Indeterministic grounding

Abstract

Grounding is sometimes thought of as metaphysical causation. If we take this analogy seriously, given the possibility of indeterministic causation we have at least prima facie reason to accept the possibility of indeterministic grounding. However, prima facie reasons are defeasible and there may be stronger reasons to reject this possibility. This paper sets out to critically examine this mostly overlooked possibility. After introducing the possibility of indeterministic grounding as analogous to indeterministic causation (Sect. 1), I clarify further the notion of indeterministic grounding by relating it to failure of supervenience (Sect. 2). I then construct an argument for the logical or conceptual possibility of indeterministic grounding, and defend it against a few possible objections (Sect. 3). Next, I explore and reject various reasons for dismissing the possibility of indeterministic grounding (Sects. 4 and 5). And I conclude by considering why philosophers almost universally overlook or rule out the possibility of indeterministic grounding, by examining the case of physicalism (Sect. 6).

1 Introduction

My mouth feels like it's on fire. This fact admits of two kinds of explanations. The first kind of explanation points to the various events that brought it about, for example that I ate a red-hot chili pepper, that Capsaicin hit my tongue triggering sensory neurons sending heat and pain signals to my brain. The second kind of explanation points to more fundamental facts about reality in virtue of which my mouth feels like it's on fire—arguably some neurological fact, namely that the pain and heat receptors in my brain are fired up.¹ The first kind of explanation points to causes while the second points to what has been labeled in recent literature "grounds".

It is quite natural to think of grounding as metaphysical causation and this analogy is often used by grounding theorists.² Following this line, we could say, roughly, that causal claims aim at explaining later events by appeal to earlier events (setting backwards causation aside), and similarly grounding claims appeal to more fundamental facts in order to explain facts that are less fundamental. Just like causal claims and causal explanations presuppose that time "moves forward", so grounding claims and grounding explanations assume a layered structure of the world from the more fundamental to the less fundamental. And given that both relations are taken to be transitive, then, to use prominent imagery,³ just like creating the big bang (and the laws of nature) would be sufficient for God in order to causally bring about the physical world as it is today (through a long causal chain), so there is a minimally sufficient set of facts at some ground level (again with the laws of nature) "minimally sufficient for a God to decree in order to create the rest of reality from the ground up."⁴

Given the strong analogy, it is plausible that features of one of these relations can inform the other. In her inaugural lecture, G.E. Anscombe famously distinguishes between what she calls necessitating and non-necessitating causes:

[…] a necessitating cause C of a given kind of effect E is such that it is not possible (on the occasion) that C should occur and should not cause an E, given that there is nothing that prevents an E from occurring. A non-necessitating cause is then one that can fail of its effect without the intervention of anything to frustrate it. We may discover types of necessitating and non-necessitating cause; e.g. rabies is a necessitating cause of death, because it is not possible for one who has rabies to survive without treatment. We don’t have to tie it to the occasion. An example of a non-necessitating cause is mentioned by Feynman: a bomb is connected with a Geiger counter, so that it will go off if the Geiger counter registers a certain reading; whether it will or not is not determined, for it is so placed near some radioactive material that it may or may not register that reading. (pp. 144–145)

A necessitating cause according to Anscombe is thus a cause that can fail to cause only if there is something to prevent it, while a non-necessitating cause is a cause that can fail to cause even assuming everything else fixed. Non-necessitating causes are such that even with everything else held fixed they are not necessarily connected to their effects but only statistically so. There is something confusing about Anscombe's terminology given that even what she calls necessitating causes don't need to strictly speaking necessitate their effect, as they could fail to cause because of the presence of some hindering condition.⁵ Therefore, instead of talking about non-necessitating and necessitating causes, I think it is better to label the former indeterministic causes, and the latter deterministic causes. By analogy then, a deterministic ground is a ground that grounds unless there is something to prevent it from grounding (that is to say, given the right background conditions it necessarily grounds),⁶ while an indeterministic ground is a ground that is such that it could, under the very same conditions, fail to ground.

While I admit that the possibility of indeterministic grounding can seem very odd and hard to wrap one's mind around (more on this oddity in what follows), I do not think it is much stranger than indeterministic causation. After all, the examples available for indeterministic causation come from controversial interpretations of highly unintuitive theories in physics. Thus, the analogy with causation gives some prima facie reason to accept the possibility of indetermnistic grounding or (since prima facie reasons are defeasible) at least not to reject it off hand. And yet, this possibility has received relatively little (although slowly growing) attention in the burgeoning grounding literature.

