“Bradley’s Regress” is an umbrella term for a familyof arguments that lie at the heart of the ontological debateconcerning properties and relations. The original arguments werearticulated by the British idealist philosopher F. H. Bradley, who, inhis workAppearance and Reality (1893), outlined threedistinct regress arguments against the relational unity of properties.Bradley argued that a particular thing (a lump of sugar) is nothingmore than a bundle of qualities (whiteness,sweetness, andhardness) unified into a cohesivewhole via a relation of some sort. But relations, for Bradley, weredeeply problematic. Conceived as “independent” from theirrelata, they would themselves need further relations to relate them tothe original relata, and so onad infinitum. Conceived as“internal” to their relata, they would not relatequalities at all, and would also need further relations to relate themto qualities. From this, Bradley concluded that a relational unity ofqualities is unattainable and, more generally, that relations areincoherent and should not be thought of as real.

In the decades since its original formulation by F. H. Bradley,“Bradley’s regress” has come to refer to a widervariety of arguments. This diversification has happened in two maindirections: (i) with respect to the ontology that the argumenttargets; and (ii) with respect to the argument-type presented. (i)Bradley’s original arguments targeted a one-category ontology ofqualities, whereby the “qualities” Bradley seemed to havein mind were unrepeatable particularized properties ortropes. The same argument form, however, has been usedagainst the one-category ontology of qualities conceived as multiplyoccurring universals, as well as against the two-category ontology ofparticulars and universals. In fact, one of the most commonly citedversions of Bradley’s regress in contemporary ontological debatechallenges the possibility of appealing to relations to unifyparticulars (such as electrons, apples, chairs) with their respectiveproperty universals (negative charge,roundness,blackness). The argument aims to show that any appeal to arelationR (of instantiation, exemplification, etc.) torelate a particulara with its universalF willrequire a further relationR′ to relate the particulara, the universalF, and the relationR; andso onad infinitum. (ii) In contemporary literature,“Bradley’s regress” has been associated with anumber of arguments and problems that are not, in the way they areposed, strictly regress arguments. Some of these take the form of thegeneralproblemabout unity, i.e., the question ofthe ontological ground of the unity of a bundle of tropes/state ofaffairs as opposed to the sum/list/set of their constituents. Othersare after an explanation ofhow relations relate, i.e., thequestion of what it is about relations that makes them apt to relatedistinct relata. Still others are after an explanation oftheexistence of specific unified complexes, i.e., the questionof what makes it the case that a number of constituents of the rightkinds areactually connected so as to form an existingfact/state of affairs/bundle of tropes.

In the face of these Bradleyan arguments, philosophers have had avariety of replies. Some have opted for arejectionist routewhich involves questioning the very assumptions that Bradley’sarguments make and consequently refusing to reply to the arguments asstated (for instance, Russell, Blanshard, Alexander, and Grossman haveargued that it is a job of relations to relate and thatBradley’s relational regresses cannot get started ifrelations’ relating role is taken seriously). The majority ofphilosophers, however, have accepted some form of the Bradleyanargument and replied in one of the following ways: 1) by appealing toa non-relational tie to relate the relata (Bergmann, Strawson,Armstrong); 2) by invoking external relations in possession of somespecial features which make them better apt to relate their relata(Meinertsen, Vallicella, Maurin, Weiland and Betti); 3) by describinga special sort of mutual inter-dependence of the would-be relata(Frege, Baxter, Simons, Perovic); 4) by claiming simply that thecomplex entities themselves (such as states of affairs or facts) actas unifiers of their own constituents (Olson, Armstrong); and 5) byarguing in favor of the benign nature of an infinite regress(Armstrong, Orilia).

This entry starts with a historical background of Bradley’sregress arguments.Section 1 opens with an outline of some ofthe historical precursors of Bradley’s regress arguments inancient, medieval, and modern philosophy. It then presents in somedetail the regress arguments as they were formulated by Bradley inAppearance and Reality (1893), as well as Bradley’slater concerns with complexes and relations.Section 2discusses the two types of extensions that Bradley’s regressarguments have undergone—with respect to the ontology that theyapply to, and with respect to the exact sort of problem in view.Section 3 presents six common types of replies that can befound in the literature surrounding Bradleyan problems. AndSection 4 concludes by describing some of the recentapplications of the regress arguments in the literature on grounding,composition of objects, and unity of the proposition.

• 1. Historical Background
  • 1.1 Precursors of Bradley’s Regress
  • 1.2 Bradley’s Regress Arguments inAppearance and Reality (1893)
  • 1.3 The Bradley-Russell Debate About Relations and Complexes in 1910/1911
  • 1.4 Bradley’s Remarks on Relations in his Posthumous “Relations” (1926)
• 2. Extensions of Bradley’s Regress Arguments
  • 2.1 Bradley’s Regress vs. One and Two Category Ontologies
  • 2.2 The Regress and Associated Problems
• 3. Replies to Bradleyan Arguments
  • 3.1 Rejectionism
  • 3.2 Non-Relational Ties
  • 3.3 External Relations with Special Features
  • 3.4 Mutual Interdependence of Constituents
  • 3.5 The Brute Fact Approach
  • 3.6 Benign Infinitism
• 4. Further Applications of Bradley’s Regress
• Bibliography
• Academic Tools
• Other Internet Resources
• Related Entries

1. Historical Background

1.1 Precursors of Bradley’s Regress

The most notable ancient regress argument that is associated withBradley’s is found in Plato’sParmenides 132a-b.Therein Plato presents an argument that has come to be known as theThird Man Argument (TMA), which challenges an explanation ofsimilarity between distinct particulars that appeals to forms.Following Vlastos (1954), the regress can be reconstructed asexhibiting the following structure:

1. a,b andc are all large because thereis a Form of largenessL that they all participate in.
2. a,b,c andL are all largebecause there is a Form of largenessL₁ that theyall participate in.
3. a,b,c,L andL₁ are all large because all of them participatein a Form of largenessL₂, and so onadinfinitum.

It is commonly assumed that at least three theses underlie thisargument. The first one is “the one over many” whichstates that many things havingL in common must be explainedby the existence of the formL that all of them participatein. The second premise is implicit and it has been called the premiseof “non-self explanation”; it simply assumes, that inexplaining whata,b,c andL havein common one cannot appeal to theL itself, but needs toappeal to adifferent form of largeness,L₁. The third premise which is implied in thisargument is “the self-partaking” premise; it assumes thatthe formL is itselfL, i.e., that the form oflargeness is itself large.

It has been debated at great length amongst the Plato scholars whetherthe Third Man Argument is to be understood as a metaphysical or as anepistemic argument, an argument about the postulated entities or anargument about what is involved in our knowledge of them. (For anentry point on literature concerning the Third Man Argument, as wellas the dialogue more broadly see the entry onPlato’sParmenides). Similarly, there has been much disagreement about which of the thesesthat underlie theTMA Plato was willing to give up in orderto avoid the regress. To a modern reader the“self-partaking” premise seems like an obvious candidate,since it is quite odd to think that the form of largeness is itselflarge, the form of smallness itself small, etc.

Plato’sTMA featured prominently in Aristotle’sPeri Ideon and was later picked up and discussed by medievalphilosophers. For instance, Boethius in hisSecond Commentary onPorphyry’s Isagoge discusses a peculiar infinite regressthat could be seen to echoTMA, though it is described as aninfinite series of genus ascriptions. (See Spade (1994: 22) for anEnglish translation of the text).

