HOW THE PRINCIPLE OF SUFFICIENT REASON UNDERMINES THE COSMOLOGICAL ARGUMENT

COMO O PRINCÍPIO DA RAZÃO SUFICIENTE MINA O ARGUMENTO COSMOLÓGICO

ABSTRACT

My aim here is to show how the Cosmological Argument (CA) is undermined by one of its own premises: the Principle of Sufficient Reason (PSR). Firstly, I explain the type of CA that I am thinking about (I). Secondly, I explain a traditional modal objection against the PSR, which is ultimately based upon our intuitions in favor of contingency (II). Thirdly, I show how this modal objection begs the question against the necessitarian, and then I reformulate the CA in more neutral terms (III). Fourthly, using this more neutral version of the CA, I argue that the main problem with the PSR goes way beyond its apparent necessitarian consequences. As an argument used by Bradley shows, embracing the rationalist path that underlies the PSR seems to commit us to a form of Radical Monism too (IV). Finally, I conclude by showing how this result ultimately undermines the CA itself (V).

Keywords:
Cosmological argument; Principle of Sufficient Reason; Necessitarianism; Bradley’s regress; Monism

RESUMO

Meu objetivo aqui é mostrar como o Argumento Cosmológico (AC) é abalado por uma de suas próprias premissas: o Princípio da Razão Suficiente (PRS). Primeiramente, explico que tipo de AC tenho em mente (I). Em segundo lugar, explico uma objeção modal tradicional contra o PRS que é, em última instância, baseado em nossas intuições a favor da contingência (II). Em terceiro lugar, mostro como essa objeção modal clama por questionar o necessitário e, em seguida, reformulo o AC em termos mais neutros (III). Em quarto lugar, utilizando esta versão mais neutra do AC, argumento que o problema principal com o PRS vai além de suas consequências aparentemente necessitárias. Como mostra um argumento usado por Bradley, abraçar a via racionalista que subjaz ao PRS parece nos dedicar a uma forma de Monismo Radical também (IV). Finalmente, concluo mostrando como esse resultado, em última instância, mina o próprio AC (V).

Palavras-chave:
Argumento cosmológico; Princípio da Razão Suficiente; Necessitarianismo; Regresso de Bradley; Monismo

I

The Cosmological Argument (CA), as commonly understood (e.g., Rowe, 1998; 2007), has two parts. In its first part, it aims to demonstrate that a necessary, independent or self-explanatory being exists. In its second part, it aims to demonstrate that this being satisfies the theistic notion of God, i.e., that it is eternal, omnipresent, omniscient, omnipotent and infinitely good. Traditionally, most of the action has taken place in the first part, which starts from two alleged truths that figure as main premises, namely: the a posteriori truth that there are beings whose existence is contingent, dependent or explained by another, and the truth of some explanatory principle. Depending on which explanatory principle is chosen as a premise, we can distinguish, following Craig, at least three types of CA: those based upon the Principle of Determination, e.g., the kalām argument; those based upon the Principle of Causality, e.g., Aquinas’s arguments; and those based upon the Principle of Sufficient Reason (PSR), e.g., rationalistic arguments like Leibniz’s and Clarke’s (Craig, 2001, p. 283). The distinction is important because the power of the objections varies according to which type of CA they are directed against. I will focus here on the rationalistic understanding of the CA. Not on any particular variant of it, but, rather generally, on the type of CA that is based upon the PSR; so, hereafter, whenever I use the expression “CA”, I will be talking about this third type of argument.

Here is a pretty standard and straightforward reconstruction of the CA (cf. Gale, 2016, ch. 7; Reichenbach, 1972, ch. 1; Reichenbach, 2021, §4.1; Rowe, 2007, ch. 2; Taylor, 1991, ch. 11; van Inwagen, 2015, ch. 7):

• (1) Some contingent beings-e.g., flowers, dogs, human beings-exist.

• (2) For everything that is the case, there is a sufficient reason for its being the case.

• (3) Not every being can be contingent.

  Therefore,

• (C1) A necessary being exists.

  …

  …

  Therefore,

• (C2) This necessary being has the following attributes: it is eternal, omnipresent, omniscient, omnipotent and infinitely good.

Premise (1) is, intuitively, a plain a posteriori truth: the commonsensical piece of knowledge that there are things such as flowers, dogs and human beings, and that these things could have failed to exist: that this flower exists is, apparently, a contingent fact (or truth). Importantly for my purposes, it is quite common among the philosophers that discuss the CA-or at least among those to which I made reference above-to take the concepts contingent, dependent and explained by another as extensionally equivalent, just like they tend to take as extensionally equivalent the concepts necessary, independent and self-explanatory. In the argument, the concept exists should be understood as tenseless, actual and concrete existence, just in the sense in which God’s Creation may be said to exist.