There is a lively debate among grounding theorists regarding whether a full ground of p must necessitate p. Necessitarians hold that it must while contingentists deny this. It is obvious that necessitarians should reject the possibility of indeterministic grounding. As for contingentists, it seems that most of them hold that a full ground of p along with certain background conditions (enablers, the absence of blockers etc.) does necessitate p.⁷ That is to say, most contingentists do not even consider the possibility of indeterministic grounding, typically without arguing against it.⁸ Bennett (2017) even writes that "this is implicitly assumed by just about everyone I can think of (except Cameron, 2007)".⁹

However, in recent years a few contingentists have argued that indeterministic grounding occurs or is at least possible and that it can either solve philosophical puzzles or that it is a precondition for respectable metaphysical positions. Wasserman (2017), draws on the analogy between grounding and causation to argue that indeterministic grounding is possible and can provide an attractive account of vagueness.¹⁰ Pearce (2021), defends what he calls grounding indeterminism also on the basis of an analogy to causation in order to solve an apparent inconsistency for classical theists. And Emery (2019) and Amijee (2021) have argued for indeterministic grounding by presenting (very different) putative metaphysical positions that require its possibility.¹¹

The implications of accepting the possibility of indeterministic grounding are potentially even more far reaching. Notably, the possibility of indeterministic grounding has significant implications to debates around physicalism and specifically to the possibility of zombie worlds. If indeterministic grounding is possible and consciousness is grounded in the physical, there can still be worlds with the same underlying physical facts and the same laws of nature where consciousness does not obtain. And if such zombie worlds are possible, so it is commonly assumed, this raises a significant challenge to physicalism. On the other hand, if this is not a genuine possibility, then given the analogy with causation it is worth exploring why.

The rest of this paper will examine this possibility further. I start by clarifying the notion of indeterministic grounding by relating it to failure of supervenience (Sect. 2). I then construct an argument for the logical or conceptual possibility of indeterministic grounding, parallel to an existing argument for the possibility of indeterministic causation, and defend the argument against a few possible objections (Sect. 3). Next, I explore and reject various reasons for dismissing the possibility of indeterministic grounding. First, I argue that while there may be reasons to reject the possibility of indeterministic grounding regarding specific kinds of facts or grounding relations, these reasons do not generalize (Sect. 4). I then go on to evaluate Bennett's arguments against indeterministic grounding (Sect. 5). I conclude by considering why philosophers almost universally overlook or rule out the possibility of indeterministic grounding by examining the case of physicalism (Sect. 6).

2 Grounding and supervenience

There is a broader question that is clearly of interest even to those who reject the analogy between causation and grounding and are generally critical of grounding talk.¹² Whatever you believe the relation is between the fact that my mouth feels like it's on fire and the fact that the pain and heat receptors in my brain are fired up, that is even if you do not take this relation to be grounding, you can ask whether there can be some possible world with the same neurological facts and the same laws of nature in which I (or rather my counterpart) do not feel heat and pain. In other words, you can ask whether the mental supervenes on the neurological.

For those who do accept the layered model of the world, the question can be formulated more abstractly as asking whether the less fundamental supervenes on the more fundamental. If it does, then the more fundamental facts about reality (given the laws of nature) imply a single possible reality at any less fundamental level of reality. This is, so to speak, "grounds-up" or "vertical" determinism, much like causal determinism is the view according to which the past and the laws of nature imply a single possible future. Similarly, if the less fundamental fails to supervene on the more fundamental, this can be thought of as "grounds-up" or "vertical" indeterminism.¹³

The idea that grounding implies some sort of corresponding supervenience claim is widespread. One of the first articulations of this idea can be found in Dancy (1981, p. 382). Dancy discusses the relation between moral facts and the non-moral facts in virtue of which they obtain (he calls this relation "resultance") and writes:

I think that there is a sense in which resultance entails supervenience, since supervenience appears as a consequence of what-ever relation holds between moral and non-moral properties of particular actions. […] we know that the relationship between a moral property and those from which it is parti-resultant is necessarily repeated in another object which resembles the first in all (?) non-moral respects.

In other words, if in situation C a moral fact M holds in virtue of a set of non-moral facts S, then in every situation that is identical to C at the non-moral level, the set of non-moral facts S would ground the moral fact M. This means that if the moral is fully grounded in the non-moral then the moral globally supervenes on the non-moral. And more generally, perhaps, if A-properties are fully grounded in B-properties then A-properties globally supervene on B-properties. This entailment claim is essentially the claim that a ground can fail to ground only if there is something to prevent it from grounding at the ground level; S can fail to ground M only if the situation is different from C at the non-moral level. In other words, this entailment claim amounts to the claim that grounding must be deterministic, there cannot be indeterministic grounding.

Hence, (setting aside the problem of identifying distinct levels of reality)¹⁴ we could formulate the question about the possibility of indeterministic grounding as follows: given that α is fully grounded in Γ, is it possible for α not to obtain while all the facts at the Γ level of reality, and the laws of nature, remain as they are?¹⁵ i.e., is it possible for α to be fully grounded in Γ and yet not to supervene on all the facts at the Γ level of reality? Or, to use an example, assuming that the fact that I have a painful burning sensation in my mouth is fully grounded in certain neurological facts, is it possible that without any change in the fundamental neurological level, I don't feel a painful burning sensation? i.e., is it possible that the mental is fully grounded in but does not supervene on the neurological? That is to say, the question about the possibility of indeterministic grounding is the question of whether there can be grounding without supervenience, whether grounding necessarily implies supervenience.¹⁶ This is again analogous to indeterministic causation. The question whether causation can be indeterministic is the question whether a cause can fail to cause without something preventing it from causing, and this can be formulated as the question whether causation necessarily implies determinism: given that E is caused, is it possible for E not to obtain while the past and laws of nature remain as they are.¹⁷

