## 1. Historical Background


### 1.1 Precursors of Bradley's Regress



The most notable ancient regress argument that is associated with
Bradley's is found in Plato's *Parmenides* 132a-b.
Therein Plato presents an argument that has come to be knows as the
*Third Man Argument (TMA)*, which challenges an explanation of
similarity between distinct particulars that appeals to forms.
Following Vlastos (1954), the regress can be reconstructed as
exhibiting the following structure:


1. *a*, *b* and *c* are all large because there is a
Form of largeness *L* that they all participate in.
2. *a*, *b*, *c* and *L* are all large because
there is a Form of largeness *L*1 that they all
participate in.
3. *a*, *b*, *c*, *L* and *L*1
are all large because all of them participate in a Form of largeness
*L*2, and so on *ad* *infinitum*.



It is commonly assumed that at least three theses underlie this
argument. The first one is "the one over many" which
states that many things having *L* in common must be explained by
the existence of the form *L* that all of them participate in.
The second premise is implicit and it has been called the premise of
"non-self explanation"; it simply assumes, that in
explaining what *a*, *b*, *c* and *L* have in common one
cannot appeal to the *L* itself, but needs to appeal to a
*different* form of largeness,
*L*1. The third premise which is implied
in this argument is "the self-partaking" premise; it
assumes that the form *L* is itself *L*, i.e., that the form
of largeness is itself large.



It has been debated at great length amongst the Plato scholars whether
the Third Man Argument is to be understood as a metaphysical or as an
epistemic argument, an argument about the postulated entities or an
argument about what is involved in our knowledge of them. (For an
entry point on literature concerning the Third Man Argument, as well
as the dialogue more broadly see SEP's entry *Plato's
Parmenides*). Similarly, there has been much disagreement about
which of the theses that underlie the *TMA* Plato was willing
to give up in order to 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 itself
large, the form of smallness itself small, etc.



Plato's *TMA* featured prominently in Aristotle's
*Peri Ideon*, and was later picked up and discussed by medieval
philosophers. For instance, Boethius in his *Second Commentary on
Porphyry's Isagoge* discusses a peculiar infinite regress
that could be seen to echo *TMA*, though it is described as an
infinite series of genus ascriptions. (See Spade (1994: 22) for an
English translation of the text).



Henninger (1989) has individuated arguments by certain orthodox Muslim
theologians, the Mutakallimun, that seem to resemble closely
Bradley's regress. Apparently they believed relations to be
purely subjective, and argued that positing relations as
mind-independent entities would lead to an infinite regress. According
to Henninger (1989: 110), a version of this argument can also be found
in Harclay, Ockham, and Aureoli.



Perhaps the closest precursor of Bradley's regress arguments is
to be found in Leibniz. Mugnai (2010) has drawn attention to and
translated the following passage from a text dated "December
1676" written during Leibniz's stay in Paris:



> 
> Suppose, for example, that there is a relation between *a* and
> *b*, and call it *c*; then, consider a new relation between
> *a* and *c*: call it *d*, and so forth to the infinite.
> It seems that we do not have to say that all these relations are a
> kind of true and real ideas. Perhaps they are only mere intelligible
> things, which may be produced, i.e., that are or will be produced.
> (Mugnai 2010: 1)



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


### 1.2 Bradley's Regress Arguments in *Appearance and Reality* (1893)



Bradley's original formulation of the regress arguments can be
found in chapters II and III of his *Appearance and Reality*
(1893). Bradley starts the discussion in chapter II on
"Substantive and Adjective", by taking as an example a
lump of sugar. He notes that there appears to be such a *thing*
as a lump of sugar and this *thing* appears to have qualities
such as *whiteness*, *sweetness*, and *hardness*.
But--asks Bradley - what is this "thing" that bears
properties? On the one hand, he thinks it is odd to assume that there
is something to the lump of sugar beside its several qualities, thus
implying that postulating a property-less bearer of properties is
incoherent. On the other hand, he notes that the lump cannot merely be
its qualities either, since the latter must somehow be united. For
Bradley, unity or "coexistence" of qualities presupposes
relations, which is why he next turns to examine different conceptions
of relations.



One at a time, Bradley examines relations conceived as attributes of a
single thing; relations conceived as attributes of two or more terms;
and relations conceived as entirely "independent" of their
relata.



The trouble with the conception of relations as attributes of a single
thing or attributes of two or more things comes down, for Bradley, to
the more general problem of predication. The problem, according to
him, is expressed by the following question: "what is it that we
do when we predicate a property of a thing?" Bradley argues that




> 
> 
> if you predicate what is different, you ascribe to the subject what it
> is *not*; and if you predicate what is *not* different,
> you say nothing at all. (Bradley 1893:17) 
> 
> 
> 



To understand what Bradley means by this, we need to keep in mind that
he is here presupposing a bundle view of particulars and that he is
using "is" to indicate the identity of the subject with
the 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 thus
with the relationship between the whole, conceived as a bundle of
qualities, and the qualities themselves. He is worried that if a given
quality, say *blackness*, is *different* from the whole,
and *separate* from it (i.e., it is not in the bundle of
qualities that constitutes the lump of sugar), then it is wrong to
attribute it to the whole. But if the quality, say *whiteness*,
is not distinct from the whole, but just a part of the bundle, then
the attribution does not add anything new at all, it trivially states
what is already the case.



Equally troubling, for Bradley, is the conception of relations as
"independent" from their terms. Indeed, it leads to the
first 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 a
> relation *C*, in which *A* and *B* stand; and it
> appears with both of them.' But here again we have made no
> progress. The relation C has been admitted different from *A* and
> *B*, and no longer is predicated of them. Something, however,
> seems to be said of this relation *C*, and said again, of
> *A* and *B*. And this something is not to be the ascription
> of one to the other. If so, it would appear to be another relation
> *D*, in which *C*, on one side, and, on the other side,
> *A* and *B* stand. But such a makeshift leads at once to the
> infinite process. (Bradley 1893: 18)
> 
> 
> 



In this famous passage, Bradley does not make it sufficiently clear
what exactly generates the infinite regress. He also shifts between
the linguistic worry about "something being said" of
relation *C* and relata *A* and *B*, and the more
substantial ontological worry about the unity of qualities *A*,
*B*, and the relation *C* conceived as
"independent" from relata. Despite this, it seems clear
that for Bradley it is the assumed *independence* of the
relation *C* that generates the problem. An independent relation
is, according to him, incapable of relating *A* and *B*, and
no amount of further independent relations can do the job either, thus
generating the regress that has the following structure.



