Questions: The No False Lemmas Condition

Question 1

Smith justifiably believes 'Jones will get the job' and infers 'The person who gets the job has ten coins in their pocket' (after counting Jones's coins). Smith gets the job and happens to have ten coins. Does the no false lemmas condition explain why Smith lacks knowledge?

• A. Yes — Smith's inference passed through the false lemma 'Jones will get the job'
• B. No — Smith's belief is true and justified, so no additional condition is needed
• C. No — the no false lemmas condition applies only to deductive, not inductive, inferences
• D. Yes — but only because Smith counted the wrong person's coins

Answer: (A)

This is a canonical Gettier case. Smith's inference ran through the false lemma 'Jones will get the job.' That lemma is false — Smith gets the job, not Jones. The true conclusion happens to be true for a different reason (Smith has ten coins), making the truth of the belief accidental relative to Smith's evidence. The no false lemmas condition correctly diagnoses non-knowledge by identifying the false intermediate step in the inferential chain.

Question 2

Henry is driving and perceives what he takes to be a barn, forming the belief 'That is a barn.' The region is full of convincing barn facades, but he happens to be looking at the one real barn. According to the no false lemmas condition, does Henry know there is a barn?

• A. Yes — his belief is true, justified, and contains no false inferential lemma
• B. No — his inference passed through the false lemma 'This region contains only real barns'
• C. No — the condition correctly identifies that his perceptual process is unreliable
• D. Yes — he has knowledge because he is actually looking at a real barn

Answer: (A)

This case reveals the condition's critical limitation. Henry's belief is formed directly through perception — there is no explicit inferential lemma in his reasoning. The no false lemmas condition has nothing to diagnose because there is no inferential chain with a false step. Yet many philosophers judge this not to count as knowledge (the truth is accidental relative to Henry's epistemic situation). The condition is insufficient: some Gettier-style cases escape its reach entirely.

Question 3

The no false lemmas condition is a proposed fourth condition on knowledge, added to the traditional justified true belief account specifically to handle Gettier cases.

• T. True
• F. False

Answer: True

Gettier (1963) showed that justified true belief is not sufficient for knowledge — some JTBs are merely luckily true. The no false lemmas condition adds a fourth requirement: the justification must not essentially depend on any false intermediate proposition. It is an attempt to close the Gettier gap by requiring that the inferential route from evidence to belief be free of false steps.

Question 4

The no false lemmas condition successfully handles most Gettier cases, making it a complete theory of knowledge.

• T. True
• F. False

Answer: False

The condition handles Gettier cases where inference passes through a false lemma — a significant class. But it fails for non-inferential Gettier cases, such as barn facade scenarios where a perceptual belief is formed directly with no inferential chain. Because some Gettier cases involve no lemmas at all, the condition's scope is too narrow. This limitation motivates defeasibility approaches, which address a broader range of epistemic defeaters.

Question 5

Describe the type of Gettier case that the no false lemmas condition cannot handle, and explain why the condition fails there.

Model answer: The condition fails for non-inferential Gettier cases — situations where a true belief is formed directly through perception without passing through any explicit intermediate proposition. The barn facade case is canonical: Henry forms 'that is a barn' by looking, with no inferential chain. Since there are no lemmas, the condition has nothing to flag. Yet the belief seems not to count as knowledge because its truth is accidental relative to Henry's epistemic situation — he could just as easily have been looking at a facade. The condition's scope is limited to inferential beliefs, so it cannot diagnose cases where luck enters through the perceptual process itself.

This limitation also reveals something deeper: 'false lemma' is one type of epistemic defeater, but not the only type. Defeasibility theory generalizes the insight by asking whether any true information could undermine the justification — a broader test that captures perceptual Gettier cases too.