It’s often claimed that there is a close connection between the tacit reasoning we use in Gettier cases and the safety constraint. Here, for instance, is John Hawthorne from page 54 of Knowledge and Lotteries.
Insofar as we withhold knowledge in Gettier cases, it seems likely that ‘ease
of mistake’ reasoning is at work, since there is a very natural sense in such cases, in which the true believer forms a belief in a way that could very easily have delivered error.
I suspect that’s not true. I don’t mean to pick on John here, I think it’s a widespread view in epistemology. But it’s false.
Here’s what I’ll argue. (Step One) There are some Gettier cases where the resultant belief satisfies every safety condition we could want. In those cases we don’t tend to assign knowledge to the agent. (Step Two) The reasoning we use in those cases is the same as the reasoning we use in all Gettier cases. So, the reasoning we use in Gettier cases is not safety reasoning.
Here’s the example of a true, safe Gettier belief.
Bob and Bill are talking about a particular mathematical conjecture. Bob says, “I predict that either Fred will prove it, or it is unprovable.” A few days later, Bill is told by Frank, a trusted and generally reliable friend, that Fred has proved the conjecture. This is false – Fred merely proved a lemma that he thought would help with the proof, and in fact the conjecture is unprovable. Bill concludes, “So Bob was right, either Fred will prove it or it is unprovable.”
Now if we take the Gettier intuitions at face value, we should conclude that this is not a case of knowledge, because it is a case where the agent has concluded that a disjunction is true on the strength of gaining good evidence that the false disjunct is true. But the belief is by any measure safe.
First, the belief is necessarily true, so it satisfies Williamson’s safety requirement. Given the tight connection between Bill’s belief and Bob’s statement, there is no nearby world in which Bill’s belief has a different content, hence no nearby world in which it is false, hence it satisfies my preferred safety requirement. And since the method Bill uses, namely come to believe those predictions of Bob’s that are entailed by reports of Frank’s, yields true results in all nearby cases, it satisfies the principle only use safe methods. There’s really no sense here in which Bill’s belief is unsafe.
But it is hard to see in what ways this case differs from other Gettier cases. If safety was crucial to the Gettier reasoning, then the intuitions in this case should be much weaker than in standard Gettier cases where safety is violated. But we don’t see any such thing – the intuition here is exactly the same as in the standard case. So I think that what is central to the Gettier cases is not safety, but the fact that Bill’s final belief is supported by a false proposition.