> 
> 
> *Regress 1* - *against "independent" relations as
> unifiers of qualities*
> 
> 
> 1. Suppose that there is an independent relation *C*, in which
> qualities *A* and *B* stand.
> 2. Independent relations are different from their relata and as such
> cannot relate.   
>  
> 
> ---
> 3. Therefore, an independent relation *C* cannot relate *A*
> and *B*.
> 4. New relation *D* is needed to relate *C*, *A*, and
> *B*.
> 5. *D* is an independent relation.   
>  
> 
> ---
> 6. From 2, 4 and 5, it follows that *D* cannot relate *C*,
> *A*, and *B*.
> 7. A new relation *E* is needed to
> relate *A*, *B*, *C*, and *D*. And so on
> *ad infinitum.*
> 
> 
> 



For this argument to have some force, Bradley needs to argue in
support of his conception of "independent" relations as
relations that cannot relate. Although he offers no such argument, he
does give us a clue as to what "real" relations ought to
be like: 



> 
> 
> If it [relation] is to be real [i.e., actually relating], it must be
> somehow at the expense of the terms, or, at least, must be something
> which appears in them or to which they belong. A relation
> between *A* and *B* implies really a substantial foundation
> within them. (Bradley 1893: 18) 
> 
> 
> 



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



Bradley's "real" relations might sound like
*internal relations* to a contemporary ear. Internal relations,
following Armstrong (1989: 43) and Lewis (1986: 62), are often
characterized as relations that supervene on the intrinsic properties
of their relata and that present no ontological addition. Common
examples of such relations are *taller than*, *being the
same shade of blue*, *having the same mass*. In contrast,
external relations are frequently understood as relations the holding
of which does not depend on the intrinsic features of particulars that
they relate; they present a genuine ontological addition (for
different ways of understanding the internal/external discussion see
section 1 of SEP entry on *Relations*). Frequently cited
examples of external relations are spatio-temporal relations such as
*being 2 feet apart*, etc. Thus, in the contemporary debate,
the question concerning whether or not relations exist turns on the
question of whether or not *external* relations exist (internal
ones are considered an "ontological free 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 the terms, the internal ones. The
peculiar way that such relations are founded in their terms for
Bradley, becomes central for the second regress, which we find in
chapter III of *Appearance and Reality*.



Chapter III focuses on the relationship between qualities and
relations. The conclusion of the overarching argument in that chapter
is that the entire relational way of thought is unintelligible and
flawed. Bradley arrives at this conclusion by arguing first that
qualities need relations; he then tries to prove that qualities are
unintelligible with relations; and finally, he argues the same for
relations--i.e., that relations need qualities but are
unintelligible with them.



Bradley's starting thesis in this chapter is that qualities
*need* relations. He assumes that without relations qualities
would just collapse into an indistinguishable blob; thus qualities, in
order to exist, need relations to somehow separate them out from that
blob, i.e., to act as difference-makers. In addition, qualities need
relations to unify them. Thus, the demand on relations is to act as
both distinction-makers and as unifiers of qualities. Qualities, on
their part, also have a "a double character as both supporting
and as being made by the relation" (Bradley 1893:26). Qualities
are *made by* relations through relations'
difference-making role, but qualities also need to be related into a
unified whole.



For Bradley, as we saw above, only internal relations stand a chance
of being
 "real"[1]
 and, subsequently, of doing the double duty just described. At the
same time, *Bradley's* *internal relations* (from
now on, *internalB relations*) are meant to be
grounded in the *proper parts of qualities* (see more below on
this peculiar understanding of relations). But if different proper
parts of a quality are to be truly different, they must be *made
different* by some additional internal relations. The latter, in
their turn, must be grounded in further different proper parts of
parts of qualities. This "process of fission", as Bradley
calls it, continues *ad infinitum*, thus generating the second
infinite regress of relations in these pages, and providing Bradley
with the alleged "proof" that qualities standing in
relations are unintelligible.



> 
> *Regress 2* - *against internalB relations
> as unifiers of qualities*
> 
> 
> 1. Relating relations are *internalB* in the sense
> that they are grounded in *parts* of qualities that they
> relate.
> 2. Qualities need relations to differentiate them from other
> qualities.
> 3. Qualities need relations to unite them with other qualities.
>   
>  
> 
> ---
> 4. From (1) and (2), it follows that a given quality *A* must have
> a part *a*, which is part of the ontological ground for the
> difference-making relation *Rd*, i.e., it is a
> part on which the distinctness of *A* from other qualities is
> based.
> 5. From (1) and (3), it follows that quality *A* must have a part
> a, which is part of the ontological ground for the unifying relation
> *Ru*, i.e., it is a part on which the unity with other
> qualities is based.
> 6. Parts *a* and a of quality *A* are different.
> 7. Difference within parts of a quality requires
> *internalB* relations.
> 8. Each of the original parts of *A*, namely *a* and
> a, must have a part that grounds the distinction of *a*
> from a, say *a*' and a', respectively,
> as well as a part that grounds the unity of *a* with a,
> say *a*'' and a'', respectively.
> 9. But the parts *a*' and *a*'' are distinct
> and yet unified; and so are a' and a''. Thus,
> each of these parts must have further parts that ground such
> distinctness and unity. And so on *ad 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 time
substantiating them. This is especially needed when it comes to his
peculiar interpretation of internality of a relation as being grounded
in proper parts of qualities. For why not claim that the quality in
its entirety can act as part of the ground (the other part being the
other quality or qualities) for different internal relations? This
would certainly be more in keeping with the contemporary understanding
of internality of a relation and it could stop the regress. To this
suggestion, Bradley would probably respond by reiterating the
unintelligibility of the idea that the very same quality can serve as
part of an ontological ground for distinctness from other qualities
*as well as* part of an ontological ground for the unity with
other qualities. In response to this, one could challenge
Bradley's reliance on the assumption that relations need to
account for difference between qualities, as well as for their unity.
In fact, it would be much simpler to claim that, say,
*whiteness* and *sweetness* are different not because
there is a difference-making *part* in them, but simply because
they are, in their entirety, *intrinsically different*.
Intrinsic difference of qualities could be Bradley's bottom
line, a primitive of the theory and it would eliminate the need for
relations as difference-makers, thus rejecting premise (2) above.