Henninger (1989) has individuated arguments by certain orthodox Muslimtheologians, the Mutakallimun, that seem to resemble closelyBradley’s regress. Apparently, they believed relations to bepurely subjective, and argued that positing relations asmind-independent entities would lead to an infinite regress. Accordingto Henninger (1989: 110), a version of this argument can also be foundin Harclay, Ockham, and Aureoli.

Perhaps the closest precursor of Bradley’s regress arguments isto be found in Leibniz. Mugnai (2010) has drawn attention to andtranslated the following passage from a text dated “December1676” written during Leibniz’s stay in Paris:

Suppose, for example, that there is a relation betweena andb, and call itc; then, consider a new relationbetweena andc: call itd, and so forth tothe infinite. It seems that we do not have to say that all theserelations are a kind of true and real ideas. Perhaps they are onlymere intelligible things, which may be produced, i.e., that are orwill be produced. (Mugnai 2010: 1)

As we will see shortly, this passage very closely resembles the firstof the three regresses discussed by Bradley (1893).

1.2 Bradley’s Regress Arguments inAppearance and Reality (1893)

Bradley’s original formulation of the regress arguments can befound in chapters II and III of hisAppearance and Reality(1893). Bradley starts the discussion in chapter II on“Substantive and Adjective”, by taking as an example alump of sugar. He notes that there appears to be such athingas a lump of sugar and thisthing appears to have qualitiessuch aswhiteness,sweetness, andhardness.But—asks Bradley – what is this “thing” thatbears properties? On the one hand, he thinks it is odd to assume thatthere is something to the lump of sugar beside its several qualities,thus implying that postulating a property-less bearer of properties isincoherent. On the other hand, he notes that the lump cannot merely beits qualities either, since the latter must somehow be united. ForBradley, unity or “coexistence” of qualities presupposesrelations, which is why he next turns to examine different conceptionsof relations.

One at a time, Bradley examines relations conceived as attributes of asingle thing; relations conceived as attributes of two or more terms;and relations conceived as entirely “independent” of theirrelata.

The trouble with the conception of relations as attributes of a singlething or attributes of two or more things comes down, for Bradley, tothe more general problem of predication. The problem, according tohim, is expressed by the following question: “what is it that wedo when we predicate a property of a thing?” Bradley arguesthat

if you predicate what is different, you ascribe to the subject what itisnot; and if you predicate what isnot different,you say nothing at all. (Bradley 1893:17)

To understand what Bradley means by this, we need to keep in mind thathe is here presupposing a bundle view of particulars and that he isusing “is” to indicate the identity of the subject withthe bundle of qualities (see Wollheim (1959), Bonino (2012) and Baxter(1996) for an interpretation that reads his “is” as an“is” of identity in this context). His concern is thuswith the relationship between the whole, conceived as a bundle ofqualities, and the qualities themselves. He is worried that if a givenquality, sayblackness, isdifferent from the whole,andseparate from it (i.e., it is not in the bundle ofqualities that constitutes the lump of sugar), then it is wrong toattribute it to the whole. But if the quality, saywhiteness,is not distinct from the whole, but just a part of the bundle, thenthe attribution does not add anything new at all, it trivially stateswhat is already the case.

Equally troubling, for Bradley, is the conception of relations as“independent” from their terms. Indeed, it leads to thefirst of the infinite regresses that Bradley discusses in these pages.He writes:

Let us abstain from making the relation an attribute of the related,and let us make it more or less independent. ‘There is arelationC, in whichA andB stand; and itappears with both of them.’ But here again we have made noprogress. The relation C has been admitted different fromAandB, and no longer is predicated of them. Something,however, seems to be said of this relationC, and said again,ofA andB. And this something is not to be theascription of one to the other. If so, it would appear to be anotherrelationD, in whichC, on one side, and, on theother side,A andB stand. But such a makeshiftleads at once to the infinite process. (Bradley 1893: 18)

In this famous passage, Bradley does not make it sufficiently clearwhat exactly generates the infinite regress. He also shifts betweenthe linguistic worry about “something being said” ofrelationC and relataA andB, and the moresubstantial ontological worry about the unity of qualitiesA,B, and the relationC conceived as“independent” from relata. Despite this, it seems clearthat for Bradley it is the assumedindependence of therelationC that generates the problem. An independentrelation is, according to him, incapable of relatingA andB, and no amount of further independent relations can do thejob either, thus generating the regress that has the followingstructure.

Regress 1 –against “independent”relations as unifiers of qualities

1. Suppose that there is an independent relationC, in whichqualitiesA andB stand.
2. Independent relations are different from their relata and as suchcannot relate.

   ---

3. Therefore, an independent relationC cannot relateA andB.
4. New relationD is needed to relateC,A, andB.
5. D is an independent relation.

   ---

6. From 2, 4 and 5, it follows thatD cannot relateC,A, andB.
7. A new relationE is needed to relateA,B,C, andD. And so onadinfinitum.

For this argument to have some force, Bradley needs to argue insupport of his conception of “independent” relations asrelations that cannot relate. Although he offers no such argument, hedoes give us a clue as to what “real” relations ought tobe like:

If it [relation] is to be real [i.e., actually relating], it must besomehow at the expense of the terms, or, at least, must be somethingwhich appears in them or to which they belong. A relation betweenA andB implies really a substantial foundationwithin them. (Bradley 1893: 18)

This suggests that for Bradley, “real” relations have tobe in some way ontologically grounded in their relata. Since his“independent” relations are not conceived as grounded intheir relata in such a way, they cannot relate.

Bradley’s “real” relations might sound likeinternal relations to a contemporary ear. Internal relations,following Armstrong (1989: 43) and Lewis (1986: 62), are oftencharacterized as relations that supervene on the intrinsic propertiesof their relata and that present no ontological addition. Commonexamples of such relations aretaller than,being thesame shade of blue,having the same mass. In contrast,external relations are frequently understood as relations the holdingof which does not depend on the intrinsic features of particulars thatthey relate; they present a genuine ontological addition (fordifferent ways of understanding the internal/external discussion seeSection 1 of the entry onrelations). Frequently cited examples of external relations are spatio-temporalrelations such asbeing 2 feet apart, etc. Thus, in thecontemporary debate, the question concerning whether or not relationsexist turns on the question of whether or notexternalrelations exist (internal ones are considered an “ontologicalfree lunch”). But for Bradley, it is the other way around:according to him, the only relations that stand a chance at being“real” are the ones that are ontologically founded in theterms, the internal ones. The peculiar way that such relations arefounded in their terms for Bradley, becomes central for the secondregress, which we find in chapter III ofAppearance andReality.

Chapter III focuses on the relationship between qualities andrelations. The conclusion of the overarching argument in that chapteris that the entire relational way of thought is unintelligible andflawed. Bradley arrives at this conclusion by arguing first thatqualities need relations; he then tries to prove that qualities areunintelligible with relations; and finally, he argues the same forrelations—i.e., that relations need qualities but areunintelligible with them.

Bradley’s starting thesis in this chapter is that qualitiesneed relations. He assumes that without relations qualitieswould just collapse into an indistinguishable blob; thus qualities, inorder to exist, need relations to somehow separate them out from thatblob, i.e., to act as difference-makers. In addition, qualities needrelations to unify them. Thus, the demand on relations is to act asboth distinction-makers and as unifiers of qualities. Qualities, ontheir part, also have a “a double character as both supportingand as being made by the relation” (Bradley 1893:26). Qualitiesaremade by relations through relations’difference-making role, but qualities also need to be related into aunified whole.

