Mary knows everything there is to know about the colour red. As a scientist, it has been her life's work. If you want to know why we can't see infrared, why tomatoes are red, or why red is the colour of passion, Mary is your woman.
All this would be unremarkable, if it weren't for the fact that Mary is an achromat: she has no colour vision at all. The world, for Mary, looks like a black and white movie.
Now, however, all that is to change. The cones on her retina are not themselves defective, it is simply that the signals are not processed by the brain. Advances in neurosurgery now mean that this can be fixed. Mary will soon see the world in colour for the first time.
So despite her wide knowledge, perhaps she doesn't know everything about the colour red after all. There is one thing left for her to find out: what red looks like.
Baggini, J., The Pig That Wants to Be Eaten, 2005, p. 37.
This version of the Mary problem seems pretty innocent as it's presented, but the further implications that philosophers usually draw from this have been staggering (and quite malevolent in my view). To make that clear, and so you don't just dismiss this thought experiment too soon, here's part of the explanation that comes from Baggini when he discusses this issue.
"Most educated people don't have much time for the view that mind and body are two different kinds of stuff, which somehow coexist side by side. ... Simply rejecting one erroneous worldview, however, does not guarantee you will be left with a true one. If you kick out mind-body dualism, what is to replace it? The obvious candidate is physicalism: there is only one kind of stuff, physical stuff, and everything, including the human mind, is made of it. ... But physicalist zeal can go too far. ... This is what the story of Mary illustrates. As a scientist, Mary knows everything about red in physical terms. Yet there is something she doesn't know: what it looks like. No scientific account of the world can give her this knowledge. Science is objective, experimental, quantitative; sense experience - indeed all mental experience - is subjective, experiential, and qualitative. What this seems to show is that no physical description of the world, however complete, can capture what goes on in our minds. As philosophers put it, the mental is irreducible to the physical. This presents a challenge to physicalists. How can it be true both that there is nothing in the world apart from physical stuff, and yet at the same time, that there are mental events that cannot be explained in physical terms?"
So what do you think? As an evolutionary philosopher, I'm a confirmed physicalist who has always found this line of reasoning annoying, but how would you tackle it?