Recently, Patrick Rooney has argued that neither external relations nor their relata can have existential inertia. Many thanks to Rooney for his engagement, and I will reciprocate that engagement as I respond to his case in this post.
There are a few things to note at the outset—things that Rooney is rightly upfront about. First, as Rooney points out (p. 3), his argument only targets one account of existential inertia. Even if the argument is successful, then, other accounts of existential inertia (e.g., Beaudoin’s, Audi’s, etc.) may still be true. Second—and as Rooney again points out (p. 2)—the scope of the argument only extends to situations in which there are external relations. Thus, as far as Rooney’s argument goes, objects that aren’t externally related may still enjoy existential inertia. While Rooeny’s argument (if successful) is significant, we should bear its limitations firmly in mind.
Keep in mind, too, that the Existential Inertia Thesis (EIT), as articulated in my book, is true so long as some subset of temporal concrete objects inertially persist. Thus, even if all externally related things fail to inertially persist, EIT may still be true if non-externally-related things inertially persist. So Rooney’s case doesn’t establish the falsity of EIT as articulated in my book. Of course, this is no objection to Rooney’s case; but it’s a dialectical point worth covering nonetheless.
Can external relations enjoy existential inertia?
According to Rooney, a relation is internal iff its existence is entailed by the existence of the internal properties of its relata, and a relation is external iff it is not internal. Now, a problem immediately presents itself for Rooney’s case here: for the platonist about properties, properties are necessarily existent abstracta. And, of course, for any x, if x necessarily exists, then x’s existence is entailed by everything. For the platonist about properties, then, every relation is an internal relation. Hence, for the platonist, there are no external relations.
But there are two problems with this consequence of Rooney’s case. First, as Rooney points out (p. 4), he doesn’t defend the existence of external relations. Instead, he argues simply that if external relations exist, then neither they nor their relata can enjoy existential inertia. But this conditional implies nothing about existential inertia if there are no external relations, since the antecedent of the conditional won’t then be satisfied. Rooney’s argument, then, can do nothing for the platonist existential inertialist. Thus, so long as the inertialist adopts platonism, Rooney’s case does nothing to impugn the truth of EIT. Second, the aforementioned consequence of Rooney’s case seems absurd. Surely there are still external relations if platonism is true. Even if platonism is true, Socrates’ being 10 meters north of my house is clearly still an external relation. Hence, Rooney’s case rests on a mistaken understanding of external relations.
We’ve seen how Rooney’s case doesn’t touch the platonist inertialist view. Importantly, though, it also doesn’t touch the nominalist inertialist view. The nominalist denies the existence of properties. A fortiori, the nominalist denies the existence of external relations. Given that Rooney only argues that if external relations exist, then neither they nor their relata can enjoy existential inertia, Rooney’s case is as impotent for the nominalist inertialist as it is for the platonist inertialist. If either platonism or nominalism is true, Rooney’s argument poses no threat to EIT. This is a serious limitation on Rooney’s case, as his case is entirely impotent for the two most prominent views of properties (endorsed by about 80% of professional philosophers).
Rooney also assumes two substantive claims about external relations: first, that external relations exist over and above their relata, and second, that relata aren’t even constituents of (“component parts of”, in Rooney’s terminology) the external relation. This even further hampers the dialectical appeal of Rooney’s case against existential inertia; not only must we accept the existence of non-platonistically-conceived external relations, but we must also accept that they’re irreducible to their relata and that the relata aren’t even constituents of the external relation. Rooney’s case also requires denying the existence of states of affairs and conceiving of external relations as relata-specific (as in Betti 2015). Keeping tally of the substantive limitations of Rooney’s case, we therefore have:
- The case only targets one account (among many) of existential inertia.
- The case could only show that externally related things (as well as external relations themselves) can’t enjoy existential inertia; it’s entirely consistent with non-externally-related things enjoying existential inertia, and hence it’s compatible with EIT as I articulate it.
- The case assumes that external relations (as Rooney characterizes them) exist.
- Consequent upon (3), the case assumes that platonism about properties is false.