For Bradley, as we saw above, only internal relations stand a chanceof being “real”^[1] and, subsequently, of doing the double duty just described. At thesame time,Bradley’sinternal relations (fromnow on,internal_B relations) are meant to begrounded in theproper parts of qualities (see more below onthis peculiar understanding of relations). But if different properparts of a quality are to be truly different, they must bemadedifferent by some additional internal relations. The latter, intheir turn, must be grounded in further different proper parts ofparts of qualities. This “process of fission”, as Bradleycalls it, continuesad infinitum, thus generating the secondinfinite regress of relations in these pages, and providing Bradleywith the alleged “proof” that qualities standing inrelations are unintelligible.

Regress 2 –against internal_B relationsas unifiers of qualities

1. Relating relations areinternal_B in the sensethat they are grounded inparts of qualities that theyrelate.
2. Qualities need relations to differentiate them from otherqualities.
3. Qualities need relations to unite them with other qualities.

   ---

4. From (1) and (2), it follows that a given qualityA musthave a parta, which is part of the ontological ground forthe difference-making relationR_d, i.e., it is apart on which the distinctness ofA from other qualities isbased.
5. From (1) and (3), it follows that qualityA must have apart α, which is part of the ontological ground for the unifyingrelationR_u, i.e., it is a part on which the unitywith other qualities is based.
6. Partsa and α of qualityA aredifferent.
7. Difference within parts of a quality requiresinternal_B relations.
8. Each of the original parts ofA, namelya andα, must have a part that grounds the distinction ofafrom α, saya′ and α′, respectively,as well as a part that grounds the unity ofa with α,saya″ and α″, respectively.
9. But the partsa′ anda″ are distinctand yet unified; and so are α′ and α″. Thus,each of these parts must have further parts that ground suchdistinctness and unity. And so onad infinitum.

The main work in this regress is being done by premises (1), (2), and(3). It is thus quite unfortunate that Bradley does not spend timesubstantiating them. This is especially needed when it comes to hispeculiar interpretation of internality of a relation as being groundedin proper parts of qualities. For why not claim that the quality inits entirety can act as part of the ground (the other part being theother quality or qualities) for different internal relations? Thiswould certainly be more in keeping with the contemporary understandingof internality of a relation and it could stop the regress. To thissuggestion, Bradley would probably respond by reiterating theunintelligibility of the idea that the very same quality can serve aspart of an ontological ground for distinctness from other qualitiesas well as part of an ontological ground for the unity withother qualities. In response to this, one could challengeBradley’s reliance on the assumption that relations need toaccount for difference between qualities, as well as for their unity.In fact, it would be much simpler to claim that, say,whiteness andsweetness are different not becausethere is a difference-makingpart in them, but simply becausethey are, in their entirety,intrinsically different.Intrinsic difference of qualities could be Bradley’s bottomline, a primitive of the theory and it would eliminate the need forrelations as difference-makers, thus rejecting premise (2) above.

One possible interpretation (see Perovic 2014: 381) of why Bradleydoes not wish to take distinctness of qualities as ontologicallyprimitive is that he might already be presupposing a primitive whichis contrary to it—a monistic undifferentiated whole. From suchmonistic perspective, it would then seem that differentiation ofqualities would need an explanation and an ontological ground, whereasthe lack of differentiation would appear to be an ontological default,requiring no explanation at all. However, although this interpretationwould help us understand better why Bradley might have assumed thatrelations need to act as difference-makers for qualities, it iscertainly not terribly charitable to Bradley; that is, it would assumethat Bradley had already question-beggingly presupposed monism as thedefault ontological position in his argumentsagainstrelations.

Finally, let’s consider the third and final regress broughtforward by Bradley in chapter III. After claiming that relations areunintelligible without qualities, he wants to show that the wayrelations stand to qualities is equally unintelligible. He writes:

If it [relation] is nothing to the qualities, then they are notrelated at all; and, if so, as we saw, they have ceased to bequalities, and their relation is a nonentity. But if it is to besomething to them, then clearly we now shall require anewconnecting relation. For the relation hardly can be the mere adjectiveof one or both of its terms; or, at least, as such it seemsindefensible. And, being something itself, if it does not itself beara relation to the terms, in what intelligible way will it succeed inbeing anything to them? But here again we are hurried off into theeddy of a hopeless process, since we are forced to go on finding newrelations without end. The links are united by a link, and this bondof union is a link which also has two ends; and these require each afresh link to connect them with the old. (Bradley 1893:27–28)

The regress presented here is somewhat similar to the one expressed inRegress 1 above. In both cases relations are assumed to beincapable of relating. InRegress 1, however, Bradleyexplicitly targeted only the “independent” relations.Here, Bradley is assuming the results of his previous arguments, andattackingall relations, i.e., relations as such.

Regress 3 –against relations as such as unifiersof qualities

1. Suppose that there is a relationR uniting qualitiesA andB.
2. IfR is nothing toA andB, they arenot related.
3. IfR is something toA andB, thenR itself is something.
4. IfR is something itself then it cannot relate and needsfurther relations, such asR′ to relate it toA andB.
5. The same process is then repeated withR′ andfurther relations,ad infinitum.

In this regress, Bradley is employing the phrases “being nothingto the qualities” and “being something to thequalities,” but he doesn’t explain what he means by thesephrases. If, however, Bradley is to be consistent with his previousclaims, relations that are “nothing to the qualities” haveto be hisinternal_B relations which he dismissedwithRegress 2, and relations that are “something tothe qualities” have to be his “independent”relations which he dismissed withRegress 1. We should thusread premise (2) inRegress 3 as follows: ifR is aninternal_B relation,A andB willend up not just not related, but will instead end up in the infiniteprocess of division, as seen inRegress 2. If, on the otherhand,R issomething toA andB,as in premise (3) inRegress 3, it itself has to besomething—that is, it is, in Bradley’s terminology anon-internal, “independent” relation. And“independent” relations, as we have seen inRegress1, cannot relate and no amount of further independent relationscan relate either.

After presentingRegress 3, Bradley believes that he hassucceeded in showing that the entire relational way of thought isflawed and that relations as such should be relegated to the sphere ofappearance, rather than to reality. Central to arriving at such aconclusion has been his assumption that what he calls“independent” relations cannot relate. It seems as ifBradley simply did not know how to think of such entities and oftenresorts to metaphors and talks about links needing further links attheir ends and insists on our inability to show how “solidthings” can be joined to other “solids” (cf. Bradley1893: 28). As these metaphors indicate, Bradley’s worry seems tobe that if relations are conceived of as independent from the termsthat they relate, they themselves will become just like the terms thatneed relating and this way they will lose their relating power.

1.3 The Bradley-Russell Debate About Relations and Complexes in 1910/1911

Bradley’s arguments against relations gained a differentdimension during his debate with Russell in the journalMind,during 1910–1911. At this point, Bradley is no longer concernedjust with arguments against the relational unity of qualities; rather,he is concerned with the possibility of there being complex unitiesthat cannot be analyzed.

By the end of his paper “On Appearance, Error, andContradiction” (1910), Bradley challenges Russell to explain howhe can reconcile his pluralism of terms and external relations withhis commitment to complex unanalyzable entities which have terms andexternal relations as constituents. He writes as follows:

I encounter at the outset a great difficulty. Mr. Russell’sposition has remained to myself incomprehensible. On the one side I amled to think that he defends a strict pluralism, for which nothing isadmissible beyond simple terms and external relations. On the otherside Mr. Russell seems to assert emphatically, and to use throughout,ideas which such a pluralism surely must repudiate. He throughoutstands upon unities which are complex and which cannot be analysedinto terms and relations. These two positions to my mind areirreconcilable, since the second, as I understand it, contradicts thefirst flatly. If there are such unities, and still more, if suchunities are fundamental, then pluralism surely is in principleabandoned as false. (Bradley 1910: 179)

Bradley thinks that a pluralist who postulates two fundamental simpleentities cannot also admit a thirdfundamental entity whichis complex, i.e., constituted out of the simple entities. There is atension which must be resolved by either letting go of thefundamentality of the simples (the view that Bradley would have optedfor); or by letting go of the fundamentality of complexes (the viewthat Bradley thinks a consistent pluralist should embrace). But thereis a further way that the tension might be resolved, and this is byarguing that simples and complexes are fundamental in different sensesof the term “fundamental”. (For different senses offundamentality in this context see Perovic (2016) who distinguishesbetweenconstitutive, explanatory, andexistentialfundamentality.)

