on bradley's regress

Relations, Monism, and the Vindication of Bradleys RegressWilliam F. VALLICELLA

ABSTRACT

This article articulates and defends F. H. Bradleys regress argument against external relationsusing contemporary analytic techniques and conceptuality. Bradleys argument is usually quick-ly dismissed as if it were beneath serious consideration. But I shall maintain that Bradleys argu-ment, suitably reconstructed, is a powerful argument, plausibly premised, and free of such obvi-ous fallacies as petitio principii. Thus it does not rest on the question-begging assumption thatall relations are internal, as Russell, and more recently van Inwagen, maintain. Bradley does notattack external relations in order to affirm a doctrine of internal relations, and his monism isnot derived from the internality of all relations, but from the self-contradictory nature of allrelations. For Bradley, it is the relational situation as such that is ontologically defective.

C. D. Broad once said of F. H. Bradleys famous regress argument againstexternal relations that its use would disgrace a child or a savage.1 But someof us who are neither find the argument surprisingly resistant to refutation.2 Itis not a compelling argument, but then which argument for any interestingphilosophical thesis is compelling? It is however a good argument, indeed apowerful argument, plausibly premised, free of obvious fallacy, and worthy ofvery serious consideration. Or at least that is what I will be maintaining.

1. Overview

Bradleys attack on external relations is motivated by his concern to establishmonism, the doctrine according to which reality in the end belongs to noth-ing but the single Real.3 But we shall see that arguments against external rela-

William F. Vallicella, 5172 South Marble Drive, Gold Canyon, AZ 85218, USA; Email:[email protected]

1 Quoted from W. J. Mander, An Introduction to Bradleys Metaphysics (Oxford:Clarendon Press, 1994), p. 92.

2 Cf. F. H. Bradley, Appearance and Reality: A Metaphysical Essay (Oxford UniversityPress, 1968), Chapter III, pp. 21-29. Hereafter cited as AR. I will speak simplifyingly ofBradleys argument despite the fact that he gives several.

3 AR, p. 403.

Dialectica Vol. 56, No 1 (2002), pp. 3-35

4 William F. Vallicella

tions, even if successful, do not automatically establish monism. Thus we dowell to separate cleanly, as apparently Bradley did not, two stages within theoverall argument. The first stage, which can stand alone, aims to prove theunreality of external relations. Building on this, the second stage argues to thetruth of monism. The link between the two stages is the assumption that relat-edness requires relations. Unpacked, this slogan says that particular cases ofrelatedness, particular relational facts, require universal relations as con-stituents. Thus the fact of Monicas loving Bill, an unrepeatable entity, wouldhave among its constituents the repeatable entity, loves. The idea is that for arelatedness to exist, a universal relation must actually relate certain items.Problems with how a universal relation can actually relate its terms, problemswhich cast doubt on the possibility of such relating, will thus cast doubt on thepossibility of particular cases of relatedness. Bradleys overall argument, then,may be set forth as follows:

Relations are contradictory, hence unreal.

Relatedness requires relations.

Therefore

Relatedness is unreal, hence merely apparent.

There are two ways of resisting the conclusion of this argument. The popu-lar way is that of Russell: deny the major while accepting the minor.4 Lesspopular, but apparently equally reasonable, is the way of Fisk: deny the minorwhile accepting the major.5 But what I want to urge in this essay is that it is atleast equally reasonable to go all the way with Bradley: accept both premisesand draw the inevitable conclusion.

2. The Internal/External Distinction and Three Associated Misconceptions

In order to understand the connection between the argument against relationsand the argument for monism, we need to clarify the distinction between exter-nal and internal relations. We also need to defuse three common misconcep-tions.

The first misconception is that, for Bradley, all relations are internal. VanInwagen, for example, takes Bradleys position to be that all relations are inter-nal and hence that none is external.6 Although Bradley is often interpreted inthis way, and with some textual justification, there are passages in which hedenies that his attack on external relations is in support of the view that all

4 See note 17 below.5 See note 30 below.6 Peter van Inwagen, Metaphysics (Boulder: Westview Press, 1993), p. 35.

Relations, Monism, and the Vindication of Bradleys Regress 5

relations are internal.7 It should be clear to a careful reader of his texts that itis the whole relational way of thought, whether based on external or inter-nal relations, that is the target of his critique.8 Indeed, he says that Every rela-tion ... has a connexion with its terms which, not simply internal or external,must in principle be both at once.9 This implies that in ultimate reality theresimply is no internal/external distinction. Further details will follow below.

Closely connected with this first misconception is a second one accordingto which Bradley derives his monism from the internality of all relations. Butit is obvious that his monism must have a different source if the first miscon-ception is indeed a misconception. If Bradley does not maintain the internal-ity of all relations, then this doctrine cannot be a premise of his monism. Onthe third misconception, the only reason Bradley could have for rejectingexternal relations is the question-begging assumption that all relations areinternal. But if Bradley attacks relations as such, then he cannot be read asassuming that all relations are internal. We will see how van Inwagen, in theexcellent company of Lord Russell, succumbs to this third misconception.

A. On the First and Second Misconceptions

What exactly is an internal (external) relation? Ill begin with the way mostcontemporary analytic philosophers construe the distinction, and then proceedto the classicalunderstanding thereof. We will then be able to see that Bradleyadopts neither. Thus we must clearly distinguish among three views on inter-nal relations, the contemporary, the classical, and the Bradleyan.

The contemporary construal is refreshingly clear: An internal relation isone that holds between or among objects just in virtue of their intrinsic prop-erties, where an intrinsic property is one that is nonrelational. It will servepresent purposes to say that a property P of x is intrinsic just in case xs gainor loss of P would constitute a real changein x (Hillarys becoming angry isa real changein her; Bills becoming an object of anger is not a real changein him). Thus if a and b are both red, then simply in virtue of their instantia-tion of this intrinsic property, the two individuals stand in the same color asrelation. An internal relation, then, is one such that there are intrinsic proper-ties of its relata that determine (logically necessitate) the relations holding

7 In his posthumous essay, Relations, Bradley says it is ludicrous to impute to himthe view that real relations are internal merely. To think that this necessarily follows whenthe mere externality of relations is denied is (I submit) an obvious, if perhaps a natural mis-take. Cf. F. H. Bradley, Collected Essays, vol. II (Oxford: Clarendon Press, 1935), pp. 642-643. See also his Essays on Truth and Reality (Oxford: Clarendon Press, 1914), pp. 238-239.Cited hereafter as ETR.

8 Cf. AR 38.9 Bradley, Relations, op. cit., p. 641.


between or among the relata. In a currently fashionable jargon, an internal rela-tion is one that supervenes on the intrinsic properties of its relata.

An external relation is one such that there are no intrinsic properties of itsrelata that determine (logically necessitate) the relations holding between oramong its relata. External relations, the most plausible examples of whichinclude spatial and temporal relations, do not supervene upon the intrinsicproperties of their relata. If one thing is ten feet from another, there are pre-sumably no intrinsic properties of the two things that determine their standingin the relation in question. One could know everything there is to know aboutthe intrinsic properties of the two things and not know how far apart they are.It follows that there could be a second pair of things indiscernible from thefirst in respect of intrinsic properties that are not ten feet from one another.

We may note right away that the contemporary take on the internal/exter-nal distinction provides no purchase to monism, an implication of which is thateverything is essentially related to everything else. For if P is an intrinsic prop-erty of x, it does not follow that P is an essential property of x; P could be acci-dental to x. Thus it is consistent to maintain of internally related items boththat (i) they are internally related, and (ii) they are capable of existing apartfrom their internal relations. For example, two red balls, in virtue of both beingred, stand in the same color as relation which is internal as above defined; butthis is surely compatible with the balls existing outside of this relation: paintone blue and they will both still exist. So if all relations are internal in the con-temporary sense, and some individuals have some of their properties acciden-tally, then monism is not a logical consequence. For in the contemporary sense,to say that all relations are internal is equivalent to saying that all relationssupervene upon the intrinsic properties of their relata; and this is obviouslyconsistent with the claim that there is, at ontological bottom, a plurality of sub-stances, i.e., a plurality of entities logically/metaphysically capable of inde-pendent existence. So if Bradleys regress shows merely that there can be noexternal relations, it does not thereby show that monism is true. This is why Idistinguished above between the argument against external relations and theargument for monism.

On the classical understanding of the internal/external distinction, however,something much stronger is intended by internal relation, namely, that if anindividual stands in an internal relation, then its very existence and identity isbound up with its standing in that relation. Thus Blanshard, a representative ofthe classical view, writes that A relation is internal to a term when in itsabsence the term would be different....10 Blanshard appears to mean numeri-

10 Brand Blanshard, The Nature of Thought, vol. II (NewYork: Humanities Press, 1969),p. 451.


cally different. Thus if x is internally related to y, then x could not be x apartfrom its relation to y. This implies that if all relations are internal, then noth-ing is what it is apart from its relations to everything else. Now if each indi-viduals existence and identity is bound up with the existence and identity ofevery other individual, then we have arrived at monism, the doctrine that inultimate reality there is only one substance. For if each individual is internallyrelated to every other one, then no one of them is a substance, i.e., an entitylogically/metaphysically capable of independent existence.