- Consequent about (3), the case assumes nominalism about properties is false.
- The case assumes that external relations are something over and above their relata.
- The case assumes that the relata of an external relation aren’t constituents of that external relation.
- The case assumes that states of affairs don’t exist.
- The case assumes that external relations are relata-specific.
Let’s briefly camp out on (9) before proceeding. A relation is relata-specific “if it is only capable of relating the relata which it does in fact relate” (p. 6). That is, a relation is relata-specific if that relation essentially relates only the relata which it does, in fact, relate. So, for instance, if R relates a and b, then R essentially relates only a and b. Now, there are two ways to understand relata-specificity, and either way renders implausible Rooney’s claim that external relations are relata-specific.
Here’s the first way to understand relata-specificity: an individual n-ary relation R is relata-specific iff for some ordered n-tuple of things actually related by R, R essentially only relates that ordered n-tuple of things. So, for instance, if the individual binary relation sitting on is relata-specific, then for some ordered pair of things actually related by sitting on—say, Socrates and his chair—sitting on essentially only relates that ordered pair (i.e., sitting on essentially only relates Socrates and his chair). Now, if this is how relata-specificity is understood, it seems absurd to say that external relations are relata-specific. Consider again sitting on. This relation is external; one can fix all the intrinsic properties of Socrates and a particular chair, and it may or may not be the case that Socrates is sitting on that chair. But sitting on is surely not relata-specific in this first sense, since sitting on surely relates more than one ordered pair of things. For instance, sitting on relates not just Socrates and his chair, but also me and the chair I’m currently sitting on. So in this first sense of ‘relata-specific’, not all external relations are relata-specific, pace Rooney.
Here’s the second way to understand relata-specificity: an individual n-ary relation R is relata-specific iff for all ordered n-tuples of things actually related by R, R essentially only relates all of those ordered n-tuples of things. So, for instance, if the individual binary relation sitting on is relata-specific, then for every ordered pair of things actually related by sitting on—me and my chair, you and yours, etc.—sitting on essentially only relates those ordered pairs—me and my chair, you and yours, and every other ordered pair actually related by sitting on. But if this is how relata-specificity is understood, it again seems absurd to say that external relations are relata-specific. If sitting on is relata-specific in this second sense, then sitting on cannot relate any ordered pair of things that are not in fact related by sitting on. But that’s absurd. I easily could have sat on that one chair in my house that I never sat on. Hence, siting on easily could have related the ordered pair (me, that chair) that is not in fact related by sitting on. Hence, sitting on is not relata-specific in this second sense. But sitting on is nevertheless external. So in this second sense of ‘relata-specific’, not all external relations are relata-specific, pace Rooney.
Moving on to Rooney’s argument (which I won’t reiterate here) that external relations can’t enjoy existential inertia, I agree (with one complication—more on that anon) that if we grant all of those assumptions (each of which is very contentious, and some of which are profoundly implausible), then external relations can’t enjoy existential inertia. Alas, I don’t grant all those assumptions, and I don’t think you should either.
The complication is that Rooney’s case requires the existence of external relations to depend on the existence of their relata. But this is, in my view, unjustified. If we view external relations as necessarily existent abstracta, their existence won’t depend on their contingent relata, even though their instantiation probably will. For instance, if the sitting on relation is a necessarily existent abstract property, it clearly won’t depend for its existence on its contingent relata (Socrates and the chair)—the relation will exist whether or not its relata do.
To avoid this problem, I think Rooney would have to treat external relations as something like tropes or maybe Aristotelian accidents. But Rooney gives no justification for treating external relations in this way.
In light of all the preceding, I don’t find Rooney’s case that external relations cannot have existential inertia plausible.
 p entails q iff □(p → q) iff ~◇(p & ~q). But □q → ~◇~q, and ~◇~q → ~◇(p & ~q). Hence □q → ~◇(p & ~q). Hence, □q → □(p → q). Hence, □q → (p entails q).