Russell’s own reply to Bradley focused on clarifying the sensein which he claimed that complex unities cannot be analyzed. He wroteback the following:

It would seem that everything here turns upon the sense in which suchunities cannot be analysed. I do not admit that, in any strict sense,unities are incapable of analysis; on the contrary, I hold that theyare the only objects that can be analysed. What I admit is that noenumeration of their constituents will reconstitute them,since any such enumeration gives us a plurality, not a unity. But I donot admit that they are not composed of their constituents; and whatis more to the purpose, I do not admit that their constituents cannotbe considered truly unless we remember that they are theirconstituents. (Russell 1910: 373)

In this reply to Bradley, Russell is taking care to point out that heis using the term “analysis” to designate a processperformed byus of “discovery of the constituents ofthe complex” (Russell 1910: 374). This signifies a departurefrom his claims in thePrinciples of Mathematics, where heargued that propositional unities could not be analyzed becauseanalysis would destroy the unity of the proposition (Russell 1903:50–51). This shift in the understanding of the notion of“analysis” from ontological breaking down of unities tosomething thatwe perform when we are discoveringconstituents of complex entities, allows Russell to say that complexesare the only objects thatcan in fact be analyzed.

In addition, Russell pinpoints his disagreement with Bradley when itcomes to relations. Russell explicitly rejects the view which favorsinternal relations, that is, which holds “that the factthat an object x has a certain relation R to an object y impliescomplexity in x and y, i.e., it implies something in the‘natures’ of x and y in virtue of which they are relatedby the relation R” (Russell 1910: 373–374). Instead,Russell states his support ofexternal relations, the holdingof which cannot be derived from the terms that such relations relateor their intrinsic complexity. Instead, when we have x and y standingin an external relation R, we then have a complex or a unityxRy. What distinguishes such a complex from a “mereaggregate”, according to Russell, is that a relation in aunified complexrelates whereas in an aggregate it does notrelate and is just a member of an aggregate.

Russell’s reply was unsatisfying to Bradley, who followed upwith his “Reply to Mr Russell’s Explanations” in1911, reiterating some of the same concerns. Namely, Bradleyrepeatedly returns to the worry about external relations—hefinds them to be unobservable and unthinkable without the terms; arelation apart from its terms is indeed for Bradley an“indefensible abstraction”. In addition, he asks Russellto elaborate further on the presumed difference between an aggregateof entities and a unity of those entities. Bradley says that an appealto relating relations is unsatisfying and further asks Russell toexplain wherein the difference between relating relations andnon-relating relations lies for him. But for Russell there was nofurther story to be told; the difference between relating andnon-relating relations is a primitive on which he did not feel theneed to offer any further details.

1.4 Bradley’s Remarks on Relations in his Posthumous “Relations” (1926)

Between 1923 and the first part of 1924, Bradley returned to the topicof relations. He was working on an article that he intended to publishinMind, the first part of which was posthumously madeavailable in hisCollected Essays vol.2, under the simpletitle “Relations”. This manuscript is significant becauseBradley is, on the one hand, restating in a slightly different waywhat he takes to be the most salient arguments from his previous worksand, on the other hand, expanding his attack on relations.

Thus, we find again his regress argument against external relations,motivated by his assumption that such relations cannot relate;external relations are, he writes, no more than “mereabstractions” from relational facts and as such hold no relatingpower (Bradley 1926: 643). Internal relations are no improvement, andBradley rejects as untrue any suggestions that he might have wanted toaccept them (642). The true problem seems to be that “an actualrelation […] must possess at once both the characters of a‘together’ and a ‘between’, and, failingeither of these, is a relation no longer” Bradley 1926: 644,634). Thus, just as in hisAppearance and Reality (1893),Bradley is demanding of relations that they fulfill both an“in-between role” (what I have called above adifference-making role)as well as the “together”role (what I have called the unifying role). Failing either of theseroles amounts to not being a true relation, which in turn makes thepresumed relational experience contradictory, for Bradley:

Relational experience must hence in its very essence beself-contradictory. Contradiction everywhere is the attempt to takewhat is plural and diverse as being one and the same, and to take itso (we must add) simply or apart from any “how”. And wehave seen that without both diversity and unity the relationalexperience is lost, while to combine these two aspects it has left toit no possible “how” or way, except one which seems eithercertainly less or certainly more than what is relational. (Bradley1926: 635)

As this often quoted passage illustrates, Bradley’s skepticismabout relations takes the form of the “how” question.Bradley’s “how” question is often read as“How do relations relate?”. But taking intoaccount the wider context, his question is actually“How might relations at the same time relateand diversify their relata?”. Failing to see howrelations might doboth, Bradley concludes that relationalexperience is marred by contradiction.

Finally, by the end of “Relations”, Bradley wishes to makeit clear that what is fatal to his monism is not just a specific typeof relations (such as asymmetric relations), but an ultimate realityofany kind of relation: “For not one kind of relation,but every and any relation, if taken as an ultimate reality, would (onany view such as mine) be fatal to Monism” (Bradley 1926: 649).This is an important reminder of Bradley’s own motivation forhis repeated arguments against relations.^[2]

2. Extensions of Bradley’s Regress Arguments

In the decades since Bradley’s original discussion inAR, “Bradley’s regress” has come to referto a wider variety of arguments. This widening of scope has happenedin two main directions: (i) with respect to the ontology that thearguments target; and (ii) with respect to the type of the argumentpresented. In this section we will take a closer look at both of theseextensions.

2.1 Bradley’s Regress vs. One and Two Category Ontologies

As we have seen in section 1.2 above, Bradley’s original regressarguments targeted a one-category ontology of qualities, whereby the“qualities” Bradley seemed to have in mind wereunrepeatable particularized properties, i.e.,tropes. But thesame argument form has been used against the one-category ontology ofqualities conceived as multiply occurring universals, as well asagainst the two-category ontologies of particulars and universals, aswell as particulars and tropes.

Bradley’s regress arguments apply easily to the one-categoryontology of universals. The same problem that Bradley articulated fortrope-like qualities can be articulated for universals: namely, whatis it that unites universals ofwhiteness,sweetness, andhardness into the particularlumpof sugar? If ordinary particulars such as lumps of sugar arenothing but bundles of universal qualities, it seems important toprovide an account of unity of such bundles. The challenge isparticularly difficult in the case of universals because, unliketropes, they are conceived as multiply occurring entities that arewholly present in each of their instances. Thus, the problem ofuniting a bundle of universals such aswhiteness,sweetness, andhardness will go hand in hand withthe problem of individuation of bundles of universals, i.e., theproblem of distinguishing between this particular bundle ofwhiteness,sweetness, andhardness andanother exact duplicate bundle ofwhiteness,sweetness, andhardness.

