>but that observation isn't relevant to the mental processes of Alice and Bob

Sure. From their context, they may not be able to distinguish which is correct. But that doesn't mean it doesn't matter. When that context changes (eg. they learn something new), it matters a lot, and it's pretty relevant to their future actions and predictions. Thus it's an important aspect we want to distinguish in our epistemology. Ie. if Bob learns he was wrong, he shouldn't think his new situation is just as good as his old one just because in both cases he held "the best beliefs that can be constructed on the basis of his evidence". Something meaningful has been said, and that difference is important to encapsulate when discussing epistemology.

This distinction is independent of the internal belief states, but that's exactly why it's so important: we don't just want to talk about internal states, we want to relate these to the external reality we're talking about. The world where my belief is wrong is different in a very important way from a world where it's correct - a way I care very much about.

>Saying that Bob knew ¬X and lost that knowledge when he changed his belief centers our assessment of Bob's mental processes on the wrong thing

This is the wrong faming though. Bob never knew ¬X: ¬X was false. He thought he knew ¬X, but was mistaken. And that mistakenness is something Bob would care about, and should consider meaningful to his epistemology. If he didn't care about his truth, it'd be just as good for him to avoid learning anything, because he'd be in the same state either way wrt holding a reasonable belief. But in reality, if he's wrong, he'll want to find this out, and consider his situation improved when that happens.

>what Bob should be concerned with is what conclusions he can draw on the basis of his available evidence

The reason Bob should be concerned with this is solely because Bob wants his beliefs to be true ones. You can't discard that aspect.

>Perhaps another way of stating this would be to say that Bob ought to believe he knows X as a result of {A, B, C}, and that whether he knows X (or that he cannot know X because ¬X is true) is irrelevant.

Bob ought to believe X, but that certainly doesn't mean whether he knows it is irrelevant - epistemic contexts can change, and ones where our beliefs reflect truth are more valuable to us than ones that don't.

>but of whether we can actually be justified

Sure, but that's not an objection to the conception of knowledge, but about what criteria we consider to constitute justification. And pretty much no standard model of knowledge states that the justification criteria should be certainty, so I think you're targeting the wrong thing in your definitions here. In general, knowledge is held to be defeasible - you can be wrong about something you believe you know, and change your mind as to whether it was really knowledge. Certainty is not a requirement.

>Moving from a position of knowledge to a position of reasonability

As such, this is misunderstanding knowledge: those two are not at cross-purposes: "reasonability" is generally part of the justification part of knowledge - and there's certainly room to debate on exactly what makes something reasonable or constitutes a justified reason to believe something - but framing this as arguing against knowledge is to misunderstand what knowledge is about.

>allows for forms of justification that are rooted neither in truth nor in cohesion

Justification isn't rooted in truth for JTB - the truth criteria is entirely seperate. Certainly we believe it to be true (though not with certainty), since that's basically what belief is, but the truth criteria is considered entirely seperate from justification.

>but at least for externalist conceptions of knowledge like JTB this is not generally considered to constitute "knowledge" in the philosophical sense.

Certainly. If something is false, it's not knowledge. But I think that's absolutely something we should definitely be concerned about in our epistemology: If you believe, and are absolutely certain about something, I think there's a rather important difference depending on whether that belief is actually true. If Alice reasonably believes X, and Bob reasonably believes ¬X, I think there's something more to be said than "Well, both these people hold beliefs" - the question of which is right seems important.

I feel this article is just misdefining or misunderstanding knowledge, and conflating it with certainty. It makes claims like:

>In contrast with general conceptions of knowledge, whether or not a belief is reasonable is not contingent on truth.

But what on earth about the general conception of knowledge says reasonableness is contingent on truth? It says that knowledge is contingent on truth, but the reasonableness of a belief is a seperate matter. I think what is going on is that the author is confusing the map and the territory wrt the "true" criteria of knowledge.

>If knowledge is justified true belief, then surely we can have justified belief regardless of whether we can state authoritatively that our belief is true

Ie. this seems to mistake the "true" criteria of JTB with "can state authoratively that it is true", but one is a statement about the thing itself, and one is a statement about our own mind. True means the claim is true, not anything about our beliefs or what we can state about the claim (that's what the "J" and "B" parts are for).

>again without need to add “truth” to our definition

No - truth is a vital part of the definition, but it simply isn't what the author thinks here. You need truth to make the claim refer to something out in the world, rather than mainly in our heads. And that truth criteria matters. No matter how confidently we assert a claim, the world in which the claim is actually true differs from one where it is false.

Considering something to be knowledge doesn't require certainty, only the same regular degree of confidence belief requires. The truth criteria only distinguishes between what someone thinks is knowledge, and what actually is, in the same way that there's a distinction between something someone thinks is round, and what shape it actually is. Ie. if we find that something we justifiably believe turned out to be false, we say "I thought I knew it", not "I used to know it, but now I don't" - our claim of knowledge was simply mistaken, just like any other claim could be. That doesn't mean we need to transfer that "true in fact" criteria somehow onto our beliefs about that, and indeed to do so would be to destroy the whole point of that criteria.