One possible interpretation (see Perovic 2014: 381) of why Bradley
does not wish to take distinctness of qualities as ontologically
primitive is that he might already be presupposing a primitive which
is contrary to it--a monistic undifferentiated whole. From such
monistic perspective, it would then seem that differentiation of
qualities would need an explanation and an ontological ground, whereas
the lack of differentiation would appear to be an ontological default,
requiring no explanation at all. However, although this interpretation
would help us understand better why Bradley might have assumed that
relations need to act as difference-makers for qualities, it is
certainly not terribly charitable to Bradley; that is, it would assume
that Bradley had already question-beggingly presupposed monism as the
default ontological position in his arguments *against*
relations.



Finally, let's consider the third and final regress brought
forward by Bradley in chapter III. After claiming that relations are
unintelligible without qualities, he wants to show that the way
relations stand to qualities is equally unintelligible. He writes:



> 
> 
> If it [relation] is nothing to the qualities, then they are not
> related at all; and, if so, as we saw, they have ceased to be
> qualities, and their relation is a nonentity. But if it is to be
> something to them, then clearly we now shall require a *new*
> connecting relation. For the relation hardly can be the mere adjective
> of one or both of its terms; or, at least, as such it seems
> indefensible. And, being something itself, if it does not itself bear
> a relation to the terms, in what intelligible way will it succeed in
> being anything to them? But here again we are hurried off into the
> eddy of a hopeless process, since we are forced to go on finding new
> relations without end. The links are united by a link, and this bond
> of union is a link which also has two ends; and these require each a
> fresh link to connect them with the old. (Bradley 1893:
> 27-28)
> 
> 
> 



The regress presented here is somewhat similar to the one expressed in
*Regress 1* above. In both cases relations are assumed to be
incapable of relating. In *Regress 1*, however, Bradley
explicitly targeted only the "independent" relations.
Here, Bradley is assuming the results of his previous arguments, and
attacking *all* relations, i.e., relations as such.



> 
> *Regress 3* - *against relations as such as unifiers of
> qualities*
> 
> 
> 1. Suppose that there is a relation *R* uniting
> qualities *A* and *B*.
> 2. If *R* is nothing to *A* and *B*, they are not
> related.
> 3. If *R* is something to *A* and *B*, then *R*
> itself is something.
> 4. If *R* is something itself then it cannot relate and needs
> further relations, such as *R*' to relate it to *A*
> and *B*.
> 5. The same process is then repeated with *R*' and
> further relations, *ad infinitum*.
> 
> 
> 



In this regress, Bradley is employing the phrases "being nothing
to the qualities" and "being something to the
qualities," but he doesn't explain what he means by these
phrases. If, however, Bradley is to be consistent with his previous
claims, relations that are "nothing to the qualities" have
to be his *internalB* relations which he dismissed
with *Regress 2*, and relations that are "something to
the qualities" have to be his "independent"
relations which he dismissed with *Regress 1*.
We should thus read premise
(2) in *Regress 3* as follows: if *R* is an
*internalB* relation, *A* and *B* will end
up not just not related, but will instead end up in the infinite
process of division, as seen in *Regress 2*. If, on the other
hand, *R* is *something* to *A* and *B*, as in
premise (3) in *Regress 3*, it itself has to be
something--that is, it is, in Bradley's terminology a
non-internal, "independent" relation. And
"independent" relations, as we have seen in *Regress
1*, cannot relate and no amount of further independent relations
can relate either.



After presenting *Regress 3*, Bradley believes that he has
succeeded in showing that the entire relational way of thought is
flawed and that relations as such should be relegated to the sphere of
appearance, rather than to reality. Central to arriving at such a
conclusion has been his assumption that what he calls
"independent" relations cannot relate. It seems as if
Bradley simply did not know how to think of such entities and often
resorts to metaphors and talks about links needing further links at
their ends and insists on our inability to show how "solid
things" can be joined to other "solids" (cf. Bradley
1893: 28). As these metaphors indicate, Bradley's worry seems to
be that if relations are conceived of as independent from the terms
that they relate, they themselves will become just like the terms that
need 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 different
dimension during his debate with Russell in the journal *Mind*,
during 1910-1911. At this point, Bradley is no longer concerned
just with arguments against the relational unity of qualities; rather,
he is concerned with the possibility of there being compex unities
that cannot be analyzed.



By the end of his paper "On Appearance, Error, and
Contradiction" (1910), Bradley challenges Russell to explain how
he can reconcile his pluralism of terms and external relations with
his commitment to complex unanalyzable entities which have terms and
external relations as constituents. He writes as follows:



> 
> I encounter at the outset a great difficulty. Mr. Russell's
> position has remained to myself incomprehensible. On the one side I am
> led to think that he defends a strict pluralism, for which nothing is
> admissible beyond simple terms and external relations. On the other
> side Mr. Russell seems to assert emphatically, and to use throughout,
> ideas which such a pluralism surely must repudiate. He throughout
> stands upon unities which are complex and which cannot be analysed
> into terms and relations. These two positions to my mind are
> irreconcilable, since the second, as I understand it, contradicts the
> first flatly. If there are such unities, and still more, if such
> unities are fundamental, then pluralism surely is in principle
> abandoned as false. (Bradley 1910: 179)



Bradley thinks that a pluralist who postulates two fundamental simple
entities cannot also admit a third *fundamental* entity which
is complex, i.e., constituted out of the simple entities. There is a
tension which must be resolved by either letting go of the
fundamentality of the simples (the view that Bradley would have opted
for); or by letting go of the fundamentality of complexes (the view
that Bradley thinks a consistent pluralist should embrace). But there
is a further way that the tension might be resolved, and this is by
arguing that simples and complexes are fundamental in different senses
of the term "fundamental". (For different senses of
fundamentality in this context see Perovic (2016) who distinguishes
between *constitutive, explanatory*, and *existential*
fundamentality.)



Russell's own reply to Bradley focused on clarifying the sense
in which he claimed that complex unities cannot be analyzed. He wrote
back the following:



> 
> It would seem that everything here turns upon the sense in which such
> unities cannot be analysed. I do not admit that, in any strict sense,
> unities are incapable of analysis; on the contrary, I hold that they
> are the only objects that can be analysed. What I admit is that no
> *enumeration* of their constituents will reconstitute them,
> since any such enumeration gives us a plurality, not a unity. But I do
> not admit that they are not composed of their constituents; and what
> is more to the purpose, I do not admit that their constituents cannot
> be considered truly unless we remember that they are their
> constituents. (Russell 1910: 373)



In this reply to Bradley, Russell is taking care to point out that he
is using the term "analysis" to designate a process
performed by *us* of "discovery of the constituents of
the complex" (Russell 1910: 374). This signifies a departure
from his claims in the *Principles of Mathematics*, where he
argued that propositional unities could not be analyzed because
analysis 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 to
something that *we* perform when we are discovering
constituents of complex entities, allows Russell to say that complexes
are the only objects that *can* in fact be analyzed.



