Labyrinths of Reason (9 page)

The grue-bleen paradox is partly about
counterfactuals:
terms that talk about what
would
happen even though it
hasn’t
. A paper clip is flexible, acid-soluble, and meltable. It is all these things even if it is never bent, dissolved in acid, or melted. A grue emerald would be grue even if it is destroyed before 1999.

Counterfactuals abound in science. Following Goodman, astronomers might call the color of the sun “yelite.” The sun is an average yellow star now, and will be a white dwarf in about 10 billion years. Of course, no one has ever observed the sun change from a yellow star to a white dwarf. No one has observed any star do that. All our direct experience confirms that the sun will be yellow forever as well as that the sun is “yelite.”

What is the difference between this and Goodman’s paradox? The astronomers’ belief in the future change is not accidental. It is not the result of there happening to be a term “yelite” in somebody’s dictionary. It is based on astrophysical theory that has been confirmed in other realms.

Terms like “grue” and “bleen” are suspect because they arbitrarily delay refutation until a future time. No possible experiment
conducted in the twentieth century can distinguish a grue emerald from a green one. The future color change is a supposition that is (so far) unnecessary. For that reason we are justifiably suspicious of someone advancing a hypothesis that emeralds are grue.

True as this is, it does not make the paradox vanish. Again, the infernal symmetry of the situation rears its double head. The Gruebleen-speaking jeweler can complain that no twentieth-century experiment will aid him in deciding whether a grue emerald will turn bleen in the year 2000 (this being his definition of “green”). To resolve the paradox, even partially, you must find a way in which the situation
isn’t
symmetrical.

Maybe the problem is the
suddenness
of the change. Sudden changes generally require a cause. In a vacuum, an object may continue its motion forever, but an abrupt change of velocity can come about only through an outside agent.

If the suddenness bothers you, let “grue” describe a gradual change from green to blue over a period of a thousand years. Better yet, suppose that all the colors are changing. The artist’s color wheel is slowly rotating, so to speak, and what is green now will be blue in a thousand years, purple in 2000 years, red in 3000 years, and come full cycle back to green in 6000 years. “Grue” applies to that class of objects (emeralds, summer leaves, etc.) that are green now, blue in a thousand years, and so on.

Assuming a 6000-year cycle, the color of all things would change ever so slightly with each passing moment. The cumulative color change in a human lifespan would, however, be so minor that hardly anyone would notice. (The wizened gemologist who complained that emeralds aren’t quite the color they were in his youth would be humored. Don’t many old-timers think that winters are warmer now, baseball players inferior, etc., etc.?)

Nor could we infer the color shifting from historical evidence. Today’s green emerald would have been yellow when it graced a feudal lord’s ring and orange in Cleopatra’s crown. But how do we know what the ancients meant by their color terms? If the classical authors used such and such a word for the color of emeralds and grass and the Atlantic Ocean, we would translate it as “green.” It
might
be that if we took a time machine back to the year 1, we would find all these things orange to our eyes. We cannot be certain that the Old English “grene” wasn’t actually yellow either.

This idea blends with “inverted spectrum” thought experiments, much discussed by philosophers. Suppose that you have, from birth, seen colors exactly opposite from everyone else. That is, the color sensation you get when you look at a Red Delicious apple—the sensation you have been trained to call “red”—is actually what everyone else calls “green.” All the colors you see are the opposite of everyone else’s. Is there any way for two people to describe their subjective color sensations to each other in such a way that they can be
sure
they see the same colors?

It seems to be impossible. Colors are usually described by comparing them to something else (turquoise blue, brick red, ivory, etc.). This would not work, for the same reason mentioned above. The best case for believing that we might be able to detect inverted color sensations is the supposed correlation of colors with psychological states. We are told that light blue and light green are restful; that red incites anger or hotheadedness; that blue is for boys and pink is for girls; that some colors (blue maybe) are more popular or tasteful than others (orange and purple maybe).

It is possible that certain colors have intrinsic psychological effects that have developed through evolution. On the other hand, it is possible that these are only societal conventions that children internalize at an early age. Unlike a lot of these epistemological issues, the inverted-spectrum debate might be settled by starting a country somewhere with all the colors inverted (by extensive use of nontoxic dyes?!). Green vegetables would be dyed bright red (but still called “green vegetables”); baby clothing would be “blue” (really orange) for boys, “pink” (really olive) for girls, and so on. Companies importing artists’ pigments would have to squeeze violet paint out of its original tubes and put it in tubes labeled “yellow.” Color photographs from the outside world would be permitted, but only the negatives! The “country” would be self-contained and underground, so that the blue of the sky wouldn’t contaminate the experiment. Would people raised in this country share our color preferences? Would an indigenous work of abstract art be detectable in any way?

Whether or not it is completely impossible to detect an inverted spectrum, it is certainly difficult. So we can have a gradual gruebleen paradox in which there is no sudden change and no unobserved future change. The alleged “change” is and has been going
on all the time, and all our present and historical experience is compatible with the change. That seems to rule out any easy resolution of the paradox.

The inverted spectrum and the grue-bleen paradox probe a lot more than colors. Goodman used colors as an example of the categories into which we divide the world. Through categories, experience melds with language. Goodman’s jewelers hold empirical beliefs about emeralds that have stood the test of time—and the beliefs are radically different!

Instinctively, we know that “All emeralds are green” is a good hypothesis, and “All emeralds are grue” is somehow flawed. The question is how we distinguish reasonable hypotheses from unreasonable ones. You might answer, “By doing experiments, of course!” That is one way of distinguishing, but scientists cannot test every hypothesis, good, bad, or indifferent.