Premise (2) is a pretty standard version of the PSR. It resembles various of its formulations. For instance, van Inwagen formulates the PSR thus: “[f]or every state of affairs that obtains, there is a reason for its obtaining” (1983, p. 202), and thus: “for every truth, for everything that is so, there is a sufficient reason for its being true or being so” (2015, p. 159). In both formulations he is clearly following the understanding of the PSR embraced by Leibniz: “we can find no true or existent fact, no true assertion, without there being a sufficient reason why it is thus and not otherwise” (“The Principles of Philosophy, or, the Monadology”, §32). Della Rocca defines the PSR in similar terms: “for each thing (object, state of affairs, or whatever) that exists or obtains, there is an explanation of its existence, there is a reason that it exists” (2010, p. 1). Pruss claims that according to the PSR “[e]verything that is the case must have a reason why it is the case. Necessarily, every true or at least every contingent true proposition has an explanation” (2006, p. 3). Taylor claims that according to the PSR “in the case of any positive truth there is some sufficient reason for it” (1991, p. 101). Spinoza offers a stronger version, which covers negative existential facts too: “[f]or each thing there must be assigned a cause, or reason, as much for its existence as for its nonexistence” (“Ethics”, 1p11d2). However, Spinoza’s stronger terms are not necessary for the purposes of our discussion. What is crucial for the understanding embraced in what follows is that, according to the PSR, there seems to be only one way in which some reason can count as sufficient: if P is a sufficient reason for Q, then P entails Q, that is, Q’s obtaining must follow from P’s obtaining with the same modal force of a conceptual or logical necessity. Otherwise, that is, if Q were not entailed by P, if it were possible for P to obtain without Q obtaining, then P would not be sufficient for Q (Della Rocca, 2003; van Inwagen, 1983, pp. 202-205).¹ And if it were possible for Q to obtain without P obtaining, then Q would either be a brute fact or have a sufficient reason distinct from P.

Premise (3) seems to be a consequence of the PSR. On one hand, if there is a reason for everything that is the case, or at least for everything that is contingently the case, as the PSR claims, then there are no beings whose existence is just a brute fact. There are no inexplicable cases of existence, no cases of existence explained by nothing whatsoever. All beings that exist are either self-explanatory or explained by another. On the other hand, no contingent fact can be the sufficient reason of its own obtaining. Given the standard of explanation raised by the PSR, a case of contingent existence is not (cannot be) a sufficient reason for itself. The premise pretends to avoid the temptation of explaining the existence of contingent beings by appealing to the existence of contingent beings alone. Take the fact that I exist. I am not a self-explanatory being-let’s take this for granted for the sake of argument . So, to explain my own existence, we need to appeal to the existence of other beings. In doing so, we may be tempted to appeal to the existence of other contingent facts, involving the existence of other contingent beings, such as the existence of my parents and their activities, the existence of my grandparents and their activities, and so on. But given the existence of any contingent being Q, the question “Why Q?” remains unanswered; it still makes sense to ask “Why Q?”. Moreover, if we take the World to be the conjunction of all contingently true propositions, the vast conjunctive fact that comprises everything that is contingently the case, we can still ask: Why does the World exist at all? Why is there the World rather than nothing? And this is so because any conjunction that includes a contingent conjunct is also contingent. It seems that the only way to block this type of question under the pressure of the PSR is by appealing to the existence of some self-explanatory being, a being whose existence somehow is sufficiently explained by its own essence, something whose existence does not depend on the existence of other things, a necessary being.

II

The CA just presented has been attacked through a famous modal objection against one of its main premises, the PSR. This objection has received various formulations (cf. Almeida, 2018, §3.3; Bennett, 1984, §28; Gerson, 1987; Pruss, 2006, ch. 6; Rowe, 1998, pp. xvi-xvii; van Inwagen, 1983, pp. 202-204). The direct charge against the PSR is that it has an intolerable consequence, namely: it produces “the collapse of all modal distinctions” (van Inwagen, 1983, p. 202), in such terms “that there are no contingent truths-that this is the only possible world” (Bennett, 1984, p. 115).

The modal objection assumes the three main premises of the CA previously stated and focuses on the PSR-premise (2)-for its reductio. Here is a reconstruction of the objection:

• (1) Some contingent beings-e.g., flowers, dogs, human beings-exist.

• (2) For everything that is the case, there is a sufficient reason for its being the case.

• (3) Not every being can be contingent.

• (4) The World exists.

• (5) There is a sufficient explanation, E, of the World’s existence. [(2), (3), (4)]

• (6) Necessarily, a fact is either contingent or necessary.

• (7) Necessarily, E is either contingent or necessary.

• (8) E cannot be necessary.

• (9) E cannot be contingent.

• (10) E cannot be. [(7), (8), (9)]

  Therefore,

• (C3) Premise (5) is false.

  Therefore,

• (C4) Premises (2), the PSR itself, is false: there is at least one brute fact of existence.

Why, according to premise (8), E cannot be necessary? Because if E were necessary, then, in virtue of the PSR, E would entail the World’s existence. But then the World’s existence itself would be a necessary fact, and the existence of all its conjuncts would be necessary too, since no necessary fact can have a contingent conjunct-contrary to the assumption of there being contingent facts, in particular those facts that involve the existence of beings such as flowers, dogs and human beings, of which we have, allegedly, a posteriori awareness.