In addition, Russell pinpoints his disagreement with Bradley when it
comes to relations. Russell explicitly rejects the view which favors
*internal relations*, that is, which holds "that the fact
that an object x has a certain relation R to an object y implies
complexity in x and y, i.e., it implies something in the
"natures" of x and y in virtue of which they are related
by the relation R" (Russell 1910: 373-374). Instead,
Russell states his support of *external relations*, the holding
of which cannot be derived from the terms that such relations relate
or their intrinsic complexity. Instead, when we have x and y standing
in an external relation R, we then have a complex or a unity
*xRy*. What distinguishes such a complex from a "mere
aggregate", according to Russell, is that a relation in a
unified complex *relates* whereas in an aggregate it does not
relate and is just a member of an aggregate.



Russell's reply was unsatisfying to Bradley, who followed up
with his "Reply to Mr Russell's Explanations" in
1911, reiterating some of the same concerns. Namely, Bradley
repeatedly returns to the worry about external relations--he
finds them to be unobservable and unthinkable without the terms; a
relation apart from its terms is indeed for Bradley an
"indefensible abstraction". In addition, he asks Russell
to elaborate further on the presumed difference between an aggregate
of entities and a unity of those entities. Bradley says that an appeal
to relating relations is unsatisfying and further asks Russell to
explain wherein the difference between relating relations and
non-relating relations lies for him. But for Russell there was no
further story to be told; the difference between relating and
non-relating relations is a primitive on which he did not feel the
need 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 topic
of relations. He was working on an article that he intended to publish
in *Mind*, the first part of which was posthumously made
available in his *Collected Essays vol.2*, under the simple
title "Relations". This manuscript is significant because
Bradley is, on the one hand, restating in a slightly different way
what he takes to be the most salient arguments from his previous works
and, 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 "mere
abstractions" from relational facts and as such hold no relating
power (Bradley 1926: 643). Internal relations are no improvement, and
Bradley rejects as untrue any suggestions that he might have wanted to
accept them (642). The true problem seems to be that "an actual
relation [...] must possess at once both the characters of a
'together' and a 'between', and, failing
either of these, is a relation no longer" Bradley 1926: 644,
634). Thus, just as in his *Appearance and Reality* (1893),
Bradley is demanding of relations that they fulfill both an
"in-between role" (what I have called above a
difference-making role) *as well as* the "together"
role (what I have called the unifying role). Failing either of these
roles amounts to not being a true relation, which in turn makes the
presumed relational experience contradictory, for Bradley:



> 
> Relational experience must hence in its very essence be
> self-contradictory. Contradiction everywhere is the attempt to take
> what is plural and diverse as being one and the same, and to take it
> so (we must add) simply or apart from any "how". And we
> have seen that without both diversity and unity the relational
> experience is lost, while to combine these two aspects it has left to
> it no possible "how" or way, except one which seems either
> certainly less or certainly more than what is relational. (Bradley
> 1926: 635)



As this often quoted passage illustrates, Bradley's skepticism
about relations takes the form of the "how" question.
Bradley's "how" question is often read as
"*How* do relations relate?". But taking into
account the wider context, his question is actually
"*How* might relations at the same time relate
*and* diversify their relata?". Failing to see how
relations might do *both*, Bradley concludes that relational
experience is marred by contradiction.



Finally, by the end of "Relations", Bradley wishes to make
it clear that what is fatal to his monism is not just a specific type
of relations (such as asymmetric relations), but an ultimate reality
of *any kind* of relation: "For not one kind of relation,
but every and any relation, if taken as an ultimate reality, would (on
any view such as mine) be fatal to Monism" (Bradley 1926: 649).
This is an important reminder of Bradley's own motivation for
his repeated arguments against
 relations.[2]


## 2. Extensions of Bradley's Regress Arguments



In the decades since Bradley's original discussion in
*AR*, "Bradley's regress" has come to refer
to a wider variety of arguments. This widening of scope has happened
in two main directions: (i) with respect to the ontology that the
arguments target; and (ii) with respect to the type of the argument
presented. In this section we will take a closer look at both of these
extensions.


### 2.1 Bradley's Regress vs. One and Two Category Ontologies



As we have seen in section 1.2 above, Bradley's original regress
arguments targeted a one-category ontology of qualities, where by
"qualities" Bradley seemed to have in mind unrepeatable
particularized properties, i.e., *tropes*. But the same
argument form has been used against the one-category ontology of
qualities conceived as multiply occurring universals, as well as
against the two-category ontologies of particulars and universals, as
well as particulars and tropes.



Bradley's regress arguments apply easily to the one-category
ontology of universals. The same problem that Bradley articulated for
trope-like qualities can be articulated for universals: namely, what
is it that unites universals of *whiteness*,
*sweetness*, and *hardness* into the particular *lump
of sugar*? If ordinary particulars such as lumps of sugar are
nothing but bundles of universal qualities, it seems important to
provide an account of unity of such bundles. The challenge is
particularly difficult in the case of universals because, unlike
tropes, they are concieved as multiply occurring entities that are
wholly present in each of their instances. Thus, the problem of
uniting a bundle of universals such as *whiteness*,
*sweetness*, and *hardness* will go hand in hand with
the problem of individuation of bundles of universals, i.e., the
problem of distinguishing between this particular bundle of
*whiteness*, *sweetness*, and *hardness* and
another exact duplicate bundle of *whiteness*,
*sweetness*, and *hardness*.



Bradley's regress arguments have been most widely discussed
within the context of the realists' two-category ontology of
particulars and universals. The challenge in this context is to
provide an ontological ground of unity of particulars and universals,
and the worry is that any appeal to a relation *R* (of instantiation,
exemplification, etc.) to unify a particular *a* with its
respective property universal *F* sets off an infinite regress of
relations, similar to the regresses described by Bradley. In the light
of this problem, some realists such as Olson (1987), and Armstrong
(1997) have argued that it is a third entity - the *fact* or
*state of affairs* of *a being F* that provides the
ontological ground of unity of *a* and *Fness* as well as
the truthmaker for the truth that "*a* is *F*".
According to critics (see, for instance, Vallicella 2000 and 2002),
this approach instead of solving the problem of unity of particulars
and universals, merely reframes it as the one threatening the very
possibility of there being such entities as facts or states of
affairs. Similar worries have arisen for trope theorists that embrace
a two-category ontology of particulars and tropes. Philosophers such
as C.B. Martin (1980) and Daly (1997) have worried that an appeal to a
relation of *inherence* in the context of unfying a substratum
and its property trope would lead to an infinite regress of inherence
relataions.



