Three Pages Against Two Thousand Years: The Gettier Problem

Here is a strange piece of academic lore. In 1963 Edmund Gettier, then an untenured philosopher at Wayne State, needed publications and apparently did not have much he wanted to say. Colleagues urged him to write up an objection he had been kicking around in conversation. The result was under three pages. He never published another philosophy paper in his life, and by most accounts he did not think the little note amounted to much. That little note is "Is Justified True Belief Knowledge?" (Gettier 1963), and it wrecked a definition of knowledge that philosophers had been leaning on, in one form or another, since Plato.

What the definition said

Ask most people what knowledge is and you will get a shrug, but philosophy had a serious answer for a very long time. Knowledge is justified true belief. Plato already circles the idea in the Theaetetus, where true belief "with an account" is the last candidate standing (Plato, Theaetetus 201c–210a), and by the twentieth century versions of the formula show up in Ayer and Chisholm as something close to received wisdom (Ayer 1956; Chisholm 1957).

Each of the three parts is doing real work. Belief first: I cannot know that Paris is the capital of France while sincerely denying it. Truth second: medieval doctors believed with total confidence that disease came from imbalanced humors, and they were wrong, so whatever they had, it was not knowledge. Conviction is cheap; knowledge has to answer to the world.

The third condition, justification, is the one that earns its keep. Say I believe my lottery ticket will win because my horoscope told me so, and it wins. True belief, sure. Knowledge? Nobody thinks so. I had no real reason. Russell had already poked at this region with his stopped clock: a man glances at a clock that happens to have stopped exactly twelve hours earlier, reads off the correct time, and believes it (Russell 1948). Something has clearly gone wrong there, even though he ends up with a true belief. Justification was supposed to be the filter that keeps this kind of dumb luck out.

So: belief connects knowledge to a mind, truth connects it to the world, justification is the bridge between them. Tidy. Too tidy, it turned out.

What Gettier noticed

Gettier's point, and it really is a simple point once you see it, is that the justification filter leaks. It blocks some luck. It does not block all of it. His paper gives two cases; here is the first one, lightly modernized.

Smith and Jones are up for the same job. Smith has excellent evidence for two things. The company president told him Jones will get the job, and Smith personally counted the coins in Jones's pocket ten minutes ago: there are ten. Putting these together, Smith infers something slightly odd but perfectly valid: the man who will get the job has ten coins in his pocket.

Then reality misbehaves. The job goes to Smith, not Jones. And, as it happens, Smith also has exactly ten coins in his own pocket, though he never counted them.

Look at Smith's inferred belief now. The man who gets the job has ten coins in his pocket. True? Yes, because Smith got the job and Smith has ten coins. Justified? Yes, he reasoned carefully from strong evidence. Believed? Obviously. And yet nearly everyone who hears the story balks at saying Smith knew it. His evidence was all about Jones's pocket. What made the belief true was his own. The truth came in through the back door while the evidence was watching the front.

Chisholm has a version I like better because there is no clever inference in it at all (Chisholm 1966). You look out at a field and see what looks exactly like a sheep, so you believe there is a sheep in the field. What you are actually seeing is a dog dressed up in wool. But it so happens that behind a hill, where you cannot see it, a real sheep is grazing. Your belief is true. Your belief is justified, given what your eyes told you. And you plainly do not know there is a sheep in that field. You lucked into it.

Once you have the pattern you can generate these cases forever. Start with a justified belief, cut the wire between the justification and whatever actually makes the belief true, then let coincidence solder the truth back on. Justified true belief, no knowledge.

Fifty years in the repair shop

The reaction was fast and, in retrospect, a bit frantic. For decades "the Gettier problem" was nearly its own subfield, and the attempted fixes make a nice tour of philosophical ingenuity, each one clever, each one eventually gutted by a new counterexample.

The earliest fix was the "no false lemmas" rule: knowledge is justified true belief that does not pass through any false step along the way (Clark 1963). This kills the Smith case cleanly, since Smith's inference ran through the falsehood that Jones would get the job. But the sheep case walks right past it. You never inferred anything. You just looked, and your eyes deceived you without a single false premise being entertained.

Goldman then proposed a causal theory: you know something when the fact itself causes your belief in an appropriate way (Goldman 1967). Nice diagnosis of the sheep case, where the hidden sheep played no causal role in your belief at all. The trouble is that mathematical truths and general truths do not cause beliefs in any obvious sense, and worse, there is the barn case, suggested to Goldman by Carl Ginet and published by Goldman himself, admirably, as an objection to his own earlier view (Goldman 1976). A man drives through a district where the locals have put up dozens of hollow barn facades. By chance he looks at the one genuine barn and thinks, barn. The real barn causes his belief in the most ordinary way possible. Still feels wrong to say he knows. He would have formed the same belief in front of any of the fakes.