 Rooney seems to think that <R’s relata aren’t constituents of R> follows from <R is an external relation>. As Rooney writes, “the sitting-on relation does not include Socrates and the chair as parts of itself (since it is an external relation)” (p. 7). But this doesn’t strike me as plausible. Just because R is an external relation—that is, just because R’s existence isn’t entailed by the existence of the intrinsic properties of R’s relata—it doesn’t thereby follow that R’s relata aren’t constituents of R. Just because the intrinsic properties of the xs don’t entail the existence of y, it doesn’t follow that the xs aren’t parts of y. The existence of some parts of a whole needn’t entail the existence of that whole. (Consider: many of my current parts existed before I did. This shows that the existence of some parts of a whole needn’t entail the existence of that whole; <the xs can exist without being parts of y> is compatible with <the xs are parts of y>.) So I think Rooney is simply mistaken in his inference here.
 This is how Rooney appears to understand relata-specificity. He writes: “Since the sitting-on relation is relata-specific toward Socrates and the chair, it is in the nature of this sitting-on relation to relate only Socrates and the chair, and so it cannot exist without Socrates and the chair” (p. 7).
 Rooney’s ‘justification’ for the claim mostly consists in repeated assertions of the very thing to be demonstrated (cf. the top half of p. 7). The one justification that doesn’t so consist seems to be the following: “A relata-specific relation in itself points toward its relata, and so the relation must be explained (at least in part) in reference to these relata.” (p. 7). I’m not exactly sure what ‘points toward’ means, but assuming (quite plausibly) that representation is a species of ‘pointing towards’, the mere fact that x ‘points towards’ y doesn’t entail that x depends on y. For instance, propositions represent contingent things, but philosophical orthodoxy tells us (rightly, in my view) that propositions are necessary, not contingent. Propositions therefore exist whether or not those contingent things exist, and so propositions don’t depend for their existence on those contingent things. Propositions, then, ‘point toward’ things without depending for their existence on those things. So x can ‘point towards’ y without depending on y. Rooney is therefore mistaken to infer dependence from ‘pointing towards’. The other justifications Rooney presents seem to me to be mere re-assertions (in different parlance) of the very thing needing justification. (Perhaps Rooney takes the claim to be obvious. If so, I think he has misdiagnosed the relevant content of his sense of obviousness. What’s obvious is that the instantiation of an external relation depends on the existence of the relata. An external relation is instantiated (partly) because its relata exist and are thus-and-so. But that doesn’t mean the existence of that external relation depends on the existence of the relata. A property can exist independently of its bearers even though its instantiation in those bearers depends on the existence of those bearers.)
Can the relata of external relations enjoy existential inertia?
Rooney begins this part of his case by asking “how is it possible for the sitting-on relation R to exist between Socrates and the chair at time t?” (p. 8). He asks shortly thereafter “whether the possibility of external relations at both t and t* is explained entirely by Socrates and the chair at both t and t*. Socrates and the chair exist independently of one another at both t and t*; and so it seems that Socrates and the chair at t and t* are not the compete explanation for how any external relations can exist between them at t and t*” (p. 9). But I don’t think this is right. We can easily cite facts about Socrates alone and the chair alone to explain how any external relations can obtain between them. For instance, Socrates is by nature a spatiotemporal thing—what it is to be Socrates is to be a particular rational animal, and what it is to be an animal is to be a biological organism with such-and-such features that entail spatiotemporality. We therefore have an essence-based explanation of Socrates’ spatiotemporality; what it is to be Socrates is to be a particular spatiotemporal thing of a given kind. Similar points apply to the chair—what it is to be a chair is to be a spatiotemporal object with such-and-such externally imposed function. We therefore have an essence-based explanation of the chair’s spatiotemporality. And with the spatiotemporality of each of Socrates and the chair in hand, we have an explanation of how they’re able to stand in any external relation. For their spatiotemporality readily explains the possibility of them standing in external spatiotemporal relations to one another; it’s precisely because they’re both spatiotemporal objects that they can be such-and-such a spatial distance from one another, for instance. And being such-and-such spatial distance from is clearly an external relation. Hence, we have an explanation of how Socrates and the chair are able to stand in any external relations by starting simply with facts about Socrates and the chair. They alone suffice to explain the possibility of external relations between them; we need make no reference to other things. Rooney is therefore mistaken to infer from their ontological independence to their inability to completely explain how they’re able to stand in any external relations.