Finally, D.M. Armstrong (1979) has stated a regress argument similar
to Bradley's, as a threat to class nominalists. The thought is
that since class nominalists analyze particulars' having of
properties in terms of particulars' membership in a class of
things that all have those properties, they would incur a regress when
trying to define a membership relation. However, class nominalists
like Lewis (2002), have been adamant about not being committed to a
membership *relation* of any sort; indeed, Lewis has argued
that all we have is a "singular-to-plural *copula*:
'is one of' as in 'this is one of
those'." (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 the
context of discussing Bradley's regress but that do not take the
form of a regress argument. The three that stand out are: (1) the
problem of explaining what differentiates a unified complex entity
from a mere aggregate of its constituents; (2) the problem of
explaining how exactly it is that relations relate; and (3) the problem
of explaining how the *specific complex* comes into
existence.


### 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 the
ontological ground of the difference between the sum *a*+*F*
and the unified state of affairs *Fa*? It could be the case
that both *a* and *F* exist at a world, and thus that the
sum *a+F* exists at such a world, without it being the case
that *Fa* obtains (but, say, *a being G* and *b being
F* obtain). What then is the ground of such a difference?
Similarly, what provides an ontological ground of the difference
between the sum *a+R+b* and the unified state of affairs
*aRb*? It might be the case that all three *a*, *R*,
and *b* exist at a world, and hence that their sum is given,
without it being the case that *aRb* obtains (instead, say,
*aRc* and *bRd* obtain). The same sort of
question can be posed, of course, for other ontologies. For instance,
for a bundle trope theorist the question will be: what is the
ontological ground of the difference between the sum
*F*1+*G*1+*H*1 of
property tropes and a unified trope bundle constituted out of them?
(See Armstrong 1989, 1997; Vallicella 2000, 2002; Maurin 2010;
and Meinertsen 2008, amongst others for such a formulation of the
problem.)



It must be noted that this problem takes it for granted: (i) that
mereological 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 and
relations, tropes, etc.) *can* indeed be summed regardless of
whether such entities can exist independently of others. Similar
assumptions are made in formulations that make no reference to
mereological sums but rather contrast lists, groupings, or sets of
entities with the unified complexes such as states of affairs or
bundles of tropes.



Philosophers who pose the problem in these terms, will often move on
to generate a regress argument for any attempt to explain the
difference between a sum/list/set of entities and a unified complex
that appeals to relations. The next question becomes: what will
account for the difference between a sum/list/set of entities
*a*, *F*, and a relation *R* (of instantiation or
exemplification) on the one hand, and a unified state of affairs of
*a being F*, on the other? The implication is that any addition
of further relations will set off Bradley's regress of
relations, with no explanation in sight (see in particular Vallicella
(2000)).


### 2.2.2 The problem of explaining how relations relate



The question "How do relations relate?" can be traced back
to Bradley (1926: 635), and it fuels much of the recent discussion
surrounding Bradley's regress (see Simons 1994, Maurin 2010,
Meinertsen 2008, Wieland and Betti 2008). But, as we saw in
section 1.4 above, Bradley's "how" question was
motivated by his puzzlement over the *dual role* that he
thought relations had to fill; he saw them as having to distinguish
between different relata *and* having to unify them. Thus his
question was not so much "how do relations relate?" but
rather "how do relations relate *as well as*
differentiate their relata?"



In contrast, contemporary philosophers' puzzlement over
"how relations relate" stems from a different place. The
assumption in this case seems to be that unless some account of the
*nature* of relations adequately *explains* what makes
them apt to unite distinct relata, an appeal to relations as relating
entities is illicit. The type of explanation that philosophers are
after in this context often remains unspecified, though it is clear
that what is expected is not a causal explanation, but a metaphysical
explanation of some kind. It is assumed that an adequate explanation
will refer to some special feature of relations that makes it possible
for them to relate; absent such feature, relations are usually
considered to be relationally inert and Bradley's regress of
relations is re-introduced.


### 2.2.3 The problem of explaining the existence of a specific complex


 This problem is usually brought out by contrasting it
with the general problem of existence of complexes. The question is
not "what is it that unifies states of affairs/bundles of
tropes?" but rather "what is it that unifies this
particular bundle of *whiteness*, *hardness*, and
*sweetness* into a lump of sugar?" and "what is
that unifies this particular chair and the universal *blackness*?"
Vallicella puts the question, as it applies to facts, in the following
way: 



> 
> 
> What makes it the case that a number of constituents of the right
> kinds--constituents which are connectable so as to form a fact
> but need not be connected to exist--are *actually*
> connected so as to form an actual or existing fact? (Vallicella
> 2000: 242) 
> 
> 
> 



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



Vallicella and others who pose the question in these terms make it
clear that they are not after a causal story about how a particular
lump of sugar or a particular black chair was made. Instead, what
drives the problem as posed is the assumed contingent nature of the
connection between constituents of states of affairs. This chair is
black but it might have been some other color; and this blackness, for
realists, need not be instantiated here, it might (and in fact
*is*) present in many other states of affairs. So what is it
that "makes it so" that this particular blackness and this
particular chair are *actually* united? There is nothing in the
*natures* of constituents of states of affairs to require that
they come together, so--the thought is - something else must
bring those constituents together.


