Case 1: Smith and Jones both apply for a job. Smith has been assured Jones will get the job and has counted 10 coins in his pocket. (d)- Jones is the man who will get the job and Jones has ten coins in his pocket. This entails (e)- The man with ten coins in his pocket will get the job. However, Smith is the one who gets the job and, unknowingly to him, has ten coins in his pocket. So, we have a justified true belief, yet we would not consider this knowledge at all.
Case 2: Smith has strong evidence to believe that Jones owns a Ford. (F)- Jones has owned a Ford all the time that Smith has known him. Smith also has a friend, Brown, for which he has no idea where he lives. Based of of this, he develops the following three propositions: (g)- Either Jones owns a Ford, or Brown is in Boston. (h)- Either Jones owns a Ford, or Brown is in Barcelona. (i)- Either Jones owns a Ford, or Brown is in Brest-Litovsk 5. These propositions are accepted of the basis of (F), for which he has strong evidence. Smith is completely justified. 6. However, Jones does not own a Ford , but it turns out Brown lives in Barcelona (h)
Fake Barn country: Barney is driving through fake barn country. In fake barn country, there are a lot of fake barns, wherein there is only the front face of the barns, like a movie set. Barney, unaware that he is in fake barn country, looks out the window, at a barn on the side of the road. By doing this, Barney develops the proposition, 'there is a barn on the side of the road'. However, it turns out that this is the only real barn in fake barn country. So, Barney had a true belief that there was a barn, which was justified by the idea that it looked real and Barney was unaware he was in fake barn country.
A lemma is a point in an argument which is used to support a larger or more important point. This condition aims to make Gettier examples an invalid example of knowledge, for they rely on a FASLE LEMMA to create a situation of JTB without knowledge. So, we can create JTB+N (N meaning no false lemmas) to create definition of knowledge which avoids Gettier's two problems. However, as Zagzebski notes, we can create cases of JTB+N which we still wouldn't consider knowledge. Consider a patient, who is diagnosed with X. The patient exhibits all the symptoms of X, yet, unknown to the doctor, he actually has, the undiscovered, Y, which exhibits the exact same symptoms as X. However, the patient had actually, recently, contracted X, so recently, in fact, that it is yet to show symptoms.
In an attempt to fix the problem, we can strengthen the justification condition with infallibilism. This makes it so the justification principle is so strong, it rules out any other possibility and means the belief HAS to be true. So, JTB+ Infallibility. However, it is incredibly difficult to have knowledge, for we can always conceive of other possibilities. So, it would seem like what we would consider is now not, for it is not infallible. This seems to against what we would consider knowledge, so most people reject this idea based on what we already consider knowledge.
This theory claims that knowledge is a true belief that is produced by a reliable cognitive process. So, K=RTB. Reliabilism claims that, in the process of generating a belief, we would consider such belief as knowledge if the reliability of generating that belief is strong. So, you are more inclined to 'know' something if it comes from a reliable source, such as a reliable newspaper, rather then something that came from a dodgy website. This allows children and animals to, indeed, have knowledge. For, children and animals would not be able to have justification, yet there perception and mind offer a reliable cognitive process. However, even the Gettier cases can exploit the gap between true belief and reliabilism. So, it is not a sufficient definition for knowledge.
This theory relies on intellectual virtues and vices. It claims that knowledge is a true belief brought about by a virtuous intellectual disposition (a person's inherent qualities of mind and character). In essence, virtues motivate us to use a reliable process to gain true beliefs and, hence, gives us knowledge. So, someone that doesn't exercise their intellectual virtues, regardless of having true beliefs, do not have knowledge. While a true belief is good, if it is gained by luck (or any other means apart from virtues), then it is not as good as a true blief arrived at by intellectual virtues. So K=VTB- Intellectual virtue motivates us to pursue what is good- Intellectual virtues allow us to form true beliefs reliably. However, if we consider someone who, out of 100 times, only demonstrates their virtues once to gain knowledge, at what point would be consider him having knowledge- It seems impossible to determine the amount of intellectual virtues which warrant knowledge. We can also argue whether the motives for knowledge are necessary. As long as we go through a reliable process and the beliefs are true, do we need motives? Within Gettier's first case, we can argue, that Smith didn't exercise his intellectual virtues to come up with his proposition 'the man with ten coins in his pocket will get the job', so it is not a VTB.