The problem of exclusion suggests that one or other of the following theses should be abandoned: all non-physical properties depend on physical properties without being reduced to physical properties and all entities that exist are physical entities. In response to the problem many physicalists have subscribed to a form of property dualism or reductive physicalism (eliminativism). Others hold that properties that are non-physical are identical to physical properties yet remain legitimate features for analysis.
There are some, however, who have found promising theories that draw on finding coherent ways to analyze the structural relationship between properties. Properties, on their view, are hierarchically arranged, one depending on another, being realized by another or inherent in the other. Though promising, these arguments fail for a simple reason. Although their theories work well when talking about physical properties—one physical property can be seen to supervene on another physical property—they are unable to show how this could work when the properties in question are mental properties dependent on physical base properties.
Physicalism is the thesis that all that is real is reducible to basic categories of physics and, in turn, physics—the study of matter, energy and force and apparent motion in space and time—ultimately and comprehensively reveals what is real.
Reductive Physicalism holds that properties, facts and relations that are given in non-physical terms should, in principle, be reduced to physical terms referring to physical properties, facts and relations. Non-reductive physicalism likewise holds that all that exists is physical. However, non-reductive physicalists also believe that properties, facts and relations that are non-physical are legitimate. They are motivated by the desire to have mental properties that are multiply realizable in different physical entities. Yet those same mental properties are nothing more than, or over and above, physical properties that they are dependent upon. In general, non-physical properties are said to supervene on physical properties.
Supervenience, when applied to mental properties, holds that mental properties obtain only if certain physical properties are present. Crucially, supervenience holds that mental and physical properties co-vary such that if there is a change in one there is necessarily a change in the other. This is referred to as metaphysical supervenience. Metaphysical supervenience requires that a set A of properties supervenes on set B of properties if for any change to A properties there is a corresponding change to B properties and in every possible world in which A properties and B properties are instantiated there cannot be a change in A properties without a corresponding change in B properties.
Donald Davidson is largely credited with advancing the idea of supervenience with reference to mental and physical properties. Supervenience, according to Davidson, does not entail nomological reduction of the physical to the mental. This is true, says Davidson, because if such a reduction were possible then we would be forced to reduce moral properties to descriptive properties and truth to syntactical properties.
The idea that no strict law can predict mental phenomena led Davidson to notice an apparent inconsistency between this and two other assumptions. First, mental events are, at least in part, related causally with physical events. Perception, judgments and intentional actions, all count as causally related to physical events. Second, cause entails law. Some effect being caused requires a law to determine its outcome. Yet, these two assumptions are inconsistent with the anominalism of mental events. Mental events cannot be described in the same way as physical events according to strict deterministic laws. Laws apply to the physical whether or not they are described in those terms. Mental events, on the other hand, are description dependent. Consequently, they cannot be reduced to physical laws. In order to explain how the mental relates to the physical, Davidson employed the idea of supervenience: “mental characteristics are in some sense dependent, or supervenient, on physical characteristics.”
Further motivating the non-reductive physicalist project is the desire to show how mental properties are multiply realizable. Suppose reductive physicalism is true—every M property just is a P property. Consequently, hunger is solely a physical state. A person’s hunger state and the consequent belief state of “that a sandwich would satisfy that hunger” is a physical (or brain) state. But, if the hunger (H) state is identical to the physical state, then it is identical only to the particular state of the organism that has the H state. But we would want to ascribe the same state to multiple organisms. What makes this physical property multiply realized? If another person has the H state and ensuing belief “that a sandwich would satisfy that hunger” then we want to ascribe an identical state to both people. It seems on the reductivist view that we may not be able to leap that far.
We can note the importance for the non-reductivist program. The non-reductivist can suggest that mental states can be used to function in the role of multiple realization. A mental property can be realized by many different physical kinds. Consequently, for every “M property and every P property which necessitates M, possibly something possesses M but not P.”
It is important to note that supervenience is an explanatory theory. It can be attacked not by offering some competing evidence, but by showing that its results produce an inconsistency or over explain the phenomena. In other words, the definition is stipulated and is judged by its usefulness for analysis.
For physicalists, Jaegwon Kim observes, supervenience is an attractive picture. The trouble is, he says, it won’t work. Kim argues that, given a set of physicalist assumptions, the supervenience of mental properties cannot help but fall fowl of one or other of the following assumptions. The causal closure principle states that for every physical effect there is a physical cause. The resources available to us from physics, in principle, exhaust the explanations for all physical events. The principle of causal exclusion states that for any physical event, if the event has a sufficient cause, then no additional cause is required for the effect. Causal overdetermination is when multiple causes are posited when only one is sufficient for the effect. Correlatively, the principle of parsimony requires that any explanation for phenomena be the least complicated.
