Take Jackson's story: Mary is raised in a black and white setting, never experiencing red. She learns all there is to know about the physical constitution of the world. She leaves her black and white setting. She sees something red. She then comes to know something about the world which she didn't know before: she learns something about the experiences that other people have had. Hence the knowledge about the physical constitution of the world doesn't exhaust the possible knowledge about the world. Hence, the world is more than physical.
The standard objection to this is that this equivocates on "knowledge". Mary gains an ability, an ability to recognize and imagine red experience, say, after coming out of the black and white setting. Jackson has a rather nice answer to this, though. He supposes that Mary, after coming out of the room, toys with scepticism about other minds. But then she rejects the scepticism. In rejecting the scepticism, she does not gain any know-how. But she does gain the knowledge that others have that kind of experience, which she now has when she is looking at a tomato.
Here is a response to Jackson that has occurred to me. If Mary, before she saw red, really knew all there was about the physical world, she also knew that she will come out of her black and white setting, and that she will experience red. Before she has experience red, she can prospectively refer to that experience of red, the experience that she knows she will have (she can use "that" to ostend to that experience she will have). She also already knows that other people have had that experience. When she first sees red, she now "knows what that experience is like." But the only relevant fact in the vicinity, the fact that others have that experience, is a fact that she already knew. She now has a new way of pointing to "that experience" of hers: she can point to it introspectively, while before she could only point to it verbally ("dthat experience which I will have at t7 upon looking at a tomato"). When she toys with scepticism about other minds, she temporarily loses the belief that others have that experience, and then she regains that belief when she rejects the scepticism. So Jackson is right in thinking that Mary loses something that isn't just know-how through scepticism and regain it. But perhaps he is wrong that what Mary loses through scepticism is what she learned about the experiences of others when she saw red. What she learned by seeing red stays there—it's just a new ability to refer to an experience of hers. What she loses is a belief that doesn't bother a physicalist.
I don't know whether the response stands up. I think it depends on the synonymy relations between indexical sentences. If I stand near near x and say "This is a tetrahedron" and you stand far from x and say "That is a tetrahedron", have we said the same thing? (Or, better yet, we both say "This is a tetrahedron", but your "This" gains reference through your pointing with your eyes, and my "This" gains reference through my pointing with my nose (with me closed-eyedly smelling the tetrahedron).) If so, then I think the response to Jackson goes through—we just have two different ways of fixing an indexical. If not, then it needs more work. But even so, if the difference between what Mary knew before she saw red and after she saw red is like the difference between a "this" belief and a "that" belief about something, it might not be a difference that should bother a physicalist.
