Labyrinths of Reason (20 page)

The four remaining permutations are cases that fail in at least two criteria for knowledge. TFF is an unjustified belief that is indeed wrong: superstitions, old wives’ tales. FTF is the peculiar case of a falsehood that is disbelieved in spite of justification. This would describe the people who are skeptical of the TTF cases above. The Catholic hierarchy
disbelieved
Copernicus’
justified
but ultimately
false
belief that the sun is the center of the universe.

FFT is a truth that is disbelieved because of lack of justification: the justifiable skepticism of someone who rejects something that nonetheless turns out to be true. The generations of philosophers who rejected Democritus’ belief in atoms (since they had no reason for believing in them) is an example. At some point in every scientific revolution, justified conservatism (FFT) turns to mere reaction (FTT).

The final case, FFF, is an unjustifiable false belief that is rejected: The disbelief of perpetual-motion machine skeptics, or anyone’s disbelief of nonsense propositions like “The moon is made of green cheese.”

Some beliefs fail to fall into any of these categories. “Buridan sentences,” named after examples in fourteenth-century philosopher Jean Buridan’s
Sophismata
, challenge any definition of knowledge. One goes:

No one believes this sentence.

If this is true, no one believes it and therefore no one knows it. If it is false, at least one person believes it but no one (believer or nonbeliever) knows it because it
is
false. Consequently, no one can possibly know that the above sentence is true!

Would you believe this?

You don’t believe this sentence.

It would be silly to believe this sentence, since then you would be believing that you don’t believe it. But if you don’t believe it, then you have every reason to believe it because it is true … If the preceding sentence convinces you to believe it, that upsets the applecart again. Then it is absurd to believe it, all over again. Strangely enough, you can never arrive at a consistent position on this sentence. Yet, at any instant, an omniscient being aware of your every thought
can
say whether you believe it.

The opposite sentence (“You believe this”) is the gist of Descartes’s
Cogito ergo sum
. If only you believe the sentence, then it is true. If you disbelieve it, then it is false, and you have excellent ground for disbelieving it. No matter what your opinion of this sentence, you’re correct.

Stranger yet is the “knower’s paradox.” It centers on this assertion (which is akin to the judge’s statement in the unexpected hanging):

No one knows this sentence.

If
this
is true, no one knows it. If it is false, there is an immediate conflict: Someone knows it, but obviously no one can know a falsehood. Consequently, the sentence isn’t false. It’s an indubitably true fact that no one can ever know!

Although the three conditions of the tripartite account have already led to paradox, they are not enough. They do not guarantee knowledge. There are ways you can have a justified true belief and
not
know what you believe. These ironic situations are known as Gettier counterexamples, after the American philosopher (Edmund Gettier) who discussed them in a 1963 paper.

As with an inductive generalization, a counterexample here is something that disproves a statement or line of argument. Gettier counterexamples are (usually) fictional situations that demonstrate that the three conventional criteria do not necessarily indicate knowledge. If the psychics mentioned above may be “right for the wrong reasons,” then the essence of a Gettier counterexample is being “right for the right reasons, but the reasons don’t apply.” Errors of this type have intrigued philosophers (and storytellers) for a long time. Gettier counterexamples typically have an O. Henry flavor of farfetched coincidence.

Plato anticipated Gettier in one of his Socratic dialogues,
Theaetetus
. There he discusses a lawyer so glib he can convince jurors of his client’s innocence even if the client is guilty. Suppose the client is innocent. The jury believes the client is innocent and can cite the valid evidence they have just heard. But spellbound by gilded oratory, they would just as readily have believed a guilty client innocent. Plato contended that it is a false kind of knowledge they have. They really don’t know the client is innocent.

One of Gettier’s original illustrations was this: Smith and Jones are applying for a job with a company. Smith has just spoken to the president of the company and learned that Jones will get the job. Smith believes that Jones will get the job, and for good reason. Smith also believes that Jones has ten coins in his pocket. He just saw Jones empty his pocket looking for a quarter, and put ten coins back in the pocket. Smith has been watching him ever since and is sure he neither removed nor added any coins.

Smith muses idly to himself, “Well, it looks like the person who will get the job has ten coins in his pocket.” He justifiably believes this, since it follows logically from the beliefs that Jones will get the job and Jones has ten coins in his pocket.

Gettier realized that these beliefs could be wrong, yet Smith could still be right. Suppose Smith gets the job (the company president changed his mind), and Jones actually has eleven coins in his pocket (one was stuck in the lining). Furthermore, it turns out that Smith has ten coins in his pocket. Then “the person who will get the job has ten coins in his pocket.” It is ridiculous to say Smith knew this; it is sheer luck that it is true.

A Gettier counterexample need not be so contrived. Someone returns from lunch and asks you what time it is. You look at your watch and answer: 2:14. Your belief that it is 2:14 is certainly justified: It’s an expensive watch that has always been reliable, and (something of a fanatic about the correct time) every night you set the watch by a government radio station that broadcasts the current time to the second. In fact, it
is
2:14
P.M
., but unknown to you, your watch stopped dead at 2:14
A.M
. the previous night. By coincidence, you didn’t look at your watch until that one minute out of every twelve hours that a broken watch is correct.

Another example: You go to the Louvre to see the
Mona Lisa
. You recognize the painting from a hundred photographs, and get goose bumps because you are in the same room with the
Mona Lisa
. You later find out that the museum staff, acting on a tip that someone would try to steal the painting, replaced it with a masterful reproduction the day you were at the Louvre. But you
were
in the
same room with da Vinci’s masterpiece because the real
Mona Lisa
was cleverly hidden behind a worthless painting nearby—the last place the thieves would look for it!

