REVIEW ARTICLE

Bo R. Meinertsen, Metaphysics of States of Affairs: Truthmaking, Universals, and a Farewell to Bradley's Regress, Springer 2018, 174 + xviii pp.

Summary

Professor Meinertsen's detailed treatment of states of affairs agrees with the spirit and much of the letter of David M. Armstrong's middle period as represented in his A World of States of Affairs (Cambridge UP, 1997). States of affairs in this acceptation are not abstract objects, as they are for some philosophers, but concrete denizens of the natural world of space-time. They are “unified complexes that are instantiations of properties or relations by particulars.” (1) Unlike Armstrong, however, Meinertsen is not concerned to argue for their existence (3, 13), or to show their utility in different philosophical areas. His focus is on states of affairs themselves, their main theoretical role, the nature of their constituents, and the problem of their unity.

Their main role is to serve as truthmakers. Suppose it is contingently true that Tom is red, where 'Tom' denotes a tomato of our acquaintance. (The use and justification of such “toy examples” is nicely explained on p. 5) Intuitively, such a truth is not just true; it needs an ontological ground of its truth. What might that be? Rejecting both tropes (Chapter 3) and D. W. Mertz's relation instances (Chapter 4) as truthmakers, Meinertsen argues that states of affairs do the job. In this example, the truthmaker is Tom's being red. On Meinertsen's use of terms, all and only states of affairs are truthmakers (84-85).

A state of affairs is a complex, and complexes are composed of distinct constituents. The composition of a state of affairs, however, is non-mereological. Mereological complexes are governed by the unrestricted composition axiom of classical mereology. (8) What the axiom states is that any plurality of items composes something: the existence of some items entails the existence of the sum of those items. The constituents of a state of affairs, however, can exist without the state of affairs existing. For example, Tom's being red entails the existence of the sum, Tom + instantiation + the universal redness. But the existence of the sum does not entail the existence of the state of affairs. A state of affairs, then, is a non-mereological complex. We will return to this important point when we come to the problem of the unity of a state of affairs.

First-order states of affairs have as their constituents particulars, properties or relations, and instantiation. The particulars are bare or thin (Chapter 5). What makes them bare is not that they lack properties, but the way they have them. The bareness of a bare particular consists in its instantiating, as opposed to including, its properties. (73) The properties that enter into states of affairs are sparse as opposed to abundant: not every predicate picks out such a property. In addition, the properties in states of affairs are universals, and thus multiply instantiable. If an immanent (transcendent) universal is one that cannot (can) exist uninstantiated, then Meinertsen's universals are immanent. Immanence so defined admits of abstractness. Meinertsen's universals, however, are concrete. (Chapter 8) The concrete is that which is “spatially and/or temporally located.” (119) Given naturalism, which Armstrong endorses and to which Meinertsen “inclines” (119), every existent is concrete and therefore located, including universals. The locatedness of universals, which is unlike that of particulars, has three implications. The first is that a universal is “wholly located in many places at the same time.” (120) The second implication is that “the region occupied by any such universal is not a mereological part of the region occupied by the whole thick particular.” (121) The third implication is that “more than one universal can have the same spatiotemporal location.” (121)

I note in passing that the banishing of so-called abstract objects demanded by uncompromising Armstrongian naturalism exacts a high price. The price is paid in the coin of the three implications just listed. The abstract-concrete distinction is replaced by a distinction between two categories of concreta, particulars and universals. This replacement requires that one accept the view that universals are ones-in-many (as opposed to ones-over-many) not merely in the sense that a universal cannot exist uninstantiated, but also in the sense that, if it exists, it is wholly present in each of its many spatiotemporal instances without prejudice to its being one and the same universal. This is a highly counter-intuitive consequence, as philosophers from Plato to R. Grossmann have appreciated, but it must be accepted by a states-of-affairs ontologist who is both a naturalist and an upholder of universals. (121)

Chapter 7 is devoted to relations, but in the interests of brevity I will not report on this chapter but advance to Chapters 9 and 10 which treat the problem of unity and Bradley's Regress respectively. This is the most exciting and original part of the book.