## 3. Replies to Bradleyean Arguments



In this section, we will take a closer look at different strategies
philosophers have employed in engaging with Bradley's regress
arguments and the associated problems discussed above (I will be using
the locution "Bradleyean arguments" to refer indifferently
to both of these cateogires). The first fork in the road for
philosophers has been to either reject the argument by questioning one
or more of the assumptions that the argument makes, or to accept and
respond to the argument on its own terms. Those that have chosen the
rejectionist approach have mostly done so by challenging
Bradley's skepticism about relations' ability to relate
their relata. Russell, Broad, Blanshard, Alexander, and Grossman have
argued that it is a job of relations to relate and that
Bradley's relational regresses cannot get started if
relations' relating role is taken seriously. Many more
philosophers, however, have found Bradleyean argument compelling and
have responded in one of the following ways. They have appealed to: 1)
some sort of *non-relational tie* or *nexus* to relate
the relata (Bergmann, Strawson); 2) external relations equipped with
special features (Meinertsen's self-relating relations,
Vallicella's external relations with the power of
self-determination, Maurin's and Weiland and Betti's
relata-specific relations); 3) the mutual inter-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 Bradleyean arguments tend to question one or more
of the assumptions on which the argument rests. With respect to the
regresses, rejectionists have mainly questioned the grounds of
Bradley's skepticism about relations and their relating role. As
we have seen in section 1.3 above, Russell employed this strategy when
debating Bradley in the journal *Mind*, in 1910. On that
occasion, Russell argued in favor of *external relations* and
their relating role within complexes of the form
 *aRb*.[3]



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



> 
> It is plain that Bradley thinks of *A* and *B* as being like
> two objects fastened together with a bit of string, and he thinks of
> *R* as being like the bit of string. He then remembers that the
> objects must be glued or sealed to both ends of the the bit of string
> if the latter is to fasten them together. And then, I suppose, another
> kind of glue is needed to fasten the second drop of glue to the object
> *B* on the one side and the string on the other. And so on
> without end. Charity bids us avert our eyes from the pitiable
> spectacle of a great philosopher using an argument which would
> disgrace a child or a savage. (Broad 1933: 85)



We find a very similar take on Bradley's regress in Blanshard
(1986). He argued *contra* Bradley that "*R* is not
the same sort of being as its terms. It is neither a thing nor a
quality. It is a relation, *and the business of a relation is to
relate*" (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 less harsh
than Broad and Blanshard in their assessment of Bradley's
regress arguments, they are unambiguous in their diagnosis of the
problem as one involving the wrong conception of relations. According
to Grossmann, for instance, the correct conclusion to draw from
Bradley's regress argument is that "it is really an
argument not against relations, but against the assumption that
relations need to be related to what they relate" (Grossmann
1992: 55).



In recent debate, replies to Bradley's regress that bluntly
insist on relations' relating role have been unpopular. This is
because the debate has shifted to include the associated questions
outlined in 2.2. above, including the question: "*How* do
relations relate?". Thus, if one is after the answer to the
"how" question, simply saying that it is the job of
relations to relate is deemed unsatisfactory.



One sort of rejectionist reply to Bradleyean arguments can be found in
Perovic (2014). Perovic (2014) argues that Bradley's original
regress arguments in *AR* rest on unsubstantiated assumptions
and thus cannot be considered as successful *reductio*
arguments against relations. For example, the first regress takes for
granted that as long as unifying relations are conceived as
"independent" from their relata, they cannot relate. The
second regress assumes that unifying of qualities cannot be achieved
with "internal" relations either; for the latter are
understood as being grounded in proper parts of qualities, which
leads, according to Bradley, to an infinite regress. She points out
that it is not clear why Bradley understands internal relations as
grounded in proper parts of qualities that they relate, nor is it
clear why Bradley believes that relations, if they are to have any
standing, ought to fill a dual role of unifying their relata as well
as providing the ground of their distinctness. Perovic (2014)
concludes that without further support, Bradley's original
arguments against relations as unifiers of qualities do not establish
the unreality of relations; an appeal to external relations as
unifiers of their relata is still a perfectly acceptable option for
both realists and trope theorists.


### 3.2 Non-Relational Ties



A great number of philosophers have found Bradley's regress
arguments to be compelling as stated. Some, in fact, have taken the
regress arguments to be so threatening, that they have concluded that
only non-relational ties might be able to unify qualities. Strawson
(1959: 167-170), for instance, has appealed to non-relational
ties such as *instantial tie* and *characterizing tie*
to unify a particular with a sortal (such as *dog*) and
characterizing universal (such as *wisdom*) respectively. He
thought of these ties as being more intimate relators than ordinary
relations as well as allowing for greater heterogeneity between the
terms they bind. Bergmann (1967: 9) famously appealed to a
non-relational tie he called "nexus" and which he
introduced 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 than
ordinary relations do. Philosophers that find relations to be
suspicious entities, tend to find non-relational ties even more
suspicious and obscure. They ask: How are non-relational ties
different from relations? If they are meant to relate or
"tie" their relata, are they not sufficiently like
relations? And if there was a problem with Bradley's regress of
relations in the first place, don't we have the same problem
with non-relational ties? (Lewis (2002) has made similar remarks
against non-relational ties in the context of discussing the problem
of termporary intrinsics and the adverbialist reply to the problem.)
Vallicella (2000: 241) has attacked non-relational ties by arguing that
even if the nexus manages to save Bergmann from the regress, the unity
problem remains. The problem, as Vallicella sees it, then becomes that
*nexus* is sufficiently like a universal that it remains
unclear what it is that unites *a*, *Fness*, and
*nexus* into a state of affairs as opposed to having a mere sum
of *a*+*Fness*+*nexus*.


### 3.3 External Relations with Special Features



Philosophers impressed by Bradleyean arguments, but with the desire to
preserve relations as unifiers of complex entities such as states of
affairs or bundles of tropes, have been drawn towards postulating
relations with certain special features. Convinced that relations
ordinarily concieved would lead to a dangerous regress, these
philosophers have tried to equip their relations with characteristics
that 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 unifying
operator that connects a fact's constituents and brings facts
into existence. This external unifier *U* is described as a
"metaphysical agent" that acts as an "existence
maker" 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 upon
its operand" (Vallicella 2000: 256). In characterizing *U*
in this way, Vallicella is trying to ensure both that the connection
between *U* and what it unifies remains contingent, *and*
that such unity is grounded in *U* itself (out of worry about the
infinite regress). The only way that he can see *U* fulfill both
these roles is by construing it "along the lines of God or a
transcendental consciousness" (Vallicella 2000: 256). The
trouble with this reply to Bradleyean arguments is, of course, that
the god-like creating role of the external unifier *U* remains
quite murky and it seems to bring in consciousness into both the
operator itself as well as the creation of states of affairs.



