Nozick believes that in order to have knowledge, the belief needs to track the truth. In other words, for one to have knowledge, one must believe P, P must be true, and one’s belief’s must track the truth value of P.
For this reason, the casual account of knowledge must be false. The casual account of knowledge states that the fact that P is true causes S to believe P. However, think about a mentally ill patient who suffers from paranoia. Suppose this patient, without any proof or facts, believes that his mother is plotting to kill him; his belief is simply based on his impaired brain chemistry. Now, suppose that by coincidence, his mother very recently actually did begin formulating a plan to kill the mental patient. The mental patient’s belief would be true, however, the mother’s plan to kill him is not the reason for his belief. Therefore, P being true is not the cause for the mental patient’s belief.
So if the conditions: P is true, S believes that P, and the fact that P is true does not always cause S to believe P, is not sufficient to constitute knowledge, what is? Nozick believes that the solution can be found by adding to subjunctive statements. If P were not true, S would not believe P, and if P were true, S would believe P. If Nozick is right, the conditions for knowledge would look like this: P is true, S believes that P is true, if P was not true S would not believe P, and if P were true S would believe P. If these rules are applied to the mental patient example, it is clear that the mental patient does not know that his mother is actually plotting to kill him. If the mental patient’s mother was not trying to kill him, the patient would still believe that his mother was trying to kill him. It is evident that Nozick’s third condition for knowledge makes belief sensitive to the truth value of P’s falsity.
In the previous situation, if P was true, S would believe P. But that is purely by coincidence. Consider this situation: There is a family with a mother, father, daughter, and son. The son is a compulsive liar and tells his parents that he is going to play tennis after school. The parents believe him, but the sister believes that the brother will not play tennis after school, but will do something else entirely. In this situation, P is true, S believes that P, and if P were false S would believe P, but if P were true she would not believe P. In this case, the sister is correct – her brother is going to do something other than play tennis. The sister’s belief is not based on any supposition about the boy’s continual lying, however, but exists only because she did not hear the lie from her brother. If she had, then she, like her parents, would have believed that the brother was going to play tennis. Therefore, the sister cannot have knowledge. In order to fix the problem, Nozick created the 4th condition, if P were true, S would believe P. With this condition, belief is sensitive to both the falsity and truth of P.
Nozick’s conditions make it so that beliefs track the truth value of P. Therefore, if knowledge can be defined by the conditions of P being true, of S believing that P is true, and of S’ sbeliefs tracking the truth value of P, then Nozick has successfully defined knowledge.
Disclaimer: It is not my claim that Nozick’s definition for knowledge is true; it is that if it is, then his conditions would constitute knowledge.