Meinertsen and I agree that the problem of the unity of a state of affairs is the central problem for a states of affairs ontology. The problem arises because states of affairs have “non-mereological existence conditions” (7): the existence of the constituents does not entail the existence of the state of affairs. What then accounts for there being one state of affairs having several distinct constitutents? What makes a one out of the many? A state of affairs is not just its constituents; it is these constituents unified. Something more is needed to make of the constituents a state of affairs. “I believe that it is the relating of a unique relation that is needed.” (8)

We can call this 'something more' the unifier. On Meinertsen's approach the unifier is internal to the state of affairs: “the unifier of a state of affairs is a [proper] constituent of it.” (135, emphasis in original) I added 'proper' in brackets to underscore that Meinertsen is not maintaining that states of affairs are self-unifying either in the positive sense that they unify themselves or in the privative sense that they are not unified by another. They are truth-making unities, but not as a matter of brute fact: they need a unifier to account for their unity. The unifier U is a special sort of relation, indeed it is a unique relation as I have just quoted him as saying. It relates the material constituents in the state of affairs, but it does so by being related to them. It is not just a relator of what it relates; it is a relator of what it relates by being related to what it relates. So if U relates the constituents of R(a, b), U does this by being related to each of them, including the relation R. This implies, of course, that U is not identical to R. Some say it is the business of a material relation to relate; not so on Meinertsen's view: it is the business of the formal relation U, and it alone, to relate. We also note that a consequence of U's being related to what it relates, and not merely a relator of what it relates, is that U enters as a constituent into every state of affairs. On an externalist view, by contrast, U unifies the constituents of a state of affairs S without entering into S as a constituent.

Now U is either related by another to what it relates, or it is related by itself to what it relates. If the former, then Bradley's regress is up and running, a regress both infinite and vicious. (Chapter 10) To avoid it, Meinertsen posits that “The U-relation is related to its relata by itself.” (143). This is what makes it unique: it is the only relation that has this “ability,” a word Meinertsen employs. This view, which he dubs “self-relating internalism,” has not been maintained before as far as I know. “To emphasize this unique self-relating ability of U on self-relating unternalism, I shall call it the 'U*-relation.'” (143) Because U* is a constituent of every state of affairs whose constituents it unifies, the monadic case of a's being F may be depicted as follows: U*(U*, F, a). The occurrence of the sign 'U*' both outside and inside of the parentheses indicates that the concrete universal U* is both the bringer of unity and one of the items brought into unity. It is a constituent of every state of affairs without which there would be no states of affairs.

Is U* the same as the instantiation relation? Meinertsen waxes coy: he is “inclined” to say that it is, but this would be an “extrinsic thesis.” What he means, presumably, is that a full assay of R(a,b) might list the following constituents: U*, dyadic instantiation, R, a, and b. Or it might list the foregoing items except instantiation. In the latter case, U* is instantiation. For example, “Edinburgh's being north of London is unified if and only if the U*-relation relates itself to being north of, Edinburgh and London.”(143). Either way, it would seem that U* must be a multi-grade relation, one that can be had by a variable number of items, and which therefore has different 'adicities.' For example, if U* is the instantiation relation, then U* is tetradic in U*(U*, R, a, b) but triadic in U*(U*, F, a). If U* is distinct from the instantiation relation I, then U* is pentadic in U*(U*, I, R, a, b) and tetradic in U*(U*, I, F, a). Meinertsen is aware of all this, and of the apparent problems that arise, but he thinks that they can be adequately dealt with. (157-159) The reasoning is intricate and obscure and to save space I will not comment on it.

The main point is that U* is the master concrete universal without which no state of affairs could exist. A state of affairs exists if and only its constituents are unified, and no plurality of constituents is unified in the state-of-affairs way as a matter of brute fact; ergo, unity demands a unifier as its ground. Being a universal, the unifier U* is multiply instantiable. Being concrete implies that U* cannot exist uninstantiated. It also implies that U*, if multiply instantiated, is multiply located and 'at work' in every state of affairs as that which ties its constituents into a state of affairs. As a self-relating relation, it does its work without igniting Bradley's vicious regress. (Chapter 10) To cop a line from Armstrong, “Nice work if you can get it.”

                                                                            Critique: The Problem of Unity

I will focus my critical remarks on Meinertsen's fascinating and original internalist theory of the unifier U*. What struck me about his theory is its structural similarity to the externalist suggestion I made in a number of my writings. (I thank Meinertsen for his close attention to them.) The points of similarity are the following. Meinertsen and my earlier self both accept that there are middle-Armstrongian states of affairs; that their main role is to serve as truthmakers; that they are complexes composed of distinct constituents; that the composition of these complexes is non-mereological; that their material constituents are particulars and universals; that the unity of a state of affairs, and therewith its difference from the mere plurality of its constituents, needs accounting in terms of a unifier; and above all, that there is a very special, indeed a unique, entity that serves as unifier. The main difference is that Meinertsen's unifier is a constituent of states of affairs while mine is external to states of affairs. Not only is there a similarity, but the two theories, as different as they are, are open to some of the same objections. But before discussing these objections, I want to state my objections to Meinertsen's account of unity, and how my theory avoids them.