Can we see this classical definition of internalas but a special case of thecontemporary one, the case where the supervenience base consists solely ofessential properties? Suppose all individuals have all of their intrinsic proper-ties essentially, and all relations are internal in the contemporary sense ofsupervening on the intrinsic properties of their relata. On this supposition, willmonism be the logical upshot? I dont think so. For if all individuals have allof their monadic properties essentially, and all relations supervene uponmonadic foundations, this still seems consistent with ontological pluralism.Recall Leibniz: In his scheme, there is a plurality of substances the propertiesof which are all essential, and relations have no reality apart from theirmonadic foundations. Thus the classical definition of internalappears not tobe a special case of the contemporary one.

To understand why, on the contemporary understanding of internal, theinternality of all relations is compatible with ontological pluralism even whenthe supervenience base consists of essential properties only, we need only toreflect on the fact that the contemporary definition makes crucial use of thenotion of supervenience: internal relations supervene upon the intrinsic prop-erties (whether essential or accidental) of their relata. But to borrow a coupleof neat phrases from David Armstrong, the supervenient is an ontological freelunch and no addition to being.11 Or as Keith Campbell puts it: Superve-nient additions to ontology are pseudo-additions.12 Thus I think we can arguethat the contemporary definition of internal relation implies that, if all rela-tions are internal in this sense, then in ultimate reality there are no internalrelations, indeed, no relations at all. In the putative relational situation wheretwo balls are the same color, all you have are two colored balls, but no rela-tion between them or in addition to them, nothing that connects or uni-fies them. Of course, supervenience is not reduction: the balls being of thesame color cannot be reduced to (identified with) their both being red. If they

11 David Armstrong, A World of States of Affairs (Cambridge: Cambridge UniversityPress, 1997), p. 12.

12 Keith Campbell, Abstract Particulars (Oxford: Basil Blackwell, 1990), p. 37. I havesuppressed Campbells italics.


were both blue (or green or ...) they would still be of the same color. Never-theless, in each concrete relational situation, there is nothing but the two col-ored balls. There is no relation distinct from them that connects them.

The implication of all this is that the classical understanding of internalrelation, according to which the doctrine of internal relations entails monism,cannot be unpacked along supervenience lines. For it involves two compo-nents, only the second of which is approximated to by the supervenience def-initions. One is that an internal relation is a bona fide relation, and thus a non-supervenient universal entity that connects its terms, and is thus betweenthem (between may seem to fit only the dyadic case; but in this contextbetweensimply means that a relation is an entity in addition to its terms, i.e.,a nonsupervenient entity). Only as connecting them and thus securing theirunity could it possibly serve the cause of monism. The other component is thatan internal relation is one that affects, modifies, or makes a difference toits terms. Thus Blanshard speaks of the nature of a term being affected byall its relations.13 This could be put by saying that, for any x, the relationalproperties that x has in virtue of standing in the relations it stands in are all ofthem essential to x.

Now it is easy to see that this classical conception is highly unstable, indeedself-contradictory which is exactly Bradleys point, at least as I understandhim. On the one hand, an internal relation, as a relation, is betweenits termsas it must be if it is to do the job of tying them into a relational fact. Clearly,it cannot tie the terms into a fact unless it is an entity in addition to them. Arelation that is not between its terms cannot unify them, and a relation that can-not unify its terms cannot be of service to monism. On the other hand, an inter-nal relation, as internal, must be grounded in the nature of its terms, and insuch a way that the very existence and identity of the terms is bound up withinthe relations. Now the only sense that can be attached to this is that the rela-tions supervene upon the intrinsic properties of the terms, and these proper-ties are all of them essential to the terms. But in that case the relations are, assupervenient, precisely not betweenthe terms. Thus we have landed in a con-tradiction: internal relations, classically conceived, are and are not betweentheir terms. They are betweentheir terms as relations, but not betweentheirterms as internal.

This is why a doctrine of the internality of all relations cannot in the endbe ascribed to Bradley, either in its contemporary or in its classical construal.This is obvious with respect to the contemporary construal. As for the classi-cal construal, internal relations are as infected with self-contradiction as are

13 Blanshard, op. cit., p. 452.


external ones. Indeed, an internal relation, as a relation, must be external to itsterms; otherwise it would not be between them. So a so-called internal rela-tion must be both external and internal. This is our contradiction in anotherform. And an external relation, if it is to be a relating relation and not merelya third thing in addition to its terms, cannot be wholly external to its terms. Anexternal relation, as external, is one whose holding between its terms makesno difference whatsoever to its terms. But as a relating relation, an externalrelation must connect its terms, which is precisely what it cannot do qua exter-nal. So a relating relation (whether internal or external) must be at once bothinternal and external which is contradictory. Thus, Every relation ... has aconnexion with its terms which, not simply internal or external, must in prin-ciple be both at once.14 Bradley concludes that the external/internal distinc-tion, if taken as absolute, is untenable, which is not to deny that it has rela-tive truth as a useful makeshift.

In short, we must scrupulously distinguish among the contemporary, theclassical, and the Bradleyan view of internal relations. Once we have doneso, we discover that (i) Bradley does not attack external relations in order toaffirm a doctrine of internal relations, and that (ii) his monism is not derivedfrom any doctrine of the internality of all relations, but from the self-contra-dictory nature of all relations. It is the relational situation as such that isontologically defective.

B. On the Third Misconception

According to the third misconception, the only reason Bradley could have forrejecting external relations is the question-begging assumption that all rela-tions are internal. This is how van Inwagen, following Russell, reads Bradley.I shall first sum up Bradleys argument and then explain why van Inwagenthinks it question-begging.

If a stands in R to b, and R is an external relation, what makes it the casethat the two individuals stand in R to one another? Since R is external, theintrinsic properties of the two individuals can play no role in explaining this.And it is clear that there is nothing in the nature of R itself that can explainwhy it connects any two individuals it does in fact connect. So why do the twoindividuals stand in R to each other? Suppose c and d respectively are indis-cernible from a and b respectively, as regards all intrinsic properties, but thatR does not hold between c and d. Why does R connect the members of the firstpair but not the members of the second? The question has traction becauseexternal relations are non-supervenient.

14 Bradley, Collected Essays, op. cit., p. 641.


It is clear that introducing a further (triadic) relation R* to tie a, b, and Rinto the fact aRb would do nothing to ensure the unity of the constituents ofthe original relational fact.15 For R* is as external to its terms as R is to itsterms, and so by introducing R* we would only succeed in replacing the ini-tial problem with the problem of the unity of a, R, R*, and b. And it is clearthat introducing further relations to do the work R* was incapable of doingbegets a regress both infinite and vicious. The unity of the facts constituentsnever gets established, with the result that nothing is ever externally related toanything else. And since nothing is ever externally related to anything else, theworlds appearing to be a plurality of externally interrelated substances ismerely that, an appearance: monism is true at ontological bottom.

This is essentially how van Inwagen construes Bradleys argument againstexternal relations and in favor of monism. But the point of it depends on afurther premise: that the fact that a certain set of things stands in a given rela-tion must somehow be grounded in or explained by the intrinsic properties ofthose things.16 Van Inwagen, however, sees no reason to accept this (question-begging) premise. For to accept it is simply to accept that there are no exter-nal relations, since, by definition, an external relation is one in which thingscan stand, without their standing in it being grounded in their intrinsic prop-erties. Bradleys argument accordingly begs the question against external rela-tions. It makes the unwarranted demand that every relation should satisfy theconditions on internal relations. Russell took a similar view of Bradley:

The view [Bradleys] which I reject holds ... that the fact that an object x has a certainrelation R to an object y implies ... something in the naturesof x and y in virtue of whichthey are related by the relation R.17

The problem with the Russell van Inwagen response to Bradley is that itignores that Bradley attacks relations as such, and not merely external rela-tions. Thus he cannot be taken to be assuming a doctrine of the internality ofall relations, thereby committing a petitio principii. Equivalently, he cannot betaken to be assuming that the unity of the constituents of a relational fact mustbe grounded in the intrinsic properties of the constituents. What he is assum-ing is that the unity of the constituents of a relational fact must have some

15 This is not the way Bradley sets up the problem since for him all relations are dyadic(two-termed). But as I said, my interest is in reconstruction over exegesis. The importance ofhis argument does not hinge on a doctrinal peculiarity that most present-day philosopherswould reject. For Bradley, a dyadic relation R1 is needed to tie a to R, a separate dyadic rela-tion R2 to tie R to b, and so on infinitely and viciously. For Bradleys objections to what hecalls multiple relations, see ETR, pp. 303-309.