Why, according to premise (9), E cannot be contingent? Because if E were contingent, then E would be a conjunct of the World. But, if so, how could E be a sufficient explanation of both itself and the World? To do so, E must both entail the World and be entailed by the World. In other terms, E cannot be a constituent of the World yet it must be a constituent of the World. The only option that seems able to dissolve this tension is to take E as identical with the World. But, in virtue of the PSR, no contingent fact can be a sufficient explanation of itself. So, the World-which we are taking now to be identical with E-cannot account for its own existence. Thus, although we might well explain every conjunct of the World by appealing to another conjunct of the World or to the World itself, these moves cannot explain the existence of the World itself, because we can always exert more pressure and ask: Why does the World exist at all? Why is there the World rather than nothing?

I think the argument is valid. The PSR thus understood seems indeed to have as a consequence a strong form of necessitarianism. But is the argument sound?

Of course, one possible reaction is simply to accept the soundness of the objection and follow it where it leads. We may have intuitions that favor the PSR, but it seems clear that our intuitions in favor of the existence of contingent beings are stronger. So, we should favor the latter. Therefore, we should reject the PSR and all arguments based upon such a false premise. Therefore, we should reject the CA too. Insofar as it is based upon the PSR, the CA is not a sound argument for the existence of God. So, maybe the existence of the World is just a brute fact indeed; or maybe there is another way, distinct from the CA, to explain it; or maybe there is a distinct type of CA, one that appeals to a restricted version of the PSR or to a weaker explanatory principle, to explain it. Most philosophers take one of these paths. All of these paths, I think, are viable alternatives. But never mind; exploring them goes beyond the scope of this paper. More importantly, I think the modal objection begs the question against the necessitarian in an important sense. Why should the necessitarian be moved by this objection at all? Sure, as it has been said, commonsensical intuitions seem to favor the idea that there are contingent facts, such as that this flower exists, so, at least in principle, the necessitarian seems to have the burden of proof against those intuitions. But if those intuitions are challenged by a direct argument for the PSR, then the burden of proof shifts. If there is such an argument, we can no longer rest comfortably upon those very same intuitions. We are forced by the dialectical context to give a counterargument to the necessitarian. As it happens, there is such a direct argument for the PSR. It has been given by Della Rocca (2010). Let’s see how it works.

III

Della Rocca’s (2010) direct argument for the PSR starts by stating an uncontroversial fact: that philosophers accept as legitimate many local explanatory demands concerning various apparent features, such as colors, sounds, free will, knowledge, perception, meaning, justice, dispositions, causation, beauty, modality, etc. Underlying the acceptance of these local explanatory demands we find explicability arguments that share the following pattern: take feature X; if X is not in virtue of something, then X is not explicable; but X is not inexplicable; therefore, X is in virtue of something. When philosophers accept this type of argument, they presuppose that certain apparent, superficial or problematic feature is explicable by, or obtains in virtue of, some more real, deeper or less problematic feature.

Not all philosophers accept all explicability arguments, but most philosophers accept some explicability arguments. Now, the fact that most philosophers accept some explicability arguments does not entail that they accept the PSR. Accepting explicability arguments concerning, say, causation and free will, is compatible with rejecting explicability arguments concerning, say, knowledge and beauty, and, therefore, compatible with rejecting the PSR. However, we can see that the philosopher who accepts some explicability arguments and rejects others is under intuitive pressure: Why does she accept some explicability arguments and reject others? At this stage, she could reply “in virtue of nothing”; and, if so, the line that divides acceptable from unacceptable explicability arguments would be simply a brute, arbitrary, inexplicable fact. Or she could instead reply “in virtue of this and that”; and, if so, the line that divides acceptable from unacceptable explicability arguments would be a reasoned, principled line. By taking the first path, the philosopher begs no question: she just accepts another brute, arbitrary, inexplicable fact among other brute, arbitrary, inexplicable facts that she already accepts. By taking the second path, the philosopher does not, thereby, accept the PSR: she just accepts another local explanatory demand as legitimate, and draws a reasoned, principled line.

But what happens if we confront our philosopher with an explicability argument concerning existence? If the existence of each thing is not in virtue of something, then the existence of each thing is inexplicable; but the existence of each thing is not inexplicable; therefore, the existence of each thing is in virtue of something. In virtue of what the things that exist exist? What explains that this and that are cases of existence?

We can see how the acceptance of local explicability arguments introduces intuitive pressure for accepting an explicability argument concerning the existence of things. Now, at this stage, concerning this very explicability argument, it is no longer possible to draw a brute, arbitrary, inexplicable line to divide acceptable from unacceptable explicability arguments. Because-and here comes the main point of Della Rocca’s argument-facing the explicability argument concerning existence we have three alternatives: (i) We can accept it. If we do so, we are immediately committed to the PSR, because to claim that every case of existence is explicable is the PSR. (ii) We can go revisionary about all our initial intuitions concerning explicability arguments, and reject all of them, including the one concerning existence. This move has the merit that does not draw arbitrary distinctions; however, it does seem quite implausible, since we all, philosophers and non-philosophers alike, are receptive to at least some explicability arguments. For example, if one day you see that an elephant pops-up in your kitchen, you will not accept this as a brute, arbitrary, inexplicable fact. (iii) We can reject it by drawing a line between acceptable and unacceptable explicability arguments in such a way that the explicability argument concerning existence is left on the side of the unacceptable ones. But this time such a line must be drawn in principled, reasoned terms. Because, at this stage of the argument, drawing such a line in brute, arbitrary, inexplicable terms would be indeed to beg the question, since it would be to presuppose that the PSR is false. This might be a permissible move when we face other explicability arguments, but not when we face an explicability argument concerning existence itself, which is a direct argument for the PSR itself.