“Research is the process of going up alleys to see if they are blind,” joked biologist Marston Bates. The role of scattershot research is severely limited, however. Philosopher of science Hilary Putnam illustrated this point with his “demon theory.” The theory (really a hypothesis) is this: A demon (maybe Descartes’s) will appear before your eyes if you put a flour bag on your head and rap a table 16 times in quick succession. Now, of course, this is stupid, but it
is
a hypothesis and
is
capable of being tested. It can be tested a lot easier than most scientific hypotheses can be tested.

The above is Demon Theory No. 16. There is a Demon Theory No. 17, which is the same except that there have to be 17 raps, and a Demon Theory No. 18, and a Demon Theory No. 19, etc. There is an infinity of demon theories. Obviously, said Putnam, scientists have to be selective about the theories they test. You could spend your life testing dumb theories and never get anywhere. It is vital that you winnow out the “possibly true” hypotheses from the “not worth bothering with” ones before getting as far as experimentation.

Unlike Putnam’s demon theory, most hypotheses are motivated by experience. A snowflake falls on your sleeve. It has six sides. A reasonable hypothesis is “All snowflakes have six sides.” But why that and not “All snowflakes that fall on Tuesday have six sides” or “All things have six sides” or “Everything that melts has an even number of sides” or “All hexagonal objects have six sides?” More
important, why do we even think that something about the shape of snowflakes is generalizable? The very fact that there is a word “snowflake” presupposes the common knowledge that there is a class of tiny, cold, white objects that fall from the sky and that may have other properties in common. Without the implicit hint given by the word, one might grope for hypotheses such as “Everything in the class consisting of (this white thing on my sleeve, Queen Victoria, lasagne, and all the beach balls in the Southern Hemisphere) has six sides.”

Bad hypotheses have a way of subverting evidence. An example is the paradox often called “anything confirms anything”—a paradox that probably occurs, in the form of fallacious reasoning, more frequently than any other of those discussed in this book.

It is reasonable to think that something that confirms a hypothesis will confirm any necessary consequence of that hypothesis. If man is descended from apes, then undeniably Darwin is descended from apes. A fossil that confirms the hypothesis that man is descended from apes must also confirm that Darwin is descended from apes. So far so good.

Take a compound statement such as “8497 is a prime number and the other side of the moon is flat and Elizabeth the First was crowned on a Tuesday” (this example from Goodman). To test this, you check 8497 for divisors and conclude that is it prime. This discovery confirms the compound statement, and one consequence of the compound statement is that the far side of the moon is flat. The fact that 8497 is prime confirms that the moon is flat!

Of course, the compound statement could lump together any propositions at all. Replace them with propositions of your own choice and make your own paradox. Anything can be shown to confirm anything else.

Evidently it is easier to join hypotheses logically than to be sure that there is valid reason for linking them. This link is essential for valid confirmation. Goodman’s sentence is patently a hodgepodge, but it suggests the wide-ranging consequences of any powerful theory. Many proponents of pseudoscience use the “anything confirms anything” argument. To give just one popular example:

There is an aesthetic to science. The “beauty” of a theory is measured largely by its simplicity. A simple theory that explains a lot is preferred to a complicated theory that explains little—even though, on the face of it, there may be no particular reason to believe that the complicated theory is any less right than the simple one.

This important principle is called “Ockam’s razor.” The name comes from William of Ockam (the name is also spelled Occam and Ockham), a Franciscan monk born about 1285. (Very similar doctrines were propounded earlier by Duns Scotus and Odo Rigaldus.) A controversial figure embroiled in disputes with popes and anti-popes, Ockam was one of the most influential of medieval thinkers. He died, probably of the plague, in 1349.

Ockam is best known for something he may never have said:
Entia non sunt multiplicanda sine necessitate
, or “Entities are not to be multiplied beyond necessity.” The sentiment, if not those words, is his. He meant that you should not resort to new assumptions or hypotheses (entities) except when necessary. If a footprint in the snow
might
be explained by a bear, and
might
be explained by a previously undiscovered manlike creature, the bear hypothesis is favored.

The principle can be misunderstood. It is not a matter of choosing the less sensational explanation. One favors bears over abominable snowmen only when the evidence (such as a half-melted footprint) is so deficient that both the bear and the yeti theory account for it equally well.

Ockam’s razor is fallible. It has often favored a
wrong
hypothesis. Is the earth round? Do tiny living creatures cause disease? We now know that these hypotheses account for observations very well, but at some point the Ockam’s razor principle rejected them. A notorious case of misplaced skepticism (often cited by proponents of ghosts, UFOs, and other currently unaccepted beliefs) is the French Academy’s prolonged rejection of the reality of meteorites. On the finest scientific advice, dozens of meteorites in European museums were thrown out as superstitious relics.

Here we come to one of the most troublesome points of confirmation theory. In every scientific discovery, there is a stage where two competing theories account for observations about equally well. There is often a simpler hypothesis, A, which everyone has been believing all along, and a new hypothesis, B, which postulates some new “entity,” in Ockam’s words. Theory A could be the belief that the earth is the center of the universe, and B could be Copernicus’s heliocentric theory. Or to take an example less obviously stacked in favor of B, A could be that there are no UFOs, and B could be that UFOs exist. When does the evidence justify the new entity?

It is difficult to give a hard-and-fast answer, for we all believe many things on the basis of slight evidence. If you glance at the cover of a tabloid in a supermarket and read that a prominent actress has eloped, you probably take it for a fact. If the same tabloid the next week says in equal-sized print that UFOs abducted a woman in Arizona, you probably don’t believe it. As astronomer Carl Sagan points out, there is a significant yet usually unconscious rule of confirmation at work here: The more outrageous the hypothesis, the more evidence is needed to confirm it.