Rooney then presents his “main argument for why the mere existences of Socrates and the chair cannot be the only explanation for how there can be any external relations (e.g., R) between Socrates and the chair” (p. 10). Here’s the argument:
Let us suppose that the possibility of R existing is explained entirely by Socrates and the chair. If so, everything about R (including R’s being between Socrates and the chair) is made possible only by the mere existences of Socrates and/or the chair. But the mere existences of Socrates and the chair have nothing to do with one another: they contain nothing that is between them. Thus, the mere existences of Socrates and the chair cannot explain how it is possible for something to be between Socrates and the chair. (p. 10)
But this is mistaken. Quite clearly, the mere existences of Socrates and the chair do have something to do with one another; in particular, with the existence of Socrates comes what it is to be Socrates, which includes, in part, being a spatiotemporal thing. Ditto for the chair. And spatiotemporal things, by dint of their spatiotemporality, have something to do with one another; just by dint of both enjoying spatiotemporality, both will enjoy temporal and spatial relations to one another. So Rooney’s key claim strikes me as wrongheaded.
Since R’s being between Socrates and the chair is not made possible by the mere existences of Socrates and the chair, it must be made possible by something else U which is itself between Socrates and the chair. (p. 10)
This, of course, rests on a substantive underlying assumption—namely, that there must be something in virtue of which R’s holding between Socrates and the chair is possible. But why can’t certain possibility claims simply be primitive, i.e., not grounded in anything else? Rooney is silent on this question. And yet satisfactorily answering it is required if Rooney wants to infer that there is something else which makes possible R’s holding between Socrates and the chair. What’s more, even if we grant that there must be a ground or explanation of the possibility of R’s holding between Socrates and the chair, why must the explanation be in terms of some existent reality U as opposed to other kinds of explanations (say, structural explanations, or explanations in terms of metaphysical necessity, etc.)? Once more, Rooney is silent.
Likewise, it seems intuitively plausible that there cannot be an ontologically dependent entity (e.g., R) between Socrates and the chair unless it exists upon a deeper foundation which is already between Socrates and the chair (i.e., U). (p. 10)
This ‘seems intuitively plausible’? To whom? To everyone? To Rooney? I can at least report on my seemings: that doesn’t strike me as plausible at all. I don’t have any intuition in favor of the need for some ‘deeper foundation’ (whatever that means) in order for an ontologically dependent entity to exist between Socrates and the chair. Indeed, as I explained earlier, I find it intuitive that no such foundation is needed, since Socrates and the chair alone suffice to explain the possibility of at least some external relations between them.
Rooney’s argument might also lead to an absurd proliferation of entities between other entities.
Consider that, on p. 10, Rooney says “But the mere existences of Socrates and the chair have nothing to do with one another: they contain nothing that is between them” (p. 10). This strongly suggests that, if there is nothing between x and y, then x and y have nothing to do with one another. By contraposition, if x and y do have something to do with one another, then there is something between x and y. Now, Rooney argues for some entity U which is itself between Socrates and the chair, and Rooney tells us on p. 9 that “when something X is between Socrates and the chair, this means (perhaps among other things) that (1) X and Socrates have something to do with one another, (2) X and the chair have something to do with one another, and (3) X is distinct from both Socrates and the chair.” Since U is itself between Socrates and the chair, it follows that U and Socrates have something to do with one another. But we concluded earlier that if x and y have something to do with one another, then there is something between x and y. Hence, there is something between U and Socrates. Call that thing U*. Since U* is itself between U and Socrates, it follows that U* and U have something to do with one another. But we concluded earlier that if x and y have something to do with one another, then there is something between x and y. Hence, there is something between U* and U. Call that thing U**. You see where I’m going… We here have an infinite series of items between items—U between Socrates and the chair, U* between U and Socrates, U** between U* and U, U*** between U** and U*, and so on ad infinitum. But that’s absurd. Since Rooney’s argument leads to an absurd infinite proliferation of entities between other entities, we should reject Rooney’s argument.