3 Grounding does not imply supervenience

The possibility of indeterministic grounding is thus also the possibility that grounding doesn't imply supervenience, much like the possibility of indeterministic causation is also the possibility that causation does not imply determinism. Once it is set in these terms, we can adapt existing arguments to the effect that causation does not necessarily imply determinism (and so indeterministic causation is conceptually possible) to argue that grounding does not necessarily imply supervenience (and so indeterministic grounding is conceptually possible). The argument I have in mind comes from Van Inwagen (1983, pp.139–140) and goes as follows:

Suppose someone throws a stone at a window and that the stone strikes the glass and the glass shatters in just the way we should expect glass to shatter when struck by a cast stone. Suppose further that God reveals to us that the glass did not have to shatter under these conditions, that there are possible worlds having exactly the same laws of nature as the actual world and having histories identical with that of the actual world in every detail up to the instant at which the stone came into contact with the glass, but in which the stone rebounded from the intact glass. It follows from what we imagine God to have told us that determinism is false. But does it also follow that the stone did not break the glass, or that the glass did not break because it was struck by the stone? It is not easy to see why we should say this follows; perhaps the only reason we could have for saying this is that we accept a corollary of the standard theory of causation: that instances of causation simply are instances of universal, exceptionless laws, that the concept of the instantiation of an exceptionless law and the concept of causation are one and the same concept. But this proposition is very doubtful.

Van Inwagen goes on and argues that watching a slow-motion film of the stone hitting the window several times "should make it very hard to believe that the stone did not break the glass".

…But what about the revelation we earlier imagined God's having delivered? Could this revelation really lead us to say that, despite appearances, the stone didn't cause the glass to break? That this is a logical consequence of this revelation? Wouldn't it be more reasonable to say this: that, while the stone did cause the window to break, it was not determined that it should; that it in fact caused the window to break, though, even if all conditions had been precisely the same, it might not have?

This case convinces me that whatever the facts of the matter may be, it is at any rate not part of the concept of causation that a cause—or even a cause plus the totality of its accompanying conditions—determines its effect.

Based on this argument, I propose the following parallel argument to the effect that grounding does not imply supervenience, or that there is no conceptual or logical reason to suppose indeterministic grounding to be impossible:

Suppose that someone experiences a sense of pain and heat as they are eating a red-hot chili pepper, and suppose we perform a brain scan of that person and as they report their sensation of heat and pain, we observe certain areas of their brain light up. Suppose also, that God tells us that the person didn't have to have a heat and pain sensation under these conditions, that there are possible worlds having exactly the same laws of nature (including all psycho-physical laws) as the actual world, and precisely alike at the neural level (and all levels more fundamental than the phenomenal sensations) but where the person does not experience pain and heat (but rather a pleasant tingling sensation, or perhaps nothing at all). It follows from what we imagine God to have told us that the supervenience of the mental on the neural is false. But does it also follow that the neural state in the particular state we observe does not ground the sensation of heat and pain, or that the person doesn't feel heat and pain in virtue of the neural state? It is not easy to see why we should say this follows…; perhaps the only reason we could have for saying this is that we accept a corollary of the standard theory of grounding: that instances of grounding simply are instances of universal, exceptionless laws, that the concept of the instantiation of an exceptionless law and the concept of grounding are one and the same concept. But this proposition is very doubtful.

Furthermore, it seems that watching carefully a high-resolution scan correlated with the person and their reported sensation should make it very hard to believe that the experience does not hold in virtue of the receptors being activated. And that the revelation that the correlation is not necessary should not, or does not necessarily have to lead us to deny this. Rather, given this revelation it would be more reasonable to say this: that, while the neural state does ground the sensation, it is not determined that it should. And so, it seems that whatever the facts of the matter may be, it is not part of the concept of grounding that a ground of p (or even a ground with all enabling conditions) determines that p must obtain. Or, in other words, grounding does not imply supervenience, and so indeterministic grounding is at least logically or conceptually possible.

Before evaluating this argument, there are two points worth making. First, the argument uses the instantiation of a particular higher-level property, a kind of sensation. However, it could be constructed around different examples that don't involve consciousness or sensations at all.¹⁸ And so, although such an argument wouldn't work for just about any grounded fact (I discuss in a subsequent section why that is) still it could similarly be constructed for a subset of grounded facts. Second, if the argument is sound there seems to be no reason to suppose that indeterministic grounding only occurs in borderline cases or cases of vagueness as Wasserman (2017) seems to hold. The higher order fact that the person has a pain and heat sensation is not a borderline case of pain and heat sensation. But is the argument sound?

3.1 Evaluating the argument

If we accept Van Inwagen's argument regarding causation, what reason can we have for rejecting the parallel argument regarding grounding? I think there is one way of resisting the latter argument that suggests itself quite naturally. While causation is a natural concept familiar to laymen and philosophers alike, grounding is a term of art used only by philosophers. Since most philosophers who have used the term "grounding" have also stipulated that it was a deterministic connection relation, and since we have no independent pre-theoretical intuitions about grounding, the argument cannot get off the ground. However, I don't think this way of resisting the argument is ultimately effective. While grounding is a term of art, it aims to capture a pre-theoretical notion, that of something holding in-virtue-of or non-causally because of something else. It is this notion that we are interested in when we ask the question regarding the possibility of indeterministic grounding, and not some stipulated notion.¹⁹ The recognition of facts holding in virtue of other facts seems no less intuitive than the recognition of events occurring because of other events. It seems doubtful that one can reject the intuitiveness of the former without also rejecting that of the latter.