First Objection

If there is a constituent of a state of affairs that explains its unity, this constituent must have a unique feature: it must be self-relating. But 'self-relating' has two senses, and this duality of senses give rise to a dilemma. Either (1) U* is self-relating only in the privative sense that it is not related by another to what it relates, supposing it is actually related to what it relates, or (2) U* is self-relating in the positive sense that it actually relates itself to what it relates. If (1), then U* blocks Bradley's regress, but fails to ground unity. It fails to ground the difference between the state of affairs, which is one entity, and the corresponding plurality of its constituents, which is a mere manifold of entities. If (2), then U* is an active as opposed to an inert ingredient in the state of affairs. It is a unity-maker, if you will. It plays a synthesizing role. It brings together the constituents, including itself, which otherwise would be a mere plurality, into a truthmaking unity.

But analysis cannot render this synthesizing intelligible, and therein lies the rub. All ontological analysis can do is to enumerate the constituents of a state of affairs, or, more generally, the parts of a whole. Analytic understanding proceeds by resolving a given whole into its parts, and ultimately into simple parts. But there is more to a (non-mereological) whole than its parts. There is the unity in virtue of which the parts are parts of a whole. The whole is one entity; the parts are many entities. Now if we try to understand this 'more' analytically we can do so only by positing a further part, a unifying part. I say 'posit,' not 'find.' In Fa, one can reasonably be said to find a particular and a character, but not a distinct copulative entity that grounds the truthmaking unity of the constituents. And so Meinertsen posits a unity-grounding entity. But the attempt to understand synthesis analytically is doomed to failure. First of all, no proper part of a whole is its unity, and this for the simple reason that the unity is the unity of all the parts. What one could say, though, is that the unity of the parts, which is distinct from any part, and from all of them, is brought about by a special part, the unifier. But then that special part, without ceasing to be a proper part, would have to exercise a synthesizing function. This synthesizing is what eludes analytic understanding. Simply to posit that the unifier U* has the ability to synthesize is make a kind of deus ex machina move. Leaving God out of it, Meinertsen's U* is a principium ex machina. I will come back to this later in connection with Meinertsen's talk of “inference to the best explanation.” (144) My present point is that even if there is some occult constituent internal to states of affairs that grounds and thus explains their contingent unity, its existence and its operation must remain a mystery and cannot be rendered perspicuous by the analytic method of constituent ontology. Let me explain further.

Does Meinertsen's U* exist? If there are states of affairs as Meinertsen conceives them, then U* has to exist. But if U* exists, then it is (a) a distinct entity independent of us and our synthetic activities, and (b) a distinct item that we can single out in thought if not in perception. If I see that a book is on a table, then I see a book, a table, and possibly also the relation referred to by 'on.' What I don't see, however, is the referent of 'is': the being of the book's being on the table. Since I don't see the being of the book's being on the table, I do not see U*. I cannot single it out in perception. Can I single it out in thought? To do so I would have to be able to distinguish U* from S, the state of affairs the unity of whose constituents U* grounds. There is a problem here. The ordinary (material) constituents in a state of affairs S are weakly separable: each such constituent could exist apart from every other one in S and apart from S itself, but not apart from every other entity. For example, let S = Fa. If Fa is a Meinertsenian state of affairs, then a can exist without instantiating F, and F can exist without being instantiated by a, and each can exist without being constituents of S. (The separability is said to be weak because a cannot exist without properties, and F cannot exist uninstantiated.) Now the immanent universal relation U* can exist apart from a and apart from F provided it is instantiated elsewhere, but not if it is the actual unifier of a and F. As the latter, as the active ingredient in S, it is inseparable from a, from F, and from S. But then U* is quite unlike the material constituents in S, which are all inert, and it is unintelligible in what exact sense U* is a constituent of S. The analytic assay lays out the constituents of a state of affairs, but it can do this only because of the logically antecedent unity of the constituents in virtue of which there is a state of affairs to assay. To understand this unity analytically by positing a special unifying constituent would make sense only if said constituent were inert like the material constituents. But of course it cannot be inert if its is to be a unity-grounder.