First, Kim challenges the idea that the mental property can cause the physical property. A mental property, M1, at t1 causes another mental property, M2, at t2. Since both M1 and M2 instantiate because of a more fundamental properties, P1 and P2 obtaining there are competing cause for M2, that of M1 and P2. To avoid this problem Kim suggests that we should say that M1 causes M2 by causing P2. This, however, leads us to think that mental properties cause physical properties in order to cause mental properties. Isn’t this, however, what the physicalist wants to avoid?
Second, Kim points out that mental properties lose their explanatory power since one can explain the cause and effect without invoking mental properties at all. Physicalism, because it adopts the causal closure principle, maintains that P1 causes P2. If mental properties supervene on physical properties then M1 supervenes on P1. Mental properties, on this view, are not mere appearances, but have causal powers. We decide on actions and carry them out. So, M1 causes P2. Since, according to the completeness principle, if a physical property has a cause then it has a physical cause, and because no effect can have more than one sufficient cause at one time we are left with a competition of causes. To be more precise, there is one cause that must be excluded according to the principles of the physicalist. Since it cannot be the physical cause that should be excluded it must be the mental cause.
Responses to the exclusion problem usually land on a scale between emphasizing the autonomy of mental properties and emphasizing the identically of mental and physical properties. There are some solutions that fall roughly in the middle of the scale. Responses of this kind focus on the hierarchical structure of properties, how one property is grounded in another property, instead of focusing on the relation between properties in terms of “closeness” as identity theorists and property dualists tend to do. These solutions attempt to show how both mental and physical properties are structured vertically in a hierarchical arrangement showing how one property is grounded in or obtains in virtue of another more fundamental property. Their attempts are promising since the emphasis shifts from an emphasis on the categorization of existent entities to an analysis of their hierarchical structure.
Theories that focus on the hierarchy of properties fail for a simple reason. There seems to be no easy way to make a connection between a mental property and a physical property such that there is any way to tell that the former connects to the latter. Physical properties and mental properties are just too different.
However, Yablo interrupts the simple tale to tell us that there is an additional property of the triangle. The triangle is a particular shade of red – scarlet. What appeared to be a simple description of a determinate property quickly became muddied by an additional property. The property in question does not negate the original property of red since scarlet is a shade of red. However, since the exclusion principle says that we need only one property that is causally relevant, “every other property was irrelevant.” Yablo concludes that the exclusion argument is subject to this criticism. It seems that whenever we find a sufficient cause we are able to find another candidate. Even those “ultimate determinates” that do not avail themselves of further determination are likely to include other causally relevant properties.
To see why one needs to understand what we mean by determination. There is a distinction between a determinate property and a determinable property. Consider the sentence: “the triangle is red by being scarlet.” The determinate property is the latter—scarlet—while the determinable property is the former—red. Applied to mental and physical properties, Yablo says:
If the determinate is physical and the determinable [is] mental…Inferring the causal irrelevance of, say, my dizziness, from the causal sufficiency of its physical basis, is not appreciably better than rejecting the redness as irrelevant on the ground that all the causal work is accomplished already by its determinate scarlet.
The determinate-determinable idea lead Yablo to suggest that mental and physical properties supervene such that S being in physical state, P, is determinate of the determinable of S being in pain. Since mental properties are multiply realizable S being in physical state, P, is one way in which S can be in pain just as being scarlet is one way to be red. Furthermore the particular physical state S finds herself in is what necessitates being in pain.
The problem with this view, argues Funkhouser, is that Yablo provides no explanation as to why a determinate does not exclude the determinable it falls under. If determinates and determinables are not identical, thus counting as individual sufficient causes, then the most we can say is that we are blind as to which cause we should exclude. If, on the other hand, they are identical then we should reduce one to the other.
Consequently, Funkhouser suggests that determinable-determinate relations require a determination dimension, that is to say what it is that differs in pain-ness. Funkhouser suggests that the determination dimensions of color are hue, saturation and brightness. Likewise, triangles differ on the lengths of their sides. Consequently, it makes sense to describe scarlet and red related in such a way. There can be scarlet and red such that scarlet occupies red space in the determination dimension. Scarlet can be red and yet differ from red.
However, Funkhouser argues that this relation does not hold between mental and physical properties. In the case of belief it is not necessary to refer to any physical state in order to arrive at the determination dimensions for that belief. Funkhouser asks us to consider any single, multiply realizle belief. What determination dimensions are available for such a belief? It appears that all we have available are the content of the belief and the confidence with which it is held. Yet neither of these dimensions requires any reference to physical states in order to determine mental properties. Funkhouser concludes:
Any psychological law relating that belief to another mental state or to action would be indifferent to the physical hardware. And this observation generalizes to other mental states: content, attitude, phenomenology and similar psychological-level features are the only determination dimensions for mental properties.