16 Ibid., p. 36.17 Bertrand Russell, Some Explanations in Reply to Mr. Bradley, Mind, vol. XIX

(1910), pp. 373-374.


ontological ground or other, but not necessarily one in the intrinsic propertiesof the constituents. Thus charity bids us reconstruct Bradleys argument so asto eliminate the circularity.

3. A Non-Circular Reconstruction of Bradleys Argument

What follows is, I think, a good argument in the spirit of Bradley. Whetheror not it adheres to the letter of his text is a matter of no great concern to me:my interest is philosophical, not exegetical. 1. There is a difference between the relational fact aRb and the set or sum or

list or ordered triple of its constituents. Equivalently, there is the differ-ence between a relation which relates in fact and one which does not sorelate....18

2. This difference requires an ontological ground: it cannot be a brute fact.3. Because R is external, the difference between the fact and its constituents

can be grounded neither in the intrinsic properties of the relata, nor in theintrinsic properties of the relation.19

4. The difference between the fact and its constituents cannot be grounded inany further constituent of the fact on pain of a vicious infinite regress.

Therefore,5. The ontological ground of the difference between the fact and its con-

stituents, and thus the ontological ground of the existence of the fact, mustlie outside the fact.20

Therefore,6. Facts and the external relations they presuppose do not exist as independ-

ent reals: depending as they do on a condition external to them, they lackultimate reality and so belong to appearance.

18 F. H. Bradley, Reply to Mr. Russells Explanations, Mind, vol. XX (1911), p. 74.19 Suppose that (i) an n-ary relation is a set of order n-tuples, and (ii) sets have their

members essentially. One might then think that the difference between a relational fact and itsconstituents could be grounded in an intrinsic property of the relation. Let R = {, }. It is intrinsic to R that it contain just these pairs. But although it makes sense to think ofthe extension of a relation as a set, it makes no ontological sense to think of a relation itself asa set, quite apart from the impossibility of this as an interpretation of Bradley. A relation is auniversal: a binary relation relates different pairs at different times and in different possibleworlds. Consider the phrase, the set of all pairs such that x is to the left of y. This phrase couldvery well pick out different sets in different possible worlds. But the relation is the same acrossthese worlds. David Lewis has a way of responding to this sort of argument, but it involves hisextravagant doctrine that there is a plurality of equally real possible worlds (Cf. his On thePlurality of Worlds (Basil Blackwell, 1986), p. 52).

20 What about the possibility that the ontological ground lies in extrinsic properties of a,R, or b? An extrinsic property is a relational one parasitic upon a relation, which would haveto be a further constituent of the fact.


I submit that this is a very powerful argument that does not beg the questionagainst external relations, and so cannot be shown the door as quickly as vanInwagen supposes. It does not assume that all relations are internal; it merelyassumes that all relations require an explanation of why they connect, or per-haps how they can connect, the terms they connect. Suppose we step throughthe argument (cautiously, as through a dialectical minefield) the better toappreciate its strength and subtlety.

4. Ad Premise (1): The Distinction between a Fact and its Constituents

Premise (1) is well-nigh self-evident: although the relational fact in questionhas a, R, and b as constituents, the fact is distinct from the set of these con-stituents, from the membership (extension) of the set of these constituents,from the extension of the list of these constituents, from the ordered triple ofthese constituents, and from their mereological sum21 (To save bytes and thereaders patience, I will often just speak of the constituents without ringingthese changes). For if the constituents exist, the set and the sum both auto-matically exist; but the constituents can exist without the fact existing. Thisis so even if we assume that relations cannot exist unexemplified, i.e., cannotexist without actually relating things. Suppose R exists in virtue of its actuallyrelating c and d, but does not relate a and b. Then a, b, and R would all existwithout constituting the fact, aRb. It follows that there is something more toa fact than its constituents. Intuitively, this something moreis the contingentunity of the constituents, their peculiar fact-making contingent togetherness.Clearly, then, (1) is true: the fact is distinct from its constituents. This is arobust distinctness unlike the anemic distinctness of a set from its members:the members of a set cannot exist unless the set exists; the constituents of afact can exist without the fact existing.

Of course, I am assuming that there are facts; if there arent any, then thereis no actual difference between a fact and its constituents. But why should wethink that there are facts? An excellent reason for positing facts is that we needthem as truth-makers for true contingent indicative sentences, for the judg-ments they express, and ultimately for our thinking, which, being unavoidablydiscursive, necessarily articulates itself in judgments. The truth-maker intu-ition is that if a is F is contingently true, it is true because22 of the way the

21 With respect to mereological sums (fusions), I assume the principle David Lewis callsUnrestricted Composition: whenever there are some things, no matter how many or how unre-lated or how disparate in character they may be, they have a mereological fusion. Parts ofClasses (Oxford: Basil Blackwell, 1991), p. 7.

22 Because here of course has nothing to do with empirical causation: it signifies theasymmetrical relation of ontological grounding.


world mind-independently is: the latter must therefore contain not only a andF-ness, but also the two together, i.e., the fact, as being F. I consider myselfabsolved from any further elaboration and defense of this truth-maker argu-ment for facts (states of affairs) since the job has been done by Armstrongwith characteristic clarity and rigor in his latest book.23 For present purposesI need add only the Bradleyan point that if there are facts, they need not beconceived as ultimately real; they can be conceived as appearances, where thelatter are to be scrupulously distinguished from illusions. An appearance is notan illusion inasmuch as it shares in reality; its just that an appearance cannotbe independently real, self-existently real, but requires an ontological groundon which it depends for its existence. At the end of this essay I will have a bitmore to say about Bradleys appearance/reality distinction, but for now themain point is that we can use the very powerful truth-maker argument to estab-lish the existence of facts at the level of appearances at least. This gives us astarting point, from which further argumentation can proceed, to show thatfacts (and the relations on which they depend) cannot be ultimately (inde-pendently) real (But it does not follow, and Bradley never says, that facts andexternal relations have no being at all as many of his critics seem to think.Facts and relations are necessarily implicated in our ordinary way of thinkingand living, having the status of a necessary makeshift). In short, we mustassume facts at the level of appearance to get the dialectic underway; but weneed not for this purpose assume that facts are ultimately real.

It is important to realize that the reasoning in the opening paragraph of thissection applies not only to relational facts narrowly construed, but also to allcontingent facts. Monadic facts are themselves broadly relational. Suppose ais contingently F. Then a and F-ness are external to each other: there is noth-ing in the nature of either to logically necessitate its being tied to the other.And yet a exemplifies F-ness. Whether exemplification is a relation (call itEX), a nonrelational tie (call it NEX), or is given a deflationary explana-tion in terms of the Fregean gappiness or Ungesttigtheit of properties (indi-cate this by __F), the problem arises: What is the ontological ground of thedifference between the fact as being F and the following mereological sums:a + EX + F-ness, a + NEX + F-ness, and a + __F? In each case the existenceof the constituents does not entail the existence of the fact. In the Fregean case,note that it is the externality of a and __F to each other that causes the prob-lem. As I see it, Bradleys problem is fundamentally a problem about unity,which is why it arises even if there is no exemplification relation and thus no

23 D. M. Armstrong, A World of States of Affairs (Cambridge University Press, 1997), pp. 113-138.


threat of an infinite regress. Not being an artifact of the inept introduction ofa tertium quid between particular and property, the problem arises even with-out the tertium quid. Hence the Fregean quashing of the quid, and its replace-ment with a slot in a property, does absolutely nothing to solve Bradleys prob-lem. This subtle point is often overlooked.24 I will return to it.

But is it really obvious that a fact, whether relational or monadic, is suffi-ciently distinct from its constituents to raise the specter of a Bradley-styleregress? Can the constituents exist apart from the fact?25 If they cannot, thenthe robust difference between fact and constituents I have been belaboring isbogus and the problem of unity cannot arise. In particular, is one perhaps mis-construing the nature of a relation if one thinks one can get it off by itself apartfrom what it relates? According to Samuel Alexander, the business of a rela-tion is to relate.....26 Bradleys difficulties therefore arise from treating rela-tions in the abstract as if they did not relate.....27 Brand Blanshard sounds thesame note:

He [Bradley] is thinking of a relation as if it were another term, as if A-R-B were threebeads on a string...But R is not the same sort of being as its terms. It is neither a thingnor a quality. It is a relation, and the business of a relation is to relate.28

To evaluate this oft-made objection, we need to distinguish two differentsenses of the business of a relation is to relate. According to the one read-ing, it is false; according to the other, the regress is not avoided.

