Edmund Gettier's Is Justified True Belief Knowledge?

Edmund Gettier’s finest work, “Is Justified True Belief Knowledge?” explains the concerns he has with the way we have formed our conditions for knowing something to be true. Many philosophers had attempted to explain the necessary conditions for someone to know a given proposition to be true, which led to Chisholm and Ayer constructing the necessary and sufficient conditions for a justified true belief, knowledge. These attempts were stated in the following form: (a) S knows that P is true, if and only if, (i) P is true, (ii) S believes that P is true, and (iii) S is justified in believing that P is true. These three conditions are necessary and sufficient enough to determine that S knows P is true. This was a problem for Gettier because Chisholm
The fact that S must be justified in believing P is a necessary condition of S knows that P is true, displays an error in their argument. It is completely possible for someone to be justified in believing a proposition that is false. For example, the proposition, we know that the world is flat, was once believed to be true. This is because to the extent of our knowledge at the time all we knew was that the world was flat because we had not journeyed nearly far enough to know that that was not the case. We believed the world was flat and we were justified in that belief because no one had come close to proving otherwise. Therefore, based on those conditions the proposition the world is flat would be true. However, we know better, that in fact, the world is not flat, and we were only limited by our justified belief in that fact to be true. That proposition was never true, yet almost every one of our ancestors believed it to be real knowledge until they proven otherwise by science and by travelers who sailed completely around the globe without falling off the edge of the
“Suppose for any proposition P, S is justified in believing P. P entails Q and S deduces Q from P, and accepts Q as the result of that deduction, then S is justified in believing Q.” (Gettier 1) This can lead to many false justified beliefs of knowledge. For example, Jeff owns a Mustang is the initial proposition and John is justified in his belief that Jeff indeed owns a Mustang. Now imagine Jeff has a friend, Jessica, and John has no idea where Jessica is right now. So he constructs three propositions at random to determine her whereabouts. (i) Either Jeff owns a Mustang, or Jessica is in Maine, (ii) Either Jeff owns a mustang or Jessica is in Kentucky, and (iii) Either Jeff owns a mustang or Jessica is in New York City. Each of those propositions is entailed with the original proposition of Jeff owning a Mustang. Therefore, it is completely correct to accept each of the three propositions made concerning Jessica’s location, and he is justified in accepting them. However, in reality, it is unknown where Jessica is and even all three of those propositions could be wrong, but they were accepted as justified knowledge. More seriously than that, they cannot all be correct in where Jessica is just because Jeff owns a Mustang because she cannot be in three places at once. Therefore, there is an issue with the logic of these conditions, which is