Belief, B, is a way of being in a certain assertive relation with certain contents of a proposition. The problem is that no physical determination dimension is relevant to B. And if no determination dimension that is physical is possible, then it is not clear how a mental determinate could have a physical determinable. There simply is no room for a physical determinable for the mental determinate. And without this connection, Yablo’s argument fails.
Sidney Shoemaker’s subset view holds that mental properties are realized by physical properties. A Physical property, P, is a realizer of a mental property, M, only if the forward-looking causal powers of M are a subset of the causal powers of P and if M and P are instantiated in an individual. Since parts and wholes do not compete for efficacy of causal powers both M and P are included without overdetermination. M and P are also not identical since they have non-identical properties. A given supervenient property has causal powers that are a subset of the base property and so are nothing “over and above” the base property, but are not identical to the base property.
Shoemaker’s theory takes the relevant aspect of properties to be their causal powers. In fact, it is the causal power of properties that Shoemaker thinks in virtue of which there is a determinate-determinable relation. In reference to Yablo’s determinate and determinable distinction, Shoemaker remarks, “the determinate property realizes the determinable in virtue of the fact that the conditional powers bestowed by the latter are a proper subset of those bestowed by the former.”
There have been a number of objections to Shoemaker’s view. Only one is needed. Kevin Morris objects to the subset view because there is no reason to accept that the mental property in question is not identical to another physical property: “where the powers of a subset-realized property M are a proper subset of its physical realizer P, we cannot identify M and P, it does not follow that there is no physical property Q such that M = Q.” There is, however, good reason to suppose that a physical property is only going to have physical causal powers since that is part and parcel of the physicalist claim – entities that exist are physical entities and cannot have non-physical properties. What makes a thing red is a combination of physical properties—hue saturation and brightness—but what makes a thing believe or hope cannot find a base set of powers that it could share that are non-physical. Just what are the causal powers of mental properties apart from non-physical causal properties? And if non-physical causal properties cannot be shared with the properties of a physical entity because physical entities have no mental properties then there is either no mental property or the physical entity is not as physical as it first appeared. It would be question begging to say that mental causal properties are had by physical entities in virtue of mental properties supervening on physical properties.
Yablo and Shoemaker’s theories have significant trouble showing how mental properties can be inherently realized by or determined by physical properties. Both arguments are weakened by the substantial difficulty that supervenience imposes on itself. While analysis of physical causal properties such as scarlet and red sheds light on how one physical property might supervene on another physical property it is much more difficult to show how a mental property can supervene on a physical property. Mental properties just don’t seem to be the kinds of things that can inhere in physical properties. On both views, the weakness is shown only when one tries to apply the theory in order to jump this gap. Whether or not this approach stands a chance depends on making the connection between the two stands up to the demands of supervenience.
 For an example of the latter see: David Robb, “The Identity Theory as a Solution to the Exclusion Problem,” in Mental Causation and Ontology eds. Gibb, Lowe & Ingthorsson (New York: Oxford University Press, 2013), 215-232.
 Michael Loux, Metaphysics: A Contemporary Introduction (New York: Routledge, 2006), 39-40.
 As opposed to local or regional supervenience that holds that properties co-vary in the actual world, given the way things are in this world, but it is metaphysically possible that mental properties are not related in this way in a different world. Few physicalists hold to this view since it fails to defeat the dualist view that the mind possibly exists without the body. Edward Feser, Philosophy of Mind: A Beginners Guide (Oxford: One World, 2005), 55-56.
 This is a strong and global supervenience thesis. Some may hold other versions, but, for the sake of brevity, this paper will focus on the most common and strongest supervenience thesis.
 Donald Davidson, “Mental Events,” in Essays on Action and Events (Oxford: Calrendon Press, 1980), 207-227.
 Ibid., 214.
 Stephen Yablo, “Mental Causation,” The Philosophical Review 101, no. 2 (April 1992), 255.
 Jaegwon Kim, Physicalism or Something Near Enough (Princeton: Princeton University Press, 2005), 15.
 Jaegwon Kim, Physicalism, or Something Near Enough (Princeton: Princeton University Press, 2005). cf. J.P. Moreland, Consciousness and the Existence of God (New York: Routlege, 2008), 14-17.
 Stephen Yablo, “Mental Causation,” The Philosophical Review 101, no. 2 (April 1992), 257.
 Ibid., 260.
 Eric Funkhouser, “The Determinable-Determinate Relation,” Nous, 40 (2006), 21.
 Ibid., 23.
 Sydney Shoemaker, “Realization and Mental Causation,” in The Proceedings of the Twentieth World Congress of Philosophy ed. Bernard Elavitch (Bowling Green: Bowling Green State University, 2000), 23-32.
 Ibid., 26.
 For example, John Heil, “Multiple Realizability”, American Philosophical Quarterly 36 (1999), 189-208.
 Kevin Morris, “Subset Realization and Physical Identification,” Canadian Journal of Philosophy 41, no. 2 (June 2011), 322.