On the one hand, the slogan could mean that the very being of a relationis its actually relating the very terms29 it does in fact relate. Thus supposingexternal relation R relates a and b only, the point would be that the being of Ris exhausted in relating a and b. But this would imply that R cannot relate anyother pair of relata, that it is essential to R that it relate just those terms. Thisis entirely too strong a reading of the slogan. For one thing, it would imply thatno relation that just happens to relate two things is a universal. Secondly, wesurely dont want to say that a relation that relates a and b, could not, by its

24 By Richard Wollheim, for example: Personally, I believe that the answer to this chal-lenge was given at about the same time as Bradley cast it down by Frege with his notion of thepropositional function. F. H. Bradley (Baltimore: Penguin Books, 1959), p. 119.

25 Of course, the constituents of a fact cannot exist as constituents apart from some factor other; but that is not the question. The question is whether or not the entities that happen tobe the constituents of a given fact could exist apart from that very fact, i.e., without being itsconstituents.

26 Samuel Alexander, Space, Time, and Deity (Gloucester, MA: Peter Smith, 1979), p.249.

27 Ibid., p. 255.28 Brand Blanshard, Bradley on Relations, in The Philosophy of F. H. Bradley, eds.

Manser and Stock (Oxford: Clarendon Press, 1984), p. 215.29 The terms of a relation are its relata. This old terminus technicus is presumably a con-

traction of the Latin terminus which in one of its senses denotes an endpoint.


very nature as a relation, have related any other pair. That would contradict thefact that R is external to its terms.

On the weaker reading, the business of a relation is to relate says thatthere are no unexemplified relations, that a relation cannot exist without actu-ally relating some relata.30 Accordingly, dyadic R cannot exist unless it isexemplified by some pair or other, but its existence does not depend on itsbeing exemplified by any particular pair. This weaker reading is very plausi-ble, but note that it doesnt stop the regress. For now R is sufficiently like athird term to cause a problem. For the weaker reading allows that a relation ismore than its relating of specific relata; it is a universal capable of enteringinto different relational facts. Necessarily, a relation must have some terms orother. But it is not necessary that a relation have the very terms it has. Now ifit is not necessary that a relation have the very terms a and b that it has, if itis a contingent fact that R relates a and b, Bradleys problem legitimatelyarises: what is the ontological ground of the difference between aRb and themere sum, a + R + b? What both Alexander and Blanshard fail to see is that arelation can exist without relating the specific objects it does in fact relate.Relations are not put out of business by their failure to do their business inspecific cases. Bradleys challenge cannot be met simply by holding that a rela-tion cannot exist without terms.

This defense of premise (1) assumes that relations are universals, repeat-able, and thus that a relation such as loves is distinct from a relatedness (rela-tionship, relational fact) such as Monicas loving Bill which is in every case aparticular, an unrepeatable. It is because relations are universals that theirbeing is not exhausted in their relating the specific objects they do in factrelate. And it is because relations are not exhausted in relating specific objectsthat the unity problem arises. So one might think to question the assumptionthat relations are universals. But to no avail: if relations are, or are reducibleto, particulars, then there are no relations as distinct from relational facts.31 Ifrelations exist at all, then they must be universals. Note first that one cannoteliminate universal relations in favor of universal properties. For as waspointed out three paragraphs back, if a exemplifies universal F-ness, then

30 Compare ETR, p. 295 ff. and p. 302 where Bradley argues that no relation is realapart from all terms.

31 A referee suggested that relations could be irreducibly relational tropes. But if thereare relational tropes, they must be reducible to, or at least dependent on, monadic tropes. AsKeith Campbell (op. cit., p. 99) puts it, Monadic tropes require no bearer, polyadic ones callfor at least two, which will have to be themselves tropes, and in the most elementary casesthese terms will be monadic tropes. Thus no relational trope can stand on its own, whichimplies that there cannot be any distinction in reality between a relational trope and a relationalfact.


exemplification, no matter how you construe it, will give rise to the Bradleyanproblem. So one might try to eliminate universal relations in favor of such par-ticulars as property-instances, accidents, tropes and the like.32 SupposeSocrates is whiter than Alcibiades. One might try the following analysis:Socrates has the relational accident, whiteness-in-respect-of-Alcibiades, andAlcibiades has the distinct relational accident, darkness-in-respect-of-Socrates. On this foundationist analysis, to give it a name, the original rela-tional fact reduces to a conjunction of two non-relational facts. Each fact isnon-relational in both the narrow and the broad senses lately distinguished.Thus each substance has its relational accident without exemplifying it, with-out in any sense being externally related to it, or even externally non-relatedto it (as in the non-relational tie and Fregean variations). Substance S andaccident A are so related (speaking loosely) that although S can exist with-out A (though presumably not without some accidents or other), A cannot existexcept in S. This implies that A is neither repeatable nor transferrable. It seemsthat Bradleys problem cannot arise in a substance-accident metaphysics. Butthis wont succor the friend of relations; for on such a metaphysics there can-not be any irreducible relations either! Therefore, if there are relations, thenthey must be universals.

So for premise (1) to be true, we must assume the existence of (external)relations, which, I have just shown, cannot fail to be universals. It is only ifthere are relations that we have the problem of their connection to their terms.But this may seem puzzling. How can Bradleys argument assume the exis-tence of relations if the whole point of the argument is to deny their existence?The answer is that the argument assumes relations (or else takes facts and therelations on which they depend as having been supplied by the truth-makerargument) in the realm of appearance in order to impugn their status as ulti-mate (independent) reals.

But there is still a gap we need to plug. Why not take Bradleys reasoningas a reductio ad absurdum of the assumption that relations are irreducible uni-versals instead of taking it as an argument for monism that consigns universalrelations to appearance? This would contravene his intentions of course, butwhy not see this as the sound core of his reasoning? In other words, why nottake Bradley to be willy-nilly supporting foundationism as sketched above, thedoctrine that relations reduce to their monadic foundations, rather than as sup-porting a form of monism according to which irreducible universal relationsexist but only at the level of appearance? For if foundationism is true, then

32 I will ignore the view that a relation is a set of ordered n-tuples. This is fine as a set-theoretic representation or model, but preposterous as the sober ontological truth about rela-tions. See note 19 above.


there can be cases of relatedness without relations.33 One might argue some-what as follows: (i) If there are universal relations, then there is the problemof how they can combine with their terms to form relational facts. (ii) Thistogetherness or connectedness cannot on the one hand be a brute fact, but itcannot on the other hand be grounded in the nature of the relation, the natureof the terms, or any further constituent on pain of a vicious infinite regress.((ii) is the sum and substance of premises (2), (3) and (4) supra.) Therefore,(iii) there are no universal relations: relational facts do not require relations.Thus would Bradley be harnessed to the cart of foundationism.

It is obvious that if there can be relatedness without relations, then theworld at ontological bottom could be a plurality of interrelated substances,which is precisely what Bradley is out to deny. To arrive at monism, therefore,Bradley needs the plausible supplementary premise that particular cases ofrelatedness require relations. Only then will the attack on relations be an attackon relatedness, and concomitantly an attack on pluralism. In other words, whathe needs is the assumption that foundationism is false.

Is foundationism false? Although this is too large a question to discuss herein any detail, foundationism is reasonably rejected (Recall that my thesis is notthat Bradleys argument against relations and for monism is absolutely com-pelling, but only that it is reasonably premised and free of obvious fallacy.) Assuggested above, a sentence like Socrates is shorter than Simmias, might beanalyzed as a conjunction: Socrates has shortness-with-respect-to-Simmiasand Simmias has tallness-with-respect-to-Socrates. One problem is that analy-ses such as these presuppose the existence of at least one relation.34 For theproperty Socrates has is coordinated with the property Simmias has. Sincefoundations come in pairs, each foundation P is coordinated with a foundationQ and vice versa. The relation of coordination remains unreduced. Cas-taedas version of foundationism may seem to evade this problem but it facesothers. Castaeda analyzes Socrates is shorter than Simmias as Shortness(Socrates) Tallness (Simmias)where the juxtaposition of the matrices Short-ness ( ) and Tallness ( ) expresses the with-respect-to connection betweenthe two participations in the Forms making up the relation shorterness.35 Notethat Castaedas analysans, unlike the foregoing one, is not conjunctive; itexpresses a peculiar atomic fact.

33 Cf. Milton Fisk, Relatedness without Relations, Nous, vol. VI, no. 2 (May 1972),pp. 139-151. Cf. also Keith Campbell, op. cit., p. 98.

34 See Reinhardt Grossmann, The Categorial Structure of the World (Bloomington:Indiana University Press, 1983), pp. 160-161.

35 Hector-Neri Castaeda, Relations and the Identity of Propositions, PhilosophicalStudies 28 (1975), p. 241. See also his Platos Phaedo Theory of Relations in M. Bunge, ed.,Exact Philosophy (Dordrecht: D. Reidel, 1973), pp. 201-214.


