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Constant comments on Conceptual Analysis and Moral Theory - Less Wrong
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There is a reason why the Gettier rabbit-hole is so dangerous. You can always cook up an improbable counterexample to any definition.
For example, here is a counterexample to Nozick's definition as you present it. Suppose that I have irrationally decided to believe everything written in a certain book B and to believe nothing not written in B. Unfortunately for me, the book's author, a Mr. X, is a congenital liar. He invented almost every claim in the book out of whole cloth, with no regard for the truth of the matter. There was only one exception. There is one matter on which Mr. X is constitutionally compelled to write and to write truthfully: the color of his mother's socks on the day of his birth. At one point in B, Mr. X writes that his mother was wearing blue socks when she gave birth to him. This claim was scrupulously researched and is true. However, there is nothing in the text of B to indicate that Mr. X treated this claim any differently from all the invented claims in the book.
In this story, I am S, and P is "Mr. X's mother was wearing blue socks when she gave birth to him." Then:
P is true. (Mr. X's mother really was wearing blue socks.)
S believes that P. (Mr. X claimed P in B, and I believe everything in B.)
If it were the case that (not-P), S would not believe that P. (Mr. X only claimed P in B because that was what his scrupulous research revealed. Had P not been true, Mr. X's research would not have led him to believe it. And, since he is incapable of lying about this matter, he would not have put P in B. Therefore, since I don't believe anything not in B, I would not have come to believe P.)
If it were the case that P, S would believe that P. (Mr. X was constitutionally compelled to write truthfully about what the color of his mother's socks were when he was born. In all possible worlds in which his mother wore blue socks, Mr. X's scrupulous research would have discovered it, and Mr. X would have reported it in B, where I would have read it, and so believed it.)
And yet, the intuitions on which Gettier problems play would say that I don't know P. I just believe P because it was in a certain book, but I have no rational reason to trust anything in that book.
ETA: And here's a counterexample from the other direction — that is, an example of knowledge that fails to meet Nozick's criteria.
Suppose that you sit before an upside-down cup, under which there is a ping-pong ball that has been painted some color. Your job is to learn the color of the ping-pong ball.
You employ the following strategy: You flip a coin. If the coin comes up heads, you lift up the cup and look at the ping-pong ball, noting its color. If the coin comes up tails, you just give up and go with the ignorance prior.
Suppose that, when you flip the coin, it comes up heads. Accordingly, you look at the ping-pong ball and see that it is red. Intuitively, we would say that you know that the ping-pong ball is red.
Nonetheless, we fail to meet Nozick's criterion 4. Had the coin come up tails, you would not have lifted the cup, so you would not have come to believe that the ball is red, even if this were still true.
Both of your Gettier scenarios appear to confirm Nozick's criteria 3 and 4 when the criteria are understood as criteria for a belief-creation strategy to be considered a knowledge-creation strategy applicable to a context outside of the contrived scenario. Taking your scenarios one by one.
You have described the strategy of believing everything written in a certain book B. This strategy fails to conform to Nozick's criteria 3 and 4 when considered outside of the contrived scenario in which the author is compelled to tell the truth about the socks, and therefore (if we apply the criteria) is not a knowledge creation strategy.
There are actually two strategies described here, and one of them is followed conditional on events occurring in the implementation of the other. The outer strategy is to flip the coin to decide whether to look at the ball. The inner strategy is to look at the ball. The inner strategy conforms to Nozick's criteria 3 and 4, and therefore (if we apply the criteria) is a knowledge creation strategy.
In both cases, the intuitive results you describe appear to conform to Nozick's criteria 3 and 4 understood as described in the first paragraph. Nozick's criteria 3 and 4 (understood as above) appear moreover to play a key role in making sense of our intuitive judgment in both the scenarios. That is, it strikes me as intuitive that the reason we don't count the belief about the socks as knowledge is that it is the fruit of a strategy which, as a general strategy, appears to us to violate criteria 3 and 4 wildly, and only happens to satisfy them in a particular highly contrived context. And similarly, it strikes me as intuitive that we accept the belief about the color as knowledge because we are confident that the method of looking at the ball is a method which strongly satisfies criteria 3 and 4.
The problem with conversations about definitions is that we want our definitions to work perfectly even in the least convenient possible world.
So imagine that, as a third-person observer, you know enough to see that the scenario is not highly contrived — that it is in fact a logical consequence of some relatively simple assumptions about the nature of reality. Suppose that, for you, the whole scenario is in fact highly probable.
On second thought, don't imagine that. For that is exactly the train of thought that leads to wasting time on thinking about the Getteir problem ;).
A large part of what was highly contrived was your selection of a particular true, honest, well-researched sentence in a book otherwise filled with lies, precisely because it is so unusual. In order to make it not contrived, we must suppose something like, the book has no lies, the book is all truth. Or we might even need to suppose that every sentence in every book is the truth. In such a world, then the contrivedness of the selection of a true sentence is minimized.
So let us imagine ourselves into a world in which every sentence in every book is true. And now we imagine someone who selects a book and believes everything in it. In this world, this strategy, generalized (to pick a random book and believe everything in it) becomes a reliable way to generate true belief. In such a world, I think it would be arguable to call such a strategy a genuine knowledge-creation strategy. In any case, it would depart so radically from your scenario (since in your scenario everything in the book other than that one fact is a lie) that it's not at all clear how it would relate to your scenario.
I'm not sure that I'm seeing your point. Are you saying that
... or are you saying that
... or are you saying something else?
Nozick apparently intended his definition to apply to single beliefs. I applied it to belief-creating strategies (or procedures, methods, mechanisms) rather than to individual beliefs. These strategies are to be evaluated in terms of their overall results if applied widely. Then I noticed that your two Gettier scenarios involved strategies which, respectively, violated and conformed to the definition as I applied it.
That's all. I am not drawing conclusions (yet).
I'm reminded of the Golden Rule. Since I would like if everyone would execute "if (I am Jiro) then rob", I should execute that as well.
It's actually pretty hard to define what it means for a strategy to be exceptionless, and it may be subject to a grue/bleen paradox.
I thought it sounded contrived at first, but then remembered there are tons of people who pick a book and believe everything they read in it, reaching many false conclusions and a few true ones.