Still, although both causation and grounding are pre-theoretical notions, and despite their similarities, they are nonetheless distinct notions. And, the objection might go, it is due to the difference between the two notions that Van Inwagen's argument is sound but the parallel argument regarding grounding isn't. That is to say, given the revelation that there is a possible world where the fundamental level obtains but not the grounded fact, it would follow that in the actual world the person doesn't feel heat and pain in virtue of the neural state. What kind of difference between causation and grounding could justify this difference? Merely stating that the best way to distinguish between the notions is that causation can be indeterministic while grounding cannot,²⁰ though it might be true, seems dubiously ad hoc. A better line is to point to another difference between the pre-theoretical notions. Here I consider three such potential differences.

A first possibly relevant difference between causation and grounding has to do with the role of time. In the case of causation, the direction of time provides an asymmetry which, arguably, is independent of the causal asymmetry. In the case of grounding, on the other hand, there is no asymmetry aside from the grounding relation itself from the more fundamental to the less fundamental. And fundamentality (relative or absolute) is standardly understood in terms of grounding.²¹ Thus, despite the possibility of indeterministic causation we still have reason to assume that causation goes in the direction that it does (namely, time). However, if indeterministic grounding is possible, what reason would we have in any such case to assume that the grounding goes in the direction that it does, rather than in the other direction? If, say, the mental doesn’t supervene on the physical, one might argue that there is no reason to think that the mental is grounded in the physical, rather than the physical is grounded in the mental. And so, if God had told us that there is a possible world where the person does not experience pain and heat despite having the same underlying neurological state, we would have no reason to think that the neural state in the particular state we observe grounds rather than is grounded by the sensation of heat and pain. Hence, we would be justified in such a case to at least doubt the claim that the neural state in the particular state we observe grounds the sensation of heat and pain. And this doubt is sufficient to block the argument.

The suggestion is thus that failure of supervenience undermines the directionality of grounding and thereby undermines grounding. It undermines the directionality of grounding because some indication of directionality of grounding is necessary and without supervenience there would be no such independent indication. The crucial move in this line of reasoning is that lack of independent indication of the direction of grounding should prompt skepticism about the direction of grounding. However, friends of grounding should not accept this assumption, as accepting it would shed doubt not merely on cases of indeterministic grounding but also on paradigmatic cases of deterministic and even necessitating grounding. Supervenience, unlike time, does not always provide directionality as it can be symmetrical. Think of the following paradigmatic example of grounding: the relation between a thing and its singleton set. Here, the former grounds the latter, but the supervenience relation goes both ways. Should we then be skeptical about the directionality of grounding in this case? I think not. We seem to have some intuitive reason to hold that grounding goes in one direction and this should be enough. The absence of an external indicator of directionality should not prompt us to doubt the apparent directionality. Therefore, God's revelation does not justify us doubting the claim that the neural state in the particular state we observe grounds the sensation of heat and pain.²²

A second difference between causation and grounding has to do with the tightness of the relation. As Segal (2021, p. 1100) puts it, grounding is "a more deeply explanatory relation" than causation. So much so, that standard examples of grounding seem to involve things that are "not wholly distinct". Or, as Schaffer (2016, pp. 94–95) puts it: "causation connects distinct events but grounding connects indistinct entities". That is to say, as opposed to causation which points to a relation between distinct entities (events), grounding points to a relation between entities (facts) that are not wholly distinct.²³ And so, if God had told us that there is a possible world where the person does not experience pain and heat despite having the same underlying neurological state, it would follow that the neural state in the particular state we observe is wholly distinct from the sensation of heat and pain, and so the relation between the two cannot be that of grounding.

However, even if we accept it as a general feature of grounding that its relata are non-distinct entities, the objection is not successful. This is because a failure of supervenience does not imply that the relation is one where the relata are wholly distinct. It only implies that their being not wholly distinct is contingent rather than necessary. In another possible world one could exist without the other. Take another kind of example, the fact that Joe Biden is currently the president of the United States and the fact that Joe Biden exists are not wholly distinct facts, but the latter could have held true without the former. Similarly, then, if God had told us that there is a possible world where the person does not experience pain and heat despite having the same underlying neurological state, it would not follow that the neural state in the particular state we observe is wholly distinct from the sensation of heat and pain. But rather it would follow that if those facts are not wholly distinct this is a contingent matter. There is a possible world where the former holds but not the latter.

A related way of resisting the argument could perhaps come from thinking about what underlies grounding connections.²⁴ Some grounding theorists hold that it is not merely that grounding relations are mediated by laws of metaphysics (which, the argument contends, we have no reason to believe are universal and exceptionless),²⁵ but also that grounding relations are intimately connected to essences.²⁶ Thus, the objection goes, for the neurological state to ground the fact that one has a heat and pain sensation, part of the essence or nature of the fact that one has a heat and pain sensation must be that if someone is in a certain neurological state then they are also (by virtue of being in this state) in a state of feeling heat and pain. And so, if one could be in this neural state without having this sensation, this would show that the connection is not one of essence and so it is not a case of grounding.

