Restricting The PSR

In these notes I look at some recent arguments from Shamik Dasgupta for restricted forms of PSR, along with a set of counterarguments from Michael Della Rocca that the PSR cannot be “tamed.”

1 Dasgupta on Limiting the PSR

Dasgupta argues for a version of PSR concerning facts that is also in an important sense restricted. His aim is to show that what he calls a “metaphysical rationalist” can accept PSR without having to accept its putatively objectionable or absurd consequences, such as that everything is necessary (“necessitarianism”), that God exists (indeed, must exist), or that everything that is conceivable exists.

1.1 Ground as Metaphysical Explanation

The set {Socrates} (i.e. “singleton Socrates”) exists because Socrates exists. The table exists because a group of particles is arranged in a particular way (i.e. “table-wise”). What does “because” mean in statements like these? The contemporary metaphysics literature contends that “because” here indicates a dependence relation of a particular kind – “metaphysical dependence”. This relation is contrasted with causal dependence. What is the contrast? For our purposes there are two salient differences. The first is that the notion of ground is a notion of constitution, or constitutive dependence.¹ Hence Q ← P (“P is the ground of Q”) just in case P is constitutive of Q. This is in contrast to causal forms of dependence, which construe P and Q as (typically) distinct events that are non-constitutively related.

1.2 PSR & Ground

The version of PSR with which Dasgupta is concerned is one about facts. So the version of PSR is roughly one which denies that there are any brute facts, or alternatively, one where every eligible fact (in a sense to be explained below) has a ground. What is a fact? A “fact” is understood roughly in the sense outlined by Gideon Rosen:²

The grounding relation is a relation among facts. We may say that A is F in virtue of B’s being G, but this is shorthand for the claim that the fact that A is F obtains in virtue of (is grounded in) the fact that B is G.

I shall suppose that facts are structured entities built up from worldly items—objects, relations, connectives, quantifiers, etc.—in roughly the sense in which sentences are built up from words. For my purposes, facts might be identified with true Russellian propositions (cf. King 2007). Facts are individuated by their constituents and the manner of their composition. This yields a very fine-grained notion. If p and q are distinct propositions, then the fact that p ∨ ¬p is distinct from the fact that q ∨ ¬q. And this is as it should be. The fact that p ∨ ¬p might obtain in virtue of the fact that p. But p cannot possibly ground the fact that q ∨ ¬q except in special cases.

Dasgupta, however, says that his reference to facts is merely “a convenient shorthand” (Dasgupta 2016, 382), and that he considers the notion of “ground” as a sentential operator, that is, an operator such as `or’ or `if - then -’. Such operators combine with different sentences (for ground, those indicating the grounds and what is grounded) to produce a further sentence (for ground, specifying the relationship of ground). The ground operator has the logical form of `φ because Γ’, where φ is a sentence, Γ is a list of sentences, and `because’ specifies the relationship of ground.³

For our purposes, nothing much should turn on whether we understanding “ground” in terms of an operator as opposed to a predicate, or in terms of facts rather than propositions, etc. But there are technical issues here, so see the sources cited above for discussion of the pros and cons of different approaches.

1.3 Autonomous Facts

Above I put Dasgupta’s version of PSR in terms of the idea that every eligible fact has a ground. This is the core of Dasgupta’s restricted PSR. He contends that some facts are eligible for having a ground, and some facts are not. A coherent but restricted form of PSR is one according to which all and only the eligible facts have grounds.

