Quoting Paul & Patricia Churchland, Victor Reppert describes three kinds of reductionism: conservative, reforming and eliminative reductionism (ER).
Victor cites examples of the three different types of reductionism. However, I noticed that one of these examples is not like the others, and two of these examples are kinda the same!
The reduction of temperature to mean kinetic energy is given as an example of conservative reduction. Let's look at what these terms are. Temperature is something that is sensed more or less directly. Temperature is not an explanation. Temperature is simply being explained by the reduction to mean kinetic energy.
The reduction of Newtonian mass to relativistic mass is cited as an example of reforming reduction. Mass (or, weight, at least) is directly sensed, like temperature. Mass is not an explanation. The reduction replaces on explanation with another that is simply more precise.
The cited example of eliminative reduction is the replacement of phlogiston in favor of chemical oxidation. However, phlogiston isn't directly sensed. Combustion is sensed. Phlogiston is an explanation for something sensed (the combustion), and one that happens to be wrong. In this case, the eliminative reduction completely eliminates one explanation that doesn't work and replaces it with one that does.
We see a pattern here. Reduction is a form of explanation. Either we:
a) Introduce an explanation for something sensed, (conservative reduction)
b) Refine an existing explanation for something sensed, (reforming reduction)
c) Replace a failed explanation for something sensed with an effective explanation. (eliminative explanation)
The problem arrives if we mistakenly think that ER replaces the thing sensed with an explanation instead of replacing the faulty explanation for that sensed thing. I believe this is the mistake made by dualists when they cite ER in their arguments.
ER is invoked by dualists who claim that the reduction of certain human mental qualities to material systems eliminates those qualities. The argument sort of runs like this:
1) I feel X.
2) X is explained by a physical theory.
3) X is eliminated because it is merely the action of atoms (or whatnot).
4) Ignoring X as a delusion is unimaginable or threatens my ability to perform this syllogism.
5) Therefore, it is better to trust (1) than accept (2).
The flaw in the argument is in step (3). The direct sensations and experiences are not eliminated by ER. They are explained and predicted by ER. The only thing being eliminated are competing explanations that don't fare as well.
Let's look at free will in particular. Here' I'm talking about free will as a sensation or direct experience, not as an explanation for experiences.
The direct experience of free will is this: I perceive a selection of possible actions, I predict the outcome of each possible action, choose the action that I prefer, and see that my choice generally results in the intended effect. In this way, my choices have made a difference, and I have displayed apparent agency.
If my thinking process and my preferences were shown to be material mechanisms, this direct experience is unaltered. The direct experience is simply explained in terms of a prediction of physics. Free will is not eliminated.
What is eliminated? What is eliminated is the "idea" that there is some alternative to determinism and randomness known as "free choice". Yet this idea of "free choice" is not a direct experience. We don't directly sense that the world is non-deterministic. Rather, "free choice" is a supposed explanation for our actual experiences. (I hesitate to call "free choice" an explanation at all because it is neither predictive, nor logically coherent.)
So, a mechanistic theory of mind does not eliminate direct experiences free will. It eliminates a faulty and incoherent explanation for those experiences. And it is the role of every good explanation to displace poor ones.