However, even if we accept that there is a difference here between causation and grounding in that only the latter but not the former is mediated by essences, this objection too is ultimately unsuccessful. That is because while there is reason to think that if an essential fact obtains then it is necessary that it obtains,²⁷ there is no reason to think that essential facts have any particular structure. And so, it might be that part of the essence or nature of the fact that one has a heat and pain sensation is that (necessarily) if someone is in a certain neurological state then there is a probability p that they are also (by virtue of being in this state) in a state of feeling heat and pain. The assumption that essential connections must be deterministic rather than probabilistic is no less doubtful than the assumption that laws of metaphysics must be such.²⁸

In sum, the underlying differences we considered between causation and grounding don't seem to justify the rejection of the parallel argument that grounding doesn't imply supervenience. Yet importantly, even if the argument is sound, what the argument aims to show is that the very concept of grounding doesn't necessarily imply supervenience, and so doesn't necessarily imply that indeterministic grounding is impossible. The idea of indeterministic grounding is coherent. Van Inwagen argues that there seems to be no other reason to think causation implies determinism. However, there may perhaps be other reasons to deny the possibility of indeterministic grounding.

4 When indeterministic grounding seems impossible

While the idea of indeterministic grounding is not incoherent, it seems that there are reasons for rejecting this possibility in certain types of cases. Here I go through two types of cases in which there seems to be reasons for rejecting the possibility indeterministic grounding and argue that these reasons are either controversial or do not generalize or both.

I start with the most obvious type of cases. Some grounding relations seem to hold necessarily for conceptual or logical reasons. For example, the dress is red in virtue of being scarlet. It is conceptually incoherent for a dress to be scarlet and for it not to be red. Likewise, if conjunctions are grounded in their conjuncts, then it is logically impossible for the conjuncts to hold and for the conjunction not to hold. So, in these and similar cases, indeterministic grounding is impossible due to logical or conceptual constraints.

Many grounding theorists seem to think that such constraints are a general feature of grounding relations. This has to do with grounding being intimately tied with explanation, and with the intuition that a complete explanation needs to leave no explanatory gap between the explanans and explanandum. The thought then is that if there is no explanatory gap then once the explanans is given in full the explanandum simply follows, and so given the full ground of x, x simply follows.²⁹ So, for example, the complete explanation of the particular moral fact that this action is wrong would include the wrong-making features of the case as well as the necessary background conditions and a true conditional stating that if these features and conditions obtain then the action is wrong. From these, together, the wrongness of the action necessarily follows.

However, even if we accept these requirements of complete explanation,³⁰ it doesn't follow that such an explanation is always available. It doesn't follow, that is, that if there is an explanation at all there has to be a complete explanation of this kind.³¹ On the contrary, it seems that we have reason to reject this claim. Causation is similarly intimately tied with explanation, and yet we do not think that for there to be a causal explanation at all, there has to be a complete causal explanation admitting of no gaps. Given that complete causal explanations are not always necessarily out there, why should we assume that complete metaphysical explanations always are? Appeal to explanation alone cannot justify this difference and so, again, it is not clear why we should assume that complete metaphysical explanations are always necessarily out there if we accept that complete causal explanation are not.

The objector may respond in one of two ways. First, she might insist that the kinds of explanations at play are distinct, and that this makes a difference such that only metaphysical explanation requires that there is a complete metaphysical explanation. But then she would have to explain what makes metaphysical and causal explanations distinct in this particular respect. What is it about metaphysical explanation as opposed to causal explanation that makes it so that complete metaphysical explanation must always be available? Alternatively, the objector might opt to bite the bullet. She might maintain that complete explanation must always be available, and so appeal to explanation motivates the rejection of indeterministic grounding and indeterministic causation alike. Surely, if one has independent reason for thinking that such complete explanations are always available, this reason would also rule out the possibility of indeterministic grounding (and by the same token the possibility of indeterministic causation). However, such an independent reason for thinking that complete explanations are always available is precisely what we are missing here. And while the human aspiration for such explanation is apparent especially since the scientific revolution, this does not provide a reason for accepting the dogma as truth.³²

And yet, at least regarding moral facts it seems that there is a different kind of reason for supposing that a complete explanation that leaves no gap (or something very close to it) must be available in principle.³³ Indeterministic grounding seems objectionable when applied, for instance, to the moral worth of an individual or an action. That Joe is a bad person is grounded in certain non-moral facts (and perhaps also some more fundamental moral facts). Suppose there is some other person Joe* who is precisely the same in all underlying relevant respects. Or if you think situations can never be perfectly identical in all relevant respects, suppose that there is a possible world W that is precisely like the actual world in all of its fundamental facts (whether moral or not), and in the laws governing the relation between the fundamental and non-fundamental facts. Suppose further, that in the actual world some of these underlying facts (including all facts about Joe's motivations, and the consequences of his actions) make it the case that Joe is a bad person. However, in some possible world W these same facts make it the case that Joe's counterpart Joe* is not quite as bad, or perhaps not bad at all. It goes without saying that this possibility seems objectionable, but it is harder to explain why exactly.

The first response that suggests itself is that if Joe and Joe* differ in their moral worth, there has to be something to metaphysically justify this difference, there has to be an explanation in the form of a difference in the more fundamental features of reality that accounts for this difference. We can think about this as a more general kind of reductio argument: if there were indeterministic grounding, there would be two worlds with exactly the same underlying facts and the grounded fact obtaining in one rather than the other, without there being any further fact that metaphysically explains the difference between them, but that is absurd so there cannot be indeterministic grounding.

