Labyrinths of Reason (10 page)

The rationale is that a prosaic hypothesis is partially confirmed by all our prior knowledge of similar occurrences. An incredible hypothesis is not. This, however, raises the possibility of being tricked into believing a series of wrong prosaic hypotheses over a less prosaic truth (as in the French Academy’s dismissal of meteorites). There is, for instance, a lot of evidence for the existence of ghosts. Many thousands of people have reported seeing them, and not all of them are kooks; there are even some fuzzy photographs. There is no categorical explanation for the reports of ghosts (other than that ghosts exist). It is maintained that there is always a “logical explanation,” but this explanation is in one case a branch scratching against a window, in another a hallucination, in another mice in the attic, in still another a hoax. In yet other cases, none of these explanations can be offered, but still it is maintained that some cause not involving the paranormal exists.

In sheer quantity, the evidence for ghosts is probably greater than that for the existence of will-o’-the-wisps, the strange lights seen over marshes. Yet science believes in will-o’-the-wisps and not in ghosts. Ultimately, more theories are refuted by the poor quality of their own evidence than by contrary evidence. There is usually something wrong with a theory that has lots of supporting “evidence,” all of it dubious. This seems to be the case with the theory
that there are ghosts. On the other hand, some of the time will-o’-the-wisps are visible for all to see.

But in Goodman’s paradox, we are skeptical of one hypothesis (emeralds are grue) even though it has precisely the same supporting evidence as another (emeralds are green). The problem rests with the hypothesis, not the evidence.

“All emeralds are grue” speaks of an entity, grueness, that we can do without. Invoking Ockam’s razor, we can say, “Hold it! We already have all the color words we need. It is pointless to add a term like ‘grue’ until you produce something that is grue (and not just green).”

BUT
—once again—the Gruebleen speaker can throw these words right back in our faces. He has all the colors he needs, has no need for “green,” won’t have until he sees something that actually is green (not grue).

Lively debate on the grue-bleen paradox continues. For the time being, most analyses concur that our preference for “green” rather than “grue” is based on simplicity. The difficulty is finding a way out of this vicious cycle whereby the Gruebleen speaker can parrot our every argument! Here is one way.

Ask yourself what will happen on the semantic day of judgment, January 1, 2000 A.D. There are four possibilities.

1. Everyone might wake up and find that the sky is green and the grass is blue! We’ll realize that “green” was the misleading term and “grue” was right—

Otherwise, the speakers of Gruebleen will have to accept the sameness of colors after the zero hour in one of three ways:

2. Gruebleen speakers could wake up and be
surprised
to find that the (still blue) sky has “changed” from bleen to grue. This is what Goodman facetiously implied.

3. Or Gruebleen speakers could go to bed the previous night
fully expecting
the “change.” It would be like resetting a watch for daylight saving time or travel across time zones. The Gruebleen speakers would realize that their color terms don’t jibe with the way the world works.

4. Finally, the Gruebleen speakers might not recognize the “change” at all (through failure to understand the time clause in the definitions cf “grue” and “bleen”). For
how do Gruebleen-speaking parents teach their children the language?

Many philosophers believe that no one could really learn the Gruebleen language as their first language. Sure, parents would point to the grass and say “grue,” point to the sky and say “bleen.” But there is more to grue and bleen than that. The perceptual change (you shouldn’t call it a color change, since grue and bleen are colors to those using those words) at midnight, December 31, 1999, has to be communicated at some point in the process of acquiring language. At some point, a parent or teacher has to sit a Gruebleen-speaking child down and tell him the facts of grue and bleen.

Here the symmetry breaks down. No one has to tell an English-speaking child that green things
don’t
turn blue in the year 2000 to prevent him from getting a wrong idea of what “green” means. It comes naturally. There is an irrelevant reference to time in the definition of “grue” after all.

Goodman’s riddle has radically changed thinking on induction. Goodman talked of the “entrenchment” of terms in language. There is a word for green and not for grue because one agrees with the way of the world and the other doesn’t. The differing color distinctions of some other natural languages agree with Goodman’s precept. Choctaw does not make our distinction between green and blue, but no single word of any natural language means grue or anything like it.
²

A problematic attribute like grueness is said to be
nonprojectable
. An attribute is projectable if it can be used validly in inductive reasoning. Greenness is projectable, in that an instance of a green emerald confirms the obvious generalization that “all emeralds are green.”

There are, however, three types of situations where positive instances of a hypothesis are nonprojectable. One is that of the gruebleen paradox; another is “anything confirms anything.”

The third nonprojectable case is a lemma to the grue-bleen paradox. Consider the hypothesis “All emeralds have been observed.” Every emerald ever seen has been observed, of course. Projecting all these instances of observed emeralds leads to the absurd conclusion that we have observed all the emeralds that exist—that there are no
unseen emeralds. In this case, there is nothing artificial about the attribute of being observed. “Observed” is entrenched in the language as well as “green.”

Scientists must be wary of nonprojectable terms. Quarks are hypothetical entities said to reside deep inside protons, neutrons, and other subatomic particles. Quarks are counterfactual: Not only has an isolated quark never been observed, but (under most theories) an isolated quark is impossible. Quarks are what a proton
would
split into,
if
it could be split, which it
can’t
.