The barn case pushed people toward reliabilism and later toward "safety" and "sensitivity" conditions, the rough idea being that knowing requires you could not easily have been wrong, that your method holds up in nearby possible situations and not just this one (Goldman 1976; Nozick 1981; Sosa 1999). There is something genuinely deep here. There is also, for every precise formulation anyone has offered, a purpose-built counterexample somewhere in the journals.

Zagzebski eventually argued that this endless whack-a-mole is not bad luck but destiny (Zagzebski 1994). Define knowledge as truth plus any condition that is even slightly independent of truth, and the daylight between the two can be exploited. Some story can always be told in which the condition is met and the truth holds anyway, by accident. On her diagnosis, Gettier cases are not a flaw in this or that definition. They are what happens whenever you try to build knowledge out of parts.

Williamson took the hint and went further: stop trying (Williamson 2000). On his "knowledge first" view, knowledge is not assembled from belief, truth, and something else. It is itself basic, a fundamental relation between a mind and the world, and the whole analytic project had things backwards. You cannot patch the definition because there never was a correct definition to patch.

Why I think it matters

I will admit the raw materials look silly. Coins, costumed dogs, fake barns. It would be easy to shelve the whole thing as a parlor game. But strip away the props and the problem underneath is about as serious as they come: it is about the relation between truth and our methods for getting at truth, which is the working problem of every science and arguably of ethics too.

Put it this way. Truth is a matter of how things stand. Justification is a matter of how things look from where we happen to be standing. The old definition quietly assumed that when the two line up and we believe accordingly, that is knowledge. Gettier showed that mere lining up is not enough. The alignment has to hold for the right reasons. Coincidence between evidence and truth is not connection between evidence and truth.

If you are any kind of realist, about mathematics, about the physical world, about morality, this should feel less like a paradox and more like a description of the human condition. Realism just is the view that the facts do not depend on our procedures for finding them. But then a gap between fact and procedure is not some exotic failure mode. It is the default, and our methods are devices for narrowing it, never for closing it. Evidence can be excellent and still hit the truth by accident. Proof can be rigorous and still leave truths forever out of reach, which is not a metaphor: Gödel showed that any consistent formal system rich enough for arithmetic contains true statements it cannot prove (Gödel 1931). Provability is our handle on mathematical truth, not the truth itself. Gettier's little stories make the same point in miniature that Gödel's theorems make at scale. The map is not the territory, and no map certifies its own accuracy from the inside.

That "from the inside" is the unsettling part. Smith's reasoning felt exactly like knowing. The driver in barn country felt exactly like someone seeing a barn, because he was one. The failure is invisible at the point of failure. Most of our knowing feels like that too.

None of this argues for skepticism, and I want to be clear about that. Smith's careful inference is still incomparably better than reading horoscopes, and methods that reliably track truth remain the best things we own. What the Gettier problem earns you is something more like permanent double vision: full commitment to your best justified beliefs, held together with the standing awareness that justification is our achievement and truth is the world's, and that these two things, however close they usually run, are never the same thing.

Gettier himself watched the enormous literature his three pages spawned with what colleagues describe as amused detachment, and never wrote a word in reply. Maybe he understood something about problems: that some of them are worth more open than solved, because the difficulty itself tells you what kind of creature you are. A believer, reaching with good but imperfect instruments toward truths that are under no obligation to bend toward you.

References

Ayer, A. J. 1956. The Problem of Knowledge. London: Macmillan.

Chisholm, Roderick M. 1957. Perceiving: A Philosophical Study. Ithaca, NY: Cornell University Press.

Chisholm, Roderick M. 1966. Theory of Knowledge. Englewood Cliffs, NJ: Prentice Hall.

Clark, Michael. 1963. "Knowledge and Grounds: A Comment on Mr. Gettier's Paper." Analysis 24 (2): 46–48.

Gettier, Edmund L. 1963. "Is Justified True Belief Knowledge?" Analysis 23 (6): 121–123.

Gödel, Kurt. 1931. "Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I." Monatshefte für Mathematik und Physik 38: 173–198.

Goldman, Alvin I. 1967. "A Causal Theory of Knowing." The Journal of Philosophy 64 (12): 357–372.

Goldman, Alvin I. 1976. "Discrimination and Perceptual Knowledge." The Journal of Philosophy 73 (20): 771–791.

Nozick, Robert. 1981. Philosophical Explanations. Cambridge, MA: Harvard University Press.

Plato. Theaetetus. Translated by M. J. Levett, revised by Myles Burnyeat. Indianapolis: Hackett, 1990.

Russell, Bertrand. 1948. Human Knowledge: Its Scope and Limits. London: George Allen and Unwin.

Sosa, Ernest. 1999. "How to Defeat Opposition to Moore." Philosophical Perspectives 13: 141–153.

Williamson, Timothy. 2000. Knowledge and Its Limits. Oxford: Oxford University Press.

Zagzebski, Linda. 1994. "The Inescapability of Gettier Problems." The Philosophical Quarterly 44 (174): 65–73.