Bradley’s regress arguments have been most widely discussedwithin the context of the realists’ two-category ontology ofparticulars and universals. The challenge in this context is toprovide an ontological ground of unity of particulars and universals,and the worry is that any appeal to a relationR (ofinstantiation, exemplification, etc.) to unify a particularawith its respective property universalF sets off an infiniteregress of relations, similar to the regresses described by Bradley.In the light of this problem, some realists such as Olson (1987), andArmstrong (1997) have argued that it is a third entity – thefact orstate of affairs ofa being F thatprovides the ontological ground of unity ofa andFness as well as the truthmaker for the truth that“a isF”. According to critics (see, forinstance, Vallicella 2000 and 2002), this approach instead of solvingthe problem of unity of particulars and universals, merely reframes itas the one threatening the very possibility of there being suchentities as facts or states of affairs. Similar worries have arisenfor trope theorists that embrace a two-category ontology ofparticulars and tropes. Philosophers such as C.B. Martin (1980) andDaly (1997) have worried that an appeal to a relation ofinherence in the context of unifying a substratum and itsproperty trope would lead to an infinite regress of inherencerelations.

Finally, D.M. Armstrong (1979) has stated a regress argument similarto Bradley’s, as a threat to class nominalists. The thought isthat since class nominalists analyze particulars’ having ofproperties in terms of particulars’ membership in a class ofthings that all have those properties, they would incur a regress whentrying to define a membership relation. However, class nominalistslike Lewis (2002), have been adamant about not being committed to amembershiprelation of any sort; indeed, Lewis has arguedthat all we have is a “singular-to-pluralcopula:‘is one of’ as in ‘this is one ofthose’.” (Lewis 2002: 10, italics mine).

2.2 The Regress and Associated Problems

There are a number of problems that tend to be brought up in thecontext of discussing Bradley’s regress but that do not take theform of a regress argument. The three that stand out are: (1) theproblem of explaining what differentiates a unified complex entityfrom a mere aggregate of its constituents; (2) the problem ofexplaining how exactly it is that relations relate; and (3) theproblem of explaining how thespecific complex comes intoexistence.

2.2.1 The problem of explaining what differentiates a unified complex entity from a mere aggregate of its constituents

For a proponent of particulars, universals, and states of affairs,this problem takes the form of the following questions: what is theontological ground of the difference between the suma+F and the unified state of affairsFa? Itcould be the case that botha andF exist at aworld, and thus that the suma+F exists at such a world,without it being the case thatFa obtains (but, say,abeing G andb being F obtain). What then is the groundof such a difference? Similarly, what provides an ontological groundof the difference between the suma+R+b and the unified stateof affairsaRb? It might be the case that all threea,R, andb exist at a world, and hencethat their sum is given, without it being the case thataRbobtains (instead, say,aRc andbRd obtain). The samesort of question can be posed, of course, for other ontologies. Forinstance, for a trope bundle theorist the question will be: what isthe ontological ground of the difference between the sumF₁+G₁+H₁of property tropes and a unified trope bundle constituted out of them?(See Armstrong 1989, 1997; Vallicella 2000, 2002; Maurin 2010; andMeinertsen 2008, amongst others for such a formulation of theproblem.)

It must be noted that this problem takes it for granted: (i) thatmereological sums are unproblematic and a metaphysical default,whereas complexes are problematic and in need of an explanation; and(ii) that all kinds of entities (particulars, universal properties andrelations, tropes, etc.)can indeed be summed regardless ofwhether such entities can exist independently of others. Similarassumptions are made in formulations that make no reference tomereological sums but rather contrast lists, groupings, or sets ofentities with the unified complexes such as states of affairs orbundles of tropes.

Philosophers who pose the problem in these terms will often move on togenerate a regress argument for any attempt to explain the differencebetween a sum/list/set of entities and a unified complex that appealsto relations. The next question becomes: what will account for thedifference between a sum/list/set of entitiesa,F,and a relationR (of instantiation or exemplification) on theone hand, and a unified state of affairs ofa being F, on theother? The implication is that any addition of further relations willset off Bradley’s regress of relations, with no explanation insight (see in particular Vallicella (2000)).

2.2.2 The problem of explaining how relations relate

The question “How do relations relate?” can be traced backto Bradley (1926: 635), and it fuels much of the recent discussionsurrounding Bradley’s regress (see Simons 1994, Maurin 2010,Meinertsen 2008, Wieland and Betti 2008). But, as we saw in section1.4 above, Bradley’s “how” question was motivated byhis puzzlement over thedual role that he thought relationshad to fill; he saw them as having to distinguish between differentrelataand having to unify them. Thus his question was not somuch “how do relations relate?” but rather “how dorelations relateas well as differentiate theirrelata?”

In contrast, contemporary philosophers’ puzzlement over“how relations relate” stems from a different place. Theassumption in this case seems to be that unless some account of thenature of relations adequatelyexplains what makesthem apt to unite distinct relata, an appeal to relations as relatingentities is illicit. The type of explanation that philosophers areafter in this context often remains unspecified, though it is clearthat what is expected is not a causal explanation, but a metaphysicalexplanation of some kind. It is assumed that an adequate explanationwill refer to some special feature of relations that makes it possiblefor them to relate; absent such a feature, relations are usuallyconsidered to be relationally inert and Bradley’s regress ofrelations is reintroduced.

2.2.3 The problem of explaining the existence of a specific complex

This problem is usually brought out by contrasting it with the generalproblem of the existence of complexes. The question is not “whatis it that unifies states of affairs/bundles of tropes?” butrather “what is it that unifies this particular bundle ofwhiteness,hardness, andsweetness into alump of sugar?” and “what is it that unifies thisparticular chair and the universalblackness?”Vallicella puts the question, as it applies to facts, in the followingway:

What makes it the case that a number of constituents of the rightkinds—constituents which are connectable so as to form a factbut need not be connected to exist—areactuallyconnected so as to form an actual or existing fact? (Vallicella 2000:242)

(Note that a similar formulation of this problem can be found inMaurin 2010).

Vallicella and others who pose the question in these terms make itclear that they are not after a causal story about how a particularlump of sugar or a particular black chair was made. Instead, whatdrives the problem as posed is the assumed contingent nature of theconnection between constituents of states of affairs. This chair isblack but it might have been some other color; and this blackness, forrealists, need not be instantiated here, it might (and in factis) present in many other states of affairs. So what is itthat “makes it so” that this particular blackness and thisparticular chair areactually united? There is nothing in thenatures of constituents of states of affairs to require thatthey come together, so—the thought is – something elsemust bring those constituents together.

3. Replies to Bradleyan Arguments

In this section, we will take a closer look at different strategiesphilosophers have employed in engaging with Bradley’s regressarguments and the associated problems discussed above (I will be usingthe locution “Bradleyan arguments” to refer to both ofthese categories). The first fork in the road for philosophers hasbeen to either reject the argument by questioning one or more of theassumptions that the argument makes, or to accept and respond to theargument on its own terms. Those that have chosen the rejectionistapproach have mostly done so by challenging Bradley’s skepticismabout relations’ ability to relate their relata. Russell, Broad,Blanshard, Alexander, and Grossman have argued that it is a job ofrelations to relate and that Bradley’s relational regressescannot get started if relations’ relating role is takenseriously. Many more philosophers, however, have found Bradleyanarguments compelling and have responded in one of the following ways.They have appealed to: 1) some sort ofnon-relational tie ornexus to relate the relata (Bergmann, Strawson); 2) externalrelations equipped with special features (Meinertsen’sself-relating relations, Vallicella’s external relations withthe power of self-determination, Maurin’s and Weiland andBetti’s relata-specific relations); 3) the mutualinter-dependence of the would-be relata (Frege, Baxter, Simons); 4)complexes as brute unifiers of their constituents (Olson, Armstrong);and 5) the benign nature of the regress in question (Armstrong,Orilia).

