Here is another example of a Gettier case taken from an actual occurrence. While in high school, a friend of mine named Pat threw a big party when his parents were out of town. His neighbor, a busy-body, took surveillance photos of the partying kids. Some of the pictures showed party-goers smoking on the side of the house. When Pat’s dad saw these pictures, he thought that he saw was a picture of kids smoking weed. Based on what he saw in the pictures, he had justification to believe that kids at the party were smoking weed.
His belief that kids were smoking weed at the party was, indeed, a true belief. However, the picture upon which this belief was based was actually a photo of kids smoking cigarettes. Pat’s dad had a justified and true belief. Pat’s dad did not, however, have knowledge. First, it seems that his belief was true because he was lucky. Second, if we imagine a close possible world where the camera used to take the pictures had a slightly better zoom lens or that the picture was taken from a better vantage point, it could be the case that the photo would show enough detail so that Pat’s dad could see that the pictures actually showed people smoking cigarettes. The belief that kids were smoking pot would still be true but Pat's dad would no longer believe it. The truth of the proposition stays the same but it is no longer believed! Because truth and belief do not covary across possible worlds, this is not a proper case of knowledge!
One may argue that in this case, Pat’s dad did not have justification for his belief that kids at the party were smoking weed. Indeed, the justification condition for knowledge is the most controversial and is difficult to agree upon. However, if Pat’s dad’s belief was unjustified, this does not disprove Gettier’s main point. All we have to acknowledge is that there are cases where one can have a justified and true belief that is not knowledge.
Imagine, for example, that instead of smoking cigarettes, the people in the photo were smoking tobacco out of a large water bong. In this case, it would seem that Pat’s dad had really good justification to believe that kids were smoking pot at the party (it is very rare for someone to smoke tobacco out of a bong!). In this case, Pat’s dad has a justified true belief that is not knowledge. His belief is true because he happened to be lucky! Gettier thinks that this means that Pat's dad's belief is not knowledge.