Here’s a new (or at least new to me) schema for solving the Mary problem. For reasons that will become clear below, it isn’t yet a solution. But someone who knows more about consciousness will be able to convert it into a full solution. The following ideas grew out of some discussions after Derk Pereboom’s talk here last Thursday, and he (and the discussants at the talk) probably deserve the credit for what value there is in it.

We start with some facts about defeaters.

At t₁, S knows that p, and indeed knows that she knows that p. At t₂, she acquires some kind of defeater for her knowledge, and recognises this fact, so she now takes herself to not know that p. It won’t matter if this is an undercutting or rebutting defeater, but let’s say it is a rebutting defeater, say some strong (but inconclusive) evidence that ~p. It is a common human failing, indeed I don’t know how one could really avoid it, for someone in S’s position to infer that she didn’t know that p at t₁. This is a failing because it is compatible with what’s happened to her that she really did know that p, and she merely now fails to know it. But it is hard not to think that the defeater defeats not only her current claim to knowledge, but by rebutting her old evidence, defeats her old claim to knowledge. I’ll assume from now on that this is how we fallible humans react to acquiring defeaters.

Now imagine a very special case of this. At t₁, Suzy knows that ∃x Fx, because she knows that Fa, and has inferred ∃x Fx. At t₂, she acquires strong evidence that ~Fa & Fb. This defeats her old claim to knowledge that ∃x Fx, while simultaneously giving her new reason to believe, indeed possibly grounds to know, that Fb. In fact both Fa and Fb, and Suzy was acquainted with these two facts at t₁ and t₂ respectively, to know that ∃x Fx. Nevertheless, from Suzy’s perspective it will seem that she learned that ∃x Fx at t₂, not at (or before) t₁, when she really came to know it. Note that if learning that p at t requires not knowing that p at least for a short time before t, then Suzy is just wrong to think she learned that p at t₂, no matter how much that seems to be the case from her perspective.

The application to Mary should be obvious. When she’s in the black and white room, she knows what it’s like to see red. She knows p, that seeing red is like this (for a suitable perceptual demonstrative). When she comes out of the room, her visual acquaintance with a red thing simultaneously defeats her ‘old’ knowledge that p and provides her with strong evidence that p. She learns nothing new, but like Suzy she takes herself to have learned that p when she came out of the room, not when she last came to know that p. The crucial idea here is that a single experience can simultaneously defeat knowledge that p and ground knowledge that p. We know that such a thing is possible, as in Suzy’s getting strong evidence (from a single event) that ~Fa & Fb. The hypothesis here is that seeing red performs both of those roles.

Why might we think this? I don’t know, which is why this is a schema not a solution. My position is that we have no idea what it would be like to be Mary, so we shouldn’t be leaning too hard on her for philosophical wisdom. But to the extent I can peer through the fog of philosophical war, the following tripartite reasoning seems at least plausible.

Case One: Mary is never a physicalist
If inside the room Mary never takes physicalism for granted, then she won’t really take herself to know that p. At most she’ll know that if physicalism is true, then p. But if she thinks there are possibly non-physical processes going on in consciousness, then she’ll be sceptical that all there is to seeing red is grounded in what’s happening in the brain, so she won’t believe that p. In this case she really might learn that p when she leaves the room, but that’s because knowing all the physical facts isn’t enough to know that p. No physicalist should ever have said it was – some facts rely on there being no non-physical facts, and p might be one of them. (In fact I rather suspect that it is.)

Case Two: Mary is a physicalist, but loses her nerve on seeing red
The intuition behind the knowledge argument is that conscious states don’t look like physical events. Let’s run with that seriously. Mary knows the physical events that are going on in her brain when she sees red, but she now has at least prima facie evidence that there is something non-physical going on as well. Not compelling evidence, say we physicalists, but prima facie evidence. In this case Mary will know p when in the room on the basis of physicalistic reasoning, this reasoning will be defeated when she sees red, but she’ll instantly ‘regain’ the knowledge that p through perception. This case mirrors the case of Suzy. Mary thinks she learns something, but she’s making the mistake all defeated knowers make.

Case Three: Mary’s physicalist nerve holds
It’s really hard to imagine this case (which is why the argument has force) but I take it in this case Mary won’t really take herself to come to know anything. I suspect this is the most likely case, and I have no idea what it would be like to be like that, because I have no idea what it would be like to know that much about the working’s of one’s own brain. (Would one feel like a free agent if one knew how one made decisions? I don’t know, because I really don’t know how that feels either. But I have a better sense of that than I have of what it’s like to be Mary.)