The Futility of Reduction
The idea of reduction is rampant in contemporary philosophy, particularly in relation to the mind. Thus we hear talk of reductive materialism or reductive behaviorism, or of reductionism about the mental. Likewise, though less frequently, we have reductive views of the moral or even the physical (as with reductive phenomenalism). It is supposed that there is a viable notion of reduction and that this notion might be invoked in philosophical theories of various subject matters. Where did this notion come from? Supposedly from science: science is thought to contain examples of successful reduction, these providing the model for philosophical reductions. We are told that pain can be reduced to C-fiber stimulation in just the way heat has been reduced to molecular motion or water reduced to H2O or light reduced to a stream of photons. So we know what it would be to provide a reduction and then the question is whether such a reduction might be true of the mental: it’s just like that. I think this whole approach is mistaken: in fact, there have been no successful reductions in science, and the case of the mind is not analogous to the kinds of cases that have been cited. The notion of reduction has been misunderstood and mischaracterized; there is really no such thing, as commonly conceived. This is actually quite obvious on reflection.
Consider the standard example: heat and molecular motion. The claim is that scientists have reduced heat to molecular motion. But why use the word “reduced”? They have identified heat with molecular motion, to be sure—they have discovered what heat is. Similarly, astronomers identified Hesperus with Phosphorus, discovering the truth of an identity statement, but did they reduce Hesperus to Phosphorus? That sounds like a strange thing to say. The reason is not far to seek: as the dictionary reports, “reduce” means “make or become smaller or less in amount, degree, or size”, with “reduction” meaning “the action of reducing”. That is, there has to be some sort of elimination to count as a reduction—some removal, some subtraction. Mere identification is not sufficient: that is just saying what something is, not saying that it isn’t after all. In general there has to be an impression of diversity in order to speak of reduction—it has to seem as if there is more than one thing there. If I seem to see two dogs in front of me and form the belief that there are two dogs there, but then discover that I have double vision, I can conclude that there are fewer dogs than I thought: I have reduced the number of things I believe in. But in the case of heat is there any such impression? Am I under the illusion that heat is different from molecular motion—that there are two things here not one? Does it seem to me that heat is not identical to molecular motion—as it seems to me that blue is not identical to red or square is not identical to triangular or space is not identical to time?  It does not—heat gives me no such impression, nor do my senses. It is simply that I have discovered an identity and can therefore make a “theoretical identification”: but where is the reduction here? You might say that the sensation of heat is distinct from molecular motion, and that is perfectly true: but no one is claiming that the sensation of heat is identical with molecular motion—only that heat is. If you were very confused, you might suppose that the discovery that heat is molecular motion is the discovery that the sensation of heat is molecular motion, and thus that you have reduced the sensation to its object—got rid of it as an independent reality. But that is simply a gross misunderstanding (“a non sequitur of numbing grossness”): it is heat that is claimed to be molecular motion not the sensation of heat (which might be a brain state or a state of an immaterial substance). The scientist takes this distinction for granted and merely claims to have discovered what heat is—and similarly for water, light, etc. There is no cutting down on what the world apparently contains, because there was no impression that heat isn’tmolecular motion—though there is certainly an impression that the sensation of heat isn’t molecular motion. Who could have thought that it is? Heat is in the object; the sensation is in the subject: there is no impression of identity here. In fact, we can imagine beings that investigate the physical world and have no sensations of heat at all—though they observe what hot objects do in the physical world. These beings can discover that the thing they call “heat” is molecular motion, but there is no question in their mind about the identity of the sensation of heat, which they don’t have. Once we distinguish heat from the sensation of heat we can see that there is no putative and problematic identification of the sensation with a condition of hot objects. All that is happening is that an empirical identification is being made—but there is nothing that is aptly described as reductive going on. In the same way, scientists have discovered that genes are constituted by DNA molecules, but this is not a case of reduction in the ordinary dictionary sense: there was no lessening of the number of things thought to exist. The truth is that putative reductions are always eliminative in the sense that they reduce the number of things apparently contained in the world: this is why the word “reductionism” is typically used pejoratively—because it is a denial of reality to what appears perfectly real. Strictly speaking, we should restrict ourselves to talk of theoretical identification, or maybe constitutive explication. It is finding out what stuff is made of. These are not instances of successful reduction. Perhaps the removal of vital spirits from biology counts as reduction, because it is plausible to say that organisms give an impression of something beyond the merely physical (mechanical, machinelike); but here again it is elimination that is really in question—such vital spirits are declared fictional, i.e. non-existent. It is not that biologists have discovered that vital spirits are in fact identical to mechanical processes; they have discovered that there are no vital spirits. It is really a choice between identification and elimination; the concept of reduction occupies a poorly defined middle ground. It would be better to drop the word altogether, because it conflates identification and elimination. You can discover that Hesperus is identical to Phosphorus, or you can discover that Vulcan doesn’t exist, but there is nothing hovering between these two—say, discovering that Vulcan is reducible to Mars. This is why I say that there have never been any successful reductions (in the contemporary sense) in science—though there have been plenty of theoretical identifications (and some eliminations: vital spirits, phlogiston etc.). The concept of reduction is a misbegotten concept. 