Another way of appreciating the problem is by asking what the difference is between U* as an active ingredient in S, and S. Clearly, S cannot exist without U*. But it is also true that U*, as the active ingredient in S that unifies precisely a and F, cannot exist without S. This is because U* is a unifying unifier only when instantiated/located in a state of affairs with determinate material constituents. In every state of affairs S in which the in rebus immanent universal U* exists, it unifies precisely the constituents of S, and cannot do otherwise. So U* and S are mutually inseparable. It follows that U* both is and is not weakly separable from S. As a constituent of S, U* is weakly separable from S. As an active ingredient and unity-maker, however, U* is not weakly separable from S. We ought to conclude that it is unintelligible how a (proper) constituent of a state of affairs could serve as its unifier. As a constituent, U* must be inert in S; as unifier, U* must be active. But it can't be both because it cannot be both weakly separable from S and not weakly separable from S.

An analogy may help clarify my criticism. The existence of two boards and some glue does not entail the existence of two boards glued together. That is obvious. It is also obvious that there would be no need for super-glue to glue the glue to the boards should someone glue the boards together. If there were a need for super-glue, then one would need super-duper-glue to glue the super-glue to the glue and to the boards, and so on. We can express this by saying that ordinary glue glues itself to what it glues; it is not glued by another to what it glues. In this sense, ordinary glue is self-gluing. This is in analogy to Meinertsen's claim that U* is self-relating. But note that 'self-gluing' can only be taken in a privative, not a positive, sense. The same goes for 'self-relating.' By 'privative' I simply mean that the self-gluing glue is not glued by another. If the glue and the relation U* were self-gluing and self-relating in a positive sense, then they would be agents of an action. They would be active as opposed to passive or inert. But surely self-gluing glue does not do anything: it does not apply itself to the boards or bring it about that the two boards are glued together; self-gluing glue is merely such that if the two boards are glued together by a genuine agent, no further glue would be needed to glue the glue to what it glues. Likewise, self-relating U* does not do anything: it does not bring it about that U*, a, and F are 'cemented' into a state of affairs; it is merely such as to insure that if U*, a, and F are brought together to form a state of affairs, no further formal U-type relations are needed to do the job.

Meinertsen credits me with appreciating that the problem of regress-avoidance and the problem of unity are two and not one. “As Vallicella (2004, p. 163) . . . eloquently puts it: 'A regress-blocker is not eo ipso a unity-grounder, pace Russell, Alexander, Blanshard, Grossmann, et al.'” If I am right, however, Meinersten has not really taken this insight on board. My point against him is that his U* can do only the regress-blocking job but not the unifying job. The problem is that no constituent of a state of affairs can do the unifying job. A fortiori, no relational constituent can do the job. By my lights, Meinerten fails to appreciate this, and it may be that he fails to appreciate it because he illicitly slides from the privative sense to the positive sense of 'self-relating.'

Second Objection

On Meinertsen's internalist theory, the unifier U* is a constituent of every state of affairs. Now corresponding to every state of affairs there is the sum of its constituents. So, corresponding to a's being F, there is the sum a + U* + F. Clearly, the particular a in the state of affairs is numerically the same as the particular a in the sum, and the universal F in the state of affairs is numerically the same as the universal F in the sum. The state of affairs and the sum share these material constituents and do not differ in respect of them. But what about the concrete universal U*? Is it numerically the same entity in the state of affairs and in the sum? If yes, then trouble, and if no, then trouble.

States of affairs are contingent. The contingency of a state of affairs derives from the contingent unity of its constituents. So it must be possible that the same constituents exist either unified or not unified. Thus the state of affairs and the sum must have the same constituents. Now U* is a constituent. It follows that U* must be be numerically the same in both the state of affairs and the corresponding sum. Two items, x, y, are numerically the same just in case thay have all the same properties. So U* must be either inert in both state of affairs and sum, or active in both. Now if U* is inert in both, then no state of affairs is constituted. If, on the other hand, U* is active in both, then the unity of the state of affairs is necessary. (For if U* is active in both, then there is no difference between the state of affairs and the sum. ) Either way, no contingent state of affairs is constituted. Therefore, U* cannot be numerically the same in both state of affairs and corresponding sum.

If, on the other hand, U* is active in the state of affairs, but inert in the sum, we get the same problem. A state of affairs is contingent just in case its constituents can exist without forming a state of affairs. It must be possible for the same constituents to be either unified into a state of affairs or not so unified. But active U* is not the same as inert U*. It follows that the state of affairs and the sum do not have the same constituents, which implies that the state of affairs is not contingent, but necessary. We ought to conclude that the unifier of a state of affairs cannot be a constituent thereof.