The problems don’t end there, though. Rooney writes:
U cannot be ontologically on par with Socrates and the chair [where x is ontologically on par with y iff neither x nor y ontologically depends on the other], otherwise, we would need to explain how three entities (i.e., Socrates, the chair, and U) can be related to one another, and so we have only made the problem worse. (p. 11)
I don’t see how this makes the problem worse, and Rooney offers no justification for this claim. Indeed, I see at least one way how it may very well solve the original problem. In particular, we can solve the problem of how Socrates and the chair can be externally related by appealing to U to explain that possibility. We’ve only re-located the original problem if the relation among U, Socrates, and the chair is an external relation. For only then do we have a relation the obtaining of which (allegedly) cannot be explained just by the relata. By contrast, if the relation among U, Socrates, and the chair is an internal relation, then we can simply cite the intrinsic characters of U, Socrates, and the chair to explain that relation’s holding among them. (After all, when a relation is internal, its obtaining is guaranteed by the existence of the relevant relata with the relevant intrinsic properties.) Hence, we’ve only made the problem worse—indeed, we’ve really only re-located the problem—if the relevant relation is external. But Rooney hasn’t at all shown why the relation must be external. For all Rooney has shown, it may be internal. Hence, for all Rooney has shown, U may very well be ontologically on par with Socrates and the chair. Hence, Rooney fails to establish something upon which Socrates and the chair depend. Since that’s needed to refute the thesis that Socrates and the chair inertially persist, Rooney fails to establish that Socrates and the chair don’t inertially persist.
Another potential problem for Rooney’s case is that U doesn’t appear able to explain precisely what Rooney posits it to explain. Rooney writes, “We have indicated that the explanatory power of U (whereby it is possible for there to be anything between Socrates and the chair) consists in (among other things) the fact that U is itself between Socrates and the chair in some way” (p. 12). Rooney appears to be saying that U is able to explain how it’s possible for there to be anything between Socrates and the chair by virtue of the fact that… wait for it… U is itself between Socrates and the chair. If this is what Rooney is saying, it is manifestly inadequate as an explanation; indeed, the ‘explanation’ is flatly circular. One cannot cite something’s being between x and y in order to explain how anything at all could be between x and y in the first place. By doing so, you simply take for granted the very thing you sought an accounting of. You offer, in other words, a circular explanation—which, of course, is no explanation at all. It’s like citing a penguin to explain how there could be any penguins at all, ever, in the first place. It’s no explanation at all.
But suppose we grant—as we shouldn’t—that Rooney’s case succeeds up until this point. Still, there’s the question: why think the relevant relata concurrently depend on U? Why not think the dependence is instead transtemporal? After all, something can inertially persist while transtemporally depending on something.
Rooney assures us that there are at least two problems with this suggestion. Here’s Rooney’s precise statement of the first problem:
The relation R cannot exist at t without Socrates and the chair existing at t. From this it follows that R is an ontologically dependent entity at t. Thus, everything about R at t (including R’s “being between Socrates and the chair at t”) must be made possible by explanations at t. But R’s “being between Socrates and the chair at t” cannot be made possible by the mere existences of Socrates and the chair at t, since the mere existences of Socrates and the chair at t do not contain anything between them at t. From this it seems that R’s “being between Socrates and the chair at t” must be made possible by something that is between Socrates and the chair at t; and the best candidate for this is something U upon which Socrates and the chair both ontological depend at t. (p. 12)
I’ve bolded the key claim. Surprisingly, Rooney gives no reason whatsoever for thinking the key claim actually follows from the preceding sentence. To be sure, the “Thus” implies that Rooney thinks (and asserts) that the key claim follows from the preceding sentence. But Rooney offers nothing more than assertion here. We already knew that R is dependent at t. Our question was precisely why we should think of this relation of dependence as concurrent rather than transtemporal. It’s no good, then, to simply assert that this relation of dependence must be made possible by explanations at t, i.e., by concurrent explanations as opposed to transtemporal explanations. That is to assert the very thing in need of demonstration. Rooney’s first ‘problem’ for the suggestion, then, is no problem at all.