Still, it may be said, we can continue to draw an analogy between heat and pain: both are cases of successful theoretical identification (constitutive explication). We can drop the misguided idea of reduction but retain the benefits of citing scientific precedent. But there is a reason why people so readily invoke the concept of reduction in this connection: for the mind does give the impression that it is not identical to the brain and body. So if it turns that it is, that is tantamount to denying that it has the kind of existence we thought—as with biology and vital spirits. It seems to us that the mind is not the brain—but it doesn’t seem to us that heat is not molecular motion (though it does seem to us that the sensation of heat is not molecular motion). So this would count as a genuine reduction, if it were true. We wouldn’t nonchalantly say, “Oh, it turns out that the mind is the brain, by the way–an interesting discovery perhaps, but nothing to get in a tizzy about”. On the contrary, a tizzy would be fully warranted—because it sure as hell seems to us that this is not the case. It would be tantamount to a deep revision in our ontological assumptions—a dramatic form of eliminativism no less. Things would be different if pain were distinguishable from the sensation of pain, as heat is distinguishable from the sensation of heat: for then we could happily identify pain with C-fiber stimulation while insisting that the sensation of pain is no such thing. But that is exactly what we cannot do, for reasons made clear by Kripke and others: pain just is the sensation of pain—as heat is emphatically not the sensation of heat (Hesperus is certainly not the sensation of Hesperus!). If the sensation of heat turned out to be identical to molecular motion, then we would have a real reduction on our hands—the world would be less populous than we were led to believe—but that is not what anyone is claiming. Likewise, if the sensation of pain turned out to be identical to C-fiber stimulation, that too would pack a reductive punch; but then the pain case is not analogous to the heat case. The crucial point of dissimilarity is that we can’t separate pain from the sensation of pain, as we can separate heat from the sensation of heat. So we have no precedent in science for the kind of identification of mind and body that is being proposed. That would be a type of reduction, unlike the heat case, but then it isn’t analogous to the heat case: in the case of heat we have no qualms about identifying heatwith molecular motion, because it never seemed not to be (though the sensation of heat certainly did). But we have plenty of qualms about identifying pain with C-fiber stimulation, precisely because pain is the sensation of pain. In other words, identifying the sensation of heat with molecular motion would be exactly as revisionary as identifying pain with C-fiber firing. So the heat case affords no encouraging scientific precedent for so-called reductive materialism: the former is not reductive at all while the latter surely is—and hence clearly eliminative. If pain turned out to be C-fiber stimulation, that would be like nothing else that has ever been discovered—a peculiar hybrid of genuine reduction (i.e. elimination) and straightforward ontologically conservative theoretical identification. It may be doubted whether this makes any sense: how could the identity theory be both ontologically conservative and eliminative? It would have to be both reductive and non-reductive: reductive because eliminative, and non-reductive because merely identifying. You can’t have it both ways. This is why nothing in science sets the stage for so-called reductive materialism: the cases usually cited are all cases of non-reductive identification, once we analyze them correctly. They simply identify one physical phenomenon with another (heat with molecular motion, water with H2O, and light with a stream of photons), while being careful to distinguish these things from the corresponding sensations. But this is not what is being envisaged for mind and brain—quite the opposite. Thus there is no precedent in science for what is being proposed—and hence no conferred respectability or antecedent plausibility deriving from that quarter. Worse, the very idea of psychophysical reduction is deeply confused, wavering incoherently between identification and elimination. There is no such thing as non-eliminative reduction—as the very words imply. The idea was foisted on the philosophical community by a misguided analogy to certain scientific discoveries that were never reductive (reductionist) to begin with. The scientist would be within his rights to protest at being called a reductionist: “I am no reductionist, young man—for I abhor such denials of manifest reality—I am merely an honest inquirer who tries to find out what things are beyond their appearance”. Why should it be thought reductionist (or even reductive) simply to say what heat really is: where is the reducing here? There is no lessening, no winnowing, and no rejecting—just finding out what things really are. The project of philosophical reduction is therefore futile: no such thing is possible or desirable. Indeed, it is contradictory under a normal interpretation of terms. 
