1.
Many experiences have two different kinds of features: representational features (For instance, your visual experience may represent that there is something red in front of you), and qualitative features (There is "something it is like" to have them).  So, if you suffer from Daltonism, my seeing a green square and your seeing the same green square have the same (or similar) representational features, but different qualitative features (you see a shade of grey while I see green).  By qualia one means the qualitative features of experiences, what's like to have them.  Jackson claims that qualia cannot be reduced to

2.
Two positions:

1. Physicalism = the doctrine that all psychological information can be given in physicalist terms (biology, chemistry, physics, etc).
2. Epiphenomenalism = the doctrine that mental states or some aspects thereof are the effect of brain (soul) activity but are totally causally inert (even with respect to other mental states) or are causally inert with respect to the brain (soul).

3. Jackson's argument against Physicalism
Mary, A colorblind neurophysiologist knows all the physiology of sight.  Yet  she does not know something about seeing colors: were she to be cured, she  would learn something about seeing she did not know.  Hence, there is more  to know than physicalism can ever tell us.  Hence, physicalism is incomplete.
More precisely:

1. While still colorblind, Mary knows all the physical information there is to know about other people and their experiences.
2. When Mary is cured and sees something red for the first time, she learns something new about other people. She learns what their experiences of red are like. She acquires knowledge about what qualitative features their experiences have.
3. So before being cured, there was some knowledge that Mary lacked. She did not know everything there is to know about other people's experiences.
4. So there is some fact about other people's experiences of which Mary was ignorant when she was still colorblind. This fact was not captured by the physical information about those other people: it is a non-physical fact.

NOTE: Jackson distinguishes his argument from

• The Modal Argument: it's logically possible for an exact physical replica of me to lack consciousness.  Hence, there's more to me than mere physiology

Problem: the premisde is debatable
• Nagel's bat argument: we cannot know what's like to be a bat even if we know their physiology because their point of view is too radically different from ours

Problem: whatever the merits of the argument, it isn't an objection to Physicalism, which makes no assumptions about our capacity to imagine what's like to be something or other.

1. When Mary is cured and first sees something red, does she genuinely acquire a new piece of knowledge (knowledge of information)
2. This new piece of knowledge, is about some new fact about our experiences (the quale of red) of which she was previously ignorant

• One may claim that (1) is true, but (2) is false. Suppose you know that sugar dissolves in water, but don't know that it dissolves in H2O.  Later, when you learn that water dissolves in H2O, you don't learn a new fact  because water is H2O.  What you learn is a new way ok knowing the same fact.  Similarly, Mary merely comes to know an old fact in a new way: all that's going on is that you have two different concepts ("water" and "H2O") for the same thing.  Experiencing the quale of red can still just be having such and such neurophysiological feature (Horgan).

Reply: The best explanation for having two concepts ("water" and "H2O") for the same thing is that there are some properties one associates with one and not with the other.  But this is not the case with Mary.  She is supposed to know all the neurophysiological properties our experiences have.
• One may deny (1) and claim that Mary's new piece of knowledge is not a case of 'knowing that', but a case of 'knowing how' i.e., the acquisition of new abilities.  On this view, what an experience of red is like (the quale of it) is nothing but the possession of certain abilities to remember experiencing red, to visualize red, to recognize red things by sight.  So, Mary's new knowledge is not a knowledge of a new fact because it's not a case of 'knowing that.' (Lewis)

Reply:  Having an ability is not the same as exercising it.  Imagine locking yourself in a room in which you cannot see red.  Suppose also that while in the room, although you retain the ability to visualize red, to remember experiencing red, etc., you never exercise these abilities.  You stay in the room for many years, and when you come out, upon seeing a red tomato you could justifiably say: "I had forgotten what's like to see red! Now I know again."  This shows that you may forget what's like to see red while having the abilities Lewis describes. (Thau)

• qualia (not mental states but certain properties of mental states) are inefficacious.
• the qualia of a mental state x may be causally efficacious to another mental state y, although no quale is physically efficacious.

• hurt is responsible for taking the hand away from the fire.  But how can this be if hurt has no physical effect?

Reply: behavior after but not caused by hurtfulness.  Rather, causally linked brain events produce both.
• If qualia have no physical effect, how can natural selection account for them?

Reply: they are the by-product of brain activities w/c have survival value, like having a heavy coat (no or adverse survival value) is the byproduct  of having a warm coat (great survival value).
• I know others have minds (and qualia) from their behavior.  But unless I believe that qualia cause behavior, how could this be?

Reply:  I argue from effect to cause to other effect of same cause: from  behavior, to cause in brain state, to effect (the quale) of same brain state.
• Why have qualia if they are a mere excrescence which does nothing and explains nothing?  We don’t understand why they are there.

Reply: so what?  we are the product of evolution and understand what matters to our survival. Since qualia don’t matter to it, why  should we understand anything about them?  Physicalism is an excessively optimistic doctrine about our powers of understanding ourselves.