In his essay "Knowledge and Skepticism," Nozick shows that skeptical possibilities violate his conditions and so, on his theory, we cannot know that skeptical possibilities aren’t realized. (You cannot know that you are not in the matrix, but in the movie some characters do know this, so is the movie incoherent?)
Skepticism, the view that little or nothing is known, does not follow unless we assume the principle of closure: you know whatever you correctly infer from what you know.
The inability to know one is not in the matrix does not preempt ordinary knowledge if one can have ordinary knowledge without being able to know what is correctly inferable from ordinary knowledge.
Nozick protects ordinary knowledge against skepticism by rejecting the closure principle.
On his theory, closure fails because propositions that satisfy his subjunctive conditions for knowing have logical consequences that do not. We may now entertain several possibilities:

1. Nozick is right about what it takes to know and closure fails. Although I do not know that I am not being manipulated into believing p falsely, nevertheless (amazingly) I do know P.

2. Nozick is wrong about what knowledge is and closure holds. Since I do not know that I am not manipulated I can’t know anything whose truth depends on my not being manipulated. A very general skepticism then holds.

3. Nozick is wrong about knowledge and closure holds, but I can know that I am not manipulated, and so ordinary knowledge is unthreatened. Even though things would seem the same if I were manipulated, still I can know that I’m not. Skepticism is false.

4. Nozick is right about knowledge but wrong about closure, because the belief that one is not a victim of manipulation satisfies Nozick’s conditions for knowledge after all.

In your paper on Nozick pick an option above (or another if you think of one you prefer) and defend it.
Here is one thought to help you select.
The entire discussion of skepticism and closure ignores the method or process that produces the belief whose knowability is at issue.
The method was earlier said to be crucial to whether one knows, but subsequently is neglected.
Does reintroducing it help?
Does how one forms the belief that one is not a victim matter to whether this belief satisfies Nozick’s conditions for knowledge?

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In his essay entitled "Knowledge and Skepticism" Nozick rejects the theory of closure and holds that "knowledge is not simply justified belief" (p. 3). Closure holds that inference about knowledge can be made from already known facts. In this account of knowledge, belief about what is true can be deductible logically from what is already known about one's surroundings and the world....

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