If Della Rocca’s argument for the PSR is sound, then we can no longer dismiss its necessitarian consequences based upon our commonsensical intuitions alone. These intuitions have been directly challenged by an argument that also starts from plausible intuitions against the brutality of facts such as there being an elephant popping-up in your kitchen. Now the burden of proof has shifted.

So, considering that there is a direct argument for the PSR, why don’t we adopt a more neutral attitude about the modal status of those a posteriori truths that work as a first datum for the CA, such as that roses exist, that dogs exist, and that human beings exist? After all, remaining silent about the modal status of these facts shouldn’t count, in principle, against the CA itself. All what the CA requires for running is to accept that the facts that work as a point of departure are known a posteriori and are not self-explanatory. But these features don’t require from us prejudging their modal status. The truth is that, firstly, there is no a posteriori datum that counts against the necessary character of facts such as that roses, dogs and human beings exist; and, secondly, although, as I said above (I), it is quite common among philosophers that discuss the CA to equate contingent, dependent and explained by another, there is no conceptual or logical barrier against the idea that there are entities whose existence is both dependent or explained by another yet necessary. Moreover, nowadays, with the revival of grounding, we are quite open to accept that something, say Y, obtains in virtue of something else, say X, in such terms that Y is both explained and necessitated by X. In fact, the standard way of understanding full grounding is as a relation that obtains between distinct facts; that carries metaphysical necessity; and that imposes a strict partial order on the entities of its domain (i.e., that grounding is an irreflexive, asymmetric and transitive relation).² Thus, if X fully grounds Y, we can say that X is numerically distinct from Y; that Y does not fully ground X; that X fully explains or fully accounts for Y; and that X metaphysically necessitates Y. If this is so, then it is possible for Y to obtain necessarily and yet be dependent on X, at least in the sense of being explained by another, by X. Whether Y obtains or not will depend on whether X obtains or not. But if X obtains, then Y thereby obtains. Of course, this doesn’t show that there are self-explanatory facts but only that it seems possible for some facts to obtain both in virtue of other facts and with metaphysical necessity. As it has been shown by Dasgupta (2016), the form of metaphysical determination involved in full grounding is already akin to the form of explanation involved in the PSR.

As we saw, according to the modal objection, the PSR collapses all modal distinctions and makes every truth a necessary truth. As we also saw, the modal objection begs the question against the necessitarian, though we must admit that the commonsensical intuitions against necessitarianism have more weight than the intuitions that may favor it. But the burden of proof shifts, this time in favor of the necessitarian, if there is a direct argument for the PSR, like the one offered by Della Rocca. Now the commonsensical fellow needs to draw a reasoned, principled line to undermine the argument for the PSR.

Having the PSR back in its place, we can bite the bullet and accept the necessitarian consequences of the PSR with more confidence. What is more important: we can still run the CA. We just need to make some minor adjustments. Instead of using the notion of contingent and equate it with the notions of dependent or explained by another, we better stick with these latter terms, which don’t prejudge the modal status of the a posteriori truth that triggers the CA. All what appearances tell us is that beings such as flowers, dogs and human beings are not self-explanatory or independent beings, and all what the PSR forbids us at this point is to take the facts concerning their existence as brute facts, as facts explained by nothing whatsoever. Thus, the revised CA should look something like this:

• (1*) Some dependent beings-such as flowers, dogs and human beings-exist.

• (2) For everything that is the case, there is a sufficient reason for its being the case.

• (3*) Not every being can be a dependent being.

  Therefore,

• (C1*)There must be an independent or self-explanatory being.

  …

  …

  Therefore,

• (C2*)This independent or self-explanatory being has the following attributes: it is eternal, omnipresent, omniscient, omnipotent and infinitely good.

Within this revised version of the CA, the existence of flowers, dogs and human beings, which is the a posteriori datum that triggers the CA, needs only to be understood as involving beings whose existence is dependent or explained by another, without prejudging their modal status: premise (1*). Thus, what I labeled in sections I and II as “the World” is, under this new understanding, something different: rather than being a vast conjunctive fact involving all contingent facts, it is like a vast conjunctive fact involving all dependent or grounded facts. Premise (2) remains intact: it is the PSR itself. But now it seems that it forces us to admit also premise (3*). Why so? Because the existence of dependent beings alone is not a sufficient explanation of the World. Underlying this premise is the thought that for there being an explanation of the existence of a collection of dependent beings it is necessary that (i) “there is an explanation of the existence of each of the members of the collection of dependent beings”, and (ii) “there is an explanation of why there are any dependent beings” (Rowe, 2007, p. 28; emphasis in the original). If every being were a dependent being, only (i) would be satisfied. If, for the sake of argument, we assume that there are only dependent beings, then explaining the existence of each one of those beings is not sufficient for explaining why there are any dependent beings at all. In order to explain this second fact, we must transcend the whole collection of dependent beings. Thus, the existence of any dependent beings must be explicable by the existence of something whose existence is not explained by another being, some other being which is not a dependent being. This ultimate “other” must be an independent being, a self-explanatory being that explains both its own existence and the existence of all dependent beings. In Spinozistic terms, dependent beings such as flowers, dogs and human beings are like the many modes of the one substance. The one substance, the one independent being, fully grounds its many modes, the many dependent beings that depend upon it. The one substance is self-explanatory; its modes are not. The modes can only be sufficiently explained by the substance upon which they depend. For some, this might be a shocking picture. But it seems the picture that results from an untamed commitment to the PSR. It seems to be the result of taking the rationalist path without constrains. It gives us a less common picture of God and the World. But still: it preserves both God and the World as distinct beings and a rational link between them that allows us to infer the existence of God from the existence of the World, just as the CA wants.

