For those of you keeping score at home, there were three counterarguments in opposition to Jackson's Knowledge Argument (the one about Mary).

Papineau provides two of them:

1. Jackson's epiphenomenalism denies the obvious truth that conscious experience causes physical effects. For example, when I have a headache, I take aspirin.

2. "Ontological danglers" are not found anywhere else in nature, so why should the mind be special? An ontological dangler is something that is causally impotent. It is the end of the line for a causal chain. It is something that is caused, but does not cause anything else. This is the upshot of Jackson's epiphenomenalism.

A Digression: Why be an epiphenomenalist?

If you remember, it makes sorting out the relationship between the mind and the brain a lot easier for someone who maintains that the mind is not a material thing. Otherwise you would have to explain how something nonphysical (the mind) has causal effects on something physical (the body). Daniel Dennett compares this to an explanation of how Casper the Ghost can fly through walls one minute and carry a mop the next. Maybe it works in cartoons, but making consistent science out of it is a problem.

So that's why Jackson decides to take another route and go epiphenomenalist.

3. Churchland's criticism of the Knowledge argument is that Jackson is equivocating two different meanings of knowledge. Equivication is a fallacy, to find out why, read more here. Churchland's contention is that there are two different types of knowledge at play in Jackson's thought experiment. The first kind of know means something like "has mastered the relevant set of neuroscientific propositions." This is what Mary knows when she learns all the facts of a complete visual neurophysics. The second kind of knowledge, what she learns when she sees red for the first time, Churchland calls "having a prelinguistic representation of redness in her mechanisms for noninferential discrimination."

To put this more simply, Churchland claims that physicalism does not depend on Mary's complete knowledge of visual neurophysics entailing that she also has knowledge of what it's like to see red.

Jackson's Reply to Churchland

Jackson says that Churchland is knocking down a strawman, a misrepresentation of the Knowledge Argument.

Here is how Churchland has been describing it:

1. Mary knows everything ther is to know about brain states and their properties.
2. It is not the case that Mary knows everything there is to know about sensations and their properties.
Therefore, by Leibiniz's law (remember the stuff Churchland cites in the text about Clark Kent and Superman being the same, even though Lois doesn't know that they are the same,)
3. Sensations and their properties are not identical with brain states and their properties.

Here is Jackson's formulation of what he is actually saying:

1'. Mary (before her release) knows everything physical there is to know about other people.
2'. Mary (before her release) does not know everything there is to know about other people (because she learns something about them on her release).
Therefore,
3'. There are truths about other people (and herself) which escape the physicalist story.

Jackson: "What is immediately to the point is not the kind, manner, or type of knowledge Mary has, but what she knows. What she knows beforehand is ex hypothesi everything physical there is to know, but is it everything there is to know? That is the crucial question."