My position on evidence is I think fairly similar to the position Clayton Littlejohn takes when he says evidence is non-inferential knowledge. I think, as I say in this old paper, that evidence is basically knowledge that is the output of a Fodorian module. The differences between our positions aren’t great. But I think there are some differences. This kind of case brings out some of these differences.
Graham, Crispin and Ringo have an audience with the Delphic Oracle, and they are told ¬ p ∨ q and ¬ ¬ p. Graham is a relevant logician, so if he inferred p ∧ q from these pronouncements, his belief in the invalidity of disjunctive syllogism would be a doxastic defeater, and the inference would not constitute knowledge. Crispin is an intuitionist logician, so if he inferred p ∧ q from these pronouncements his belief in the invalidity of double negation elimination would be a doxastic defeater, and the inference would not constitute knowledge. Ringo has no deep views on the nature of logic, but has accepted the classical theory he learned in an undergrad intro class because he doesn’t know there’s any dispute about it. Moreover, in the world of the story classical logic is correct. So if Ringo were to infer p ∧ q from these pronouncements, his belief would constitute knowledge. Now Graham’s and Crispin’s false beliefs about entailment are not p ∧ q-relevant evidence, and Ringo doesn’t have more evidence about logic than Graham or Crispin. So all three of them have the same p ∧ q-relevant evidence, but only Ringo is in a position to know p ∧ q.
This case is meant to do two things. First, it is an argument against a kind of evidentialism about knowledge. It isn’t true that what you know, or even what you’re in a position to know, supervenes on the evidence you have. Graham, Crispin and Ringo have the same evidence, but only Ringo is in a position to know that p ∧ q. That’s because Graham and Crispin’s false beliefs about entailment are defeaters in this context. In general, knowledge doesn’t supervene on evidence because defeaters don’t supervene on evidence.
The other thing it is supposed to do is draw out the idea that there is something problematic about treating logical knowledge as evidence. Ringo knows that ¬ p ∨ q and ¬ ¬ p entail that p ∧ q. Graham and Crispin don’t know this. But this isn’t an extra piece of evidence that Ringo has. Indeed, it isn’t an extra piece of evidence Ringo has for two reasons.
First, Graham and Crispin have all the evidence that Ringo has. They know that logic professors in intro classes say that ¬ p ∨ q and ¬ ¬ p entail that p ∧ q. They just don’t believe that these professors are right. This doesn’t seem like the kind of thing that destroys evidence.
Second, there are reasons tracing back to Lewis Carroll’s “Achilles and the Tortoise” for distinguishing between logical rules and logical axioms. Similar reasons suggest that we should distinguish between between empirical evidence and inferential rules that licence inferences from that evidence. That’s especially true when the inferential rules just are logical rules. So I don’t think that what licences Ringo’s inference of p ∧ q is an extra bit of evidence, it’s rather a rule of logic.
But Ringo knows that rule is correct. Indeed, it might even be a non-inferential piece of knowledge for him. (If need be, make Ringo smart enough in the example that he can simply see that certain inferences are valid.) Basic inferential rules aren’t things we know inferentially, they are things we use to get inferential knowledge. So if evidence is non-inferential knowledge, they are evidence. But I suspect they are not evidence for the reasons I’ve given here. So I think there’s a downside to the equation of evidence with non-inferential knowledge.