3.1 Rejectionism

Rejectionists about Bradleyan arguments tend to question one or moreof the assumptions on which the argument rests. With respect to theregresses, rejectionists have mainly questioned the grounds ofBradley’s skepticism about relations and their relating role. Aswe have seen in section 1.3 above, Russell employed this strategy whendebating Bradley in the journalMind, in 1910. On thatoccasion, Russell argued in favor ofexternal relations andtheir relating role within complexes of the formaRb.^[3]

C. D. Broad (1933) also objected to Bradley for his treatment ofrelations; he thought that the main problem had to do withBradley’s treatment of relations as if they were particulars inneed of being related themselves. He wrote, rather harshly:

It is plain that Bradley thinks ofA andB as beinglike two objects fastened together with a bit of string, and he thinksofR as being like the bit of string. He then remembers thatthe objects must be glued or sealed to both ends of the bit of stringif the latter is to fasten them together. And then, I suppose, anotherkind of glue is needed to fasten the second drop of glue to the objectB on the one side and the string on the other. And so onwithout end. Charity bids us avert our eyes from the pitiablespectacle of a great philosopher using an argument which woulddisgrace a child or a savage. (Broad 1933: 85)

We find a very similar take on Bradley’s regress in Blanshard(1986). He arguedcontra Bradley that “R isnot the same sort of being as its terms. It is neither a thing nor aquality. It is a relation,and the business of a relation is torelate” (Blanshard 1986: 215).

More of the same can also be found in Alexander (1920 [1966], vol. 1,249, 256) and Grossmann (1992: 55–56). Though they are lessharsh than Broad and Blanshard in their assessment of Bradley’sregress arguments, they are unambiguous in their diagnosis of theproblem as one involving the wrong conception of relations. Accordingto Grossmann, for instance, the correct conclusion to draw fromBradley’s regress argument is that “it is really anargument not against relations, but against the assumption thatrelations need to be related to what they relate” (Grossmann1992: 55).

In recent debate, replies to Bradley’s regress that bluntlyinsist on relations’ relating role have been unpopular. This isbecause the debate has shifted to include the associated questionsoutlined in 2.2. above, including the question: “How dorelations relate?”. Thus, if one is after the answer to the“how” question, simply saying that it is the job ofrelations to relate is deemed unsatisfactory.

One sort of rejectionist reply to Bradleyan arguments can be found inPerovic (2014). Perovic (2014) argues that Bradley’s originalregress arguments inAR rest on unsubstantiated assumptionsand thus cannot be considered as successfulreductioarguments against relations. For example, the first regress takes forgranted that as long as unifying relations are conceived as“independent” from their relata, they cannot relate. Thesecond regress assumes that unifying of qualities cannot be achievedwith “internal” relations either; for the latter areunderstood as being grounded in proper parts of qualities, whichleads, according to Bradley, to an infinite regress. She points outthat it is not clear why Bradley understands internal relations asgrounded in proper parts of qualities that they relate, nor is itclear why Bradley believes that relations, if they are to have anystanding, ought to fill a dual role of unifying their relata as wellas providing the ground of their distinctness. Perovic (2014)concludes that without further support, Bradley’s originalarguments against relations as unifiers of qualities do not establishthe unreality of relations; an appeal to external relations asunifiers of their relata is still a perfectly acceptable option forboth realists and trope theorists.

3.2 Non-Relational Ties

A great number of philosophers have found Bradley’s regressarguments to be compelling as stated. Some, in fact, have taken theregress arguments to be so threatening, that they have concluded thatonly non-relational ties might be able to unify qualities. Strawson(1959: 167–170), for instance, has appealed to non-relationalties such asinstantial tie andcharacterizing tieto unify a particular with a sortal (such asdog) andcharacterizing universal (such aswisdom) respectively. Hethought of these ties as being more intimate relators than ordinaryrelations as well as allowing for greater heterogeneity between theterms they bind. Bergmann (1967: 9) famously appealed to anon-relational tie he called “nexus” and which heintroduced to tie the qualities directly, without mediation. Armstrong(1978: 110, 1989: 109) too embraced something he called a“non-relational fundamental tie” of instantiation.

Two objections are frequently brought against non-relational ties: (1)they are found to be more obscure than full-blooded relations; and (2)they are accused of not being able to stop the regress any more thanordinary relations do. Philosophers that find relations to besuspicious entities, tend to find non-relational ties even moresuspicious and obscure. They ask: How are non-relational tiesdifferent from relations? If they are meant to relate or“tie” their relata, are they not sufficiently likerelations? And if there was a problem with Bradley’s regress ofrelations in the first place, don’t we have the same problemwith non-relational ties? (Lewis (2002) has made similar remarksagainst non-relational ties in the context of discussing the problemof temporary intrinsics and the adverbialist reply to the problem.)Vallicella (2000: 241) has attacked non-relational ties by arguingthat even if the nexus manages to save Bergmann from the regress, theunity problem remains. The problem, as Vallicella sees it, thenbecomes thatnexus is sufficiently like a universal that itremains unclear what it is that unitesa,Fness, andnexus into a state of affairs as opposed to having a mere sumofa+Fness+nexus.

3.3 External Relations with Special Features

Philosophers impressed by Bradleyan arguments, but with the desire topreserve relations as unifiers of complex entities such as states ofaffairs or bundles of tropes, have been drawn towards postulatingrelations with certain special features. Convinced that relationsordinarily conceived would lead to a dangerous regress, thesephilosophers have tried to equip their relations with characteristicsthat would enable them to relate their relata and answer the“how do relations relate?” question.

For instance, Vallicella has argued in favor of an external unifyingoperator that connects a fact’s constituents and brings factsinto existence. This external unifierU is described as a“metaphysical agent” that acts as an “existencemaker” for facts (Vallicella 2000: 250); it does so due to“the power of contingent self-determination”, i.e., it has“the power to contingently determine itself as operating uponits operand” (Vallicella 2000: 256). In characterizingU in this way, Vallicella is trying to ensure both that theconnection betweenU and what it unifies remains contingent,and that such unity is grounded inU itself (out ofworry about the infinite regress). The only way that he can seeU fulfill both these roles is by construing it “alongthe lines of God or a transcendental consciousness” (Vallicella2000: 256). The trouble with this reply to Bradleyan arguments is, ofcourse, that the god-like creating role of the external unifierU remains quite murky and it seems to bring in consciousnessinto both the operator itself as well as the creation of states ofaffairs.

Another novel relation has been proposed by Meinertsen (2008). He hasargued for a self-relating relation to do the uniting of particularsand universals into states of affairs. According to this proposal,what makesR related to the pair (a,b) isa unifying self-relating relationU* which unitesitself toR,a, andb. Thus, astate of affairsR (a,b) turns out to beidentical to the state of affairsU* (U*,R,a,b) and a state of affairsFais just a short forU*(U*,F,a)(cf. Meinertsen 2008: 12). The self-relating relationU*occurs twice in the states of affairs it unites: the first time,outside the brackets,U* occurs in its “active”relating role; the second time, inside the brackets,U*occurs in its “passive” role as one of the constituentsbeing related (cf. Meinertsen 2008: 15).

All this evokes Russell’s talk of relations having dual nature,i.e., being able to occur as terms of relations as well as relatingrelations. The trouble with such dual roles, is to explain, as Bradleyasked Russell: “What is the difference between a relation whichrelates in fact and one which does not so relate?” (Bradley1911: 74). Or for Meinertsen: What is the difference between arelation occurring in its passive role and it occurring in its activerole? If we are willing to accept as a primitive that thereis such a difference and that it is thanks toU*’s dual role as a self-relating relation that it isable to unify constituents of a complexa,b, andR, then why exactly is such a view an improvement upon a viewthat takes it that a relating relationR simply relates itsrelata?

