Fred Dretske in The Philosopher's Magazine:

Prior to Gettier it was more or less assumed (without explicit defence) that knowledge, knowing that some proposition P was true (when it was in fact true), was to be distinguished from mere belief (opinion) that it was true, by one’s justification, evidence, or reasons for believing it true. I could believe – truly believe – that my horse would win the third race without knowing it would win. To know it would win I need more – some reason, evidence or justification (the race is fixed?) that would promote my true belief to the status of knowledge. Gettier produced examples to show that this simple equation of knowledge (K) with justified true belief (JTB) was too simplistic. His examples triggered a widespread search for a more satisfactory account of knowledge.

Gettier’s counterexamples are constructed on the basis of two assumptions about justification, both of which were (at the time he made them) entirely uncontentious. The first of these was that:

1: The justification one needs to know that P is true is a justification one can have for a false proposition.

Almost all philosophers who aren’t sceptics accept 1 without hesitation. After all, if one can, as we all believe we can – sometimes at least – come to know (just by looking) that there are bananas in the fruit bowl and (by glancing at the fuel gauge) fuel in the automobile tank, then given the existence of wax bananas and defective gauges, the justification, the kind of evidence, needed to know is clearly less than conclusive. It is something one can have for a false proposition.

Nonetheless, despite the overwhelming appeal of 1, accepting it lands one in the epistemological soup. Well, almost in the soup. The added push is supplied by Gettier’s second assumption:

2: If you are justified in believing P, and you know that P entails Q and accept Q as a result, you are justified in believing Q.

The idea behind 2, of course, is that one does not lose justification by performing deductive inferences one knows to be valid. If you have reasons to believe P is true, and you know P can’t be true unless Q is true, then you have equally good reasons to believe Q is true. It is difficult to see how 2 could be false if logic is to be regarded as a useful tool for expanding one’s corpus of rationally held beliefs.

But, alas, accepting both 1 and 2 lands you in deep trouble. Gettier explains why.