However, when presented this way it's clear that the general argument fails because it merely assumes the absurdity of indeterministic (moral) grounding. When we genuinely raise the question regarding indeterministic grounding, we also genuinely raise the possibility that the difference between the worlds is unexplained and brute, it is unsatisfactory to reply by merely insisting that this is absurd. Surely, the denier of indeterministic grounding can dig her hills in this way, but this should do nothing to sway those who are unsure, and given the analogy with causation we have some prima facie reason to be unsure. The denier of indeterministic grounding needs to do more than offer a restatement of the idea that there cannot be indeterministic (moral) grounding. Furthermore, if the argument were successful, then so would be the analogous armchair argument against the possibility of indeterministic causation: suppose that in the actual world the ball broke the window, then it is impossible for there to be a possible world that is identical to the actual world right up to the moment the window broke but in which the window didn't break. Such a world is impossible because there has to be a difference in terms of past events that would account for the different outcome in W and there is none. But this is hardly an argument and more a restatement of determinism.

I think that the possibility of identical underlying characteristics with varying moral worth seems objectionable because of constraints specific to moral facts and judgments. Let me consider two such constraints. First, the possibility may seem objectionable because it strikes us as deeply and acutely unfair, wrong, or immoral. It's not fair to judge identical people or cases differently. It seems unfair to Joe that he should be deemed bad given that Joe* isn't. And in order as to avoid this blatant unfairness, we need our moral judgments to be such that what explains them is not merely ground floor probabilities (or the arbitrary decision of a divine being conferring or withholding grace), but relevant differences. The thought is then, that fairness is a conceptual prerequisite for appropriate moral judgment and for the obtaining of the moral facts that correspond to them.³⁴ Alternatively, perhaps the relevant constraint is a justificatory constraint. If there is no underlying difference between Joe and Joe* then there is no way for me to justify to others the judgment that the former is good and the latter bad. The thought might be then, that the ability to justify one's judgement to others is a fundamental requirement for morality.³⁵ Similarly, the constraint might be that morality has to be intelligible.³⁶.

However, I don't think either of these proposed reasonings can generalize to a broader argument for rejecting the possibility of indeterministic grounding of all kinds of facts. Indeterministic grounding, like indeterministic causation, introduces some randomness, some unjustified brute luck.³⁷ Why is it that the ball broke the window in the actual world and not in world W? In explaining this difference, we can typically do no more than state ground floor probabilities (or the opaque will of God). In a sense, it isn't fair and it is an unjustified brute fact that the window in the actual world broke while the window in world W was left intact. But the world is rife with such instances of cosmic unfairness and brute luck so it introduces no new difficulty. Likewise, suppose that some mental facts hold in virtue of neurological facts, and that Jill and her counterpart have the same underlying neurological state but that Jill is in pain while her counterpart isn't. Granted, it is unjustified bad luck for Jill that she isn't pain free (like her counterpart), and we might even be tempted to say that it's not fair, but there is no presupposition that such facts need to be luck-free in the first place.³⁸

So, we may have reason for rejecting the possibility of indeterministic grounding when it comes to moral facts in that the grounding of moral facts is subject to certain constraints. And we may plausibly find similar constraints for some other types of normative facts (perhaps, for instance, facts about what is rational). However, these constraints don't seem to carry over to all other types of facts. And, although the idea that some non-normative facts depend on or can be sensitive to normative facts is not unheard of,³⁹ in this context I see no reason to think that such considerations justify rejecting wholesale the very possibility of indeterministic grounding (especially if one doesn't take them to justify rejecting the very possibility of indeterministic causation).

5 Bennett's arguments against indeterministic grounding

Most contemporary philosophers seem to simply assume that there cannot be such a thing as indeterministic grounding without explicitly arguing for this assumption. The exception to this rule is Karen Bennett (2017, pp. 49–52), who acknowledges that one could hold that there can be genuinely indeterministic grounding (in her terminology: indeterministic building):

One way to deny that full builders necessitate what they build is to deny that anything necessitates the built entities. This is to claim that there can be genuinely indeterministic building: there are entire worlds just alike but for the fact that some built entity exists or obtains in one and not the other. It is to claim, that is, that built entities fail to strongly globally supervene on the rest of the world. (49)

Bennett goes on to argue that this kind of claim "is false; genuinely indeterministic building is not possible" (p. 50). She offers two arguments to this effect:

To fix ideas, let world w1 contain, among other things, a and b (perhaps they are objects, perhaps they are facts, perhaps they are something else). Let world w2 be an exact duplicate of w1 except that b does not exist or obtain there.

Argument 1: from luck. If both w1 and w2 are possible, it’s a matter of chance whether or not b exists (or obtains, etc.). It just does or it doesn’t. Certainly, nothing a is doing (as it were) makes the difference between worlds where it exists and worlds where it doesn’t. Neither a nor anything else is really accounting for b, or making b exist. So b just isn’t accounted for or made to exist—it isn’t built at all. (Note that the intuition in play here directly contradicts one of Anscombe’s intuitions about the causal analogue (1971, pp. 91–2).)

