Grounding and Metaphysical Explanation

The intermediate article on supervenience ended with a debt. Supervenience says there is no difference of one kind without a difference of another, and that is a claim about covariation: it records which patterns can and cannot occur across the possible worlds. It does not say which side of the pattern is responsible for the other. When a philosopher says that the mental supervenes on the physical, she nearly always means something more, that a person is in pain because of what is happening in her nervous system and not the other way round. Supervenience was being asked to carry that "because", and it could not.

This article is about the relation the "because" was reaching for. It now has a settled name, grounding, and a good part of the advanced tier is organised around it. The questions here are what it is, how it behaves, why no modal relation could stand in for it, and whether it is needed at all.

The in-virtue-of relation

The notion is easier to recognise than to define, so begin with cases.

The set whose only member is Socrates exists in virtue of Socrates' existing. Given the man, the set needs nothing further, and nobody thinks that Socrates exists because his singleton does.

A disjunction is true in virtue of a true disjunct. "Either it is raining in Leeds or seven is even" is true, if it is, because it is raining in Leeds. The truth of the disjunction is nothing over and above the truth of the disjunct that makes it true.

A thing is red in virtue of being scarlet. Scarlet is one determinate way of being red, as crimson is another, and a scarlet postbox is red by being that shade. It is not red and also, as a separate matter, scarlet.

A person is in pain in virtue of her neural state, if physicalism is true. An act is wrong in virtue of being a betrayal, if moral facts hold in virtue of natural ones.

The cases share a shape. In each, one thing holds in virtue of another. The connection is not causal: the set does not come into being a moment after Socrates is born, and the postbox's redness is not an effect of its scarlet. It is directed, running one way only. And it is explanatory, since citing the first answers the question why the second holds. Philosophy has long had words for it: "makes it the case that", "consists in", "nothing over and above", and a metaphysical use of "because".

The idea is far older than the word. Plato's Euthyphro turns on a question of exactly this form, whether the pious is loved by the gods because it is pious or pious because the gods love it. Grant that the gods love all and only pious things and the question survives, because it is not about which things are pious but about which fact holds in virtue of which. Bernard Bolzano, in the Wissenschaftslehre (1837), separated the relation of ground and consequence between truths from mere deducibility, since one truth can follow from others without being explained by them. What is recent is a systematic logic for the notion.

Three writers set the terms. Kit Fine, in "The Question of Realism" (2001) and then "Guide to Ground" (2012), used ground to state what realism about a domain amounts to, and worked out a logic for it. Gideon Rosen, in "Metaphysical Dependence: Grounding and Reduction" (2010), argued that the idioms of dependence are intelligible, that they cannot be paraphrased in purely modal terms, and that reduction is best understood with their help. Jonathan Schaffer, in "On What Grounds What" (2009), argued that metaphysics should be reorganised around the relation.

They differ over its form. Rosen treats grounding as a relation between facts, and this article follows him. Fine prefers a sentential connective, "p because q", which carries no commitment to facts as things standing in relations. Schaffer lets grounding relate entities of any category, so that the set itself is grounded in the man; dependence between objects returns in the later article on ontological dependence.

Schaffer's paper shows why the notion seemed to matter. Most existence questions, he argued, are easy: there are prime numbers, so there are numbers. The questions worth asking are which existing things are basic and which derivative, and grounding is the relation that orders them.

Explanation without causes

"Because" does two jobs. "The window broke because the stone hit it" cites a cause: an earlier event, connected to the later one through laws that could have been otherwise. "The postbox is coloured because it is red" cites nothing earlier and no law. The redness does not produce the colouredness; both hold at once.

Causal explanation typically runs across time, goes through contingent laws, and links distinct existences. Metaphysical explanation is synchronic, holds whatever the laws are, and links things that are not wholly separate: the truth of the disjunction is not a second item added to the truth of the disjunct.

How grounding relates to explanation is disputed. Fine treats ground as itself a form of explanation, objective and independent of what any audience wants to know. Others model it on causation, which is a relation in the world that causal explanations cite. On that view grounding is a worldly relation that backs metaphysical explanations without being one. The logic below is the same on both views, but the dispute returns when transitivity comes under pressure.

Full and partial ground

Some grounds work alone and some need company. The fact that the postbox is red does not, by itself, make it the case that the postbox is red and cylindrical. The fact that it is cylindrical has to be added, and the two together do the job.

Both definitions are Fine's, and on them a full ground counts as a limiting case of partial ground.