The most obvious difficulty with this analysis, as Grossmann points out,36

is that it is not clear how Shortness (Socrates) Tallness (Simmias) is to beread and understood in English. It cannot be read as a conjunction; neither asSocrates is short and Simmias is tall nor as Socrates has shortness-as-com-pared-to-Simmias and Simmias has tallness-as-compared-to-Socrates. Howthen is the expression, which seems to have two parts, to be read? Replacingthe and with a comma or semi-colon of course changes nothing as regardslogical form. Could it be read as: Socrates has shortness with respect to Sim-mias has tallness? But that makes no sense. So it is not at all clear what factCastaedas analysans is supposed to express.

A second difficulty, also pointed out by Grossmann,37 is that since Short-ness and Tallness both occur together in the fact in question, the relation ofoccurring together in the same fact must go unreduced. This is just the coor-dination relation under a different guise.

Finally, how is the matrix, Shortness ( ) to be understood? Does Socratesexemplify Shortness? That would introduce the relation of exemplification.Castaeda, as a sophisticated bundle-theorist, has a way of avoiding exempli-fication; but to follow this out would land us deep within the bowels of hisontology with its commitment to nonexistent objects, the Identity of Indis-cernibles, and other controversial theses. Suffice it to say that foundationismis reasonably rejected, and that it is therefore reasonable to hold to Bradleysview that relatedness requires relations.

Premise (1) thus stands up well under scrutiny. Relatedness requires rela-tions, which must be universals. Relations are therefore not exhausted in theirrelating of what they relate, and so are sufficiently distinct from what theyrelate to engender the problem of how they can form fact-unities with theirterms.

5. Ad Premise (2): Could a Relations Actual Relating of its Relata be a BruteFact?

According to premise (2), the something more, the contingent fact-makingtogetherness which distinguishes a fact from the mere sum of its constituents,requires an ontological ground. But why must there be a ground? Why cantthe difference between the fact and its constituents be a brute fact? Equiva-lently, why cant Rs actual relating of a and b be a groundless, inexplicableultimate? Van Inwagen takes the brute factview: The fact that a given exter-nal relation holds between two objects, therefore, has to be a kind of brute

36 Grossmann, op. cit., p. 161.37 Ibid.


or ultimatefact.38 This implies that the difference between a fact and its con-stituents is a brute fact and so has no explanation. So van Inwagen would rejectpremise (2) with its demand for an ontological ground. Surely there must besome brute facts somewhere in the World?39

Nevertheless, I believe there is good reason to accept premise (2), a reasonthat does not require the truth of any version of the principle of sufficient rea-son (PSR).40 Let us first reflect on what is implied by saying that the differ-ence between a fact and its constituents is a brute fact.41 For the difference tobe a brute fact is for it not to have an ontological ground. To say this is to saythat there is nothing internal or external to the fact that unifies its primary con-stituents.42 Nothing internal to the fact: there is no special unifying constituentsuch as a relation of exemplification, a non-relational tie (Strawson) or anexus (Bergmann) whose office is to tie the primary constituents into a factand which succeeds in faithfully executing the duties of this office. Nothingexternal to the fact: there is no unifier of a facts constituents outside of thefact, such as the synthetic activity of a transcendental consciousness (and ofcourse a fact cannot unify itself, a point to which I shall return). To say thatthe difference between a fact and its constituents has no ground, then, is to saythat the unity of the facts constituents has no unifier, either internal to the factor external to it. There is unity but no unifier; connectedness but no connec-tor.

But there are reasons to be uneasy with this. I will present three arguments(A1, A2, and A3) why unity demands a unifier, and then argue (A4) that onemay admit brute facts while also holding that unity demands a unifier: paceRussell, Bradleys argument (at least as here interpreted) does not presupposeany version of the principle of sufficient reason.43

38 Van Inwagen, op. cit., p. 37.39 Ibid., p. 37.40 Van Inwagen and others reject PSR for what I take to be a bad, or at least inconclu-

sive, reason. See my On an Insufficient Argument against Sufficient Reason, Ratio, vol. 10,no. 1 (April 1997), pp. 76-81.

41 Since fact is getting quite a work-out in this paper, perhaps brute givenis prefer-able to brute fact. But Ill stick with the latter expression trusting that no one including theauthor will become confused. Note, however, that if Rs relating of a and b is a brute fact, itdoes not follow that aRb is a brute fact, even though Rs relating of the two individuals in ques-tion is the fact, aRb. For this fact may well have a causal explanation in terms of some otherfact or facts. I will have more to say about this below when I distinguish between empirical andontological brute facts.

42 In our example, a, R, and b are primary constituents; any further constituents invokedto tie together the primary ones are secondary. Thus a relation of exemplification would be asecondary constituent, and so would any non-relational tie one cares to introduce.

43 Cf. Bertrand Russell, art. cit., p. 374.


A1. The first argument aims to show that the brute fact view, according towhich the unity of a facts constituents has no unifier, issues in a contradic-tion, namely the contradiction that a fact both is and is not a whole of parts.This contradiction will be taken to show, not that there are no facts, but thatthe brute fact view of facts is mistaken. Accordingly, the unity of a facts con-stituents must have an ontological ground.

A fact is a whole of parts in that there is nothing in it but its parts. For afact is a complex, and a complex is composed of constituents. Analysis of aRbcan yield nothing beyond a, R, and b. A fact is not a whole of parts in that theexistence of the parts does not entail the existence of the whole. Thus a fact ismore than the mere sum of its parts. This more is something real, and yet itcannot be, or be grounded in, any further constituent of the fact. Thus one nat-urally concludes, along with Hochberg44 and Armstrong,45 that a fact is anentity in addition to its constituents, an entity irreducible to them. The diffi-culty with this is that it seems to be a contradiction to say of a whole that it isan entity in addition to its parts when it is composed of them. It is not helpfulto say that facts are special unmereological wholes, for this does not eliminatethe suspicion of contradiction. I share David Lewis intuition that unmereo-logical comnposition is a contradiction in terms.46 But can the contradic-tion be evaded?

One might be tempted to say that there is no contradiction because althougha fact is a whole of its primary and its secondary parts, it is not a whole of itsprimary parts. We have already seen why this wont work: a + R + b + EX (orNEX) does not add up to a fact. Thus, although it is true that a fact is not awhole of its primary parts, it is also not a whole of its primary and secondaryparts. The contradiction remains: a fact, being a complex, is a whole of its pri-mary and secondary parts and, being a unity, it is not a whole of its primaryand secondary parts.

Thus the contradiction is genuine since both limbs are self-evident. It isself-evident that a fact, being a complex, is composed of its constituents andis thus nothing more than them. But it is also self-evident that a fact, being theunity of its constituents, is more than its constituents. Faced with this contra-diction, we must either deny the existence of facts altogether, thus setting asidethe very appealing truth-maker argument, or look beyond facts to something

44 Herbert Hochberg, Thought, Fact, and Reference: The Origins and Ontology ofLogical Atomism (Minneapolis: University of Minnesota Press, 1978), p. 339: Facts must,therefore, be recognized as existents in addition to constituents of facts.

45 David Armstrong, A World of States of Affairs, op. cit., p. 118.46 David Lewis, Critical Notice of Armstrong, D. M., A Combinatorial Theory of

Possibility, Australasian Journal of Philosophy, vol. 70, no. 2 (June 1992), p. 213.


that can remove the contradiction. Note also that to deny the existence of factsis to deny the existence of external relations. For a relation cannot exist with-out relating (which is not to be confused with the falsehood that a relation can-not exist without relating the very items it does in fact relate), and what is con-stituted by such relating is just that which we mean by a fact or state of affairs.Hence, anyone who denies the existence of facts will presumably have to holdthat there can be relatedness without relations, a view we found fault with inour defense of premise (1) supra.

We can avoid this denial of facts if we are prepared to recognize an exter-nal unifier upon which facts depend for their unity and thus their existence(the existence of a fact being just the unity of its constituents). If there is anexternal unifier, then we can reconcile both the proposition that a fact is notan entity in addition to its constituents with the proposition that it is a unity ofits constituents. For with an external unifier we can accommodate the unity ofa facts constituents without treating the fact itself as an entity in addition toits constituents. In this way, we remove the contradiction. Actually, what weare doing is showing that what are logical contradictories (A fact is a wholeof parts, A fact is not a whole of parts), on the assumption that facts are inde-pendent reals, self-existent structures, are logical contraries (A fact reducesto its constituents, A fact is an entity in addition to its constituents), on theassumption that facts depend for their existence on an external unifier distinctfrom them and their constituents. Logical contraries can both be false; thus itis false both that a fact reduces to its constituents, which reduction cannotaccommodate unity, and that a fact is in addition to its constituents, which can-not accommodate a facts being a complex.

