Suppose that there was a class of particles called P-particles that are identified by the fact that they decay into a burst of gamma radiation after 10 seconds. And let us further suppose that this classification was developed at the beginning of research into atomic physics, when it was even harder than it is now to look at what is really going on at the subatomic level. Because of their distinctive properties P-particles are likely to figure into a number of different theories and explanations of particular events.
However let us suppose that later investigations reveal that P-particles aren’t really one kind of particle at all. Instead there are really two kinds of particles that exhibit the decay characteristic of P-particles. Let us call them A and B particles. What is it proper to say in this case? Have we reduced P-particles to A and B particles? Have we eliminated them? Are they a real but non-reducible class of particles?
The anti-reductionist might say that P-particles cannot be properly reduced to talk about A and B particles. We may not simply be able to get rid of the need to talk about P-particles; we may not have the resources to determine whether A particles, B particles, or some combination of the two is responsible for the phenomena that we previously attributed to P-particles. And, moreover, we may not want to do away with talk about P-particles; perhaps it is simply too convenient linguistically to get rid of. Finally, they might argue that the concept of P-particles is simply not properly captured by any talk of A particles or B particles.
But the reductionist may respond to this and point out that P-particles, strictly speaking, no longer exist. What exists is A particles and B particles, since these are the only entities that we need to construct our explanations. P-particles can of course still exist, in a sense, but only as a label for some kind of phenomena that evolves entities that are involved in our best explanations. And, according to the reductionist (rightly in my opinion), such labels can only be part of satisfactory explanations if there is a reductive relation between them and the phenomena they describe. Thus, says the reductionist, either P-particles reduce to A and B particles in some way, or P-particles don’t exist.
I think that the reductionist has the better of the anti-reductionist here, quite possibly because the anti-reductionist has a too narrow understanding of what counts as reduction. The reductionist sees X being reducible as meaning only that X can be said to convey some information about what is going on with what it is being reduced to in particular cases, and that this information explains how X can have its characteristic effects. Anti-reductionists on the other hand see reduction as establishing a one-to-one correspondence between what is being reduced and what it is being reduced to. (Peter Smith has a great paper entitled “Modest Reductions and the Unity of Science” explaining why reduction should be understood as looser than this.) So perhaps the real problem is that the two are talking past each other.
I think the real lesson here is not that reductionists have the upper hand on anti-reductionists, if you grant them a broader definition of reduction than the anti-reductionist uses, but that the reductionist/anti-reductionist dispute in general is orthogonal to the real issues. The real issue is constructing a theory that explains all the phenomena in question. Whether you can reduce other terms to terms in the final theory is irrelevant to the final theory itself. (The final theory being one that perfectly explains all the phenomena.) And the final theory, by its very nature, explains everything that needs explaining. This makes the existence of entities that don’t play some role in the final theory (such as P-particles) irrelevant. Of course this seems extremely unintuitive. How can the existence of these things not matter? But given a final theory that doesn’t contain them the existence of such things is a best a linguistic matter (is there something that exists (is part of the final theory) that we wish to describe using the term?). And whether we wish to continue discussing things using such terms, and whether we wish to continue to frame our explanations using them, is simply a matter of practicality. And so worries about whether they reduce, whether they exist, are not relevant to understanding the world. And if understanding the world is what we are after then we can leave such questions to linguists.