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Knowledge is traditionally defined as justified true belief: in order for S to know P, S must believe P, P must be true, and S must be justified in believing P. Now this definition has been criticized by invoking various "Gettier cases", supposed examples of justified true belief which are not knowledge. The defenders of a "justified true belief" understanding of knowledge have responded by showing that these Gettier cases are not really cases of justified true belief, by clarifying exactly what constitutes a justification. Here is the philosopher Robert Nozick's theory of justification, according to this Wikipedia article:

Nozick's Four Conditions for S's knowing that P were:

  • P is true

  • S believes that P

  • If it were the case that (not-P), S would not believe that P

  • If it were the case that P, S would believe that P

Nozick's third and fourth conditions are counterfactuals. He called this the "tracking theory" of knowledge.

I understand the first three conditions; the first two conditions just specify a true belief, and the third one is a straightforward counterfactual conditional. But I don't understand the fourth condition. What kind of conditional is that? P is true, so this can't be a counterfactual conditional. And it's presumably not a material conditional, because the material conditional "If P then S believes P" is trivially true given the first two conditions.

So what is the point of the fourth condition, and what does it mean?

Any help would be greatly appreciated.

Thank You in Advance.

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The fourth condition is a subjunctive conditional. However, I believe that Nozick tentatively proposed a slightly different set of truth-conditions for subjunctive conditionals. He endorsed the following:

“If it were the case that P, S would believe that P” is true iff, in every close possible world in which P is true, S believes that P.

You are correct that this is different from standard usage, which only looks at the closest possible world. Under standard usage, the fourth condition is trivial under the first two conditions, since the closest possible world is the actual world. The intuition behind this, I think, is that if you were a brain in a vat caused to believe that you were a brain in the vat you would lack knowledge in this case because in close possible worlds where you are a brain in a vat you don't believe you are a brain in a vat.

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