What about Rooney’s second problem for the suggestion? Let’s take it bit by bit.
Second, the deist proposal implies that Socrates graduates from “an ontologically dependent entity” at t* to “an ontologically non-dependent entity” at t. (p. 13)
No. The proposal only entails that Socrates graduates from concurrently dependent at t* to transtemporally dependent at t. As articulated in my book, EIT only debars an inertially persistent temporal concrete object from concurrently depending (at any non-first moment m of its life) on concrete non-parts of that object. It is entirely compatible with that object transtemporally depending (at m) on concrete non-parts of those objects—i.e., depending at m on something before m. So Rooney is simply mistaken here.
But let’s suppose that Rooney were right. Suppose the suggestion at hand did require a graduation from dependence to independence. What does Rooney have to say against that?
But this is impossible. Being ontologically dependent is not a hat that you can wear on some days but not on other days. At the core of his being, Socrates is either an ontologically dependent entity or an ontologically non-dependent entity. Put more formally, the attribute of “being ontologically dependent” is either essential to Socrates at t* or it is not essential to Socrates at t*. If “being ontologically dependent” is essential to Socrates at t*, then he can never become ontologically non-dependent at t. But if “being ontologically dependent” is not essential to Socrates at t*, then he is not truly ontologically dependent at t* since he can exist at t* with or without his so-called “ontological dependence” on U. (p. 13)
Once more, this is mistaken. For being ontologically dependent at t* (or at its first moment) might be essential to Socrates even though being ontologically dependent (simpliciter) is not essential to Socrates. In that case, Socrates would be truly ontologically dependent on U at t* (and Socrates wouldn’t be able to exist at t* without dependence on U), and yet there is no pressure to admit that Socrates must thereby be ontologically dependent at times after t*, since being ontologically dependent isn’t essential to Socrates (and, further, nothing forces us to posit that being ontologically dependent at times after t* is essential to Socrates).
Thus, Rooney’s two problems for the aforementioned suggestion are no problems at all. In my assessment, then, just about every turn of Rooney’s argument in this section is mistaken.
 Even if one supposes that they’re denizens of disjoint spatiotemporal manifolds, this very fact implies a binary external relation between them—namely, occupying a disjoint spatiotemporal manifold from. (Note that fixing their intrinsic characters doesn’t entail their relatedness in this manner, since their intrinsic characters are obviously compatible with occupying the same spatiotemporal manifold. Hence this relation is an external relation.)
 Note that U, U*, U**, U***, U****, etc. are, indeed, all distinct, since an entity’s being between x and y entails that this entity is distinct from x and y. At least, that’s precisely how Rooney defined the notion in the case of Socrates and the chair, and it’s also how between is colloquially used—nothing can be between itself and itself, or between itself and another! (Also, on the top of p. 12, Rooney appears to reason that, since Socrates himself may be identical to his own relation of dependence on U, Socrates’ relation of dependence on U needn’t be between Socrates and U. This reasoning appears to rely on the following claim: if x is identical to some relation R that x bears to y, then R is not between x and y. By contraposition, if R is between x and y, then x is distinct from the relation x bears to y. And, of course, if R is between x and y, then R is between y and x, and so R is also distinct from y. Hence, an entity’s being between x and y entails that this entity is distinct from x and y.)
 You’ll have to forgive me if this is a misinterpretation; I certainly don’t intend to misinterpret. The quoted sentence isn’t altogether clear to me, and I’m doing my best to parse it.
Rooney’s case is riddled with problems. I see nothing therein that should worry the existential inertialist. Nevertheless, I’m deeply grateful to Rooney for his engagement. His article is fascinating, thought-provoking, and innovative. It’s always wonderful exploring the depths of reality with fellow inquirers. 🙂