Maria sees a clock showing 4:00 PM. The clock stopped exactly 12 hours ago. It is, in fact, 4:00 PM. Does Maria know it is 4:00 PM, according to the justified-true-belief analysis?
AYes — she has a true belief with reasonable justification, satisfying all three conditions.
BNo — this case is a counterexample to the JTB analysis: she satisfies all three conditions yet clearly lacks genuine knowledge because her belief is only accidentally true.
CNo — her belief is not justified, because a stopped clock is never an acceptable source of evidence.
DYes — whether the justification is causally reliable is irrelevant; true belief plus justification is sufficient.
This is a Gettier-style counterexample. Maria satisfies every condition the JTB analysis requires — the belief is true, and she has the normal kind of justification for it — yet we recognize she does not genuinely know the time; she got lucky. The case proves the analysis is incomplete because it identifies a situation where all three conditions hold but knowledge is absent. Option A states the very view this scenario refutes. Option C is wrong: clock-reading is standard justification; the problem is that her justification is disconnected from the fact that makes her belief true.
Question 2 Multiple Choice
Someone argues: 'All mammals are warm-blooded; all dolphins are warm-blooded; therefore all dolphins are mammals.' What is the logical status of this argument?
AValid and sound — the premises are true and the conclusion is also true.
BValid but unsound — the argument form is correct but a premise is false.
CInvalid — a counterexample shows the form can have true premises and a false conclusion.
DInvalid — the premises contradict each other.
The form 'All A are B; all C are B; therefore all C are A' is invalid, even though the conclusion happens to be true in this instance. Counterexample: 'All dogs are mammals; all cats are mammals; therefore all cats are dogs.' True premises, false conclusion — proving the form invalid. Option A is the key distractor: a true conclusion does not rescue an invalid argument. Validity concerns whether the form guarantees the conclusion, not whether the conclusion happens to be true.
Question 3 True / False
A single genuine counterexample is sufficient to refute a universal generalization.
TTrue
FFalse
Answer: True
True. A universal generalization claims something holds for every member of its domain. One genuine exception — one case where all the required conditions are met but the conclusion fails — proves the claim false. This asymmetry is fundamental: a thousand confirming instances cannot prove a universal claim, but one disconfirming instance disproves it. This is why Gettier needed only two brief scenarios to overturn a widely accepted account of knowledge that had stood for decades.
Question 4 True / False
An unusual or exotic counterexample carries less logical force than a common, everyday one.
TTrue
FFalse
Answer: False
False. The force of a counterexample comes entirely from its logical structure — whether it genuinely falls within the scope of the claim and genuinely violates the conclusion. How rare or unusual the case is has no bearing on its logical power. A single black swan refutes 'All swans are white' just as decisively as a thousand would. Frequency matters in probabilistic reasoning but not in testing universal claims.
Question 5 Short Answer
What makes a Gettier case a genuine counterexample to the justified-true-belief analysis, rather than merely an expression of doubt about the theory?
Think about your answer, then reveal below.
Model answer: A Gettier case is a specific, constructible scenario that satisfies every condition the JTB analysis requires — the belief is true, and the person has a justification that meets ordinary epistemic standards — yet the case is one where we clearly judge the person does not know. It does not merely raise vague skepticism; it provides a concrete instance that fits the definition perfectly while falling outside the concept. That precision is what makes it a counterexample: it proves the analysis is extensionally incorrect — it includes cases it should not.
Compare: saying 'I doubt JTB is right about knowledge' is an expression of uncertainty. Constructing a case where JTB is satisfied and knowledge is absent is a counterexample. You cannot dismiss it by saying 'knowledge is complicated' — you must either accept the case counts as knowledge (contradicting intuition) or accept the analysis fails. The counterexample forces the issue in a way that mere doubt cannot.