The Gettier Problem

I shall argue that Keith Lehrer’s fourth condition for knowledge fails to account for all Gettier-like cases and places implausible restrictions on knowledge. I shall first explain the Gettier problem and Lehrer’s response and show how Lehrer appears to solve the problem. After, I shall use Randolph Carter’s criticism to show how Lehrer fails to solve every Gettier-like case before arguing that Lehrer’s concept of potential defeaters places too many epistemic demands on the agent.

Edmund Gettier proposes two case examples to contest the commonly held notion of knowledge. The view of knowledge was that three necessary conditions formed a jointly sufficient condition needed for one to be knowledgeable of P (these conditions adequately entail the definition of knowledge) (Gettier, 1963, p. 121):

1. S believes that P
2. S is justified in believing P
3. P is true

Gettier first makes two claims:

1. Being justified in believing P does not entail its truth
2. If S is justified in believing P, P entails Q, S deduces Q from P, then S is justified in believing Q

From this, Gettier formulates two cases to show that the ‘justified true belief’ conception of knowledge is inadequate.

Case 1

(Gettier, 1963, p. 122): Gettier supposes two employees, Smith and Jones, with Jones having ten coins in his pocket and Smith having reliably heard that Jones will be promoted. Thus, Smith believes that the man with ten coins in his pocket will receive the promotion. Yet, unbeknownst to Smith, he also has ten coins in his pocket and will receive the promotion. Thus, the belief that the man with ten coins will receive the promotion is true, yet the premise from which it was drawn (that Jones will be promoted and that Jones has ten coins) is false.

Case 2

(Gettier, 1963, p. 123): In case 2, Smith has a justified belief that Jones owns a Ford. Additionally, Smith is unaware of Brown’s current location. Thus, Smith claims three disjunctions (Gettier, 1963, p. 123): either Jones owns a Ford, or Brown is in Boston; either Jones owns a Ford, or Brown is in Barcelona; either Jones owns a Ford, or Brown is in Brest-Litovsk. All these propositions are entailed by the belief that Jones owns a Ford. Upon realising this, Smith also recognises he is justified in believing each disjunction. However, suppose that Jones does not currently own a Ford (he crashed it yesterday, unbeknownst to Smith) and that Brown just happens to be in Barcelona. If this is true, then Smith cannot be said to know the second disjunct, despite his justified (because he was justified in believing Jones owned a Ford), true belief (because Brown was in Barcelona).

Gettier’s two cases show that the JTB conception of knowledge does not provide a sufficient definition of what it means to know something. There are instances where one can be said to have a justified true belief in P yet not know it. Gettier’s counterexamples are meant to disrupt the so-called supremacy of the ‘justified true belief’ account of knowledge.

Lehrer recognises the issues of the Gettier problem – when a person is justified in “believing or accepting some false proposition which transmits justification to some true proposition” (Lehrer, 1979, p. 65). Lehrer provides an alternate definition of knowledge (Lehrer, 1979, p. 65): S knows h iff (i) h is true, (ii) S accepts h, (iii) h is evident for S, and (iv) there is no false proposition f such that if f were doubtful for S, then h would not be evident for S.

Lehrer distinguishes between acceptances and beliefs (Lehrer, 1979, p. 66). One’s beliefs are natural endowments, not necessarily volitional decisions, whereas one’s choice to accept something reflects a conscious decision made by the agent to purposefully assent or refuse something (Lehrer, 1979, p. 67). This is crucial as it fits better with Lehrer’s conscious, evidence-based approach to tackling knowledge.

Secondly, Lehrer clarifies what it means for something to be evident. A proposition’s evidence depends on its relation to other propositions. Proposition h is evident to S iff it beats other proposition c or if c is neutralised by h in respect to S (Lehrer, 1979, p. 67). For a proposition to beat another, it must first compete with it. For two propositions to compete, they do not have to contradict – rather, one must “diminish the epistemic worth” of accepting the other (Lehrer, 1979, p. 67). Thus, c competes with h iff it was less reasonable for S to accept h if c were certain for S than if the denial of c were certain for S. Lehrer can now define how propositions beat others. h beats c if it is more reasonable for S to accept h than to accept c. Competitor c is neutralised if there is a proposition n such that the conjunction of n and c no longer competes with h, and it is as reasonable for S to accept the conjunction as it is to accept just c (Lehrer, 1979, p. 68). Thus, for proposition h to be evident to S, it must beat or neutralise any competing propositions.

Finally, Lehrer clarifies his fourth condition. By ‘doubtful’, he means that proposition f is doubtful for S iff “it is more reasonable for S to decline p than accept it” (in other words, it is more reasonable for S not to accept p, but rather question accepting its denial) (Lehrer, 1979, p. 70). Thus, for something to be considered knowledge, there must not be a potential defeater for S’s belief that p. There is a potential defeater for S’s belief that p, iff there is some q, such that q is false, and if S learned that q was false, S would not believe p.