There have been Gettier counterexamples in the history of science. One is the alchemists’ belief that metals can be transmuted into gold. This belief was founded on more than a mere hunch. As the first to systematize knowledge of substances, the alchemists were rightly impressed by how one substance may change into a profoundly different substance in chemical reactions. They further realized that the world is not infinitely diverse but is made of a relative few basic substances. If cinnabar can be turned into mercury, why not a base metal into gold? It seemed to be only a matter of hitting on the right combination of substances.

Even in retrospect, this was a plausible speculation. It just happened to be wrong. Brittle red cinnabar can be turned into silvery liquid mercury because it is a compound of mercury and sulfur (both elements). It
would
be possible to turn common substances into gold provided that gold is a compound of common elements, or else that some common substance is a compound of gold and something else. In fact, gold is an element and, unfortunately, no common substance is a compound of gold. Chemists can make gold from, say, gold chloride, but gold chloride is rarer than gold itself.

Despite this, it so happens that other elements can be transmuted into gold (or any element) in atomic reactions—of which the alchemists knew nothing. The alchemists had a justified true belief, yet it is surely wrong to say they “knew” other elements can be transmuted to gold.

One reaction to Gettier counterexamples is that they are really just unusual cases of being right for the wrong reasons. In each situation, the “justified” belief is not justified beyond all doubt. The likely is being confused with the certain.

Smith’s conversation with the company president must not have been adequate grounds for believing that Jones would get the job. It was reason for assigning a high probability to Jones’s getting the job, but not for believing it with certainty. Smith should have realized that executives are capable of reversing a decision and of purposely misleading a job candidate about his chances.

On the other hand, Gettier situations can be devised even for beliefs as certain as any belief about the external world can be. What are you most sure of right now, this very instant? You may be pretty sure that this book is in front of you right now. But you could be a disembodied brain in a vat. A laboratory janitor left a
book in front of your vat while cleaning up, and by a wild coincidence, the book was
this
book.

The point is that if we demand that a “justified” belief be one of which we are certain, we short-circuit our attempt to define knowledge. Then one of the criteria for being certain of something would be to have reasons that make it certain. Even worse:
Nothing
in the external world is incontestably certain. If we have to be 100 percent certain of something to know it, then we don’t know anything (not even the true things we justifiably believe).

Much effort has gone into finding a “fourth condition” of knowledge. This would be an additional criterion that, combined with the first three, guarantees knowledge. It would have to eliminate all Gettier counterexamples, and not permit even more exotic counterexamples.

No one has yet come up with a fourth condition so obviously right that everyone has rushed to accept it. Of several attempts to frame a fourth condition, the most discussed holds that a justified true belief must also be
indefeasible
—it cannot be disqualified by extenuating circumstances.

Gettier’s victims of false knowledge end up hitting themselves on the side of the head and saying, “If only I had known!” The victims could have avoided error if they had known—or just believed—certain information (that the painting was removed; that the watch had stopped; etc.). These disqualifying facts are called defeaters. Had Gettier’s victims believed the defeaters, they would not have had justification for believing the paradoxically true statements.

It is 2:14
P.M
.; you believe it is 2:14
P.M
., having looked at your watch; you also believe that your watch stopped last night and hasn’t run since. Then your belief that it is 2:14 is irrational. It is irrational because the defeater casts the original evidence of the time (your watch’s hands indicating 2:14) in an entirely new light. The watch’s hands are now irrelevant. The condition of indefeasibility requires that there
not
be an extenuating circumstance like this.

No one ever really knows when a belief is threatened by a defeater like this. The condition of indefeasibility may satisfy a theoretical need for a fourth condition, but it cannot help us avoid Gettier’s false knowledge.

Now back to prisoner, judge, and executioner. You can argue from the tripartite account that the prisoner’s “knowledge” is an illusion. W. V. O. Quine felt that
all
the prisoner’s (or attorney’s) deductions are wrong. Even the first deduction, that the prisoner cannot be hanged the last day, is invalid.

When the judge said the prisoner must not be able to predict the day of his execution, he evidently meant that a perfectly logical prisoner would be unable to deduce the date with certainty. A regular, not so logical prisoner has greater freedom. He may have a hunch that it will be a certain day, and may even be right (an unjustified true belief). No choice of execution date is proof against a lucky guess. Assuming the judge’s order has any meaning at all, it must prohibit only a rational determination of the date.

For simplicity, use the two-day version of the paradox. Suppose for the sake of argument that the prisoner
can
logically determine that he must be executed on Saturday to fulfill the judge’s instructions. The executioner (who is just as bright as the prisoner) can likewise deduce this. He then has no reason to hang the prisoner on Saturday rather than Sunday. See why? The prisoner expects Saturday (that’s the premise of this reductio ad absurdum); but even if by some miracle he
isn’t
hanged on Saturday, he can deduce it will be on Sunday. That leaves the executioner no reason to prefer one day over another. He is damned if he does hang him on Saturday, and damned if he doesn’t.

Consequently, the executioner is equally free to execute the prisoner on either day. That means the prisoner is
wrong
to conclude he will be hanged on Saturday.

If you prefer, you can assume that the prisoner deduces Sunday as the only logical day of execution. This gives the executioner equal reason to hang him on Saturday, and the prisoner is wrong again.

The result is a Gettier situation with a twist. Let’s say the prisoner
is
hanged on Saturday. On the surface, the prisoner seems to have been right. The prisoner has a justified true belief. It fails to be genuine advance knowledge, though. The prisoner does not realize the defeater of his belief: that just as good a justification exists for him being hanged on Sunday. As stated above, the assumption that the prisoner
must
be hanged on Saturday leads to the conclusion
that he can equally well be hanged on either day. The defeater of the prisoner’s belief is the belief itself.