Weiland and Betti (2008) on the one hand, and Maurin (2010) on theother, have argued for relata-specific relations as unifiers of tropesin trope bundles (Weiland and Betti hint at a possible extension ofthis idea to relations unifying particulars and universals in statesof affairs). They have argued that the relational trope ofcompresence construed as asymmetrically dependent on specificrelata is the way to solve the Bradleyan unity problem. It is part ofthe very nature of the relation of compresence to relate specificrelata; thus, there would be a different compresence trope for eachspecific bundle of tropes. As Weiland and Betti put it:

If a relation is relata-specific, it necessarily relates its relata,butonly if it exists. To put it in possible-worldsterminology: ifR holds betweena andb inthe actual world, it holds betweena andb in allpossible worlds in whichR exists (and not in any possibleworld in whicha andb exist, or in any possibleworld whatsoever). (Weiland and Betti 2008: 519)

Hakkarainen and Keinänen (2023) have recently argued against therelata-specific relations as an adequate answer to Bradley’sregress. They worry that such relations are too complex and obscure todo the explanatory work required of them in the trope theoreticalframework.

3.4 Mutual Interdependence of Constituents

In “Function and Concept” (1891), Frege famously describeda concept-object distinction as a special case of thefunction-argument distinction. Concepts, according to Frege, wereunsaturated and incomplete entities, in need of completion by objects.Because of such natures of concepts and objects, the two wouldpresumably “fit” together without any intermediaries.

Taking a cue from Frege, some philosophers have argued in favor of atwo-sided dependence of constituents of states of affairs (and amany-sided dependence of property tropes in trope bundles) as anon-relational way of accounting for the unity of such complexes.Baxter (2001), for instance, has proposed that the unity of particularand universal should be analyzed aspartial identity. ForBaxter, both particulars and universals have “aspects”.Different instances of one and the same universal are differentaspects of a universal; spatial parts of particulars aretheir different aspects. Particulars and universals can bepartially identical by overlapping in their aspects. Baxterwrites:

Suppose Hume is a particular, Benevolence is a universal, and Hume isbenevolent. Then Hume has as an aspect, Hume insofar as he isbenevolent. Also Benevolence has as an aspect, Benevolence insofar asHume has it. These are the same aspect—Hume’s benevolence.(Baxter 2001: 454)

Hume’s benevolence in Baxter’s example is whatArmstrong calls astate of affairs. In fact, Armstrong wastemporarily swayed by Baxter’spartial identity view ofstates of affairs, but then went on to object to the view on thegrounds that partial identity cannot be merely contingent. Thus, forlater Armstrong, “once one has identity, even if only partialidentity, there will be found necessity” (Armstrong 2005: 317).A particular, thus,necessarily has all the properties thatit in fact has, and the universalnecessarily has theinstances that it has. This outcome secures the unity of particularsand universals but at a cost of embracing a strong version ofnecessitarianism.

Inspired by earlier Armstrong, Perovic (2016) has proposed anon-necessitarian dependence model for particulars and universals instates of affairs. On this model, the constituents of most states ofaffairs such asthis chalk being white exhibitmutualgeneric existential dependence. This simply captures the ideathat a particular piece of chalk presumably cannot exist withouthaving some color or other, it is generically existentially dependentupon some color universal. Similarly, the universalwhitenessisgenerically existentially dependent on some concreteparticular, for it cannot exist without inhering in some concreteparticular or other, but it need not be the particular piece of chalka. However, the state of affairsthis particular chalkbeing white exhibits the strongest kind of dependence on itsconstitutive particular and universal—namely, it seems toexhibitone-sided specific existential dependence on itsconstituents. The reason why specific states of affairs seem toexhibit such strong existential dependence, is because of the simplefact that any change in a particular or in a universal would bringabout a different state of affairs.

Simons (1994) put forward a similar proposal within the framework ofhis “nuclear theory” of tropes. He thinks of bundles oftropes as having different levels of unity. Property tropes that areessential to a particular are tightly woven through mutual dependenceon one another, whereas property tropes that are accidental are moreloosely dependent upon the tight bundle tropes in the nucleus.

One might find these sorts of proposals wanting since they onlycharacterize the types of dependence that hold between constituents ofunified wholes (whether they are states of affairs or nuclear bundlesof tropes). But, the objection goes, they do not account for thedifference between constituents considered outside of such unities andconstituents in a unified whole. Here, Perovic (2016) is happy toadmit that she is not trying to provide such an account in the firstplace. Following Armstrong, she takes the world to be exhausted bystates of affairs and takes particulars and universals to exist onlyin states of affairs.

3.5 The Brute Fact Approach

The term “brute fact approach” is slightly ambiguous. Itcan be identified with the rejectionist view sketched along the linesof 3.1 above, where to say that relations’ job is to relate isto take that fact about relations as primitive or “brute”.However, the expression, as it is used here, is intended to refer tothe view that takes complexes such as states of affairs or facts asunifiers of their own constituents. This view was defended by Olson(1987) and Armstrong (1989, 1997), and challenged by Vallicella(2000).

Olson finds that the upshot of Bradley’s arguments was not somuch areductio of relations, but to show that facts shouldbe taken as irreducible entities. The word “relation”, forOlson, is ambiguous between two senses: the first one is to designatean entity that can be multiply instantiated by various pairs ofrelata, whereas the second sense is to designate the fact ofrelatedness. In place of “relation”, Olson prefers theword “connection”, since it “can only mean beingconnected. There is not the same temptation to think of it as anadditionalthing that does the connecting. The connection isnot a constituent of the fact; it is the fact itself” (Olson1987: 61). Armstrong seems to have something similar to this in mindwhen he says that states of affairs “come first”. But thenhe also adds that they “hold their constituentstogether in a non-mereological form of composition, a form ofcomposition that even allows the possibility of having differentstates of affairs with identical constituents” (Armstrong 1997:118, italics added).

Vallicella (2002) has objected to this sort of brute fact approachthat it is mysterious and incoherent. He even accuses the proponentsof the brute fact approach as being committed to the followingcontradiction:

It is self-evident that a fact, being a complex, is composed of itsconstituents and is thus nothing more than them. But it is alsoself-evident that a fact, being the unity of its constituents, is morethan its constituents. Faced with this contradiction, we must eitherdeny the existence of facts altogether […] or look beyond factsto something that can remove the contradiction. (Vallicella 2002:20–21)

This objection, of course, presupposes that the only non-controversialform of composition is the mereological kind and that facts are“nothing more than their constituents”. Armstrong’sand Olson’s facts openly go against these assumptions: they areunities that are more than just the sum of their constituents. Butfailing to provide further ground for the difference between the sumand the fact makes such facts brute and unacceptable toVallicella.

3.6 Benign Infinitism

In the context of discussion of states of affairs as unifiers of theirconstituents, Armstrong anticipated Vallicella’s objection justdescribed. His reply was to claim that even if he had to concede thatit was necessary to introduce a relation or a “fundamentaltie” to account for the peculiar unity present in states ofaffairs, the resulting regress would not be vicious. In fact, such aregress would be closer to the benign truth regress—many truths,but only one truthmaker, just like with “p”, and “itis true that p”, and “it is true that it is true thatp”, etc. Treating the instantiation regress in the same way, wewould have the first instantiation relation uniting the constituentsof the state of affairs, but all further relations would supervene andnot present any further ontological addition.