IV

The main problem of accepting the PSR as a premise of the CA is not that it entails necessitarianism. If it only were this, perhaps we could accept a version of the CA as the one made explicit in the last section, one that has as a result a Spinozistic picture of God and the World, where the latter it explained by the former in terms of full grounding or something similar. However, as I will argue in this section, a commitment to the PSR not only leads us to that Spinozistic picture: it leads us way beyond it to a stage in which the distinction between God and the World simply collapses, that is, to a form of Radical Monism that goes beyond Spinoza’s monism. Let’s see why.

The PSR is not only famous for being a fundamental premise of the CA. The PSR, or at least a particular application of it, is a fundamental piece of another famous argument, or family of arguments, that Bradley made against the very idea, the very possibility, of relations and pluralism (Bradley, 1914, ch. IX; 1930, chs. 2 and 3 and Appendix B; 1935).

Bradley’s main argument can be reconstructed thus:

• (11) If there is really more than one being, there is really at least one relation; conversely, if there is really at least one relation, there is really more than one being.

• (12) If relations are really inexplicable, then there are really no relations.

• (13) Relations are really inexplicable (“self-contradictory”, “unintelligible”, etc.).

  Therefore,

• (C5) Really, there is only one being (the Absolute, the Unconditioned, or better: just undifferentiated, seamless Being).

Premise (11) makes the fairly reasonable assumption that real pluralism entails at least one real relation, such as the relation of difference, instantiation, grounding, being two feet apart from, being the father of, being caused by, etc., and that a real relation entails real pluralism. As it can be appreciated, premise (12) is just a particular application of the PSR: to accept that relations exist, these must be explicable, there must be a reason for their existence or obtaining; that is, there are no brute relations or relational situations.³ What about premise (13)? Why, according to Bradley, relations are really inexplicable (“self-contradictory”, “unintelligible”, etc.)? Because, according to Bradley, there is no plausible account of how relations ultimately relate their terms. For Bradley, the very idea of relatedness, the very idea of a relational situation, is ultimately inexplicable, self-contradictory, unintelligible.

Bradley gives various arguments for supporting premise (13). I will only focus on two of them. The first one (Bradley, 1930, ch. 2; cf. Baxter, 1996) attacks the relation between a thing and its properties or nature, the very idea of real definition or explanatory identity. How can one entity be (identical with) many entities, that is, not one, without contradiction? It is an important difficulty of the general dilemma that we face when we try to give a real definition or explanatory identity of something, an account of the thing that both preserves truth and goes beyond triviality. The problem affects any sort of complex unity. Take a lump of sugar (Lump) and assume it has (only) three qualities (Sweetness, Whiteness, Hardness) which exhaust its nature. When we attempt to give a real definition of Lump in terms of its qualities, a trilemma arises. First horn: Lump cannot be identical with its qualities taken individually. That is, Lump cannot be identical with Sweetness, nor with Whiteness, nor with Hardness. Because if Lump were identical, say, with Sweetness, then it couldn’t be identical neither with Whiteness nor with Hardness, which are distinct from Sweetness. The truth is that Lump cannot be simply Sweetness; it must be, somehow, Whiteness and Hardness, too. Second horn: maybe Lump is identical with its qualities taken collectively. But this cannot be the case. The secret of the thing lies in its unity. Lump is one thing, not many things, yet Sweetness, Whiteness, Hardness are many things, not one. And a single thing, on pain of contradiction, is not (cannot be) identical with many things, that is, not one. So, here comes the third horn: surely, then, Lump is identical with its many qualities being or standing in a “one-making relation” (Baxter, 1996), say R1.⁴ But this cannot be the case, since when we try to give an account of how R1 does its job, the following dilemma arises.

Either:

(a) We give a question-begging (brute, dogmatic, arbitrary) response: R1 relates its relata in virtue of the fact that R1 relates them, or the relata are R1-related in virtue of the fact that they are R1-related. As it can be appreciated, this is like bringing to the scene some “virtus relativa” (MacBride, 2011, p. 170), or like having “a John Wayne moment”, as when we claim that “a man’s gotta do what a man’s gotta do” (Della Rocca, 2020, p. 34). We are giving an “explanation” that says nothing.

Or:

(b) We embark ourselves in an infinite or circular sort of explanation, which we can only block by giving a brute response at some stage of it: R1 relates its relata in virtue of another one-making relation, R1*. If in virtue of R1*, then R1* relates R1 and its relata in virtue of another one-making relation, R1** (or in virtue of R1 again, in which case we face a circular explanatory chain), or in virtue that it relates them (back to (a)); and so on, ad infinitum.

