Reducibility

Reducibility

Some things are said to be reducible, others irreducible. I wish to consider two questions about such claims:  (a) what their modal status is and (b) what their explanation is. I won’t be interested in whether the claims are true or false but only in whether their truth is necessary or contingent and in why they are true when they are true. I will focus on the irreducibility of mind to body, assuming that this is a genuine case of irreducibility.

The first question, then, is whether the mind is necessarily irreducible or only contingently so. We are accepting that nothing about the brain as it actually exists affords an adequate reduction base for the mind—not neurons, axons and dendrites, chemical transmitters, etc. It doesn’t follow from this that no brain properties couldserve as an adequate reduction base: maybe there are possible worlds in which the mind is reducible to properties of the brain that don’t exist in our world. Maybe brains have a richer set of properties in some other world and these properties allow a successful reduction of the mind. For example, assume that panpsychism is false in our world, so that such properties cannot be appealed to as a possible reduction of the mind as we experience it—there just are no such properties of matter in the actual world, inside the brain or outside. That is consistent with accepting that in some other world the brain might be endowed with micro-mental properties and that these provide a successful reduction. Suppose that in that world we have ample evidence for the existence of these micro-mental properties and that physics has long since recognized their existence (they might even affect the behavior of elementary particles). It then turns out that a combinatorial scheme can generate macro-mental properties from these more basic micro properties—the case is structurally just like the atomic theory of matter. There is a mental chemistry that relates the mind reductively to its micro-constituents. Whether we choose to call those constituents “mental” or “physical” matters little; the important point is that there exists a set of facts that provides a satisfactory reduction. Or again, there might be some hitherto undreamt of set of properties that exists in a possible world that can provide a reduction, even though nothing in the actual world can perform this role. If so, though the mind is actually irreducible, it might not be necessarily irreducible (though we could still say that it is necessarily irreducible in the actual world).

Similarly, something may be reducible in the actual world but not in all possible worlds. Thermodynamics is reducible to statistical mechanics in the actual world, but is it so reducible in all worlds? What if a world contains heat phenomena but no molecular motion (the molecules stay still in this world)? Maybe heat is reducible to something else in this world, or maybe it is reducible to nothing. What if chemistry is not reducible to physics in a possible world because there are no negatively charged particles in that world? Just as the same things can have different explanations in different possible worlds, so natural phenomena can be differently reducible in different worlds. Does liquidity always have to reduce to sliding molecules in all worlds? Maybe it is a primitive property in some worlds, or maybe it reduces to perturbations in a continuous substance. Just because X is reducible to Y in our world doesn’t imply that the same reduction obtains in all possible worlds. Reduction is contingent.[1]

If these reflections are correct, Descartes could have been right about the mind as it exists in the actual world but not as it exists in all worlds. Maybe in some worlds matter is richer than Cartesian mechanism allows so that there is less of a gap between it and thought (the essence of mind). Maybe functionalism stands more chance of being true in a world that contains more subtle kinds of functional role than what obtains in the actual world (experiences of red may have a different functional role from experiences of green in this world, so that we don’t have inverted spectrum problems). None of this would imply that in our world functionalism is true, but some version of it might be true in another world (relative to the kinds of mind that exist there). Even something deserving the name “materialism” might be true in world in which the physical world is richer than our physical world. If this is so, we could say that it just happens that the mind is irreducible in our world—it might have been otherwise. Reduction is a metaphysical possibility.

But if it is merely contingent that the mind is irreducible in our world, why is it the case that it is so irreducible? If the mind is not intrinsically irreducible, then presumably something must explain why it is irreducible as things are—there must be something about our world that makes it so. There must be a reason for the irreducibility. There is a reason for reducibility when it obtains, which is not difficult to discover: roughly, things are generally combinations of simpler things. The universe starts with a range of basic ingredients and then these combine to form more complex structures, but nothing fundamentally new comes into the world—thus stars, planets, galaxies, rock formations, mountains, and continents. Molecules form from atoms, ever more complex. Primitive organisms form from molecules (we don’t yet know precisely how). Simpler organisms give rise to more complex ones. There is an unbroken chain, an intelligible and predictable sequence. It all hangs coherently together. Reduction, then, is only to be expected; it is certainly not something to be surprised about—no one says, “How amazing, mountains are reducible to rocks!” Nor are we stunned to find that water is H2O and heat is molecular motion. Things are composed of other things according to laws and intelligible modes of combination. It is irreducibility that is surprising from a cosmic perspective: how does the universe contrive to create novel types of entity? For example, granted that the mind is irreducible, why should that be so? Couldn’t it have been reducible? In some worlds it may be. What is the explanation of irreducibility in our world? Why does the universe indulge in it? This may seem like a strange question, but perhaps considering some possible answers will make it less strange.

