Some of our mental states are conscious. There is some peculiar way it feels to be in those mental states. There is no special way it feels to be 6 feet tall, on the other hand. The statue is 6 feet tall, but it doesn't feel anything.
Although some of our mental states are conscious, many philosophers will argue that not all of them are. We seem to have many mental states which aren't conscious.A noteworthy fact about many of our mental states, especially the conscious ones, is that we seem to be able to know about them in an especially direct way. Our knowledge of our own mental states is not usually based on any evidence or observation. You can just tell that you're thinking about elephants. You don't have to infer it from any evidence. But other people do have to infer what you're thinking, from your behavior and from what you say. So you have a kind of special or privileged access to your mental states which other people lack. You don't have any privileged access of that sort to your height or weight or shoe size. In principle, other people could be in a better position to know your height than you are.
It's not clear whether we have privileged access to all our mental states. For instance, other people might be in a better position than you are to know whether you're jealous of your friend's success, or what your unconscious motivations are. But we do seem to have privileged access to some of them.
That may be enough to generate an argument for dualism. The argument goes like this:As we said, we have a special sort of privileged access to some of our mental states. But physical objects and their physical properties are all publicly accessible. In principle, it is possible for someone else to know more about my height, and my weight, and the physical state of my brain, than I know. So if my mental states were just physical states of some sort, like neurophysiological states of my brain, then that would make my mental states all publicly accessible. The only way to retain our belief that we have privileged access to our own mental states, the dualist argues, is to say that our mental life takes place in a special, private realm that nobody else has direct access to. The dualist can make sense of these "private realms"; but the materialist cannot.
A related line of argument here is brought up by the character Mouse in The Matrix:
Mouse: Do you know what it really reminds me of? Tasty Wheat. Did you ever eat Tasty Wheat?
Switch: No, but technically neither did you.
Mouse: That's exactly my point. Exactly. Because you have to wonder now, now how do machines really know what Tasty Wheat tasted like. Maybe they got it wrong. Maybe what I think Tasty Wheat tasted like actually tasted like oatmeal or tuna fish. That makes you wonder about a lot of things...
Mouse is proposing here that maybe the way Tasty Wheat tastes to people outside the Matrix is different from the way Tasty Wheat tastes to people inside the Matrix, and how would the machines ever know that they had gotten it right? The machines can only examine the physical state of the humans' brains. Perhaps that doesn't fully determine the nature of the humans' sensory experiences. Only the humans are really in a position to know what their own experiences are like. This suggests that the nature of our experiences is not some publicly accessible, physical fact about our brains. Rather, it's a distinctive mental fact about us.
Philosophers often tell this story using inverted color spectrums. They say, suppose there are two guys, Bert and Invert, and the way tomatoes look to Bert is the way that grass looks to Invert, and vice versa. Both of these guys have learned to call the tomatoes "red" and they've both learned to call the grass "green"; so no one will be able to tell from their behavior that there is any difference between them. Perhaps it's possible for people to have color experiences which differ in this way even though their brains and bodies are physically just the same. If so, then materialism must be false. For materialism says that what mental properties someone has just depends on what that person is like, physically. According to the materialist, it could not possibly be the case that Bert and Invert have all the same physical properties but nonetheless have different experiences. The dualist argues that this is possible. We can readily imagine the situation with Bert and Invert being as it was just described. This poses a problem for the materialist.
One kind of question these "inverted spectrum" cases raise are questions about what we could know. How can we know what each other's experiences are really like? (And if our experiences are different, how can we tell whose experience represents the true colors of objects? Do objects have true colors?)
Another kind of question these cases raise are questions about whether it really is possible for our spectrums to be inverted--regardless of whether we'd know that this is so. If it really is possible for two people to be physically just alike but to have inverted color experiences, then the materialist story about our color experiences cannot be correct. There must be more going on than just the physical state of our brain--for Bert and Invert are in the same physical state but they have different experiences.
The dualist appeals to these kinds of possibility to support her position. The materialist has to find a way to argue that cases like Bert/Invert aren't really possible, after all.