Notice that we stopped talking about Lump and we ended up talking about qualities-in-relation. So, here comes a natural second stage in Bradley’s attack (1930, ch. 3), which undermines the very idea of qualities-in-relation, a move that Bradley is clearly willing to apply to the very idea of any relational situation, to the very idea of relata-in-relation. It happens, according to Bradley, that relations seem impossible without relata and relata seem impossible without relations (premise (11)). When we try to explain such arrangement, we face a dilemma that can be stated either from the side of the relata or from the side of the relations in more or less the same terms (support for premise (13)). Let’s see it from the side of the relations. On one hand, a relation taken without its relata is a relation that does not relate anything, a relation that makes no fact of relatedness, a relation that gives place to no relational situation at all, unless in brutal terms. Such a relation is inexplicable, “nothing intelligible”, “a phrase without meaning”, “a false abstraction”, something “which loudly contradicts itself” (1930, p. 27). In other words, relations are not self-explanatory beings. They must, at least partially, be explained by their relata, just like the relata must, at least partially, be explained by their relations. As Bradley puts it, “there must be a reason why this and that appear together” (1930, p. 517), we must look for “the ground, the how and why” (1930, p. 521) of any relation that relates. However, on the other hand, a relation taken with its relata, a relation that is allegedly really something for its relata, a relation that is somehow grounded (at least partially) in its relata, is unintelligible too, because we cannot explain how it manages to relate its relata and yet still remain something distinct from them.⁵ When we attempt to explain this, we are bewildered:

But if it is to be something to them, then clearly we now shall require a new connecting relation. For the relation hardly can be the mere adjective of one or both of its terms… And, being something itself, if it does not itself bear a relation to the terms, in what intelligible way will it succeed in being anything to them? But here again we are hurried off into the eddy of a hopeless process, since we are forced to go finding new relations without end. (1930, pp. 27-28)

Why Bradley rejects the alternative of a relation being “a mere adjective of… both of its terms”? Isn’t this, after all, the common way to understand relations? It might be so, but, as Bradley argues, it is a response that begs the question, because it presupposes what is under discussion: that relations relate their relata. It says, brutely, dogmatically, arbitrarily, that relations relate their relata. In contemporary terms, such an answer presupposes that the relata instantiate the relation. Any fact whatsoever is a relational situation: if something is the case, then some constituents are, allegedly, related in a particular way, something instantiates something. So, Bradley is not saying that there really are facts and that these real facts are inexplicable. In perfect alignment with the rationalist demand that underlies the PSR, he is trying to say that facts, qua relational situations, are really, ultimately, impossible beings, since they are really, ultimately, inexplicable beings. Bradley is rejecting, in virtue of its inexplicability, the very idea, the very possibility, of any relational situation. Try to conceive a simple relational situation, say Rxy, and then try to make sense of it in terms of the PSR: Why Rxy? In virtue of what, ultimately, Rxy obtains? Not in virtue of any of its constituents, whether we take them individually or collectively, because none of its constituents, however we take them, is sufficient for Rxy to obtain. That is, Rxy is not explained by R, nor by x, nor by y, nor by R and x, nor by R and y, nor by x and y, nor by R and x and y. And it is not explained by being and adjective of any of its terms or both, that is, neither by Rx, nor by Ry, nor by Rx and Ry. Lastly, Rxy is not explained by Rxy itself. To use again Della Rocca’s eloquent image, taking Rxy as an explanation of Rxy itself would be to have “a John Wayne moment”, to give a question-begging response, an explanation that says nothing at all. We are trying to explain what is not self-explanatory, we are trying to explain how is it that x and y are R-related. Therefore, it must be something else. But what? The obvious candidate is a relation, a “one-making relation”, say R1, that is, a relation capable of putting all these ingredients together into a single relational situation, a single fact. But now we should ask: Why R1(Rxy)? How is it that R1 does its job? In virtue of what, ultimately, R1(Rxy) obtains? And we can immediately see that the introduction of R1 to explain Rxy is futile: either we face an infinite or circular chain of insufficient explanations; or we must declare that R1 or some other relation of the explanatory chain of insufficient explanations relates because it relates, that is, we must accept a question-begging (brute, dogmatic, arbitrary) response.

At this point, Bradley is confident that he has proven the inexplicability of relations, pluralism and relational situations.

The reader who has followed and has grasped the principle of this chapter, will have little need to spend his time upon those which succeed it. He will have seen that our experience, where relational, is not true; and he will have condemned, almost without a hearing, the great mass of phenomena. (1930, p. 29)

And he is not alone: various contemporary philosophers have vindicated or at least appreciated the compelling character of Bradley’s way (e.g., Candlish, 2007; Della Rocca, 2020; Hylton, 1990; Vallicella, 2002).

