PHILOSOPHICAL PERSPECTIVES

Philosophical Perspectives, 25, Metaphysics, 2011

RELATIONAL vs. CONSTITUENT ONTOLOGIES

Peter van Inwagen

The University of Notre Dame

In a companion piece to this essay, an essay entitled “What is an Ontological

Category?”,1 I have tried to give an account of the concept of an ontological
category, and I have suggested that ontology is the discipline that attempts to
answer Quine’s “ontological question” — ‘What is there?’ — in terms of a system
of ontological categories. And I have suggested that an ontology is any given such
attempt at an answer.2 Very roughly speaking, in that essay I have defended the
view that there are natural classes — classes whose boundaries are not simply
matters of arbitrary convention — and I have contended that the ontological
categories are natural classes that are in a certain sense very “high” or very
comprehensive.
In the present essay, I’m going simply to assume that we have some sort
of intuitive grasp of these concepts — “natural class”, “ontological category,”
“ontology” (mass term), and “ontology” (count-noun).
I will begin by presenting a classification of ontologies. (This classification ig-
nores the fact that one way to divide ontologies is into “Meinongian” and “Non-
Meinongian” ontologies. In the sequel, I will proceed on the assumption that
existence and being are the same thing and that everything exists/is. I leave for
another occasion the task of setting out a more general classification of ontolo-
gies, a classification that takes into account the fact that the Meinongian/non-
Meinongian opposition is at least as important for the taxonomy of ontologies
as is the relational/constituent opposition that is the focus of the present
essay.)
The major division my proposed classification recognizes is a division of
ontologies into monocategorial and polycategorial ontologies. A monocategorial
ontology is an ontology that implies that there is only one primary ontological
category — that there is only one ontological category that is not a subcategory
of any other ontological category,—and that everything belongs to that category.3
That is to say, a monocategorial ontology implies that the universal class is an
ontological category. A polycategorial ontology, of course, implies that there are
two or more primary categories.4
390 / Peter van Inwagen

Here are some examples of monocategorial ontologies:

• “Austere” nominalism: there exist only concrete particulars.5

• The “New Bundle Theory,” invented by — but by no means endorsed
by — James Van Cleve: there exist only properties (and these properties
have no fusions or mereological sums; concrete particulars — including
adherents of the New Bundle Theory—do not exist).6
• The ontology that is being worked out by L. A. Paul: there exist
only properties (but the members of any non-empty set of properties
have a fusion; the fusion of any set of properties is itself a property;
among the various fusions of properties are concrete particulars — like
L. A. Paul; thus certain objects that traditional ontologies would place
in other categories than “property” do exist, but, whatever else they may
be, whatever non-primary ontological categories they may belong to, they
are one and all members of the only primary ontological category, the
category “property”).7

I will give examples of polycategorial ontologies in connection with the subdi-

visions of that division. Polycategorial ontologies may be divided into relational
and constituent ontologies.8 This distinction — central to the present essay — is
best explained in terms of the concept of “ontological structure.”
Let us say that a relation is quasi-mereological if it is either the part-whole
relation or is in some vague sense “analogous to” or “comparable to” the part-
whole relation. And let us say that a constituent of an object is either one of its
parts or some object that is not, in the strict sense, one of its parts, but stands in
some quasi-mereological or part-like relation to it.
Let us say that to specify the mereological structure of an ordinary particular
(substance, individual, concrete thing) is to specify the other ordinary particulars,
if any, that are its parts in the strict and mereological sense — by saying which
other ordinary particulars bear the part-whole relation to it —, and perhaps
by saying something about how those other ordinary particulars stand to one
another in respect of certain relations thought to be “structure relevant” (spatial
relations, it may be, or causal relations). And let us say that to specify the
ontological structure of an ordinary particular (etc.) is to specify the objects in any
categories other than “concrete particular” that bear some quasi-mereological
relation to it.
A relational ontology is a polycategorial ontology (one of whose primary
categories is “concrete particular” or something in the ontological neighborhood,
something to very much the same ontological purpose: substance, individual,
concrete thing . . . ) that implies that concrete particulars have no ontological
structure — that implies that concrete particulars are, in Armstrong’s termi-
nology, blobs. (This is a feature that relational ontologies share with austere
nominalism.) According to any relational ontology, the only structure that
 Relational vs. Constituent Ontologies / 391

concrete particulars have is good, old-fashioned everyday structure: mereological

