine camel’s hair brush, (l) others, (m) those that have just broken a flower vase, (n) those that resemble flies from a distance.”

Man is the animal that invents categories. Science is a litany of phyla, genera, and species; eras and epochs; elements and compounds; leptons, mesons, and hadrons. The irony is that many of
the categories judged scientifically valid appear just as arbitrary to the nonspecialist as the
Celestial Emporium’s
. Biologists divide the animal kingdom into about twenty-two phyla. Of these broad divisions, all “regular” animals (foxes, chickens, hippopotamuses, man) form a small subcategory of one phylum. Most of the other phyla enumerate the varieties of worms.

Borges’s essay describes the ambitious and perhaps insane artificial language devised by British scientist and educator John Wilkins (1614–72). Wilkins’s language divides the world into forty categories. Each category is divided into subcategories and sub-subcategories as in a library’s cataloguing system. Wilkins associated a letter or two with each category. The words for things in Wilkins’s language are assembled by stringing together the letters for the successive categories that define it. It is as if the title of each book in a library was also its catalogue number; or as if people’s names were composed of letters from their ancestors’ names.

“The word
salmon
does not tell us anything about the object it represents;
zana
, the corresponding word, defines (for the person versed in the forty categories and the classes of those categories) a scaly river fish with reddish flesh,” Borges writes. “Theoretically, a language in which the name of each being would indicate all the details of its destiny, past and future, is not inconceivable.”

In 1953 American philosopher Nelson Goodman posed what he called the “new riddle of induction.” The “grue-bleen” paradox, as it is better known, challenges our thinking about categories. A jeweler examines an emerald. “Aha,” he says, “another green emerald. In all my years in this business, I must have seen thousands of emeralds, and every one has been green.” We think the jeweler reasonable to hypothesize that all emeralds are green.

Next door is another jeweler having equally comprehensive experience with emeralds. He speaks only the Choctaw Indian language. Color distinctions are not as universal as might be thought. The Choctaw Indians made no distinction between green and blue—the same words applied to both. The Choctaws
did
make a linguistic distinction between
okchamali
, a vivid green or blue, and
okchakko
, a pale green or blue. The Choctaw-speaking jeweler says: All emeralds are
okchamali
. He maintains that all his years in the jewelry business confirm this hypothesis.

A third jeweler speaks Gruebleen, a strange, Esperanto-like language.
The Gruebleen language has its own terms for colors, just as English and Choctaw do, but it has no word for green as such. Instead it has the word “grue.” “Grue” can be defined in English as follows: If something is green before midnight, December 31, 1999, and blue thereafter, then it is grue. The Gruebleen-speaking jeweler naturally concludes that all emeralds are grue.

Put the question “What color will this emerald be in the year 2000?” to the jewelers. All three shake their heads and say they never knew an emerald to be any other color than what it is right now. The English speaker confidently predicts that the emerald will be green in the year 2000. The Choctaw speaker says it will be
okchamali
. The Gruebleen speaker asserts that the emerald will be grue in the year 2000 … but wait! “Grue in the year 2000” means blue in plain English. (It means
okchamali
in plain Choctaw.)

The paradox is that all three jewelers have had identical experiences with emeralds, and all have used the same inductive reasoning. Yet the Gruebleen speaker’s prediction is at odds with the English speaker’s. (The Choctaw speaker’s prediction is compatible with either of his fellow jewelers’.) The paradox can’t be swept away as meaningless. Come the turn of the century, at least one prediction will be wrong.
¹

The paradox can become as absurd as you wish. Let “grurple” mean green before a designated “zero hour” and purple thereafter. Let “emerow” mean something that is an emerald before the zero hour and a cow thereafter. Then the green emerald confirms “All emerows are grurple,” which is to say, the green emerald will be a purple cow in 2000 A.D. By suitable choice of terms and zero hour,
anything
confirms that it will be
anything
else at
any
later time.

As with Hempel’s paradox, there is an obvious “resolution” that fails miserably. The problem sure seems to be that gimmicky word “grue.” “Grue” is inherently a more complicated word than “green”—look at its definition above! Grue is a “gerrymander” category, to borrow a term from politics. It has no natural significance;
it was constructed by Goodman with the sole aim of creating a paradox. It makes irrelevant reference to a specific point in time.

We do use some rather artificial categories in the real world. When a person in Chicago says it is 5 o’clock, he is actually saying that it is 5 o’clock in the region west of 82.5 degrees west longitude and east of 97.5 degrees west longitude, except as these boundaries are amended by local observances of Central Standard Time. It’s 6 o’clock in the Eastern time zone, 4 o’clock in Mountain Time, and assorted other times at other places in the world. It’s every hour—someplace—all the time. This definition sounds at least as cockeyed as that of “grue.” It makes reference to geographic location, which is irrelevant to what time it is.

How much more sensible it would be to use Greenwich Mean Time all over the world. When it was 5:30
P.M
. in São Paulo, it would also be 5:30
P.M
. in Tokyo, Lagos, Winnipeg, and everywhere else. We might then regard the current method of stating time a patchwork out of a logic paradox.

And is “green” any less arbitrary? As logician W. V. O. Quine has pointed out, the concept of color is, to a physicist’s way of looking at things, arbitrary. Light comes in a continuum of wavelengths, and there is no special distinction to those wavelengths that we call “green.” Were we explaining what “green” means to a being from another planet, we would have to say something like “Green is what we experience when viewing light of wavelength greater than 4912 angstrom units but less than 5750 angstrom units.” Why 4912 and 5750 rather than some other cutoff points? No reason—that’s just the way things are.

Of course, “grue” inherits the spectral arbitrariness of “green” (and “blue”). “Grue,” however, is arbitrary in a way that “green” is not. “Grue” supposes a
change
in color. It is not that nothing in the world changes from green to blue. Unripe blueberries do. But a simultaneous and universal change is quite unprecedented. “Grue” asks us to believe in this change, a change that has never been observed.

This sounds like a strong objection. But it sounds just as sensible inside out from the other side of the looking glass. The third jeweler’s idiosyncratic tongue has another color word, “bleen.” Something is bleen if is blue until midnight, December 31, 1999, and green thereafter.

In order to explain the English word “green” to the Gruebleen-speaking jeweler, we have to say that something is green if it is grue before midnight, December 31, 1999, and bleen thereafter. To him,
raised on grue and bleen from the cradle, “green” is the artificial term. It is
green’s
definition that makes reference to a specific time.

The cross-definitions are as symmetric as bookends. Look in an English-Gruebleen/Gruebleen-English dictionary, and count the number of words in the definitions of “green” and “grue.” “Grue” can be defined using “green” and “blue,” or “green” can be defined using “grue” and “bleen.” Asking which is the more fundamental term is like asking whether the chicken or the egg came first.

To get the full impact of this, imagine that “grue” and “bleen” are not made-up terms of a logic paradox but the very real terms of a natural language. Native speakers routinely say grass is grue and the sky is bleen. To them, saying that a dress is bleen does not raise the question of how, physically, it is going to turn blue at the turn of the century. (Any more than our saying that a banana is yellow implies that it will never turn brown but will be yellow forever.) When they say a dress is bleen it is because it is being perceived as bleen
right now
. It is the same color as the portion of a color chart that is labeled “bleen”; the color of the bleen sky or the first bleenbird of spring. The only difference between their bleen and our blue is that this time clause is built into the definition (or is it?).