The Gettier Problem: Disproving Plato's Theory of Knowledge
In ancient times, Plato developed a theory on knowledge which claimed that knowledge is made up of justified true belief. (For an in-depth explanation of Plato's Theory see the article Plato on Knowledge). Plato's argument was generally accepted by the philosophic community until 1963, when Edmund Gettier came on the scene. In his paper "Is Justified True Belief Knowledge" Gettier exposed a fundamental flaw in Plato's logic. Gettier created a hypothetical situation in which justified true belief fails to lead to knowledge, leading to the presumption that some other element would need to be present in order to facilitate knowledge. While Gettier used the now-famous example of "Smith, Jones and the Ford car," other philosophers have invented similar situations with have come to be known as "Gettier Problems."
Gettier Problem: Smith, Jones and the Ford Car
Smith believes that his neighbor Jones owns a Ford. Smith has regularly seen Jones pulling out of his garage in the Ford on the way to work for over a year. Thus Smith is justified in believing that Jones owns a Ford.
One weekend Smith, not knowing where his friend Brown is, states "Either Jones owns a Ford or Brown is in Barcelona" (Statement A). Unknown to Smith, Jones sold his Ford after work on Friday, and does not currently own a car. In addition, Brown actually is in Barcelona, but has not shared this information with Smith.
In this example Smith does indeed believe that Statement A is true, and is justified in his belief. Furthermore, Statement A is actually true, though not for the reason that Smith believes it is. Although all of Plato's requirements for knowledge are present (justified true belief), Smith does not possess the knowledge that Brown is in Barcelona and Jones does not own a Ford. Smith has justified true belief about his statement, but is lacking the essential knowledge that proves it as true.
Through a case of accidental circumstance, the truth that Smith imagined in his idea of the scenario, that Jones owned a Ford, was not actually true. Rather than this falsity negating the proposition (Statement A), the accidental circumstance has allowed for another version of truth to replace Smith's version.
The problem is that what Smith is referring to, the facts in question, are incorrect. Smith is being led by inaccurate premises, namely the idea that Jones owns a Ford, towards a true conclusion.
Elements of a Gettier Problem
In a Gettier problem, an individual is led to a true conclusion by premises that they believe to be true, but actually happen to be false. In addition, a set of circumstances exists that are similar enough to the individual's premise to uphold the element of truth, though the individual in question is unaware of these other circumstances.
In short, multiple conditions exist which could fulfill the requirement for truth. The individual whose knowledge is in question is only aware of a condition that does not satisfy the truth requirement.
While Gettier accepts Plato's position that justified true belief need to be present in order to have knowledge, he believes that a missing variable is necessary in order to account for the cases of accidental circumstance creating justified true belief without knowledge, as seen in the Gettier problem.