Another novel relation has been proposed by Meinertsen (2008). He has
argued for a self-relating relation to do the uniting of particulars
and universals into states of affairs. According to this proposal,
what makes *R* related to the pair (*a*, *b*) is a
unifying self-relating relation *U\** which unites
*itself* to *R*, *a*, and *b*. Thus, a state of
affairs *R* (*a*, *b*) turns out to be identical to the
state of affairs *U\** (*U\**, *R*, *a*,
*b*) and a state of affairs *Fa* is just a short for
*U\**(*U\**, *F*, *a*) (cf. Meinertsen 2008:
12). The self-relating relation *U\** 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 constituents being 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 relating
relations. The trouble with such dual roles, is to explain, as Bradley
asked Russell: "What is the difference between a relation which
relates in fact and one which does not so relate?" (Bradley
1911: 74). Or for Meinertsen: What is the difference between a
relation occurring in its passive role and it occurring in its active
role? If we are willing to accept as a primitive that
there *is* such a difference and that it is thanks
to *U\**'s dual role as a self-relating relation that it
is able to unify constituents of a complex *a*, *b*,
and *R*, then why exactly is such a view an improvement upon a
view that takes it that a relating relation
*R* simply relates its relata?



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



> 
> 
> If a relation is relata-specific, it necessarily relates its relata,
> but *only* if it exists. To put it in possible-worlds
> terminology: if *R* holds between *a* and *b* in the
> actual world, it holds between *a* and *b* in all possible
> worlds in which *R* exists (and not in any possible world in
> which *a* and *b* exist, or in any possible world
> whatsoever). (Weiland and Betti 2008: 519)
> 
> 
> 


### 3.4 Mutual Interdependence of Constituents



In "Function and Concept" (1891), Frege famously described
a concept-object distinction as a special case of the
function-argument distinction. Concepts, according to Frege, were
unsaturated and incomplete entities, in need of completion by objects.
Because of such natures of concepts and objects, the two would
presumably "fit" together without any intermediaries.



Taking a cue from Frege, some philosophers have argued in favor of a
two-sided dependence of constituents of states of affairs (and a
many-sided dependence of property tropes in trope bundles) as a
non-relational way of accounting for the unity of such complexes.
Baxter (2001), for instance, has proposed that the unity of particular
and universal should be analyzed as *partial identity*. For
Baxter, both particulars and universals have "aspects".
Different instances of one and the same universal are different
aspects of a universal; spatial parts of particulars are
*their* different aspects. Particulars and universals can be
partially identical by overlapping in their aspects. Baxter writes:




> 
> 
> Suppose Hume is a particular, Benevolence is a universal, and Hume is
> benevolent. Then Hume has as an aspect, Hume insofar as he is
> benevolent. Also Benevolence has as an aspect, Benevolence insofar as
> Hume has it. These are the same aspect--Hume's benevolence.
> (Baxter 2001: 454)
> 
> 
> 



*Hume's benevolence* in Baxter's example is what
Armstrong calls a *state of affairs*. In fact, Armstrong was
temporarily swayed by Baxter's *partial identity* view of
states of affairs, but then went on to object to the view on the
grounds that partial identity cannot be merely contingent. Thus, for
later Armstrong, "once one has identity, even if only partial
identity, there will be found necessity" (Armstrong 2005: 317).
A particular, thus, *necessarily* has all the properties that
it in fact has, and the universal *necessarily* has the
instances that it has. This outcome secures the unity of particulars
and universals but at a cost of embracing a strong version of
necessitarianism.



Inspired by earlier Armstrong, Perovic (2016) has proposed a
non-necessitarian dependence model for particulars and universals in
states of affairs. On this model, the constituents of most states of
affairs such as *this chalk being white* exhibit *mutual
generic existential dependence*. This simply captures the idea
that a particular piece of chalk presumably cannot exist without
having some color or other, it is generically existentially dependent
upon some color universal. Similarly, the universal *whiteness*
is *generically existentially dependent* on some concrete
particular, for it cannot exist without inhering in some concrete
particular or other, but it need not be the particular piece of chalk
*a*. However, the state of affairs *this particular chalk
being white* exhibits the strongest kind of dependence on its
constitutive particular and universal--namely, it seems to
exhibit *one-sided specific existential dependence* on its
constituents. The reason why specific states of affairs seem to
exhibit such strong existential dependence, is because of the simple
fact that any change in a particular or in a universal would bring
about a different state of affairs. 



Simons (1994) put forward a similar proposal within the framework of
his "nuclear theory" of tropes. He thinks of bundles of
tropes as having different levels of unity. Property tropes that are
essential to a particular are tightly woven through mutual dependence
on one another, whereas property tropes that are accidental are more
loosely dependent upon the tight bundle tropes in the nucleus.



One might find these sorts of proposals wanting since they only
characterize the types of dependence that hold between constituents of
unified wholes (whether they are states of affairs or nuclear bundles
of tropes). But, the objection goes, they do not account for the
difference between constituents considered outside of such unities and
constituents in a unified whole. Here, Perovic (2016) is happy to
admit that she is not trying to provide such an account in the first
place. Following Armstrong, she takes the world to be exhausted by
states of affairs and takes particulars and universals to exist only
in states of affairs.


### 3.5 The Brute Fact Approach



The term "brute fact approach" is slightly ambiguous. It
can be identified with the rejectionist view sketched along the lines
of 3.1 above, where to say that relations' job is to relate is
to take that fact about relations as primitive or "brute".
However, the expression, as it is used here, is intended to refer to
the view that takes complexes such as states of affairs or facts as
unifiers 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 so
much a *reductio* of relations, but to show that facts should
be taken as irreducible entities. The word "relation", for
Olson, is ambiguous between two senses: the first one is to designate
an entity that can be multiply instantiated by various pairs of
relata, whereas the second sense is to designate the fact of
relatedness. In place of "relation", Olson prefers the
word "connection", since it "can only mean being
connected. There is not the same temptation to think of it as an
additional *thing* that does the connecting. The connection is
not a constituent of the fact; it is the fact itself" (Olson
1987: 61). Armstrong seems to have something similar to this in mind
when he says that states of affairs "come first". But then
he also adds that they "*hold their constituents
together* in a non-mereological form of composition, a form of
composition that even allows the possibility of having different
states of affairs with identical constituents" (Armstrong 1997:
118, italics added).



Vallicella (2002) has objected to this sort of brute fact approach
that it is mysterious and incoherent. He even accuses the proponents
of the brute fact approach as being committed to the following
contradiction: 



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



This objection, of course, presupposes that the only non-controversial
form of composition is the mereological kind and that facts are
"nothing more than their constituents". Armstrong's
and Olson's facts openly go against these assumptions: they are
unities that are more than just the sum of their constituents. But
failing to provide further ground for the difference between the sum
and the fact makes such facts brute and unacceptable to
Vallicella.