So, Bradley’s argument against relations, just like the CA, starts with what seems to be an a posteriori commonsensical fact: that there are relata standing in relations, that there are relational situations. Then, just like the CA, adds as another main premise the PSR, at least to the case of relations. And being unable to find a satisfactory explanation of relations, it leads us to a form of monism that goes way beyond Spinoza’s monism, since for Bradley all relations, regardless their ontological category, are unreal; even instantiation or inherence is, for him, “self-contradictory” (1930, p. 649). This shows that he is willing to go far beyond Spinoza, who accepted the distinctions of substance, attributes and modes, and the relations of inherence, distinctness, and grounding or dependency as part of the ultimate metaphysical make-up of reality. Bradley’s path is a “Parmenidean Ascent” (Della Rocca, 2020, ch. 3), an attack on all real distinctions, all real relations, within Being. Bradley’s Absolute, the supra-relational unity, is more like a Parmenidean whole, a seamless, undifferentiated, non-relational Being; or like Aquinas’ God: “since God is absolute form, or rather absolute being, He can be in no way composite” (“Summa Theologica”, 1.3.7). We can call it “Radical Monism”.

V

As it can be appreciated, Bradley’s argument against relations undermines the very presuppositions of the CA. Firstly, the CA presupposes that God is distinct from the World. Secondly, the CA presupposes that the World has distinct parts or constituents. In fact, only some tiny parts or aspects of the World (i.e., some flowers, dogs, human beings, etc.) work as constituents of the a posteriori datum that triggers the CA: we never perceive the World as a whole. Thirdly, the PSR is meant to be the premise that establishes an explanatory relation between the existence of the World and the existence of God. Fourthly, the second part of the CA is supposed to establish that God has many properties, all of which contribute to explain the fact that such God brings into existence the World. But none of these presuppositions makes any sense if Bradley’s argument against relations is sound. Because if Bradley’s argument is indeed sound, then there is no distinction between God and the World, not even in Spinozistic terms-such as the distinction that allegedly holds between a substance and its modes. And there are no real distinctions within the World itself: no really distinct flowers, dogs, human beings, etc. And there is no explanatory relation between God and the World, not even in terms of instantiation, dependence or grounding, because there is no explanatory gap to be filled between God and the World. And there are no distinctions whatsoever within God itself-such as the distinctions between God’s many alleged properties-, because, ultimately, there are no relata and distinctions whatsoever. There is just seamless, undifferentiated, non-relational Being.

Della Rocca (2020, chs. 1, 9) argues that we should take Bradley’s argument against relations as something like Wittgenstein’s ladder (“Tractatus LogicoPhilosophicus”, 6.54). The ascent to seamless, undifferentiated, non-relational Being would be through relational means, because all discursive thought is relational through and through. And we should throw away this relational ladder once we have arrived to Being, once we have seen the world aright. Thus, the contemplation of Being would be more like a mystical experience, something impossible to articulate in conceptual, i.e., relational, terms.

However, I think this solution doesn’t work. If the ladder is somehow illusory under the light of the point of destiny, then it could hardly have worked as a means for getting us there. As Blanshard puts it: “If you ask us to accept your conclusion because it has been reached on a series of solid rungs, you cannot also expect us to accept it once you dismiss them as worm-eaten” (1984, p. 224). If we attempt to accept both means and end, the ladder and the place that is beyond it, we face paradox. We must combine discursive, logical, relational thought with a non-discursive, mystical, non-relational result. Yet we cannot combine them: they are incompatible. On one hand, the very idea of explanation seems to presuppose distinct relata standing in some relation(s). To explain something is to relate it (Briceño, 2021; Della Rocca, 2012). When we are asked to give an explanation of X itself, we engage in the process of unfolding the very nature of X, what X really is; and this unfolding is nothing but making explicit the relations that X has with its inside (its parts, properties, structure) or with its outside (with other things, their parts, properties, structure). This happens when we claim that X instantiates F; or that X is grounded upon G and H; or that X is constituted or composed by G and H; or that G and H compose X, etc. It even happens when we claim that X is ontologically independent of other beings. This latter definition is relational too: it presupposes at least distinctness of X from other beings. In fact, even calling X one seems to be a relational business (Della Rocca, 2020, p. 78), since how can we make sense of numerical identity and individuation without presupposing numbers and, therefore, relations holding between them? On the other hand, as Bradley’s argument reveals, the very demand of radical explanation, i.e., the PSR itself, forces us to wipe out from reality all relations, and shows us that the only thing which can give us rest in the search for explanations is something whose nature and existence does not presuppose relations of any sort, i.e., just seamless, undifferentiated, nonrelational Being. Because only Being in this sense has no other requisites than itself, is absolutely unconditioned by the existence of otherness, is a sufficient reason of itself, is self-explanatory. Thus, the PSR not only supports Bradley’s argument for Radical Monism, but also Radical Monism is the only result that seems to satisfy the strict explanatory demands of the PSR.

Thus, it seems that if we are committed to the PSR and to the a posteriori truth that triggers the CA, then we must both accept and reject Bradley’s argument for Radical Monism. This position is self-undermining. On one hand, if we accept the argument for Radical Monism, we must reject Radical Monism. Because such argument, as any argument, with its distinct concepts and propositions, with its premises and conclusion, presupposes relata and relations. On the other hand, if we accept Radical Monism, we must reject the argument that allowed us to get there. Because if we accept that there is just seamless, undifferentiated, non-relational Being, then we must accept as nonsensical the very idea of explanation that we used to get there, because the very idea of explanation is relational. If relations are unintelligible, if reality is only seamless, undifferentiated, non-relational Being, then how can any philosophical argument or position be even articulated or stated? How can the very argument for Radical Monism be deployed? If the PSR-the key premise of both the CA and Bradley’s argument-has Radical Monism as a logical consequence, then the PSR undermines not only the very arguments in which it figures as a key premise but it also undermines itself.

