1
A Gettier case has all three conditions
The belief is justified, true and held, and the person does not know. The definition says the person knows, so it admits a case that should be excluded. That is the direction called too broad.
Lesson · Knowledge and Evidence · Analysing knowledge
Gettier Cases and the Fourth Condition
Gettier cases are rows where all three conditions hold and the verdict is still that the person does not know, so the definition is too broad. A fourth condition can be added to remove the failing row, and a new case can then be found that the fourth condition cannot separate.
J, T and B all hold, and no knowledge
the definition is too broad on that row
a fourth condition removes the row
a new case breaks the fourth condition
Too broad, then repaired, then too broad again
Core ideas
What this lesson establishes
The previous lesson tested a definition against four cases, and it survived. These cases are the ones it was not tested against.
2
A fourth condition is a new column
To exclude the failing row the table needs a way to tell it apart from ordinary perception. A new condition is a new column that is 1 on the failing row and 0 on perception.
3
A repair is itself a definition
A repaired analysis is tested the way the original was. The cases that broke the first version are not the only cases, and the repair must meet the ones that follow.
The material
Smith’s coins, the stopped clock and the fake barns
Two cases that the three conditions cannot tell apart from perception, and a third that the repair cannot.
In Gettier’s own case Smith has strong evidence that Jones will get the job, and that Jones has ten coins in his pocket. Smith therefore believes that the man who will get the job has ten coins in his pocket. In fact Smith himself gets the job, and Smith himself has ten coins. The belief is justified, true and held. Almost nobody thinks Smith knew it.
Russell’s stopped clock is the same shape with a simpler mechanism. You look at a clock that stopped twelve hours ago, read the time off it, and believe it is a quarter past two. By chance it is. You had good reason to trust the clock, the belief is true, and you hold it.
case J T B knows?
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ordinary perception 1 1 1 yes
Smith's coins 1 1 1 no
stopped clock 1 1 1 no
lucky guess 0 1 1 no
Two rows of this table are identical in all three columns and different in the verdict. Whatever the definition says about perception it must say about Smith’s coins, and the verdicts disagree. The lab’s search over one and two conditions finds no formula that fits, and none of any length could, because the inputs of two rows are the same and the outputs are not.
A fourth condition
The usual repair adds a condition that is true of the failing rows and false of perception. In both cases the belief depends on something false along the way: that Jones will get the job, that the clock is running. Call the condition L, for “relies on a false lemma”, and require it to be absent: J ∧ T ∧ B ∧ ¬L. In the lab’s list of candidate definitions, not is written as a tilde.
case J T B L knows?
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ordinary perception 1 1 1 0 yes
Smith's coins 1 1 1 1 no
stopped clock 1 1 1 1 no
lucky guess 0 1 1 0 no
fake barns 1 1 1 0 no
The fourth condition now separates Smith’s coins and the stopped clock from perception, and the lab now reports agreement on four of five rows. The last row is why it does not end there. Henry drives through country dotted with barn facades and looks at the one real barn. He sees a barn, believes it is a barn, and is right. He relies on no false lemma at all, so L = 0, and most people think he does not know, because he could easily have been looking at a facade.
Perception and fake barns now agree on every column, J = 1, T = 1, B = 1, L = 0, and differ in the verdict. This is the same trouble as before at a new place, and the lab names the row. Fixing it takes a fifth condition, and the literature has tried several.
Theorem · What the cases show and what they do not
They show that the three conditions are not jointly sufficient. They do not show that knowledge is impossible, and they do not show that justification is irrelevant: the lucky guess row still needs J, because without it the repaired definition calls the guess knowledge.
Interactive
The method of cases
A definition tested against every case in the table
Method
Working a Gettier case
Constructing a case and then testing a repair, in the order the lab expects.
1
Start from an ordinary case of knowing
Take a case you are sure about, such as seeing a cup on the table, and write its row. Everything else is a variation on it.
2
Break the connection but keep the three conditions
Add luck that sits between the justification and the truth. The evidence points the right way for the wrong reason, so J, T and B stay at one.
3
Record the verdict and classify the failure
If you judge that the person does not know, the definition is too broad on this row. Say so: it is the direction that tells you the repair must add a condition.
4
Propose a fourth condition
Choose a condition that is present on the failing row and absent on ordinary perception, and add its negation or itself to the definition.
5
Look for a case the new condition cannot separate
Build a case with the same four values as perception and a different verdict. If you can, the repair is too broad on that row, and you are back at the second step.
Gettier rows
Score 0 / 0Choose the answer you can justify.
Smith’s coins through the lab
Row by row, with L standing for a false lemma.
Smith's coins: J=1 T=1 B=1 verdict no
J ∧ T ∧ B: says knows -> too broad
add ¬L: L=1 on the coins -> now says no
fake barns: J=1 T=1 B=1 L=0, verdict no
J ∧ T ∧ B ∧ ¬L: says knows -> too broad again
The repair did what it was built to do and removed one row. It did not stop the failure; it moved it. That is the usual history of a proposed fourth condition.
Common mistakes
1
Taking Gettier to show that knowledge is impossible, or that justification is irrelevantThe ordinary perception row still has all conditions and the verdict yes, so cases of knowing survive. The lucky guess row still needs justification excluded, and the lab shows the repaired definition calling the guess knowledge as soon as J is dropped. What the cases refute is the claim that the three conditions are enough. A definition that is too broad on some rows is not a definition of nothing.
2
Believing a fourth condition ends the matterA repair is a new definition and meets the same test. The false-lemma condition removes the coins and the clock and then fails on the fake barns, where there is no false lemma. The failure moves to a case the repair did not anticipate, and the lab’s search finds no formula of one or two of the listed conditions that fits the table; the two rows that agree in every column and differ in the verdict show that none of any size could.
3
Reading “justified” as “certain”Smith is not careless. His evidence is strong, and it is only the luck between evidence and truth that fails him. Raising the standard of justification does not help, because any standard short of the truth itself can be met by a case with this structure.
Check your understanding
✓
Finish when you can build the row and classify it.
You should be able to write down a case with all three conditions present and the verdict no, say that the definition is too broad on it, propose a fourth condition, and construct a case with the same values as perception that the new condition cannot separate. A case described in prose without its row of values has not yet been tested.
Note: The labs search only the conditions that you list. If the table has no column that separates two rows, no search can succeed, and finding what the missing column would be is the philosophical work the lab leaves to you.