There are those facts that are apt for having a ground but lack one. These are the so-called “fundamental” or “brute” facts. And there are those that are apt for having a ground and have one. These are the so-called “derivative” facts. And finally there are those that are not apt for having a ground in the first place. These are what I call “autonomous”.⁴

So Dasgupta understands PSR’s claim, that everything has an explanation or reason, in terms of a restricted claim that everything that is eligible (or “apt”) for explanation has an explanation.

we can distinguish brute facts from essentialist facts. Both are groundless, but there is a difference. The former are apt for being grounded; it is just that they lack a ground. By contrast, the latter are not apt for being grounded in the first place, in roughly the same sense that arithmetic facts are not apt for causal explanation and that definitions are not apt for proof. I am using ‘autonomous’ to label the latter category, and ‘brute’ or ‘fundamental’ to mark the former. Thus the brute facts play an analogous role vis-`a-vis metaphysical explanation as the initial conditions play vis-`a-vis causal explanation and the axioms play vis-`a-vis proof. The autonomous facts play a different role, one more analogous to the role that definitions play in proof.⁵

1.4 Essence & Autonomy

Autonomous facts are ungrounded facts but they are not brute, because they are not eligible or “apt” for explanation. Dasgupta’s proposal is that only essentialist facts are autonomous. What are essentialist facts?

An essentialist fact is one that specifies what a thing is “in its most core respects”.⁶ Dasgupta leaves this notion of a “core respect” pretty vague. But the idea seems to be that a core respect is that (i) without which the thing would not exist; (ii) that determines the kind to which the thing belongs. So for any fact of form E,

E:

it is essential to x that φ (where x is an item of any ontological category and φ is a sentence)

it is the case that x would not exist, and would cease to exist as a member of that kind were it to lack φ. So, consider the fact that (e.g.) it is essential to the number four that it is the successor of three. The number four would not be what it is without the property of being the successor of three. It would not exist, and would not exist as a number (or as even, or as a natural number, etc.).⁷ All “non-essentialist or ”substantive“ facts are thus grounded in essentialist facts, and all essentialist facts are ungrounded, but also ineligible for being grounded. They are ”autonomous“.

When we glossed rationalism as the view that “everything” has an explanation we meant that everything that is apt for being explained (given the particular notion of explanation in play) has an explanation. For us—using (as we are) the notion of ground—this means that every substantive [i.e. non-essentialst fact] fact has an explanation. Which is precisely what my PSR implies.

1.5 A PSR Within Limits?

There are questions as to whether metaphysical rationalism is compatible with the PSR as Dasgupta understands it, and whether Dasgupta’s version avoids all the putatively negative or absurd consequences associated with more traditional versions of PSR. But for our purposes I focus on the specific issue of limitation by appeal to autonomous facts. I consider two questions. The first is whether essentialist facts ultimately satisfy the conditions set out for a fact’s being autonomous. The second is whether the notion of an autonomous fact (whatever else such facts might be) is ultimately compatible with the kind of intelligibility constraints that are usually considered part and parcel of any form of PSR.

1.5.1 Against Autonomous Essences

Dasgupta contends that essentialist facts are not apt for explanation or grounding. To ask why it is that four is essentially the successor of three is invite the answer “that’s just what it is to be four”. For essentialist facts no further answer beyond “that’s just what it is to be x” is forthcoming.

In virtue of what is it part of what water is that it is composed of H₂O? It is again hard to know what to say other than that is just what water is! And in saying this one is again most naturally heard as sidestepping the question rather than giving it a serious answer.⁸

But is it right to think that essentialist facts are ungrounded in the manner required for autonomous facts? Consider the singleton Socrates case again. Here Dasgupta contends that there is nothing further to say as to why {Socrates} essentially depends on the existence of Socrates. But this is not because it is a brute fact, but rather because it is an autonomous fact, and we can see this because brute facts, unlike autonomous facts, are arbitrary.

