The view that knowledge was justified true belief was widely held by philosophers, but Gettier showed that there were cases of justified true belief that did not appear to be knowledge. Thus, the Gettier problem shows that justified true belief is not a sufficient condition[?] for knowledge (in other words, something else is needed as well).
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Gettier provides two actual examples of his problem, both of which rely on the fact that justification is preserved by entailment. For example, if a belief that P is justified, and the truth of P entails Q, then a belief that Q is also justified.
Gettier's first example:
Gettier's second example:
In both of Gettier's actual examples, the justified true belief came about as the result of entailment from justified false beliefs. This led some early responses to Gettier to conclude that the definition of knowledge could be easily adjusted, so that knowledge was justified true belief that depends on no false premises.
More general Gettier-style problems
The "no false premises" (or "no false lemmas") solution was not the end of the matter, however, as more general Gettier-style problems have also been proposed, in which the justified true belief does not seem to be the result of a chain of reasoning from a justified false belief.
For example:
Other responses to Gettier include externalist responses, such as the theory that knowledge is justified true belief that is caused (in the right sort of way) by the relevant facts, or Robert Nozick's view that knowledge is a belief which is true, and which the believer would not have had if it was false. There are also many other theories of knowledge.
Finally, one can say that knowledge really is justified true belief, but "justification" must be understood in such a way that justified beliefs are never false. Since very few beliefs are justified to the extent of absolute certainty, this implies philosophical skepticism - the view that knowledge is usually impossible.
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