Thus we can argue that the brute fact view is mistaken as follows. Factsexist, by the truth-maker argument. But if the unity of a facts constituents isa brute fact (if the difference between a fact and its constituents lacks an onto-logical ground), then facts are contradictory structures and do not exist. There-fore, the unity of a facts constituents is not a brute fact. Unity demands a uni-fier. Since the unifier cannot be internal, and since no fact can unify itself,which would be the fact-theoretic equivalent of causing oneself to exist, theunifier must be external. The possibility of an external unifier (a possibility tobe elaborated upon later and defended against objections) gives us good rea-son to reject the brute fact view of facts. This completes our first argument forpremise (2) in the master argument.

A2. Consider two facts, (F1) aRb and (F2) cR*d, which have no constituentin common.

On the brute fact view, each is a connectedness of constituents without aconnector responsible for the connectedness. And yet each fact is precisely


a fact, which suggests that they have the universal being a fact (facthood) incommon. Now this is puzzling. If F1and F2 have no constituent in common,then facthood is not a common constituent; how then do we explain the cir-cumstance that they are both facts? How do we explain the common categor-ial status? Realist ontologists cannot suddenly go nominalist at this point.There must be something in reality, i.e., something extralinguistic, thataccounts for the sameness of F1 and F2 in point of their being facts, and thattherefore grounds the applicability of fact to both of them. The two factssurely cannot be wholly ontologically disjoint: they both exist, and they bothexist as facts. This is no problem for the ontologist who posits a special uni-fying constituent in both; he can say that they are both facts because one andthe same constituent such as the exemplification nexus ties their respective pri-mary constituents into facts. Both are facts because both have the same fact-making constituent which is a universal, or at least has the one-many fea-ture.47 But one cannot say this if one says that the togetherness of primaryconstituents is a brute fact. For that implies the denial of any special fact-mak-ing constituent. How then do we explain what all facts have in common justinsofar as they are facts? Could that be a brute fact? Could it just happen tobe the case without ground that F1 and F2 are both facts? Obviously not; thatwould amount to saying that they have nothing in reality in common. Plainly,they are both facts because they exhibit the same ontological structure: eachis a unity or togetherness of fact-appropriate constituents. Since it cannot bea brute fact that F1 and F2 are both facts, the difference between either andthe sum of its constituents cannot be a brute fact.

A3. We just considered a case in which two facts share no constituent, andyet are both facts. The argument was that there must be an ontological groundof this commonality. Now consider the opposite case in which two facts shareall constituents. Is such a case possible? My third argument proceeds as fol-lows: (i) If the difference between a fact and its constituents is a brute fact,then it is possible that two facts share all constituents. (ii) But it is not possi-ble that two facts share all constituents. Therefore, (iii) the difference betweena fact and its constituents is not a brute fact; it has an ontological ground.

To see that (i) is true, consider that if the difference between fact and con-stituents is a brute fact, then there is no constituent, indeed nothing at all, inwhich this difference resides. So the difference must be that a fact just differsholus bolus from its constituents, despite the circumstance that a fact is entirelycomposed of its constituents (Isnt this just incoherent? The fact, not being

47 For Gustav Bergmann, exemplification, though not a universal, has the one-manyfeature. See his New Foundations of Ontology (Madison: University of Wisconsin Press,1992), p. 78.


entailed by the constituents, is something in addition to them; and yet, beinga complex, it is wholly composed of them! It is easy to sympathize with DavidLewis claim that such an unmereological composition is a contradictionin terms.48 But with this we are back to argument A1 supra). So if the dif-ference between a fact and its constituents is a brute fact, a facts being a factis what distinguishes it from its constituents. But then it should be possible fortwo distinct facts to share all constituents. For if a facts being a fact is whatdistinguishes it from its constituents, then a facts being a fact is what ulti-mately distinguishes it from other facts even if there also happens to be a dif-ference in constituents. Each fact, just in virtue of its being a fact, differs fromevery other fact. The difference becomes a brute difference unaffected by thediffering facts constituents. (Compare: each thin particular, just in virtue ofbeing a thin particular, differs from every other thin particular regardless ofwhether or not the differing particulars agree in the properties they exemplify.)And so if the difference between a fact and its constituents is a brute fact, thenit is possible that two distinct facts share all constituents. So (i) is true.

But surely it is not possible that two distinct facts share all constituents. Afact is a complex; a complex is composed of its constituents; it is thereforeimpossible to see how two complexes can differ without a ground to their dif-ference. For example, two sets cannot differ unless they differ in an element;two sums (fusions), unless they differ in a part. There cannot be two or morenull sets, since there is nothing that could distinguish them. Similarly for mere-ological sums. Consider a bicycle and (the sum of) its disassembled parts. Herethe ground of difference is obviously not a further part. But it doesnt followthat the bicycle and its unassembled parts are just distinct without anythingthat makes them distinct. The distinctness is due to an external entity, anassembler. A ground of difference need not be a part or constituent. We maytherefore hazard the generalization that no two complexes can differ withouta ground of difference whether this be a constituent or an external entity. Thisstrikes me as an intuitively evident principle. Now if two facts differ, they can-not differ in respect of the ground of their unity, for this is the same for both.Therefore, they must differ in a constituent.

One might counter this with the assertion that facts are an exception or elsea counterexample to the intuitively evident principle: it is just the nature ofthese critters to differ whether or not any constituent makes the difference. Insupport of this one might adduce apparent cases in which two facts differ with-out differing in a constituent. Where R is a non-symmetrical relation, loves for

48 David Lewis, Critical Notice of David Armstrongs, A Combinatorial Theory ofPossibility, Australasian Journal of Philosophy, vol. 70, no. 2 (June 1992), p. 213.


example, aRb and bRa, which are clearly different facts, seem to differ with-out differing in a constituent. If there are complexes that differ without differ-ing in a constituent, perhaps the difference between a fact and its correspon-ding sum is but another instance of this. Indeed, in one place Armstrong arguesfor states of affairs or facts from the premise that there are complexes that dif-fer without differing in a constituent.49 Since aRb and bRa (R either non-symmetrical or asymmetrical) are different states of affairs that share all con-stituents, they differ only by being different states of affairs. Hence we requirestates of affairs in our ontology.50

This is not a satisfactory argument for states of affairs. For one thing, it isquestion-begging.51 And as Armstrong later came to realize under the influ-ence of Reinhardt Grossmann, it is not at all clear that our two relational factsdo not differ in a constituent.52 Arguably, ...R--- is different from ---R.... Non-symmetrical and asymmetrical relations have a directionso that, e.g., xs lov-ing y is distinct from ys loving x. These are two different relations. Thus thereis something internal to the two states of affairs that distinguishes them; theydo not just differ as states of affairs.

With the concession to Grossmann, Armstrong loses an independent rea-son for accepting states of affairs as unmereological compositions (but a badreason is one well lost). He is thrown back upon the truth-maker argument asthe sole support for non-reductionist (non-supervenient) states of affairs. It istherefore puzzling when he writes that If we have to choose between the (intu-itively quite attractive) Nominalist principle [a system is nominalistic ... ifno two entities are generated from exactly the same atoms.] and the truth-maker argument that leads us toward states of affairs, then my judgment is thatthe truthmaker principle is by far the more attractive.53 Well, they are bothattractive, and there is no need to choose between them. To reject the notionthat facts supervene upon their constituents, it is not necessary to hold thatfacts can differ without differing in a constituent; it is only necessary to graspBradleys point that a fact is more than its constituents. It is consistent to main-tain both that (a) facts are more than their constituents and (b) facts cannot dif-fer without differing in a constituent. Indeed, I claim that both (a) and (b) are

49 D. M. Armstrong, A World of States of Affairs, In Philosophical Perspectives 7(1993), pp. 430-431.

50 Ibid., p. 431.51 As Herbert Hochberg points out in Facts and Classes as Complexes and as Truth

Makers, The Monist, vol. 77, no. 2 (1994), p. 187. Or at least it appears to be question-beg-ging. One cannot know the premise (aRb and bRa differ without differing in a constituent) tobe true without knowing the conclusion (States of affairs exist) to be true.

52 D. M. Armstrong, A World of States of Affairs, pp. 121 ff.53 Ibid. p. 122.


true. Armstrong may be confusing two different senses of unmereological. Iffacts are unmereological in the sense that the existence of their constituentsdoes not entail their existence, it does not follow that facts are unmereologi-cal in the sense that two facts can differ without differing in a constituent.

The upshot is that it is unintelligible to suppose that two distinct complexesjust differ as a matter of brute fact. So (ii) is true: it is not possible that twofacts share all constituents. Hence by Modus Tollens, (iii) the differencebetween a fact and its constituents is not (and we may add: cannot be) a brutefact. Equivalently, it cannot be a brute fact that a relation holds between oramong its relata. There is need of an explanation, not so much of why the rela-tion holds, but of how it is possible that it holds.