The difficulty is not confined to attempts at psychophysical reduction. Take the doctrine of reductive phenomenalism: the idea (roughly) is to reduce material objects to sense data. But is this merely a case of theoretical identification—are material objects simply identical to collections of sense data? It doesn’t feel like that—it feels more…rejectionist. Why? Because we are under the firm impression that material objects are more than sense data—that they are mind-independent, substantial, and objective. And those impressions are being denied: there aren’t really any objects like that, but only subjective, wispy, mental things. By attempting to reduce material objects to sense data we are denying their essential nature, thus eliminating them from our ontology. The alleged reduction is accordingly felt as disguised elimination: the inhabitants of reality are radically reduced, cut down. We are being offered metaphysical depopulation. But this is not true of standard scientific “reductions”: nothing in our ordinary conception of heat rebels at the suggestion that heat is molecular motion, since there is nothing about heat that can’t be captured in terms of molecular motion (again, distinguishing heat from the sensation of heat). Phenomenalism really is a form of reductionism, precisely because it is tacitly eliminative: it is not merely conservatively explicative—a mere analysis of what we ordinarily believe. It is not just a matter of straightforward identification. But it can’t be both: it can’t be reductive and merely identifying (explicative). Thus the notion of reductive phenomenalism, as normally understood, is inherently confused, even contradictory—unless it is clearly offered as outright elimination. The same can be said of reductive efforts with respect to morality: attempts to reduce values to facts, to put it crudely. If this is offered as merely explicative, it is apt to meet with anti-eliminative resistance: for it feels eliminative, given the way we ordinary conceive of morality. It might, on the other hand, be offered in a frankly eliminative spirit, and then there would be no objection of disingenuousness or incoherence. But if we are told that it is not intended in that spirit, but only as an account of what moral values actually are, we are apt to protest that the real thing is being denied. Why? Because values don’t seem to us antecedently to be identical to non-value facts—they seem like something above and beyond such facts. If this seeming is veridical, then no reduction is possible, because it would involve denying the essence of the moral. Again, the idea of conservatively reducing the moral to the factual emerges as incoherent, since that could not be anything other than disguised elimination. This is not so for the scientific cases, which is why they don’t have an eliminative flavor. So no precedent can be found in them for the kind of philosophical reduction being mooted. The conclusion I would draw from this is that the whole idea of a philosophical reduction is a monster—a mythical monster. So is the philosopher’s idea of a scientific reduction: there is no such thing (except in the rare eliminative sense). Identifications, yes: reductions, no. The real problem with putative reductions is not that they are guilty of reductionism; it is that they are conceptually confused. We can certainly analyze water into its constituent molecules and heat into the dynamic constituents of hot objects and light into its photonic composition, but none of these qualifies as a reduction—they are not at all reductionist. They are more amplifying than reducing. The same is true of philosophical analysis: we can analyze knowledge as true justified belief (etc.), but this is not a reduction of knowledge to true justified belief. The concept of reduction (as opposed to analysis) really has no place in philosophy, as that concept is customarily intended. This is not to say that the mind could not be the brain (under some description), just that it is wrong to speak of this as an instance of “reduction”. And if it is the brain (somehow conceived) this has to be a truth of a quite different order from that found in science as we now have it. The alleged scientific precedents are mischaracterized as reductive, and are not
 In the case of time, restating everything in terms of space-time is apt to come across as eliminative, since it appears to deny the essence of time, as we normally understand it. We normally regard time as something quite separate from space, clearly so. Anything that denies this is bound to seem eliminative (the same is true of attempts to replace talk of time with talk of clocks). In any case, time certainly seems different from space, which is why the concept of space-time strikes us as revolutionary–however things may be theoretically.
 There is another notion of reduction that is sometimes employed—theory reduction. This is conceived as defined over sentences or statements or propositions, not objects or properties: it is a relation between language-like items. The thought is that we can replace one theory with another, thus eliminating the reduced theory in favor of the reducing theory. This is in accordance with the dictionary definition of “reduce”, since we are reducing the number of sentences that need to be included in our theory of the world; the reduced sentences can be eliminated without theoretical loss. But this notion clearly does not entail any reduction of the denoted objects or properties. If we make a use-mention confusion, however, we can find ourselves speaking of the reduction of the entities referred to in a theory. In any case, I am not here addressing the question of theory reduction, which I don’t regard as a solecism.
 It is an interesting question whether physical accounts of color qualify as reductive. Are they perhaps the only examples of successful genuine reduction? The matter is controversial but I would say that they are reductive in the proper sense, i.e. eliminative not conservative. This is because our ordinary concept of color links colors constitutively to sense experience, and physical reduction to wavelengths and the like severs this connection. Thus the reductive claim involves denying that colors exist in the ordinary sense (as properties of the surface of objects)—there aren’t really any colors in objects but only color experiences in minds. So the alleged reduction is not really conservative, simply identifying what colors intrinsically are, but tacitly eliminative (which is how it intuitively strikes us). If we insist on incorporating the experiential connection, on the other hand, we deny the possibility of reductive (sic) identification. So, again, this doesn’t count as a successful piece of philosophical reduction: it is either tacitly eliminative or false. I do, however, think that the dualistic leanings of color are less obvious than in the case of the mind: they don’t seem as non-physical, if I can put it simply.