There is nothing arbitrary about the fact that {Socrates} is by definition the unique singleton containing Socrates: this is, after all, just what {Socrates} is⁹

So while both brute and essentialist facts putatively lack any further basis to answer why questions concerning them, they are supposed to differ in the sense in which this is arbitrary. However, it actually seems like we can say more as to why an essentialist fact of the sort above is not arbitrary. The reason why {Socrates} is a unique singleton is that set identity essentially depends on its members. But Dasgupta has to deny that this fact is a ground for the fact that {Socrates} is the unique set having Socrates as its sole member. He contends that the nature of set membership merely implies that the identity of a set depends on its members, it does not ground any essentialist fact about this or that set.¹⁰ Unfortunately he seems to lack any clear reason or (non ad-hoc) argument for doing so.¹¹

Consider the point that Dasgupta makes against other views of ground, that they are inadequate because they provide only a single explanation where different explanations are required. For example, the “simple reductionist” view contends that

if P obtains then P grounds P ∨ Q. And suppose (as is also customary) that P grounds ¬¬P. Then simple reductionism implies that what grounds the fact that P grounds P ∨ Q is exactly the same as what grounds the fact that P grounds ¬¬P, namely, P. And this is wrong: the grounds are surely different and involve something about disjunction in the first case and negation in the second. It is because of the way disjunction works that P is a sufficient explanation of why P ∨ Q, while it is because of how negation works that P is a sufficient explanation of why ¬¬P. The point is emphasized by noting that even if P ∧ Q obtains, P does not (on its own) ground P ∧ Q. So why is P ∨ Q different? What is it about P ∨ Q in virtue of which it is sufficiently explained by P but P ∧ Q is not? Surely the answer has something to do with disjunction (perhaps its truth-table).¹²

The point being made here is that the ground of P ∨ Q must be different from the ground of ¬¬P. They cannot both be grounded in P alone, or at least it seems reasonable to ask why they are the same rather than different. Dasgupta makes the plausible point that the difference lies in the differing natures of the logical connectives. The natures of those connectives (or their truth tables) along with the nature of P, ground the different complex logical truths. But if that is correct then why not say that the nature of set membership and the nature of its elements jointly ground essentialist claims such as it is essential to {Socrates} that it is the unique set containing Socrates as its sole member? It is entirely ad hoc to say that this relation to the essentialist fact is merely implication and not ground. But if that is right then at least some essentialist facts do have grounds after all. Moreover, it looks like this point generalizes. For any fact, including essentialist ones, we can ask why it is the way that it is, and any answer to such a why question is going to require appealing to the nature of the constituents of the fact in question, up until we get to the nature of being as such. And while this is still an essentialist fact, this is no comfort for the brute essentialist, since the whole point of basing ground claims in autonomous facts about essences was that we don’t end up having the PSR push us towards the unity of all answers to such why questions in the nature of being as such.

1.5.2 Autonomy & Intelligibility

If essentialism isn’t going to provide a convincing means of restricting PSR, is the more general appeal to autonomy going to fare better? There may be other candidates for autonomy to which one might appeal. But we can also ask about the position of autonomy itself. Is it plausible to say that there are ungrounded facts that are not brute (as opposed to explanatorily ineligible)? Take the position above, that all essentialist facts ultimately bottom out in some fact (or facts) concerning being as such. Is this a good candidate for an autonomous fact?

On the one hand, it’s hard to see what else could be a candidate for autonomy if not being as such, since (particular beings aside) there is literally no other candidate. Perhaps here the “this is just what x is!” strategy is appropriate. But on the other hand, as Spinoza argues, it is the same impulse driving us to understand being as such as it is driving us to understand any other particular being. All things must be explained in terms of being (and being conceived) in themselves or another (E1a1-2). The difference between a reply like that of the Brute Essentialist and a reply of the kind that Spinoza gives is that the latter, but not the former, respects the demand for thoroughgoing intelligibility. From this point of view it seems that the kind of stopping point advocated by the Essentialist is no different from that advocated by any proponent of brute facts. In this sense the Brute Essentialist fails to find a way of restricting PSR in a satisfactory manner.

2 Della Rocca’s Anti-Taming Argument

Michael Della Rocca (MDR) argues that there is no middle ground for PSR, either one applies it wholly unrestrictedly, or one rejects it. There are no other alternatives.¹³ MDR’s argument is a general one, and applies to any proponent of any form of PSR. His contention is that any endorsement of PSR, however limited, will lead to a radical monism in which all distinctions of any kind must be denied.

