A physicalist wants to be able to say the following:
(A) There are no mental properties.
(B) S believes p.
There is an apparent inconsistency in these two claims. Most physicalists consider it implausible to suggest that (B) is false and so concede that (A) is false. In order to maintain the physicalist worldview they say that mental properties are nothing over and above physical properties. This is usually stated in terms of supervenience, something like this: 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.
In recent literature there has been a plethora of discussion about metaphysical grounding. As a paradigmatic case, contemporary grounding theorists, point to the grounding of a non-physical fact in a more fundamental physical fact. On this view, the exclusion argument shows not that physicalists should be elimitivists, but that they are asking the wrong question. Instead of asking what exists we should be asking how reality is structured. Reality is structured in layers with one fact obtaining in virtue of a more fundamental fact. To be a metaphysical fundamentalist is to commit to the belief that there are levels of ontology that ground other levels such that some level is fundamental to all the others. The motive for thinking this way is spurred on by the intuition that things are dependent in some way. And if most things are dependent then something grounds them fundamentally. “There cannot be turtles all the way down.” Grounding statements, then, are about relating one fact to a more fundamental fact.
According to some grounding theorists we should also remain neutral on what we mean by fact. Perhaps a fact should be understood as picking out existent entities or perhaps it is related to the logical form of the fact. Either way non-reductive physicalists want some way to say that mental properties are picked out by it being the case that “S believes p” or that it is true that “S believes p.”
Let us take, as a simple statement of ground, Kit Fine’s definition:
Ground = df. “if the truth that P is grounded in other truths, then they account for its truth; P’s being the case holds in virtue of the other truths’ being the case.”
Rather than treat the exclusion problem as a matter of causation, these theories suggest there might be a way to avoid the problem by considering what grounds what. As Kit Fine puts it: “Ground… stands to philosophy as cause stands to science.” The metaphysical ground explains, or accounts for, an apparent fact.
But is there really any difference between grounding and supervenience? Some philosophers have supposed that grounding is identical to supervenience. To say that the mental is grounded in the physical just is to say that the mental supervenes on the physical. Davidson, for example, appeared to assume that supervenience was the same as, or a way of describing, metaphysical dependency. Kim, on the other hand, notes that the concept of supervenience implies some “deeper” metaphysical dependency relation.
Of particular relevance to the exclusion problem are causative explanations and supervenience.  Kit Fine suggests that both causal determination and supervenience fail to capture what we have in view when we think of the relationship between physical and mental:
It will not do, for example, to say that the physical is causally determinative of the mental, since that leaves open the possibility that the mental has a distinct reality over and above that of the physical… Nor is it enough to require that the mental should modally supervene on the physical, since that still leaves open the possibility that the physical is itself ultimately to be understood in terms of the mental.
Kit Fine suggests that the problem lies in wanting to hold either to a realist view or an anti-realist view. If one is a realist one is forced to find some way to have a mental property without it gaining the upper hand. If one is an anti-realist (read: elimitivist or reductivist), then one is forced to consider statements about mental properties to be false. Yet the non-reductive physicalist wishes to avoid this dilemma.
Fine suggests that we should adopt a metaphysically neutral concept that is open to realist and anti-realist alike. Recall that the distinction in question is which truth is fundamental to another truth. Consider a table. One might want to say that “it is a table” is true, but affirm that there are no real tables. Fine’s suggestion is that if a fact is grounded and there is no other reason to treat it as real then one should treat it as unreal. 
One should, as a point of departure, be a minimalist about facts. An anti-realist of this type wants to say that what is fundamentally real are atoms and these atoms are arranged table-wise. Strictly speaking there is no table, only atoms. Yet “it is a table” remains true if it is grounded in a fundamentality statement. So, “it is a table in virtue of it being atoms arranged table-wise” grounds the apparent fact, “it is a table”, in a fundamental fact, “there are atoms arranged table-wise.” Without the operator, “in virtue of” one is left to say that “it is a table” can only be analyzed in terms of the more fundamental statement, “there are atoms arranged table-wise.” Fine asks why we should be obliged to impose this reduction. Surely one can consistently hold that tables are not real while “it is a table” remains a true statement. This “enables us to distinguish, within the sphere of what is the case, between what is really the case and what is only apparently the case.”
The problem that the exclusion argument brings up is that because one thing—the physical—is fundamental and does not reduce to anything else, an explanation that includes reference to mental properties suffers from including reference to too many entities. Fine, however, suggests that statements about reality do not need to include only entities that exist, but should include reference to how what is fundamental accounts for what is apparent. Even if what is apparent is not real, reference to unreal entities can be referred to, and be true, only if they are accounted for by reference to what is fundamentally real.