To sum up: A2 showed that if the difference between a fact and its con-stituents is a brute fact, then there is no accounting for the facthood of facts,for what is common to them. But then we are left in darkest ignorance as tothe very nature of facts. A3 showed that if the difference between a fact andits constituents is a brute fact, then there is no accounting for the differencebetween any two facts. The difference between any two facts becomes a brutedifference which allows distinct facts to share all constituents. Both conse-quences are unacceptable. What is needed is both a ground of the facthood offacts, as well as a ground of the difference between any two facts. The exter-nal unifier, as the ground of what is common to facts as facts, ensures thatfacts cannot differ as facts, and so must differ in a constituent.

At the root of both A2 and A3 is the essentially Bradleyan thought thatfacts, dependent as they are on relations, are contradictory structures whentaken by themselves as independent reals. This thought was articulated in A1.From this we may infer that if there are facts, then they must have an ontolog-ical ground; the unity of a facts constituents cannot be a brute fact. To arriveat this conclusion all we need are facts (supplied by the truth-maker argument),the recognition that taken as independent reals they are self-contradictory, andthe logical acumen to infer that they therefore depend for their existence on acontradiction-removing ontological ground external to them.

A4. But if the difference between a fact and its constituents is not a brutefact, are we thereby committed to saying that there are no brute facts at all,that the principle of sufficient reason is true? To answer this question we needto make some further distinctions.

If an external relation R relates a and b, but does not relate c and d, thenone question call it Q1 is: Why does R hold between the members of thefirst pair, but not between those of the second? Perhaps van Inwagen is rightthat the answer to this question is that it is just a brute fact that the relationholds in the one case but not in the other. But note that Q1 presupposes that


R does in fact connect a and b; it presupposes in other words that there existsthe fact aRb and thus that there are external relations. It presupposes that theconstituents form a fact-unity, and thus can form such a unity. You cannot sen-sibly ask why a relation holds unless it does hold. Q1 therefore begs the ques-tion against Bradley who is out to deny that there are external relations in ulti-mate reality. So Q1 is not Bradleys question. He cannot be charitablyinterpreted as asking a question a presupposition of which is that he is com-mitted to the negation of his own thesis.

The other question in the vicinity call it Q2 is: How is it possible for anumber of fact-appropriate constituents a, R and b in our example to con-stitute a fact in the first place?54 To ask how it is possible for there to be anyfacts at all is clearly different from asking, of any fact presupposed to exist,why it exists. The how of possibility is different from the why of actuality. Q2is the more radical of the two questions impugning as it does the very possi-bility of facts as independent reals.

Suppose we delve a bit further into this. Since Q1 presupposes that aRbexists as a unitary structure in which R has done its work of relating the terms,the answer to Q1 can only proceed by finding another fact that is the empiri-cal cause of aRb, or else by denying that there is any such further fact, i.e., byholding that aRb is a brute fact. Let us say that a fact lacking an empiricalcause (a causefor short) is an empirical brute fact. Suppose we grant to vanInwagen that there are empirical brute facts, e.g., a photons passing throughslit A rather than slit B. This amounts to granting that the principle of suffi-cient reason is false, something van Inwagen holds in any case.55 But if a factis an empirical brute fact, it does not follow that it is an ontological brute fact.A brute fact of the latter stripe is one that is categorially immune to either hav-ing or lacking an empirical cause but does lack an ontological ground. Forexample, there is no ontological ground of the numerical difference betweenany two of Armstrongs thin particulars, or any two of Bergmanns bare par-ticulars: they just differ. Such differences are ontological brute facts. It wouldmake no sense to say that they are empirical brute facts for the simple reasonthat they are categorially debarred from either having or lacking an empiricalcause. They are situated at a level deeper than that of empirical causation/lackof causation. Causation is plausibly taken to link facts; hence what is involved

54 One referee finds this a strange question to ask in the context of realism about facts.But it is a strange question only if one fails to see that said realism does not imply that factsare irreducible sui generis entities in addition to their constituents. Indeed the central point isthat, although we need facts to serve as truth-makers, facts cannot be independent reals on painof contradiction (see A1 above) and so depend for their existence on something external tothem.

55 Van Inwagen, op. cit., pp. 104 ff. For a critical discussion, see my article, On anInsufficient Argument against Sufficient Reason, op. cit.


in the very constitution of facts (thin particulars, universals, nexus, etc.) liesdeeper than empirical causation. By contrast, the sameness of color of two redspots has an ontological ground in the presence of one and the same universalin both spots. The universal grounds, but does not cause, the sameness of colorin the two spots. Presumably the sameness of color also could have an empir-ical cause: I might have painted them both red.

The point of the distinction between empirical and ontological brute factsis that aRb may well be an empirical brute fact without being an ontologicalbrute fact. It may lack a cause there may be no other fact that stands in thecausal relation to it but have a ground: there is an entity that unifies the factsconstituents and so assembles them into a fact. Causation is horizontal;grounding is vertical: causes and grounds do not compete. But if a fact (tobe precise: the unity of a facts constituents) lacks a ground, then the fact wontexist and so wont be in a position to cause or be caused. A ground of a factis a ground of its existence (the unity of its constituents); a cause of a fact can-not be a cause of its existence. This is because the causal relation like anygenuine relation cannot obtain unless both its relata exist. Since the exis-tence of two facts is a precondition of their standing in the causal relation toeach other, empirical fact or event causation cannot be causation of existence.In contrast, for the relation of ontological grounding to obtain, only one ofthe terms need exist and can exist. If the grounded term exists independentlyof the grounding relation, then it is precisely not grounded in the groundingrelation but presupposed by it. The grounding relationis not strictly a rela-tion any more than the intentional relation is: if I am in an intentional statevis--vis x, it doesnt follow that x exists. Quine can want a sloop whether ornot there exists a sloop he wants. Thus unifier Us grounding of fact F is nota relation to F, but at most a relation to Fs constituents: it operates upon themto produce F. Since F is produced (caused to exist), U is not related to F. If Uwere related to F, Bradleys problem would arise once again.

The operator schema: U = F1, where U is an ontological opera-tor that operates upon an ordered triple of fact-appropriate constituents, pro-vides a way of answering Q2 and showing how it differs from Q1. Thus theanswer to Q2 would be that the constituents form a fact because (ontologically)operator U operates on them (I am not saying or implying that this answer isunproblematic; I am merely illustrating an ontological ground). A condition ofthe possibility of there being facts is that there exists the ontological operatorU, which is of course not an empirical cause. Consistent with giving thisanswer, one can either say that F1 is a brute fact in the sense that there is nofact G such that G causes F1, or that F1 does have an empirical cause. Thisdemonstrates how Q2 cuts deeper than Q1.


Once we see that Bradleys question is best construed as Q2 rather than Q1,we are in a position to see that premise (2)s demand for an ontological groundof the difference between a fact and its constituents is a demand for an accountof the very possibility of facts. Clearly this demand cannot be satisfied byclaiming that aRb is an empirical brute fact. For even if that is so, it does notfollow that it is an ontological brute fact. It therefore seems that Bradleys argu-ment can be mounted without assuming the Principle of Sufficient Reason. Itis consistent with a denial of this principle. Russell take note! Furthermore, anempirical brute fact is a fact; but it is the possibility of this that needs to beunderstood and so cannot be assumed. For if facts are not possible, then thetogetherness of their constituents can neither have nor lack an empirical expla-nation. One begs the question against Bradley if one argues from the actual-ity of facts to their possibility without addressing the difficulties inherent intheir possibility.

To sum up this section, what I have argued is that the difference between afact and its constituents requires an ontological ground. I have also argued thatthis demand for an ontological ground is not to be confused with the demandthat every fact have an empirical explanation. There may well be empiricalbrute facts. But if aRb is an empirical brute fact, it does not follow that it isan ontological brute fact. I have shown that it cannot be an ontological brutefact.

6. On the External Unifier and Whether it Avoids the Bradley Regress

There are facts according to the truth-maker argument. Since the unity of afacts constituents cannot be a brute fact, this unity must derive from a unifier.Since the unifier can be neither internal to the fact nor the fact itself (as weshall see more clearly below), the unifier must be external. So from the exis-tence of facts we may infer the existence of an external unifier U on whichthey depend for their existence. As we shall see in section 8 below, this exis-tential dependency suffices to make facts appearances in Bradleys sense.

It is perhaps not strictly necessary for the limited purposes of this paperthat I give a theory of U. But if I dont say a bit more about it, the reader maybe left wondering whether the same Bradleyan objection that can be broughtagainst an internal unifier can also be brought against an external one. In show-ing how U avoids the Bradley regress, I will be concomitantly showing oneway the theory of U could be developed.