Orilia (2006, 2007) develops this sort of response a bit further. Heagrees with Armstrong (1997) that Bradley’s regress is anexplanatory regress that is, in fact, benign. What makes it benign forOrilia is that at each step of an explanation the added fact explainsthe previous one via an additionalexternal relation. Heargues that despite it being the case “that at any given stagewe can continue the explanatory task”, it “doesnot show that no knowledge or no understanding is provided at anystage”. According to Orilia, this “merely shows that at nostage we know/understand everything that there is to know/understandabout theexplicandum that gives rise to the expalantorychain. And noting that theexplicandum in question gives riseto such an infinite chain may be considered part of our understandingof it” (Orilia 2007: 160).

Even if one were to grant Orilia that there can be infinite dependencechains of facts, for Maurin (2015) a crucial problem remainsunresolved. According to her, Orilia’s account does nothing toanswer what she calls the “how” question, i.e., thequestion “how can there be a situation in which thestate of affairsthat a is F exists?”. She argues thatthe infinitist’s reply already presupposes thatthereis unity of states of affairs before explainingwhat itsexistence depends upon—that is, a further state of affairs, etc.But the all-important “how” question, according to Maurin,remains unanswered.

4. Further Applications of Bradley’s Regress

Grounding. The metaphysical debate about the nature ofgrounding and metaphysical explanation has taken an interest inBradley’s regress from a different perspective. Here, the mainBradley-inspired issue has been whether or not it should be one of therequirements for a metaphysical explanation that it “must groundout”. The problem with Bradley’s regress in this contextis that it appears to be committed to an infinite chain of facts, eachone ontologically dependent on the subsequent one for its explanation.This is the situation described positively by Orilia (2006, 2007)above. The unity of a state of affairsFa is explained byappeal to another higher-order factR<Fa>, andthis one in turn is explained by appeal to a further factR′<R, <Fa>>, and so onad infinitum. However, Cameron (2008) has found such adependence chain to be very problematic. He believes that there is astrong intuition in favor of there being “a metaphysical ground,a realm of ontologically independent objects which provide theultimate ontological basis for all the ontologically dependententities, and a realm of basic facts which provide the ultimatemetaphysical ground for all the derivative facts” (Cameron 2008:8).

Cameron admits that it is hard to argue for this intuition by appealto a further, more basic metaphysical principle. Instead, he suggests,it can be supported by appeal to theoretical utility; a unifiedexplanation of the same sort of phenomenon seems preferable to aninfinite descending chains of separate explanations. In response toCameron, Orilia (2009) has pointed out weaknesses in Cameron’sappeal to a unified explanation as a way of supporting the thesis ofwell-foundedness of all chains of ontological dependence(WF); thus, Orilia has concluded thatWF cannot yethave a claim of being a contingent truth.

Another interesting question inspired by Bradley’s regressarguments, has been posed by Bennett (2011). Her question is: isgrounding itself fundamental? Prima facie, it seems that it canneither be fundamental, nor grounded. But if it is neither, then thegrounding would have to be rejected, which is an unattractive outcomethat Bennett does not want to embrace. Inspired by Armstrong’s(1989) discussion of the Bradley problem and relations ofinstantiation as internal and supervenient upon their relata, she thenexplores whether the grounding relation itself could be treated in asimilar fashion. There is one important difference: rather than havegrounding supervene on two or more relata, Bennett proposes that it betreated as a relation that supervenes upon only on the first relatum.Such a relation she calls “superinternal”.

Debate concerning the nature of metaphysical explanation and theconcept of grounding is quite prolific and ongoing. (For a detaileddiscussion see the entries onFundamentality and onMetaphysical Grounding.) What one must keep in mind when it comes to Bradleyan problems andgrounding is that the former debate is itself quite varied and withouta consensus on either the nature of the problem or the desiderata fora satisfactory solution. Thus, caution should be advised whenimporting conclusions from one contentious problem into the area ofanother even more abstract and contentious one.

Composition. Grounding considerations and Bradley’sregress have found their application in the discussion of the problemof composition of objects. Brzozowski (2008) has recently posed thefollowing question concerning the location of composite objects: doesthe location of a composite object derive from the location of itsproper parts, or not? (Brzozowski 2008: 193). Either way, Brzozowskitakes it that we get unappealing consequences. The first horn of thedilemma is thatif indeed the location of composite objectsis derived from their proper parts, the possibility of spatio-temporalgunk objects (composite objects whose parts are themselves compositeobjects) would have to be denied. If, on the other hand, the locationof composite objects is not derived from their proper parts, thenbrute metaphysical necessities connecting the location of compositeobjects with the locations of their proper parts must be posited.Brzozowski argues in favor of the first horn of the dilemma, and partof his argument relies on applying a Bradley-type argument to thelocation of gunk objects. His main thought is that there would be aserious problem of location of gunk objects since “even thoughat each level of the series of decomposition we can explain thelocation of a composite object by appealing to the location of aproper part, it is left unexplained howany object in theseries is located in space-time. Given the piecemeal story, there isno way for the totality of location relations to begrounded…” (Brzozowski 2008: 201). As we can see,Brzozowski here relies on some version of Cameron’sWFprinciple described above.

Philosophy of Language. Outside of the strictly metaphysicaldebates, Bradleyan arguments are often brought up when discussing theproblem of the unity of the proposition. This problem in philosophy oflanguage is usually put as follows: what is the difference between amere list of words such as “wise, Alice, is” and ameaningful sentence such as “Alice is wise”? The latterseems to possess a unity of some sort, but what is the exact nature ofsuch unity and how does it come about? In analogy with the ontologicalversion of Bradley’s regress, philosophers then worry that anappeal to a copula does not explain what it is that is special aboutthe unity present in “Alice is wise” and absent in a merelist. And no appeal to further copulas will help matters either.

There has been a tendency recently to view the problem of the unity ofthe proposition as a useful heuristic in interpreting views of Frege,Russell, and Wittgenstein. We can see this in Davidson’s (2005)posthumous work on truth and predication, where he often runs togetherthe ontological and the semantic versions of what he refers to as“the problem of predication”. More careful work on thisissue has been recently done by Gaskin (1995, 2008) and Collins(2011). The particularly obscure nature of the debate between Russelland Wittgenstein over Russell’s theory of judgment has lentitself to being interpreted as concerning the problem of the unity ofthe proposition. For such an interpretation see in particular Hanks(2007).

Philosophy of Perception. Skrzypulec (2019) has tried todevelop a perceptual version of Bradley’s regress. He notes thatour perceptual systems tend to easily distinguish between seeing a redsquare (Rs) and a green circle (Gc) in one instance, and a greensquare (Gs) and a red circle (Rc) in the other. Thecontentof our visual experiences is different in these two situations, andone way to characterize those differences is by appeal to distinctstates of affairs – in the first instance, we see Rs & Gcand in the second we see Gs & Rc. The more fundamentalconstituents of those states of affairs, however, are the same; eachstate of affairs has R, G, s, and c. So, Skrzypulec argues, thereneeds to be something to account for the difference between thesedistinct states of affairs and for our ease in perceptuallydistinguishing the two different visual contents. The metaphysicalaccount does not line up with the most recent accounts of lower- andhigher-level representations of visual content.

Similarly, Wiese (2017) has explored the problem of phenomenal unity– the problem of providing a phenomenological characterizationof the difference between phenomenally unified and phenomenallydisunified conscious experience – by analogy withBradley’s regress problem. He finds thesingle stateconception (SSC) of the unity of the phenomenal state to beunsatisfying and sketches other accounts worthy of exploration. TheSSC conception states that two events are experienced together just incase the corresponding phenomenal states are bothpart of asingle phenomenal state. This parthood relation is not sufficientlyclear, according to Wiese.

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