If one believes, for example, that numbers are fundamentally real, then reference to facts about plurality obtain in virtue of their being grounded in fundamentally real numbers. On the other hand, if numbers are not real they can be referred to as being accounted for by the fundamental reality of entities upon which the apparent number depends. Crucially, some fact can be true, even if it is not real, if its relation to what is fundamentally real accounts for its truth.
Fine’s suggestion supplies the anti-realist with a way to make meaningful statements about mental properties without committing herself to their reality: “So someone who thinks that mental states are reducible to micro-physical states thinks that there are mental states, but not in reality. In reality there are micro-physical states. She is an “anti-realist” about mental states just in that precise sense.”
Red, then, is unreal in that it is non-fundamental. Sophie, the pigeon, pecks at the red triangle. The triangle is red in virtue of its saturation, hue and brightness. Saturation, hue and brightness are fundamental truths and a thing being red is grounded in its being of a certain saturation, hue and brightness. The triangle being scarlet, of course, is grounded in its being red, which, in turn, is grounded in its being a certain saturation, hue and brightness.
While it is true that the triangle is red in virtue of its saturation, hue and brightness red is not real since it is not fundamental. Consequently, “S’s being in pain is grounded in S’s having a certain brain state” Being in pain is true, but not real. “The triangle is red” is a true in virtue of its being grounded in its physical base. It cannot stand on its own. It requires, in principle, to be grounded in a fundamental truth and it should not be reduced to another truth. Likewise, to say that the meaning of “S is in pain” is “S has a certain brain state” is to reduce one to the other. But to say “S’s being in pain is grounded in S’s having a certain brain state” is true because the non-fundamental, unreal truth is grounded in a fundamental and real truth.
However, the grounding relation upon which the anti-realist depends is threatened by an intelligibility challenge. Chris Daly notes that in order to define ground philosophers have generally listed three features. First, grounding has been assigned some properties that distinguish it from other relations. Asymmetry, reflexivity, transivity and monotonicity all count as formal properties of grounding. Second, grounding is conceptually related to other terms such as fundamentality. Finally, grounding is defined by reference to paradigmatic cases of its use in philosophy and in ordinary speech of which mental and physical facts is an example. Grounding is, therefore, primitive and useful. Daley claims, however, that it is unintelligible.
First, specifying the logical properties of grounding should not determine the logical properties of grounding. Physical facts can be said to both explain and ground mental facts. Yet, while causes explain their effects they do not ground their effects. Therefore, explanation is not the same as ground. And if that is how the definition is come upon it is determined, and not merely specified by the logical properties of grounding.
Second, either fundamentality is another way of saying grounding or it is independently analyzable or its connection to grounding is questionable. Daly argues that it is a questionable connection since the only apparent way to define fundamentality is in terms of grounding. To say the P is fundamental is merely to say that P is the end of the grounding chain. The only way to establish whether or not P is more fundamental than M is to say that P grounds M. Connecting grounding to some other concept would need to use a concept that is independently defined. Since fundamentality is only defined by reference to grounding, this argument to establish an intelligible definition fails.
Finally, Daley argues that defining grounding by extension is the strongest way grounding theorists present the idea to readers. However, Daley argues that this is indecisive. Consider someone who does not yet understand grounding. How do the class members help? They are supposed to help by clarifying the concept in question. In other words, grounding is supposed to help in understanding how some fact obtains in virtue of another fact. However, Daley argues, utility does not clarify anything; it merely shows how important it is to clarify the term one is using. But what if one does not understand the term? Daley concludes that grounding is not illuminated by the examples listed particularly if the relation of grounding is in competition with other relations such as supervenience or identity.
Paul Audi concedes the first point and says that the third point requires more work. Audi offers a partial response to Daly’s second criticism. Perhaps there is some connection between explanation and grounding such that explanation is understood independently and analytically sheds light on the concept of grounding. Since Audi sees grounding as a species of explanation he must show explanation’s independence in order to show an analytic connection that does not require the use of the concept of ground to get at. The distinction is epistemic. Explanations are things that are known whereas grounding relations are known about. An explanation that is non-causal is explained by a relation of ground: “The obtaining of the grounding relation, on this account, differs from the explanation in the same way any truth-maker differs from the truth it makes true.”
It is not clear that this does the trick. Consider another way to say the same thing: “A relation of ground explains the non-causal explanation.” All one has to see is that the function of the grounding relationship just is a non-causal explanation. If that is all it means it does not tell us what we need. In order to clarify the definition we need to know how grounding explains a non-causal relation. Consider its rival—supervenience. Supervenience explains or accounts for the presence of mental properties in a world of only physical things by suggesting 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. The difference is that Supervenience is about properties whereas grounding is about facts. Supervenience is an explanation of some relationship between some objects—in this case, properties—and thus explains their relationship. It is not clear that saying A grounds B is any more than saying A non-causally explains B. But then one wonders how grounding explains the relationship between A and B.