Formally, U is an ontological operator. Among other things, this impliesthat U is no sort of property. A property by definition is an exemplifiable entity.So if U were a property, then facts would be facts by exemplifying this sup-


posed property. But a fact cannot exemplify a property unless it is already (log-ically speaking) constituted as a fact; hence that which unifies its constituentsand thus constitutes it as a fact cannot be a property. Once a fact is on hand,and only then, is it in a position to exemplify properties; but what needsaccounting for is the move from constituents to fact, and clearly that feat can-not be accomplished by any property if we are to avoid vicious circularity.56

Furthermore, given that exemplification is a relation, or at least relation-like,it seems that a vicious regress threatens this property theory of the unifier. ButIll leave the details of this second objection as an exercise for the reader.

Since U cannot be a property, an exemplifiable entity, U is perhaps bestthought of as an ontological operator57 or as having the formal properties ofone. Accordingly, U operates upon a set or perhaps an ordered n-tuple of fact-appropriate constituents to produce a fact. There would then be three items todistinguish, operator, operand, and product: U = F1. This schemaallows us to accommodate both the insight that a fact is something more thanits constituents as well as the insight that facts qua facts have something incommon. What they have in common is the unifying operator U; the some-thing moreis the unity or togetherness of constituents in each fact that is pro-duced by U and is therefore distinct from U. U is common (universal) thoughnot in the manner of a property while the togetherness in each fact is in eachcase a particular. Since the unity of constituents in F1 is produced by U, U isnot related to F1. In particular, U is not related to F1 by the relation of exem-plification (If U were related to F1, F1 would have to exist as a preconditionof its standing in this relation; but then F1 would not be a product of Us uni-fying activity).

How then does the postulation of external U avoid Bradleys problem? Ifan internal unifier gives rise to the problem, why shouldnt an external one doso as well? Apparently, there will still be the problem of how U connects withwhat it unifies given the contingency of the connection. If the differencebetween the fact aRb and the mere sum a + R + b demands an ontologicalground distinct from these constituents, then why doesnt the differencebetween U and U + demand an ontological ground distinctfrom this second sum of items? So the question remains as to the ontologicalground of the difference between U and U + .

56 This argument has the same structure as Hector-Neri Castaedas argument to the con-clusion that particularity (individuality) cannot be a property. For suppose it were a property.Then it would be related to particulars by first-order exemplification, which is an external con-nection between properties and particulars. Since that presupposes that particulars are already(logically speaking) constituted as particulars, it cannot be in virtue of exemplifying any prop-erty that particulars are particulars. See his Individuation and Identity: A New Look,American Philosophical Quarterly, vol. 12, no. 2 (April 1975), p. 137.

57 Though not necessarily in Castaedas sense. Ibid., pp. 138-140.


The better to appreciate the difficulty, recall that I found fault with theAlexander-Blanshard line that the business of a relation is to relate on theground that it issues in a dilemma. For taken in one way, it implies that exter-nal relations are essential to their terms, which is absurd, since that wouldentail that there are no contingent relational facts. But taken in the other way,as boiling down to the plausible claim that there are no uninstantiated rela-tions, it fails to explain the difference between a relations relating specificrelata and its failing to do so. Now if this dilemma is decisive against Blan-shard, why isnt it decisive against my operator theory? Isnt a contingentlyunifying unifier strictly analogous to an externally relating relation? What isaccomplished by introducing an operator to do the work of a relation?

The dilemma my operator theory appears to face is as follows: If Us beinga unifying unifier (as opposed to an inert item that in turn needs unificationwith what it unifies) means that U necessarily unifies the sets of fact-appro-priate constituents that it does unify, then the facts that result will be neces-sarily existent which contradicts their being contingent. If, on the other hand,it remains contingent that U unifies the sets of constituents that it does in factunify, then how can U be a unifying unifier, one for which the differencebetween U qua unifying the members of set S, and the mere sum, U + the mem-bers of S, cannot arise? Thus it may appear that the preceding operator rig-marole makes no advance at all over the Alexander-Blanshard position.

But it does make an advance if we are willing to construe U robustlyenough. U must satisfy three constraints: (i) the connection between U and itsoperand must be contingent and so cannot be grounded in the nature of U; (ii)the connection cannot be brute, and so must have a ground; (iii) the groundmust lie in U itself on pain of a vicious infinite regress. Now if the connec-tion between U and its operand cannot be grounded in the nature of U, and yetmust be grounded in U, then U must have the power of contingent self-deter-mination: it must have the power to contingently determine itself as operatingupon its operand. In other words, if U is the ground of the contingent unity ofa facts constituents, then U contingently grounds its grounding of the unity ofthe facts constituents.

A model for U that satisfies the above constraints is available in our ownfreedom which of course is a power of contingent self-determination.58 Sup-pose I freely unify disparate elements in the synthetic unity of one conscious-ness: I judge that a is F, or perhaps I merely entertain the thought that a is F.The connection instituted is contingent; both the connection between the sub-ject and predicate representations, and the connection between me and the

58 I am assuming a libertarian theory of freedom of the will.


judgemental content. The connections are contingent since I could haverefrained from combining the representations. But the connections are notbrute since they have a ground in my combining activity. This satisfies the firsttwo constraints.

As for the third constraint, my consciousness C, as the unifier of the sub-ject- and predicate-representations, is not an inert ontological ingredient thatitself needs unification with what it unifies. It is not as if there must be a Cwhich unifies a, C, and F-ness, a C which unifies a, C, C, and F-ness andso on into a vicious infinite regress. A Bradley-type regress cannot arise pre-cisely because C is a unifying unifier in a way in which a relation cannot be.An external relation is not exhausted in its relating of what it relates, else itwould be essential to its terms and hence not external. But if it is not exhaustedin its relating of what it relates, then it is distinct from them and the problemarises as to how it forms a unity with its terms. You cannot say that a relation,in relating its relata, relates itself to them in such a way that it grounds not onlytheir togetherness, but also its togetherness with them. For no relation has thepower of contingent self-determination. But this is exactly the power con-sciousness exercises when it unifies disparate representations: it establishestheir togetherness, and in so doing, establishes its togetherness with them.

Thus the difference between U and U + is grounded byU itself in a way that an external relation R cannot ground the differencebetween aRb and a + R + b. This of course requires that we impute to U thepower of contingent self-determination, a power for which we have a model inour own self-consciousness in the synthesis of a manifold, to put it in Kantianterms.

What I have just offered is a mere illustrative sketch of how one might givesubstance to the notion of an ontological ground, and in a way that avoidsBradleys regress. This is one way to go, perhaps not the only way. We maynow comfortably acquiesce in the soundness of the above arguments to theconclusion that the difference between a fact and its constituents cannot be abrute fact.

I conclude that one cannot have a particular unity of fact-appropriate con-stituents without a unifier (a ground of unity); one cannot have a case of con-nectedness without a connector. Without a ground of unity there is no account-ing for what is common to all facts just insofar as they are facts. Without sucha ground there would be no accounting for the nature of facts. And obviously,no fact can be its own connector: no fact can connect its own constituents intoa fact. That would suggest the absurd schema: F1 = F1. A fact thatoperates upon its own constituents to be a fact is like a god who causes him-self to exist (I note en passant that this is not the charitable reading of causa


sui; the charitable reading takes it as synonymous with necessary being).There must therefore be something common to all facts which is the univer-sal ground of the unity of their constituents. This is the ontological ground ofthe difference between a fact and its constituents. The operator theory sketchedabove is just one way of cashing this out. I am not endorsing it; it was adducedfor illustrative purposes. The point is simply that there must be some groundor other. This completes the argument for the thesis that the difference betweena fact and its constituents cannot be a brute fact.

7. Ad Premises (3) and (4)

Premise (3) states that there is nothing in the natures of the terms or in thenature of the relation that can ground the relations holding between the terms.Sufficient support having been given for this above, I proceed to premise (4)according to which the difference between fact and constituents cannot begrounded in any further constituent on pain of a vicious infinite regress. Thistoo I think is pretty obvious from what has been said above. But perhaps a bitmore discussion is required, since one could hold that what connects a, R, andb in our example, or a and F-ness in the simple monadic case, is a non-rela-tional tie, which, being non-relational, does not sire a regress.

Accordingly, one might hold with Gustav Bergmann that exemplificationis a non-relational tie or nexus where A nexus does not need a further entityto tie it to what it ties....59 Exemplification ties directly. But as I suggestedabove, this move mislocates (dislocates?) the bone of contention. For let it begranted that exemplification is a non-relational tie or nexus, call it NEX, andthat this nexus does not spawn a regress. There will remain the problem ofaccounting for the difference between as being F and the sum, a + F-ness +NEX. Thus the problem is not primarily one of blocking a regress, but one ofensuring the unity of a facts constituents. If you try to do this with exempli-fication relations, you get for your trouble a vicious infinite regress. But if youtry to do it with a non-relational tie, you avoid the regress, but are left with theunity problem.

It might be thought that the unity problem cannot arise on Berg

on bradley's regress

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