The distinction exposes some structure. A disjunction with two true disjuncts has more than one full ground, since each disjunct grounds it alone. "Something is red" is fully grounded in the postbox's instantiating redness, and separately in the tomato's instantiating it. So grounding does not assign each fact a single ground, as a function would; a fact can be overdetermined from below, much as an effect can be overdetermined by causes. Universal claims are harder, and they are the first test case for necessitarianism below.

Most grounding claims made in philosophy are claims of partial ground. "The mental is grounded in the physical" usually means that physical facts are among the grounds of each mental fact, without promising to say exactly which ones complete it.

How ground behaves

Its logic can be set out as a short list of principles, each accepted by most theorists of ground and each questioned by someone.

Grounding is factive. If one fact grounds another, both obtain.

Grounding is irreflexive. No fact grounds itself. A fact that held in virtue of itself would explain itself, and a self-explanation is no explanation.

Grounding is asymmetric. If the fact that Socrates exists grounds the fact that his singleton exists, the fact about the singleton does not ground the fact about Socrates.

Grounding is transitive. If the postbox's being scarlet grounds its being red, and its being red grounds its being coloured, then its being scarlet grounds its being coloured. With irreflexivity, transitivity yields asymmetry, and the three together make grounding a strict partial order, which is the precise content of the familiar talk of reality as layered. Schaffer adds that every chain of grounds terminates in something ungrounded, a claim that belongs to the later article on fundamentality.

Grounding is non-monotonic. Entailment is monotonic: if some premises entail a conclusion, adding premises leaves the entailment intact. Ground is not. The fact that it is raining fully grounds the fact that it is raining or snowing, but the fact that it is raining taken together with the fact that Paris is in France does not, because the second contributes nothing. A full ground must be relevant throughout, and padding it with idle facts destroys it. That is one sign that a full ground is more than a sufficient condition.

Grounding is hyperintensional. A context is intensional when expressions can be replaced by necessarily equivalent ones without changing the truth of the whole, as in "it is necessary that ...". It is hyperintensional when even necessarily equivalent expressions cannot always be exchanged. The fact that Socrates exists and the fact that his singleton exists obtain at exactly the same worlds, yet the first grounds the second and not the reverse. For a purely logical case, p and p or p are necessarily equivalent, and the fact that p grounds the fact that p or p, not the other way round.

Why supervenience could not do the job

Now set the logic beside what the intermediate article found in supervenience. Supervenience is reflexive, since every family of properties supervenes on itself. It is not asymmetric, since necessarily coextensive families, such as being triangular and being trilateral, supervene on each other. And it is cheap where necessity is cheap: whatever holds at every world supervenes on any base whatever, so that the fact that seven is prime supervenes on the weather in Leeds.

Grounding lacks all three features. It is irreflexive and asymmetric, and it discriminates among necessary truths. The necessary fact that seven is prime or seven is not prime is grounded in the fact that seven is prime, and not in the fact that it is raining in Leeds, although the rain, like anything else, necessitates it.

These are not three defects to be patched one at a time. They have a single source. Supervenience is defined by what happens across possible worlds, and anything defined that way is blind to differences between facts that hold at exactly the same worlds.

If grounding were modally defined, the first premise would let the fact about the singleton replace the fact about Socrates in the third premise, so that the fact that the singleton exists would ground itself, which the fourth forbids. The beginner tier met an argument of this shape about essence, where Fine used the same pair to show that a thing's nature outruns its necessary properties. Here the target is explanation, and the lesson is parallel.

Doubts about transitivity

Transitivity seemed the safest of the principles, since it is what makes chains of grounds add up to layers. Schaffer himself challenged it in "Grounding, Transitivity, and Contrastivity" (2012). The best known of his cases concerns a ball with a small dent. The fact that the ball has this dent is a partial ground of the fact that it has exactly the shape it has. The fact that it has that exact shape grounds the fact that it is more or less spherical. Transitivity then requires that the dent is a partial ground of the ball's being more or less spherical. That seems false: the ball is more or less spherical despite the dent, not partly because of it.

Schaffer's diagnosis was that grounding is contrastive. A grounding claim relates one fact rather than some alternative to another fact rather than some alternative, and the chain fails because the contrasts do not link up: the dent makes a difference to which exact shape the ball has, but not to whether it is more or less spherical. A restricted transitivity holds when the contrasts at the middle link match.

Grounding necessitarianism

The last principle concerns the link between ground and modality.