Audi concludes that more work should be done on the most promising means to a definition—appeal to examples. Of course, since the project is in its infancy it may have some work ahead to build a comprehensive definition that is agreed upon. What the examples show, if nothing else, is that many philosophers already use something like the grounding relation in their arguments and that it has prima facie appeal.
 For example, Fabrice Correia and Benjamin Schnieder, “Grounding: An Opinionated Introduction,” in eds. Correia & Schnieder, Metaphysical Grounding: Understanding the Structure of Reality (New York: Cambridge University Press, 2012), 1. Jonathan Schaffer, “Grounding in the Image of Causation,” yet unpublished draft to appear in Philosophical Studies. Michael Raven, “Ground” Philosophy Compass 10 (2015), 322-333.
 Ross Cameron, “Turtles All the Way Down: Regress, Priority and Fundamentality,” The Philosophical Quarterly, Vol, 58, Issue 230 (2007), 1-14.
 Some grounding theorists disagree. Robert Audi, for example, argues that fundamentality is not a necessary component of grounding theory: Robert Audi, “A Clarification and Defense of the Notion of Grounding” in Metaphysical Grounding: Understanding the Structure of Reality ed. Correia & Schneider (New York: Cambridge University Press, 2012),101-121.
 Michael Loux, Metaphysics: A Contemporary Introduction (New York: Routledge, 2006), 144.
 Kit Fine, “The Question of Realism,” Philosophers Imprint 1 (2001), 15.
 Fine, “Guide to Ground,” 40
 Jaegwon Kim, “Postscripts on Supervenience,” in Supervenience and Mind: Selected Philosophical Essays (Cambridge: Cambridge University Press, 1993), 167
 Michael Raven provides five features of common grounding statements. Grounding explanations are irreflexive (nothing grounds itself), asymmetrical (non-circular), transitive (grounding chains), well-founded (reaching, in principle, at the end of the chain a fact which itself is ungrounded) and non-monotonicitive (non-arbitrary). Raven shows that grounding is distinct from entailment, supervenience, reduction or truthmaking. Entailment is reflexive, supervenience can be symmetrical, identity is both reflexive and symmetrical and truthmaking does not chain. Raven “Ground”.
 Kit Fine, “Guide to Ground,” Metaphysical Grounding: Understanding the Structure of Reality ed. Correia & Schneider (New York: Cambridge University Press, 2012), 41.
 Schaffer argues that such a project is consequently far more permissive about what exists: “there is no longer any harm in positing an abundant roster of existents, provided it is grounded on a sparse basis.” The debate over the mind and material, according to Schaffer, is not about whether either exists, but about whether mind is grounded in matter. Grounding, then, is an exploration of the structure of reality before it is a consideration of the content of reality. Schaffer, “On What Grounds What,” 353.
 Kit Fine, “The Question of Realism,” Philosopher’s Imprint 1 (June, 2001), 3.
 Cf. Louis deRosset, “Grounding Explanations” Philosopher’s Imprint 13 (April, 2013), 1-26.
 It should be noted that theists have often held to something like Fine’s anti-realist theory. Jonathan Jacobs persuasively argues that statements made about God are true in virtue of their being grounded in the fundamental reality of divine nature even while they are strictly unreal. Jonathan Jacobs, “The Ineffable, Inconceivable, and Incomprehensible God: Fundamentality and Apophatic Theology”, Oxford Studies in Philosophy of Religion Vol. 6 ed. Jonathan Kvanvig (Oxford: Oxford University Press, 2015), 158-176.
 Jonathan Jacobs, “The Ineffable, Inconceivable and Incomprehensible God,” in ed. Jonathan Kvanvig, Oxford Studies in Philosophy of Religion Vol. 6 (Oxford: OUP, ), 170.
 Other examples include moral facts in virtue of natural facts, legal facts in virtue of social facts, particular entities in virtue of sets of entities and parts in virtue of a whole. Cf. Fabrice Correia and Benjamin Schnieder, “Grounding: An Opinionated Introduction,” in Metaphysical Grounding: Understanding the Structure of Reality ed. Correia & Schneider (New York: Cambridge University Press, 2012), I
 Chris Daly, “Scepticism About Grounding”, in Metaphysical Grounding: Understanding the Structure of Reality ed. Correia & Schneider (New York: Cambridge University Press, 2012), 81-100.
 Ibid., 91.
 Ibid., 91-92.
 Ibid., 95-96.
 Paul Audi, “A Clarification and Defense of the Notion of Grounding”, in Metaphysical Grounding: Understanding the Structure of Reality ed. Correia & Schneider (New York: Cambridge University Press, 2012), 120.
 The most comprehensive work to date has been carried out by Kit Fine who sees ground as a sentential operator. Kit Fine, “Guide to Ground”, Metaphysical Grounding: Understanding the Structure of Reality ed. Correia & Schneider (New York: Cambridge University Press, 2012), 37-80 especially p. 46-74.