###  3.6 Benign Infinitism



In the context of discussion of states of affairs as unifiers of their
constituents, Armstrong anticipated Vallicella's objection just
described. His reply was to claim that even if he had to concede that
it was necessary to introduce a relation or a "fundamental
tie" to account for the peculiar unity present in states of
affairs, the resulting regress would not be vicious. In fact, such a
regress would be closer to the benign truth regress--many truths,
but only one truthmaker, just like with "p", and "it
is true that p", and "it is true that it is true that
p", etc. Treating the instantiation regress in the same way, we
would have the first instantiation relation uniting the constituents
of the state of affairs, but all further relations would supervene and
not present any further ontological addition.



Orilia (2006, 2007) develops this sort of response a bit further. He
agrees with Armstrong (1997) that Bradley's regress is an
explanatory regress that is, in fact, benign. What makes it benign for
Orilia is that at each step of an explanation the added fact explains
the previous one via an additional *external* relation. He
argues that despite it being the case "that at any given stage
we can continue the explanatory task", it "*does
not* show that no knowledge or no understanding is provided at any
stage". According to Orilia, this "merely shows that at no stage we know/understand everything that there
is to know/understand about the *explicandum* that gives rise
to the expalantory chain. And noting that the *explicandum* in
question gives rise to such an infinite chain may be considered part
of our understanding of it" (Orilia 2007: 160).



Even if one were to grant Orilia that there can be infinite dependence
chains of facts, for Maurin (2015) a crucial problem remains
unresolved. According to her, Orilia's account does nothing to
answer what she calls the "how" question, i.e., the
question "*how* can there be a situation in which the
state of affairs *that a is F exists*?". She argues that
the infinitist's reply already presupposes that *there
is* unity of states of affairs before explaining *what* its
existence 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 of
grounding and metaphysical explanation has taken an interest in
Bradley's regress from a different perspective. Here, the main
Bradley-inspired issue has been whether or not it should be one of the
requirements for a metaphysical explanation that it "must ground
out". The problem with Bradley's regress in this context
is that it appears to be committed to an infinite chain of facts, each
one 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 affairs *Fa* is explained by
appeal to another higher-order fact *R*<*Fa*>, and this one
in turn is explained by appeal to a further fact *R*'<*R*,
<*Fa*>>, and so on *ad infinitum*. However, Cameron
(2008) has found such a dependence chain to be very problematic. He
believes that there is a strong intuition in favor of there being "a metaphysical ground, a realm of ontologically independent objects
which provide the ultimate ontological basis for all the ontologically
dependent entities, and a realm of basic facts which provide the
ultimate metaphysical ground for all the derivative facts" (Cameron
2008: 8).



Cameron admits that it is hard to argue for this intuition by appeal
to a further, more basic metaphysical principle. Instead, he suggests,
it can be supported by appeal to theoretical utility; a unified
explanation of the same sort of phenomenon seems preferable to an
infinite descending chains of separate explanations. In response to
Cameron, Orilia (2009) has pointed out weaknesses in Cameron's
appeal to a unified explanation as a way of supporting the thesis of
well-foundeness of all chains of ontological dependence (*WF*);
thus, Orialia has concluded that *WF* cannot yet have a claim
of being a contingent truth.



Another interesting question inspired by Bradley's regress
arguments, has been posed by Bennett (2011). Her question is: is
grounding itself fundamental? Prima facie, it seems that it can
neither be fundamental, nor grounded. But if it is neither, then the
grounding would have to be rejected, which is an unattractive outcome
that Bennett does not want to embrace. Inspired by Armstrong's
(1989) discussion of the Bradley problem and relations of
instantiation as internal and supervenient upon their relata, she then
explores whether the grounding relation itself could be treated in a
similar fashion. There is one important difference: rather than have
grounding supervene on two or more relata, Bennett proposes that it be
treated as a relation that supervenes upon only one of its relata.
Such a relation she calls "superinternal".



Debate concerning the nature of mataphysical explanation and the
concept of grounding is quite prolific and ongoing. (For a detailed
discussion see the SEP entry on Grounding.) What one must keep in mind
when it comes to Bradleyean problems and grounding is that the former
debate is itself quite varied and without a consensus on either the
nature of the problem or the desiderata for the satisfactory solution.
Thus, caution should be advised when importing conclusions from one
contentious problem into the area of another even more abstract and
contentious one.



*Composition*. Grounding considerations and Bradley's
regress have found their application in the discussion of the problem
of composition of objects. Brzozowski (2008) has recently posed the
following question concerning the location of composite objects: does
the location of a composite object derive from the location of its
proper parts, or not? (Brzozowski 2008: 193). Either way, Brzozowski
takes it that we get unappealing consequences. The first horn of the
dilemma is that *if* indeed the location of composite objects
is derived from their proper parts, the possibility of spatio-temporal
gunk objects (composite objects whose parts are themselves composite
objects) would have to be denied. If, on the other hand, the location
of composite objects is not derived from their proper parts, then
brute metaphysical necessities connecting the location of composite
objects with the locations of their proper parts must be posited.
Brzozowski argues in favor of the first horn of the dilemma, and part
of his argument relies on applying a Bradley-type argument to the
location of gunk objects. His main thought is that there would be a
serious problem of location of gunk objects since "even though at each level of the series of decomposition we can
explain the location of a composite object by appealing to the
location of a proper part, it is left unexplained how *any*
object in the series is located in space-time. Given the piecemeal
story, there is no way for the totality of location relations to be
grounded..." (Brzozowski 2008: 201). 
As we can see, Brzozowski here relies on some version of Cameron's
*WF* principle described above.



*Philosophy of Language*. Outside of the strictly metaphysical
debates, Bradleyean arguments are often brought up when discussing the
problem of the unity of the proposition. This problem in philosophy of
language is usually put as follows: what is the difference between a
mere list of words such as "wise, Alice, is" and a meaningful sentence
such as "Alice is wise"? The latter seems to possess a unity of some
sort, but what is the exact nature of such unity and how does it come
about? In analogy with the ontological version of Bradley's
regress, philosophers then worry that an appeal to a copula does not
explain what it is that is special about the unity present in
"Alice is wise" and absent in a mere list. And no appeal
to further copulas will help the matters either.



There has been a tendency recently to view the problem of the unity of
the 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 together
the ontological and the semantic versions of what he refers to as
"the problem of predication". More careful work on this
issue has been recently done by Gaskin (1995, 2008) and Collins
(2011). The particularly obscure nature of the debate between Russell
and Wittgenstein over Russell's theory of judgment has lent
itself to being interpreted as concerning the problem of the unity of
the proposition. For such an interpretation see in particular Hanks
(2007).