Argument 2: from modal recombination. The joint possibility of w1 and w2 indicates that b is recombinable with a, and indeed with the rest of reality. But such modal recombinability is frequently taken as a mark of fundamentality: if nothing else modally constrains b, then b is fundamental (e.g. Schaffer 2010, p. 40). But if something is fundamental, it is not in any way built! […] In short: if something fails to supervene on the rest of reality, it is recombinable with the rest of reality; if it is recombinable in that way, it is fundamental; if it is fundamental, it is unbuilt. So b is not built by a, or by anything else for that matter. (p. 50)

I don't think these two arguments are convincing. Let me respond to them in turn. Bennett's first argument can be restated as follows: (1) If b is indeterministically grounded it is a matter of chance that it exists. (2) If the existence of b is a matter of chance, nothing accounts for its existence. (3) If nothing accounts for b’s existence, it isn’t grounded. Therefore, if b is indeterministically grounded it's not grounded at all, and so b (that is any fact) cannot be indeterministically grounded.

The weak link in this argument is premise (2). Chance doesn't have to rule out there being something that accounts for b, something that makes b the case (either a cause or a ground). This is precisely the heart of Anscombe's intuition (which Bennett acknowledges to be contradicting hers). It might be useful to get back to Anscombe's original example of indeterministic cause. Anscombe imagines a bomb that

[…] is connected with a Geiger counter, so that it will go off if the Geiger counter registers a certain reading; whether it will or not is not determined, for it is so placed near some radioactive material that it may or may not register that reading. (144–145)

Still, Anscombe maintains that in such a case

There would be no doubt of the cause of the reading or of the explosion if the bomb did go off. [..] Certainly the motion of the Geiger counter's needle is caused; and the actual emission is caused too; it occurs because there is this mass of radioactive material here. (145)

In other words, Anscombe expresses the intuition that even though the explosion is not determined by the radioactive decay and so whether it will occur or not is in some sense a matter of chance, it doesn't follow that the explosion is not caused by the radioactive mass. The same intuition that "not being determined does not imply not being caused" (ibid) also underlies Van Inwagen's argument presented above. And so, if we accept Anscombe's intuition regarding causation, and if we take the analogy between the two concepts seriously, there's no reason not to accept this intuition with regard to grounding.

Moving on to Bennett's second argument, the simplest way of restating it is as follows: (1) If b is indeterministically grounded, it is modally recombinable with a (and the rest of reality). (2) Modal recombinability is frequently taken as a mark of fundamentality. Therefore (3) if b is recombinable with the rest of reality it is fundamental. But, (4) if b is fundamental, it is not grounded, and so it cannot indeterministically grounded. In short, if b is indeterministically grounded it's not grounded at all, and so b (that is any fact) cannot be indeterministically grounded.

This argument, however, is unconvincing because of the move from premise (2) to premise (3). Even if modal recombinability is indeed frequently taken as a mark of fundamentality, it doesn't follow that if something is modally recombinable it is fundamental. What Schaffer argues in the referenced paper is that fundamental objects should be freely recombinable, not that recombinable objects must be fundamental. Fundamental facts are facts that do not hold in virtue of any other fact, and if a fact is indeterministically grounded, it is grounded nonetheless. Such a fact is not independent of its ground, it's simply not fully determined by it.

But perhaps Bennett's claim is not merely that modal recombinability is a mark of fundamentality, but that there is good reason to suppose that whatever is modally recombinable is fundamental. The intuitive idea is that what is modally recombinable is in some important sense independent of the rest of reality and what exists independently of anything else must be fundamental. On this picture, everything that God would have to create in order to ensure that the world is as it actually is, counts as fundamental.

I think the key issue here is the relevant sense of independence. If b is indeterministically grounded in a then it is independent of a in the sense that its existence is not determined or ensured by a. However, b does factually depend on a in the sense that in the actual world b holds in virtue of a. This goes back to the Anscombian intuition discussed above. If we accept this intuition, we also accept a somewhat different picture according to which once the fundamental level is in place, everything else follows, though perhaps not necessarily.

Bennett admits that her arguments are "not exactly knockdown arguments" but she believes that their conclusion is further bolstered by the fact that (1) there is little to be said in favor of the opposite view, and that (2) "the claim that built entities do supervene on the rest of the world is implicitly assumed by just about everyone I can think of." (51)

I don't think this is convincing. Regarding (1), I think the analogy with causation gives at least prima facie reason to seriously consider the opposite view. Regarding (2), even though Bennett seems to be correct here and this assumption is almost universal, this could be an indication of prejudice rather than an indication of truth. In other words, this assumption could very well be a widespread mistake. However, as I will argue in what follows, a closer look will show that the appearance of universality is perhaps misleading.

6 Physicalism

Bennett illustrates her claim that the assumption according to which indeterministic grounding is universally ruled out, by discussing the well-known zombie argument against physicalism. According to this argument, zombie worlds (i.e., worlds that are similar to ours with respect to the physical facts and the laws of nature and in which people behave exactly the same but where they have no consciousness) are possible and therefore physicalism is false. Bennett argues that if there can be indeterministic grounding then zombie worlds are possible, i.e., there can be a world with the same fundamental physical facts and the same laws of nature, but where those physical facts do not give rise to anything resembling consciousness. She further argues that according to all engaged in the debate, if a zombie world is indeed possible then it follows that physicalism must be false. That is to say that all engaged in the debate agree that the possibility of a zombie world is incompatible with physicalism. However, Bennett contends, if indeterministic grounding were possible then there would be no inconsistency between the possibility of a zombie world and physicalism. Since nobody defends physicalism in this way Bennett concludes that everybody accepts that indeterministic grounding is impossible.