Third Objection

The first objection focused on the existence conditions of states of affairs; the third focuses on the existence conditions of concrete universals, in particular, the existence conditions of U*. What I will try to show is that Meinertsen's theory is involved in an explanatory circulus vitiosus. Roughly, he attempts to explain the unity, and thus the existence, of a state of affairs by positing a special unifying constituent when that very constituent can exist only in a state of affairs. Here is my argument:

a) A state of affairs exists if and only if its constituents form a unity.
b) U* is a constituent of states of affairs that explains their unity.
Therefore
c) U* is a constituent of states of affairs that explains their existence. (from a, b)
d) U* cannot exercise its explanatory function unless it exists.
Therefore
e) The existence of U* explains the existence of states of affairs.
But
f) U* cannot exist except in a state of affairs.
Therefore
g) The existence of states of affairs explains the existence of U*
h) Given the asymmetry of explanation, (e) and (g) are contradictory, and Meinertsen's explanation of the existence of states of affairs in terms of U* is viciously circular.

The above argument rests on the following assumptions. First, there is such a procedure as metaphysical explanation. Second, it is asymmetrical: if x explains y, then it is not the case that y explains x. Third, a circular explanation, violating as it does the asymmetry of explanation, is not an explanation, or is not a successful explanation. Fourth, the unity/existence of states of affairs, being modally contingent, needs explanation, i.e., it cannot be a factum brutum. Meinertsen is committed to all four assumptions. He is committed to the first since he accepts truthmaking. The truthmaker metaphysically (not logically and not causally) explains the truth of the truth-bearer. He is obviously committed to the second and third. He is committed to the fourth because he takes seriously the problem of unity, which is the problem of explaining the difference between a state of affairs and the mere plurality of its constituents.

An External Unifier Avoids the Above Objections

I admit that the theory of my earlier self is not much better than Meinertsen's: in the final analysis they are both unsatisfactory, although for different reasons. But my theory does avoid the above objections. Meinertsen gets into trouble by making his unifier U* a constituent of states of affairs. This exposes him to the first objection because no constituent of a state of affairs could be an active, unity-grounding ingredient. Or at least it is unintelligible how anything like that could exercise a synthesizing function. A state of affairs is a synthetic unity the synthetic character of which cannot be understood by ontological analysis. Analytical understanding here reaches one of its limits. An ontological assay is merely a list of constituents. But the unity of these constituents is not a further item on the list. Nor can adding a special constituent to explain this unity avail anything. For either this further constituent is inert or it is active. If the former, no progress as been made in accounting for unity. If the latter, then the further constituent must be ascribed a special synthesizing power that nothing else has, and that nothing that analysis could reveal could have. How could analysis reveal such an occult power?

U*'s being a constituent opens Meinertsen to the second objection because a state of affairs is contingent only if the same constituents can exist either unified or not. But this sameness is impossible if U* is both a constituent and a unifier. U*'s being a constituent also exposes him to the third objection because no constituent can exist without being a constituent of some state of affairs or other. So if the unifier is a constituent, then it cannot exist unless states of affairs exist. This however gives rise to the explanatory circle. We ought to conclude that if there is a unifier, then it cannot be internal.

My external unifier unifies but without thereby entering into the states of affairs whose unity it brings about. It thereby evades all three of the objections lately listed. Kant's transcendental unity of apperception provides a model of an external unifier. That which brings about the synthesis of representations in the unity of one consciousness, thereby constituting an object of experience, is not itself a part of the object so constituted. One obvious objection from a realist, naturalist, and empiricist point of view to an external unifier, whether developed along transcendental lines or, as in my 2002, along onto-theological lines, is that it leads us away from realism to idealism. It brings mind into the picture as the synthesizing factor. But if (irreducible) mind is brought in, then naturalism is abandoned for some sort of 'spiritualism.' Empiricism too is abandoned if one invokes an external unifier along either transcendental or onto-theological lines.

The brings me to the deus ex machina objection that has been lodged against my proposal. Roughly, I put God to work to solve the problem of the unity of states of affairs. (“God has his uses,” my teacher J. N. Findlay once said.) Curiously, Meinertsen is open to a similar objection, call it principium ex machina. He does not call upon God, but upon a sui generis entity, U*, which is unique among concrete universals due to its synthesizing power. Well, what exactly is wrong with these ex machina moves? Meinertsen and I will be told that the moves are objectionably ad hoc. Meinertsen is sensitive to the criticism:

The U*-relation is of course an 'ad hoc' entity in the sense that it is only introduced to solve a problem, viz. the problem of unity. Some authors, such as Betti (2015), would consider that a big drawback of self-relating internalism. However, one man's 'ad hoc' – solution is another man's inference to the best explanation. (143)

If any of my three objections above are sound, however, Meinertsen's inference to the best explanation is an inference to an explanatory entity that cannot exist or at least cannot be intelligibly posited.