The motivation is simple. A full ground is supposed to be enough. If the grounds could obtain without the grounded fact, something further would be needed, and that something would seem to belong in the ground. Rosen states a principle of this kind in his 2010 paper, and most early theorists of ground accepted it. It concerns full grounds only: the fact that the postbox is red does not necessitate that it is red and cylindrical.

The principle repairs the relationship with supervenience rather than severing it. If every fact of one family is fully grounded in facts of another, and full grounds necessitate, there can be no difference in the first family without a difference in the second. Grounding, if necessitarianism is true, produces supervenience. That explains why the two were run together for so long, and it meets Kim's demand, reported in the intermediate article, that supervenience be treated as a pattern needing explanation. On this view supervenience is a symptom of grounding: good evidence for it, and never the same thing.

Two problems press on the principle. The first concerns generalisations. Suppose the apples on the table are a, b and c, and each is red. The facts that a, b and c are red seem to ground the fact that all the apples on the table are red. But they do not necessitate it, since there is a possible world in which those three apples are red and a fourth, green apple is also on the table. The usual repair adds a totality fact, that a, b and c are all the apples on the table, to the full ground. That restores necessitation, but it raises the question of what totality facts are and what grounds them, and it is not obvious that the totality fact helps to explain the generalisation rather than serving as a background condition on it. If it is only a background condition, the instances are the full ground, and they do not necessitate.

The second concerns emergence. A classical emergentist holds that conscious states arise from neural organisation by fundamental laws that could have been otherwise. If the neural facts ground the conscious ones, the grounds do not necessitate. The necessitarian replies that this dependence is nomic rather than metaphysical, so the emergentist has described something other than grounding. Fine allows that there may be natural and normative varieties of ground alongside the metaphysical one, and on such a view the principle might hold for metaphysical ground while natural ground carries only natural necessity. The critic's complaint is that each reply makes the principle safer by narrowing what may count as a ground, until it threatens to hold by definition.

There is also the question of where necessitation would come from. One answer looks to essence. It lies in the nature of disjunction that a disjunction holds in virtue of any true disjunct, and in the nature of a set that it exists given its members. If grounding connections flow from what things are, and what lies in a thing's essence could not have been otherwise, necessitation follows. That answer needs a conception of essence that does not reduce to necessity, which the beginner tier's modal definition cannot supply.

Sceptical voices

Not everyone thinks the notion earns its keep. The most developed objection is Jessica Wilson's "No Work for a Theory of Grounding" (2014). Wilson distinguishes the generic relation, which she calls big-G Grounding, from the specific relations metaphysicians actually invoke: type and token identity, functional realisation, the relation of determinable to determinate, part and whole, set membership. These small-g grounding relations, she argues, do all the work. Being told that the mental is Grounded in the physical leaves open what physicalists and their opponents actually dispute, such as whether mental properties are realised by physical ones or identical with them. Once the specific relation is given, Grounding adds nothing; until it is given, Grounding says too little. Wilson also notes that the formal profile of Grounding fits some specific relations badly. Identity is reflexive and symmetric, so a reductive physicalist who identifies pain with a neural state cannot state her view as a Grounding claim.

Defenders reply that a generic notion can be useful even when the specific cases differ. "Cause" stays useful although causal mechanisms are endlessly various, because it marks what the cases share and allows general claims about them. Claims about the overall shape of reality, that it has a fundamental level or that everything derivative depends on one kind of thing, need a relation general enough to span the small-g cases at once.

Thomas Hofweber, in "Ambitious, Yet Modest, Metaphysics" (2009), raised a more general worry about what he called esoteric metaphysics: inquiry conducted in special metaphysical terms that have no use outside philosophy. The worry is that such terms, a distinctively metaphysical sense of "in virtue of" among them, have no secure meaning, so that nothing assures us that we grasp them or that they apply to anything. Grounding theorists answer by pointing to the examples this article began with, which seem intelligible without any special training.

Next

The argument against modal analyses used Socrates and his singleton, a case the beginner tier first met in an argument about essence. The next article returns to that argument at full length. Fine's claim is that a thing's essence is not the collection of its necessary properties: Socrates necessarily belongs to his singleton, but belonging to it is no part of what Socrates is. In place of the modal account Fine puts real definition, the statement of what a thing is, together with the suggestion that necessity flows from essence rather than essence from necessity. If that is right, it also answers the question left open above, about where the necessity of ground comes from.