The following is an excerpt from a comment I made over at Dangerous Idea 2. The comments got a little sidetracked from the original post, but the issue at stake is what reduction is about. Does a reductionist theory eliminate phenomena or does it identify one phenomenon with a different one? No....
The watch tells the time. The watch ticks. The hands of the watch move. The watch contains movable springs and gears. The watch has a glass cover and a part that connects it to a strap or watch-chain.
The reductionist theory of watches says that the ticking and the time-telling and the hand movements are caused by the springs and gears working as a mechanism. The reductionist does not say that the hand movements and the time-telling are identical to the springs and gears in the absence of a mechanism.
When the reductionist theory is first put forward, the mechanism is unseen. So we're not saying that something we have seen is something else we have seen. We are saying that something we have yet to see (the mechanism) causes the seen phenomena.
In this case, what we have observed to date about the watch does not contradict the reduction. The ticking, the gears and springs, the time-telling are all still present after the reduction, and they don't disappear after the reduction. The reduction does not eliminate the motion of the hands or the telling of the time. It explains them.
Now, let's backtrack to a time before we decided knew the watch reduced.
A priori (before the reduction), we might think that the watch properties cannot be reduced. We might think that the external properties of the watch are the fundamental ones. For example, we might think time-telling is in the watch as a fundamental property of the whole and cannot be broken down to a mechanism of more fundamental parts.
When we propose irreducibility like this, there will generally be parts in the watch that we can remove without breaking the time-telling. For example, we can remove the glass cover or the parts that connect the watch to a chain or strap. Take off these other parts and the watch continues to tell the time.
When we open the watch and see the springs and gears moving in sync with the hand movements, we have to ask whether they are all fundamental or whether one is more fundamental than the other. For example, maybe it is the intrinsic time-telling that moves the hands, and the hands drive the gears. If that were the case, then the gears and springs are at least as likely to be unnecessary as necessary. Maybe the watch is intrinsically a time-teller, and the gears serve only to cause the ticking.
On what basis do we successfully and completely reduce the watch to a mechanism of gears and springs? Well, the watch reduction is totally successful once we understand the mechanism, and once we can build watches or show that the gears and their mechanism predict the ticking and the time telling.
However, we can make partial reductions without understanding the whole watch. If we find that the watch cannot tell time without the gears, there's (a priori) 2:1 odds that the gears cause the the time-telling (and that time-telling is not fundamental to the watch). This is because if time-telling is fundamental, the time-telling is compatible with gears moving or not moving, but if gears and mechanism are fundamental, the gears must move.
Similarly, if we find that tweaking the gears causes the time-telling to speed up or slow down, then we have another 2:1 (now 4:1) statistical advantage for the reductionist gears theory. If time-telling is fundamental, then it may or may not be possible (2 possibilities) to change the hand movements by tweaking the gears. On the other hand, if the gears and mechanism are fundamental, then it will certainly be possible to change the time-telling rate by tweaking the gears.
In cognitive science, we have performed many partial reductions. If mind or its aspects are fundamental, then we don't need physical brains, physical memories or any of the other things comparable to the gears in the watch. Yet we have them. If minds are fundamental, then we don't need circuits in our brains that function as memory, that recognize, that predict, and that emote. Yet we have all those things. It turns out that just about every function of mind can be tweaked physically or chemically. So while we don't know the whole mechanism, we ought to be well over 99% certain that the mind is not fundamental, and that the neurochemical mechanisms are fundamental to mind.