Quarks are held inside protons and neutrons by a “color force.” Most physical forces, like gravity and electric attraction, decrease with distance. The color force does not decrease with distance. It is as if all quarks are connected with rubber bands that continue to exert force from any distance. Consequently, it would take an infinite expenditure of energy to free a quark permanently from a proton. Even a less ambitious project, like pulling a quark an inch out of a proton, would take a fantastic amount of energy (and wouldn’t succeed in any case—the energy would create new particles rather than a bent-out-of-shape proton).

The way nature seemingly conspires to avoid free quarks has always been suspicious. Some fear that unseen quarks may be something like the unseen blue of twenty-first-century grue emeralds. Although the theory of quarks and the color force—quantum chromodynamics—has been confirmed in many ways that the grueness of emeralds has not, controversy rages over whether quarks are “real” particles or only a convenient shorthand for categorizing the particles said to be made up of them.

Identical questions were raised about the reality of atoms in the nineteenth century. But John Dalton’s atomic theory did not rule out detection of individual atoms—and such confirmation came eventually in the gold-foil experiments of Ernest Rutherford (1911).

Moreover, there is a weary exasperation with the increasingly complex quark model. There are different varieties of quarks. These varieties were called “colors” and “flavors.” (They have nothing to do with real colors, much less flavors, but what can you call attributes of something so removed from the world of the senses?) There are three colors (called red, blue, and green) and six flavors (called up, down, strangeness, charm, bottom, and top). That creates eighteen
types of quarks, not counting antiparticles. Then there are electrons, neutrons, gluons, Higgs particles …

Some wonder if colors and flavors may be artificial complications of a simple reality we do not yet understand. Possibly someday someone will hit on how things really are, and we will realize that our current physics is a strained way of describing this reality. We could be like a Gruebleen speaker trying to understand why the sky has turned grue on judgment day. The answer is not in the sky, but in our heads.

S
UPPOSE THAT LAST NIGHT, while everyone slept, everything in the universe doubled in size. Would there be any way of telling what had happened? So runs one of the most famous intellectual riddles of all time, posed by Jules Henri Poincaré (1854–1912), a talented popularizer as well as an eminent scientist of his day.

One’s first impulse is to assume that any drastic change like that would readily be detectable. Think again: Since
everything
has doubled in size, so have all rulers, yardsticks, and tape measures. You cannot
measure
anything and detect the change.

The vaunted platinum/iridium bar in a suburban Paris cellar, the original basis of the metric system, has doubled too and provides no clue to the change. The meter is currently defined as the length of 1,656,763.83 wavelengths of a specific orange light given off by krypton
gas. Still no good. The special fluorescent tubes containing this gas are twice as big, and so are the krypton atoms they contain. The electron orbits of the krypton atoms are twice as big, and therefore the light produced has twice the wavelength.

Wouldn’t things
look
bigger? The picture on your bedroom wall is now twice as big. But your head is twice as far from the picture (from any particular point in the enlarged room). The two factors precisely eliminate any perceptual change.

All right, try this. You’re in foggy London, looking at Big Ben. The clock is twice as big, and you’re twice as far from it, from any given vantage point. The perspective is identical. But your line of sight traverses twice as much fog. Shouldn’t Big Ben look hazier?

The trouble is, it’s really the number of fog droplets that cause haze, and this number hasn’t changed. The droplets are twice as big, and they scatter the doubled photons exactly the way they did before. Big Ben would look as clear or as hazy as it would have had there been no doubling. Similar arguments show that everything would look the same.

The real point of the thought experiment is this: Granted that it is impossible to detect the change,
is
there then a change at all? The question recalls the old metaphysical riddle asking if a tree falling in the forest with no one to hear it makes a sound.

You might say that the nocturnal doubling is real, in that God or some such being “outside” the universe would know of the change. You can imagine God sitting in hyperspace somewhere and watching our universe double in size. This misses the point entirely. Everything that exists must double in size, including God. Not even God can do anything to demonstrate the change.
Then
is the change real?

Poincaré said no. It is pointless even to talk of such a change, he felt. Here words are deceptive: “what if everything in the universe doubled in size” sounds like it describes a change, but the “change” is an illusion.

Others differ. Nocturnal doubling illustrates two competing schools of philosophy. The school called realism allows that nocturnal doubling might be real, even if unobservable. Realism holds that the external world exists independent of human knowledge and observation of it. There are truths beyond our recognition. These include not only truths that are currently unknown and seem impossible
to discern (such as what happened to Ambrose Bierce or whether there is life on Alpha Centauri) but truths that no one will ever know, no matter what. The realist school says these truths still exist. Common sense is primarily realist: Of course the tree makes a sound, even if no one hears it.

Philosophers of the antirealist school argue that there are no evidence-transcendent truths (truths that cannot be demonstrated empirically). Given that no one could ever detect nocturnal doubling, it is absurd and misleading to say that the doubling occurred. Saying that everything doubled last night and saying that everything is the same size are (at most) just different ways of describing the same state of affairs.