Considering Gettier’s first case, one can apply Lehrer’s theory to see how it fares. The original issue was that it did not feel intuitively correct to argue that Smith knew he would receive the promotion. Instead, Smith accidentally realised that he would be promoted.

Hence, Lehrer’s main issue would be Smith’s justification and the satisfaction of (iv) – there must be no potential defeater to the belief. If the agent forms a belief under the conditions of a potential defeater for said belief, they cannot have knowledge. In Gettier’s first case, there is a potential defeater for Smith’s belief that the man with ten coins in his pocket will receive a promotion. However, Smith is unaware that he will receive the promotion instead of Jones. The very existence of this fact undermines Smith’s justification completely. Smith no longer satisfies (iv). If the agent could acquire information such that there was a proposition that would make previous beliefs false, then they are not in a position of knowledge.

This analysis shows that Lehrer’s solution to the Gettier problem aligns with our common intuitions. Smith’s ‘knowledge’ relied on a defeater to his claim, thus allowing Lehrer to claim he never really possessed knowledge in the first place. However, just because Lehrer manages to overcome one of the examples put forward by Gettier, it doesn’t mean that his conception of knowledge is sufficiently suitable to overcome similar Gettier-like problems. Take, for example, Case C, put forward by Randolph Carter (Carter, 1977, p. 330) – an entomologist trapped in a village where the villagers are renowned for their brilliant hospitality. This contributes to his false belief that he can leave by a rope ladder (and thus leave the village). Furthermore, he (justifiably yet falsely) believes his climbing skills are so poor that he cannot leave the village by climbing a rope to the adjacent cliff since he recalls his poor climbing skills in previous scenarios. The ladder is removed, but he manages to leave by using the ‘roof-and-rope method’, making his original belief that he can leave the village true. Here, we have a Gettier-like case because the entomologist has a justified true belief. Yet, our intuition is that the entomologist does not know he can leave because his true belief is based on the false belief that he can use the ladder.

In this example, Carter argues that Lehrer’s conception of knowledge fails to deny that the entomologist didn’t know he could leave the village. Instead, it falsely tells us that the entomologist knew he could leave the village. To establish this, we must consider Lehrer’s four conditions. (i) and (ii) are both satisfied because the entomologist has a true belief about his ability to leave the village. Additionally, (iii) is also satisfied since the proposition that the entomologist can leave the village is more reasonable than his not being able to, thus meaning that it beats other propositions and is thus evident. The challenge, however, is whether Lehrer’s fourth condition is satisfied. To do this, one must consider the ‘verific alternative’ to the entomologist’s corrected beliefs. A verific alternative is what the agent would believe if they were to replace their false beliefs with their denials and then assess whether the justification for their belief still held (Carter, 1977, p. 327). Consequently, one can assess (iv). In the verific alternative, the entomologist believes he can leave the village, that he can leave the village by climbing the rope (since the opposite was false) and that he cannot leave by ladder (the opposite of this was also false). In this alternative, he is justified in believing that he can use the rope to leave and, therefore, leave the village. Thus, (iv) is satisfied, and the entomologist is said to have known he could leave the village (Carter, 1977, p. 331). However, this goes against the intuition that the entomologist never really knew that he could leave the village.

Moreover, having seen that Lehrer’s solution fails to resolve every Gettier-like problem, we may also criticise it for its restrictive account of knowledge. Lehrer’s fourth condition requires the agent to rule out all possible defeaters to a proposition. In applying the solution to Gettier’s first case, Smith faced an unknown defeater. According to Lehrer, the only possible way for Smith to have justifiably known would have been for him to be aware of something almost impossible to be aware of. If we require the agent to rule out every single conceivable defeater to their proposition, we may remain in a position of constant scepticism. Any number of possibilities may suggest that some fact poses a defeater to the agent’s claim. Lehrer may suggest that instead of having to consider any possible potential defeater, the agent must only consider those which are most relevant to the context. Yet this seems to be lacking. How can one decide what is relevant to the situation? Suppose that Smith only received the promotion because Jones suffered some freak accident on his way to work, leaving only Smith as the only possible candidate. At first, this may not seem relevant to Smith as it is so improbable that there was any real need to consider it. Furthermore, refining potential defeaters to unknown ones loses the scrutiny that Lehrer’s conception allegedly affords him. The worry is that making this move loses the strength of Lehrer’s fourth condition. Thus, a trade-off that Lehrer must be willing to accept is that his fourth condition, although keen to consider all possible defeaters, may prove to demand too much epistemic access and may ultimately nearly always force the agent into a position of scepticism.

In conclusion, I have shown how Lehrer’s solution fails to solve the Gettier problem. As shown in the case put forward by Randolph Carter, Lehrer’s ‘solution’ sometimes concludes that an agent knows something when we would intuitively say otherwise. Additionally, I have shown that Lehrer places too high a demand on the agent, leading to them often having to be in a position of scepticism and being unable to know anything. Thus, while we may at first think that Lehrer provides a solution to the Gettier problem, under further scrutiny, it fails to suffice in every Gettier-type case and places the agent in too confined a position to be able to attain knowledge.