I think, however, that there is an alternative explanation why almost nobody defends physicalism in that way and this explanation is due to the commitments of physicalism itself rather than to theoretical commitments regarding grounding. Naturalism or physicalism has recently come to be understood as the thesis that all facts are either physical facts, laws of nature, or facts that are fully grounded in physical facts (given the laws of nature).⁴⁰ The idea, as Dasgupta (2014, p. 558) puts it,

is that at some basic level the world is constituted by a relatively sparse basis— natural or phenomenal facts—and that this sparse basis “gives rise to” facts about normativity and the external world, respectively.

This is also the understanding of physicalism expressed in Bennett's work. However, this characterization leaves implicit a very significant element of physicalism, namely, as Kripke (1972, p. 155) puts it that all facts "are 'ontologically dependent' on physical facts in the straightforward sense of following from them by necessity." A physicalist doesn't merely believe that physical facts (given the laws of nature) "give rise to" all other facts, but that they "give rise to" all other facts by necessity. It is not merely the view that once the ground level physical facts (and the laws of nature) are set, there is no need for anything else in order for the rest of reality to follow. It is also the commitment that the ground level of physical facts (given the laws of nature) fixes everything else and thus leaves nothing to chance.⁴¹

What is the appeal of this commitment? First, understandably, it stems from the ambition to provide a scientific theory that can explain everything, without gaps, holes or exceptions, and the faith that such a theory is, in principle, available. Although I have argued that I see no general good theoretical nor observational reason to take it as a given that such a perfect theory accurately describes metaphysical reality, it seems that physicalists (perhaps impressed by the success of the modern hard sciences) typically operate under this assumption.⁴²

However, there appears to be an even deeper appeal for the physicalist to hold on to this commitment. A view that takes only physical facts to be fundamental is, to use Amijee's (2021, p. 1167) words:

compatible with at least three distinct views about the other type of fact: facts of the first type may reduce to facts of the second type (‘reductionism’), or they may be metaphysically explained by those facts without reducing to them (‘non-reductionism’), or they may be eliminated altogether (‘eliminativism’).

When someone is a physicalist about the mental, say, she doesn't merely want to say something about what explains mental facts (i.e. what grounds them or makes them the case). Rather she wants to make a claim about what ultimately mental facts are. And this claim is most plausibly understood either as an eliminative claim (there are no mental facts but only the underlying physical facts) or as a reductive claim (mental facts reduce to physical facts).⁴³ Both claims allow for no gap between the (supposed) mental fact and the underlying physical facts. Now, given the shortcomings of eliminitavism and reductionism, physicalists are pushed towards a grounding formulation of their view but they want to hold on to as much of their initial claim as possible and this is achieved if necessitation is supplemented. My suggestion is therefore, that the almost universal acceptance that the possibility of a zombie world stands in contradiction to physicalism, is not necessarily due to theoretical commitments about grounding but could rather be due to theoretical commitments regarding physicalism (as well as other philosophical views that pertain to answer questions of the form "what ultimately x's are"). This raises the suspicion that perhaps the seemingly widespread agreement that the possibility of indeterministic grounding seems at the very least very odd is somewhat attributable to the pervasiveness of physicalism in contemporary thought (not only among philosophers).

This suspicion is confirmed when we think about alternatives to physicalism. Consider an idealist view according to which everything is ultimately grounded in a perfect good rational and necessary mind, i.e., God. If you hold this position and also maintain that the physical world is contingent, then you must also accept that given the full ground (i.e., God or the existence of God) it is not yet determined that the world should exist.⁴⁴ It seems plausible that some theologians actually do hold this or a similar enough position. Surely this does not establish that indeterministic grounding is possible. Perhaps there is some other reason for which the proposed picture is ultimately incoherent (this is perhaps what Spinoza thought).⁴⁵ However, this example is enough to undermine the impression we started with that the possibility of indeterministic grounding is always odd and hard to even consider. It seems that this impression is due rather to a lack of imagination on our part and perhaps—to paraphrase on Wittgenstein's famous quote—a one-sided diet of live metaphysical alternatives.⁴⁶

In conclusion, the discussion in this paper does not establish that there can be no reason for rejecting the wide spread possibility of indeterministic grounding. What I have established is that just assuming that indeterministic grounding is impossible or applies only to borderline cases is unsatisfactory and advancing an argument for these claims is no easy task. If you'd like, this paper is intended as either a challenge to put forward an argument against the possibility of indeterministic grounding, or as an invitation to explore the far-reaching implications of the possibility of indeterministic grounding. I think either would be valuable contributions. Perhaps, for example, much like causal-indeterminism is thought by some to be what is needed to defend libertarian free will, so grounding-indeterminism could be seen as making room for a strong emergentist position according to which some higher-level properties cannot be fully accounted for by fundamental physical properties, and yet those higher-level properties are not fundamental since they are instantiated in virtue of more fundamental physical facts.⁴⁷