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Responses to Gettier fall into several families. The no-false-lemmas condition adds that knowledge may not depend essentially on any false intermediate belief, but this fails for direct Gettier cases that use no false lemmas. The causal theory (Goldman 1967) requires that the fact that p causally produce the belief that p, handling perceptual cases but struggling with knowledge of mathematical or future truths. Defeasibility theories require that no true proposition, if added to the evidence, would defeat the justification. Each response captures something right while facing its own counterexamples, motivating a shift away from the analysis project entirely toward reliabilism or virtue epistemology.
For each proposed fourth condition, construct a case that satisfies JTB plus that condition but still intuitively lacks knowledge. This systematic pressure helps explain why many epistemologists abandoned the analysis project.
From your study of Gettier problems, you know that justified true belief is not sufficient for knowledge. Gettier's 1963 counterexamples showed that a belief can be justified and true and yet fail to be knowledge because the justification and the truth are connected only accidentally — through luck. The immediate philosophical reaction was to look for a fourth condition to add to the JTB analysis that would rule out Gettier cases while preserving all genuine cases of knowledge. The history of these responses is a case study in philosophical dialectic: each proposed fix is plausible, but each is either too weak (it still admits some Gettier-like cases) or too strong (it excludes cases that do seem like knowledge). Understanding why each response fails is as important as understanding the response itself.
The no-false-lemmas condition (sometimes called the "no-false-grounds" condition, associated with Gilbert Harman) adds that knowledge requires that the belief not be inferred from any essentially false intermediate premise. This handles Gettier's original cases directly: in those cases, the agent infers a true conclusion from a false belief (e.g., infers "someone in this office owns a Ford" from the false belief "Jones owns a Ford"). Ruling out false lemmas excludes those cases. The problem is direct Gettier cases that use no false lemmas at all. The classic example: Henry is driving through the countryside and sees what looks exactly like a barn. It is a barn, and his perception is functioning normally — he has no false beliefs in his reasoning chain. But unbeknownst to Henry, he is in "Fake Barn County," where nearly all the barn-shaped structures are elaborate facades. By luck, this particular one is a real barn. Henry has a justified true belief with no false lemma, but intuitively he does not know there is a barn. The no-false-lemmas condition cannot exclude this case.
Alvin Goldman's causal theory of knowledge (1967) takes a different approach: it requires that the fact that p *causally produce* the belief that p through an appropriate causal chain. This handles perceptual cases elegantly — your belief that there is a barn is caused by the barn itself (through light, retina, neural processing), so that is knowledge. In Gettier's original cases, the causal connection between the truth (someone in the office does own a Ford) and the belief is broken or accidental. The causal theory excludes those cases. But the theory struggles with knowledge of abstract or non-causal truths: how can you have knowledge that 7 is prime if there is no causal process linking the mathematical fact to your belief? Abstract mathematical and logical truths do not cause anything, yet we clearly know them. The causal theory would either deny we know these truths (implausible) or require a strained notion of "appropriate causal chain" that threatens to swallow the original insight.
Defeasibility theories (Lehrer and Paxson, Chisholm) require that there be no true proposition which, if the subject were to learn it, would undermine the justification. In the Fake Barn case, the true proposition "most barn-like structures here are facades" would defeat Henry's justification if he learned it, so defeasibility rightly says he lacks knowledge. The problem is misleading defeaters: in some cases, there exists a true proposition that would defeat the justification if believed, but only because that proposition is itself misleading. Suppose Tom sees his friend Grabit steal a book, and Tom justifiably believes Grabit stole it. Unknown to Tom, Grabit's mother — a notorious liar — has told police that Grabit has a twin who committed the theft. The proposition "Grabit's mother said he has a twin" would, if believed by Tom, defeat his justification. Yet intuitively Tom does know Grabit stole the book. A simple defeasibility condition cannot distinguish genuine defeaters from misleading ones.
The significance of this catalog of failures is not merely negative. Each failed response isolates something real about Gettier cases — the role of false reasoning, the need for appropriate causal connection, the requirement that no defeating information lurks in the environment — without fully capturing it. Many epistemologists concluded that the analysis project itself was misconceived: the attempt to give necessary and sufficient conditions for "S knows that p" in terms of simpler notions may be an instance of what Wittgenstein called the demand for definitions where there is only family resemblance. The responses to Gettier set the stage for reliabilism (Goldman's later view: knowledge is belief produced by a reliable cognitive process) and virtue epistemology (Sosa, Zagzebski: knowledge is belief produced through the exercise of intellectual virtues), which shift the question from conditions to processes and character — and explicitly abandon the hope of a short-form analysis.
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