The Gettier Problem

Philosophy · 28 April 2016

In 1963, Edmund L. Gettier published a brief paper in Analysis. The paper challenged the traditional view of propositional knowledge as justified true belief. In this paper, I will attempt to challenge Gettier’s argument in effort to defend the traditional definition of knowledge.

Gettier raised objections against the traditional definition of knowledge. Namely, Gettier claims that:

(K) S knows that P if and only if

(1) P is true,

(2) S believes that P, and

(3) S is justified in believing that P

is insufficient for propositional knowledge.

Gettier’s Two Assumptions

Gettier’s two cases were built on two explicit assumptions. First Gettier assumed:

A1: It is possible for S to be justified in believing P, which is in fact false.

That is, Gettier assumed that while S may not know that P, condition (3) can be satisfied even if condition (1) is not.

Gettier’s second assumption is based on the principle of epistemic closure. Gettier wrote:

A2: For any proposition P, if S is justified in believing P, and P entails Q, and S deduces Q from P and accepts Q as a result of this deduction, then S is justified in believing Q. (Gettier, 1963)

This is derived from a more general deductive closure principle, “A set of objects, O, is said to exhibit closure or to be closed under a given operation, R, provided that for every object, x, if x is a member of O and x is R-related to any object, y, then y is a member of O” (Audi, 1999).

These assumptions build up the essential logic in Gettier’s cases where all three conditions are satisfied for (K) but S does not know P.

Gettier’s Objections

Case 1

Smith and Jones have applied for a job and Smith has strong evidence for the following proposition:

(a) Jones is the man who will get the job, and Jones has ten coins in his pocket

and proposition (a) entails:

(b) The man who will get the Job has ten coins in his pocket

Here, (a) logically entails (b), and since (a) is epistemically justified, by A2, Smith is justified in believing that (b).

Gettier then introduced that, as a matter of fact, Smith instead of Jones is the man who will get the job; and unknown to Smith, he also has ten coins in his pocket. In this case, (b) is true despite the falseness of (a) from which (b) is inferred. However, Smith does not know (b) because he was not aware of the number of coins in his pocket. Gettier concluded that (1)-(3) together are not sufficient for knowledge.

Case 2

Suppose Smith has a friend Brown whose whereabouts he is ignorant of. Also, Smith has strong evidence to believe that:

Smith then randomly selects three city names and entails the following:

(d) Either Jones owns a Ford, or Brown is in Boston

(e) Either Jones owns a Ford, or Brown is in Barcelona

(f) Either Jones owns a Ford, or Brown is in Brest-Litovsk

Since Smith is justified in believing proposition (c) and propositions (d)-(f) are logically entailed by (c), Smith is justified in believing (c)-(f) under epistemic closure. Now suppose that Jones does not own a Ford, and by coincidence, Brown happens to be in Barcelona. Even though Smith believes and is justified in believing that (e) is true, and (e) is in fact, true, Smith does not know (e) is true. Hence, traditional definition for knowledge as justified true belief is not sufficient for knowledge.

Responses to Gettier’s Objection

One possible defence for the traditional view of propositional knowledge is to reject Gettier’s two assumptions. A1 seems very plausible as we have learnt from the history of science, many well-justified beliefs had been proved false. An example is that the heliocentric model of the universe, which was supported by strong evidence and approved by prominent Greek philosophers at the time, turned out to be false. A2, also known as epistemic closure principle, is a fundamental logic that humanity has adopted. It would be problematic to reject this assumption because in doing so, we have to give up on most of our everyday reasoning. However, if a further condition is added to this principle, we would not need to reject the assumption itself to defend traditional definition of knowledge. Consider object x is an element of O and x is R-related to a set of objects S=[w, y, z, …]. x, by definition, exhibits closure on set S under operation R, thus S is also a member of O by deductive closure. The further condition could be that, for epistemic closure to hold, every element in set S must cohere with every element in set O. That is, if object y, z ⊆ S contradict with other elements in set O, S is not closed under operation R. Now, consider Gettier’s first case. Proposition (a) entails that Smith will not get the job, which contradicts with proposition (b) where Smith turned out to get the job. Then we can say that proposition (b) and that ‘Smith will not get the job’ are not closed under epistemic closure.

Let us assume that A1, A2 are perfectly sound, Gettier’s arguments do not necessarily follow. Followed by A2, Smith’s justified belief (a) logically entails (b) which is also justified under epistemic closure. The logic of such entailment could be:

P1: (a)

P2: If (a), then (b)

C: (b)

Then we may ask, does such logical entailment hold if the deduction itself contains a false premise. That is, the deduction which yields (b) can only be sound if its premises are true. In other words, only if that it is on true grounds that (a), can (b) be entailed. In case 1, Gettier claimed that (b) is true even though (a) is in fact false. Such claim does not follow the logic of deduction. I shall take that (a) and (b) are essentially equivalent. “The man who will get the job” in this case is Jones. When Gettier introduces that Smith is the man who gets the job, the subject “The man who will get the job” in proposition (b) still refers to Jones. If (a) were false, so is (b). In Gettier’s case, proposition (b) is not any less true than (a), hence Smith does not have a justified true belief.

The second case follows the same fashion, although Gettier introduced an “either/or” situation in propositions (d)-(f). Consider the logic behind this entailment:

P1: (c)

P2: If (c), then (d), (e) and (f)

C: (d), (e), (f)

Because of the “either/or” situation, for propositions (d)-(f) to be justified belief, Smith has to be justified in believing that Brown is not in either one of the cities. However, Smith has no idea where Brown is, thus Smith is not justified in believing proposition (d)-(f), hence Gettier’s objection does not hold.

Gettier’s objections to the traditional analysis of knowledge is not sound, even though, it implies a possibility of new perspectives of knowledge. Perhaps one way to view knowledge is to let each reasonable individual take account for knowledge when the external world needs not to be concerned. After all, our beliefs, in the perspective of others, can often be false, yet such beliefs lead us to success in carrying out everyday tasks. Or perhaps knowledge does not need a universal, fixed definition. It could be that we are to adjust our views of knowledge as we refer to it from time to time. Either way, there should not be an absolute definition for knowledge that is ultimately correct. If so, it would take beyond an ordinary being to define knowledge. Until then, we shall build our own understanding of knowledge that cohere with our demands.

Reference:

Audi, R., 1999. The Cambridge Dictionary of Philosophy. Cambridge: Cambridge University Press. Gettier, E. L., 1963. Is Justified True Belief Knowledge?. Analysis, Volume 23, pp. 121-3.