Now, if we are not willing to accept that Radical Monism is indeed a consequence of the application of the PSR to the case of relations or relational situations, then we must reject the PSR itself and accept brute, arbitrary, inexplicable relations or relational situations at some point. But if we reject the PSR itself and accept brute, arbitrary, inexplicable relations or relational situations at some point, then we must reject the CA too, since the CA has the PSR as one of its main premises.

As we can see, if the CA has some viability as an argument for the existence of God, then it must be in some distinct form than the one based upon the PSR.⁶

• 1
  For an alternative understanding, one that takes the force of the explanation demanded by the PSR to be weaker than logical entailment, see Pruss (2006, p. 104). I remain unconvinced by his arguments, but this is not the place to argue against this alternative. For arguments in favor of a strong, necessitarian, understanding of the idea of explanation demanded by the PSR, I direct the reader to Della Rocca (2003; 2014).
• 2
  Cf. Bliss and Trogdon (2016, §5). As Bliss and Trogdon explain, there is an intuitive contrast between full grounding and partial grounding. Take the fact <p>, the conjunctive fact <p and q>, and the disjunctive fact <p or q>. We can say that the fact <p> is partial ground of the fact <p and q>, whereas it is full ground of the fact <p or q>. As it is obvious, only full grounding can carry metaphysical necessity.
• 3
  Russell correctly identifies that it is Bradley’s commitment to the PSR what gives ultimate ground for his aversion against relations: “This opinion [i.e., that relations cannot be brute, “purely fortuitous”] seems to rest upon some law of sufficient reason, some desire to show that every truth is “necessary”. I am inclined to think that a large part of my disagreement with Mr. Bradley turns on a disagreement as to the notion of “necessity”. I do not myself admit necessity and possibility as fundamental notions: it appears to me that fundamentally truths are merely true in fact, and that the search for a “sufficient reason” is mistaken.” (Russell, 1910, p. 374)
• 4
  After all, what else it could be? Certainly not a bare substratum! Lump is not a naked particular. Moreover, if we add a bare substratum to the equation, we only move the problem forward: now, to account for Lump, we have to explain a unity that involves not only the qualities but also the bare substratum. Bradley’s rejection of bare substrata has to do with his commitment to the PSR too. Brute numerical identity and distinctness go against the PSR; they are facts that must be explained through qualitative identity/distinctness. A commitment to the PSR carries a commitment to the Principle of the Identity of the Indiscernibles. See Della Rocca (2003).
• 5
  In other words, Bradley’s attack on relations affects relations whether they are conceived as external or internal. External relations, that is, relations that do not supervene on the nature of the relata, relations that are independent and contingent addition of being (Armstrong, 1997, p. 87), are obviously suspicious under Bradley’s attack: they are “free-floating” entities, unintelligible brute existents. Yet internal relations are ultimately unsatisfactory too. For our purposes, we can distinguish two relevant ways of understanding internal relations. A first way is the contemporary sense in which a relation is said to supervene on the nature of the relata, “an ontological free lunch”, as when the relation of resemblance between that rose and this rose is said to supervene on the monadic facts that that rose is red and that this rose is red (Armstrong, 1997, p. 87). But this sense already presupposes pluralism in various senses (for start, two numerically distinct roses) and, therefore, some relation that is not internal in that sense (for instance, a relation of spatiotemporal distance). A second form is the more classical sense in which a relation was said to be internal if it was essential to, or constitutive of, the identity of the relata (Moore, 1920; Rorty, 1967). In this latter sense, Bradley thinks that internal relations are more real than external relations, but still somehow unstable: qua relations, they affirm the distinctness of the relata; qua internal, they deny it (Bradley, 1914, pp. 239-240; 1935, pp. 643-645; Candlish, 2007, pp. 159-161; Hylton, 1990, pp. 54-55). What is worst, internal relations in this last sense just move the problem (i.e., in virtue of what relations relate?) inside the relation or inside the relata, which now must combine a double character or role: to be something on its (their) own and to relate (be related) (Bradley, 1930, pp. 26).
• **
  Artigo foi apresentado na XVIII Conferência Internacional de Biblioteconomia 2014
• 6
  Thanks to audiences in Santiago and Paris and to an anonymous referee for their helpful comments and suggestions.
  The opinions expressed in this article are those of the author and do not necessarily reflect the views of the John Templeton Foundation.
• This article was made possible through the support of the following grants:

  • The John Templeton Foundation-Pontificia Universidad Católica de Chile: Proyecto de Investigación sobre la Existencia y Naturaleza de Dios #61559-19.

  • The John Templeton Foundation-University of Houston: LATAM Bridges in the Epistemology of Religion.

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Publication Dates

• Publication in this collection
  08 Mar 2024
• Date of issue
  Dec 2023

History

• Received
  06 Dec 2022
• Accepted
  12 June 2023