Here is how MDR states the argument:

it seems to be generally true that if one thing is built into the nature of another thing, then the second thing depends on the first. In the case at hand, because standing in a relation of grounding to one or more of its relata is built into the nature of any relation, it follows that our relation R depends not just on its relata, but also depends on the relation of grounding that it stands into one or more of its relata. Call this relation of grounding, R′ . Thus, R depends not only on its relata, but also on R′ (the relation of grounding between R and one of its relata). I will call the relatum in question “A”. So R′ is the relation of grounding between R and A.

Now, as Hume might say, in our sifting humour, we must ask: what does R′ depend on? R′, by its nature, stands in a grounding relation to its relata, R and A. Thus it is built into the nature of R′ that it stands in this further relation of grounding which I’ll call R′′ . But what does R′′ depend on? Answer: its relata plus a further relation of grounding, R′′′ between R′′ and its relata, etc. We are clearly off on an infinite regress…¹⁴

MDR contends that this regress is vicious.

We are clearly off on an infinite regress, a regress that seems to be vicious. Grounding R depends on first grounding R′ which depends on first grounding R′′ , etc. This chain of grounds not only can never be completed, but it can never even get started: the chain of grounds can never, as it were, get off the ground.¹⁵

In addition to being vicious, MDR also contends that the argument posits a circular set of grounds.

R′ depends on its relata, R and A. But, as we have seen, R, in turn, depends in part on the relation R′ of grounding which it stands in to A. So R′ ultimately depends in part on R′ itself. This is a circle. This is a problem.¹⁶

MDR states that the argument can be avoided if one rejects PSR, which he considers to play a role in the above argument in at least three key ways:

first, in the claim that if relations cannot be grounded or metaphysically explained, they don’t exist or are not real; second, in the claim that relations cannot be free-floating, they must be grounded at least in their relata; and third in the claim that being grounded in its relata is built into the nature of a relation.¹⁷

In each case MDR’s view seems to be that the problems besetting the proponent of a restricted version of PSR can be avoided by accepting some form or other of bruteness concerning relations and their grounds.

Here is a reconstruction of MDR’s regress argument:

1. If x is part of y’s nature, then y depends on x.
2. By its nature, a relation R depends on (at least) its relata (r_1 … r_n).
3. It is part of the nature of R that it stand in a relation of grounding to one or more of its relata – call this part of R’s nature “R′”.
4. ∴ R depends (at least) both on its relata and on R′. [1-3].
5. It is part of the nature of R′ that it stand in a relation of grounding to one or more of its relata (i.e. to R and to r_x) – call this latter “R′′”.
6. ∴ R′ depends (at least) both on its relata and on R′′. [1, 4-6]
7. … regress ensues.

Is there any way of replying to MDR’s regress argument (which is modeled on Bradley’s famous regress argument)? One possibility, often discussed, is to agree that there is a regress, but argue that it is benign rather than vicious. Consider the analogy with truth: if it is true that P then it is true that it is true that P and so on. Is this a problem for an account of truth? It doesn’t seem so. Instead there is one ground of truth(the truthmaker for P) and the regress supervenes on this truth and its ground – the infinite chain is merely a kind of free byproduct.¹⁸

Another alternative would be to deny one of the key premises in the argument above (i.e. premises 1-3). For example, one might argue that entities do not depend (at least in the sense of “ground”) on their natures (or the constituents of such natures) but rather are defined by their natures (this would seem to be Dasgupta’s position, for example). So if we reject premise 1 (at least under one precisification of “depends”) then we can reject the inference to premise four. Just because it is part of the nature of R (of what R is) that it be grounded in its relata, that does not mean it depends on this part of its nature, and in particular that it stands in a relation of ground to this part of its nature. If that is correct then there is no regress, vicious or otherwise, nor is there any circle of ground.

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