Suppose the mind has some functional biological property P that cannot be conferred by the brain, as the brain is constituted in the actual world.  Then natural selection could lead to the propagation of P—even though the brain has no property that can reduce P. Here we have a biological explanation of the irreducibility of the mind: it has a property that brains can’t confer that is advantageous to survival. That is the reason an irreducible reality arose.  Irreducibility could arise when a chance mutation is selected that brings a new trait into circulation. That is, the explanation of mental irreducibility is that a chance factor combines with natural selection to favor a given trait that has no basis in anything else. In general, chance can lead to new forms, which may or may not persist. According to this explanation, irreducibility arises for intelligible reasons (in so far as chance is intelligible); it is not just a brute inexplicable fact. It might even arise from basic indeterminism at the quantum level. Alternatively, it might be said that the explanation of mental irreducibility is that God intervenes in nature to inject new ingredients into the world, expressly designing it to contain irreducible elements. He doesn’t leave nature to its own combinatory devices. Whether these are good explanations, is not to the point—which is that irreducibility requires an explanation. It is not a predictable necessary truth about how things are. In fact, it is a puzzle, an anomaly, compared to reducibility. This doesn’t mean that it isn’t a reality just that it is a surprising fact about nature. Given the way nature generally works, we would expect the mind to be reducible—as bodily organs are reducible (the brain is not irreducible). Something special must be invoked to explain its existence as an irreducible being. If we say that the mind is essentially subjective and hence irreducible, then the puzzle is why the evolutionary process gave rise to a subjective entity instead of making do with the objective entities already on the menu. What does subjectivity do for the organism? Why didn’t evolution install objective traits functionally like the subjective mind, thus allowing for reduction? The lack of reducibility calls for some kind of explanation, but it is not at all clear what this explanation might be. It hardly seems like a completely chance occurrence with no underlying rationale.

Compare fact and value: why is value irreducible to fact? We might reply: because values are normative and facts are not. That is some kind of explanation for irreducibility–and notice that it applies in any possible world. But the case of mind and body is not like that because the mental-physical divide is not comparable to the fact-value divide: the former exists within a natural evolutionary process while the latter reflects the very different purposes of factual and normative discourse.[2] It is not at all surprising that values differ from facts and are irreducible to them, but it is surprising that an irreducible type of reality arose during the course of evolution. This is why the latter irreducibility cries out for explanation while the former does not. We don’t know the reason why an irreducible mind arose—though (it may be supposed) we know that it did. In general, we don’t know why the universe contains irreducible things as well as reducible ones. It seems like an eccentric proclivity, a fondness for variety for its own sake. A thoroughly reducible universe would be a lot easier to comprehend.[3]

Colin McGinn

[1] The astute reader may observe that if reduction implies identity then we will have the same reduction all worlds, since if X is identical to Y it is so in all worlds. For example, heat will always be reducible to molecular motion in all worlds since heat is molecular motion. But we need not have such a simple view of the reduction relation: what matters for reduction is that everything about the reduced domain is explicable in terms of the reducing domain. And identity is certainly not sufficient for reduction or else “Hesperus is Phosphorous” would count as a reduction (and molecular motion would be reducible to heat). In this paper I shall try to avoid presupposing any specific theory of reduction, leaving the notion at an intuitive level.

[2] I am not here attempting to give any serious account of the fact-value distinction, or even defend its reality; my purpose is merely comparative.

[3] Another way to put the question of this paper is: Why does the universe contain (non-reductive) supervenience as a well as (reductive) identity?