structure.9 A constituent ontology, like a relational ontology, includes “concrete
particular” in its inventory of ontological categories. But, unlike relational
ontologies, constituent ontologies imply that concrete particulars have an onto-
logical structure: they have constituents (perhaps parts in the strict sense, perhaps
not) that do not belong to the category “concrete particular.”
The so-called bundle theory (sc. of the nature of concrete particulars) can
serve as a paradigm of a constituent ontology — provided that we suppose
the bundle theory to imply that there really are bundles of properties (that is,
universals) and that something is a bundle of properties if and only if it is a
concrete particular. And provided, too, that we suppose that the bundle theory
assigns bundles of properties (on the one hand) and properties tout court (on
the other) to distinct and non-overlapping ontological categories. That is, only
those versions of the bundle theory that do not treat apparent singular reference
to and singular quantification over “bundles of properties” as a disguised form
of plural reference to and plural quantification over properties are examples
of a constituent ontology. And only those versions of the bundle theory that
do not treat bundles of properties as themselves properties are examples of a
constituent ontology. By “the bundle theory” I thus mean what might be called
the standard-or-garden-variety bundle theory, the classical bundle theory, and
not Van Cleve’s New Bundle Theory or Paul’s ontology. The classical bundle
theory is a constituent ontology for the simple reason that it implies that concrete
particulars have constituents — properties or universals — that do not belong to
the category “concrete particular.” And, obviously, if an ontology implies that
concrete particulars have “bare particulars” as constituents or have “tropes” as
constituents, that ontology too will be a constituent ontology. But almost all
constituent ontologies imply that among the ontological constituents of concrete
particulars are properties (although those properties may be tropes rather than
universals). And, of course, any such ontology will imply that the important
relation that is variously called ‘having’ or ‘exemplifying’ or ‘instantiating’ —
the most salient of the relations that Solomon bears to wisdom, Central Park
to rectangularity, and Arizona to aridity — is intimately related to the idea
of properties-as-constituents: the properties that a concrete particular has (or
exemplifies or instantiates) are exactly those that are its constituents: ‘the concrete
particular x has the property F’ is equivalent to ‘the property F is a constituent
of the concrete particular x’.
My own favored ontology can serve as an example of a relational ontology.10
According to this ontology, members of the primary category that can be var-
iously called “substance,” “concrete thing,” “individual thing,” and “particular
thing” are without ontological structure. Such structure as a particular thing
like a dog has is the structure that supervenes on its parts (cells, electrons) and
their spatial and causal relations to one another; and every part of a dog or
any other particular thing is itself a member of the primary category “particular
thing.” This must be, for (the Favored Ontology contends) everything that is
392 / Peter van Inwagen

not a particular thing is an abstract object or relation (a proposition, property,

or proper relation). And there is no possible sense of ‘constituent’ in which
an abstract object can be a constituent of a substance/concrete particular/
individual thing. Consider, for example, my dachshund Jack and the property
xenophobia—that is, aggressive hostility toward any living thing that one has
not been properly introduced to. Xenophobia is certainly one of Jack’s properties
(and it is certainly a universal, since he shares it with his little life-partner, my
other dachshund, Sonia), but it is in no possible sense one of his constituents. For
the proponent of the Favored Ontology, the dyadic relation “having” that Jack
and Sonia each bear to the property xenophobia is as abstract and “external” as
the variably polyadic relation “being numbered by” that they enter into with the
number 2.
According to the Favored Ontology, a property or attribute is something that
one ascribes to something by saying a certain thing about it; xenophobia, for
example, is what one ascribes to something by saying that it’s a xenophobe.
The attribute xenophobia — the thing I say about Jack or Hitler when I
say of either of them that he’s a xenophobe — is, according to the Favored
Ontology, an unsaturated assertible11 , to be contrasted with a saturated assertible
or proposition (the proposition that there are xenophobes, for example). An
attribute may be said to stand to a sentence in which one variable is free as a
proposition stands to a closed sentence. Saturated and unsaturated assertibles —
propositions on the one hand, and attributes and relations on the other —,
are much alike in many respects. Both are necessarily existent things to which
spatial, temporal, and causal concepts — and the concept “constituent of a
concrete particular,” as well — have no application. (And what does ‘has no
application’ mean in this context? Well, here’s an example that may serve as a
model for what I am trying to express by using this phrase. Johnny’s algebra
teacher asks him to “extract” a cube root; he requests a forceps to use in this
operation. His request, you will probably concede, is ill informed: the extraction
of a cube root is an operation to which the concept of a physical extracting tool
has no application. It ought to be as evident that there is no sense of ‘constituent’
in which unsaturated assertibles are constituents of concrete particulars as it is
that there is no sense of ‘extraction’ in which a physical tool can be of use in the
extraction of a cube root.)
A second example of a relational ontology is provided by David Lewis’s
ontology of properties (what he calls ‘properties’, and not what he calls
‘universals’) — or, more exactly, by any ontology that includes what Lewis called
‘properties’ and which treats these Ludovician properties as forming a natural
class.12 According to Lewis, a property is a set of possible objects. (Something
is a property if and only if it is a set all of whose members are possible objects.)
The property of being a pig or porcinity, Lewis says, is simply the set of all
possible pigs — a set far larger than the set of actual pigs. Consider an actual
pig, Freddy. Freddy of course has porcinity. And what is this relation “having”
that holds between the pig and the property? Why, simply set-membership. And
 Relational vs. Constituent Ontologies / 393

the relation that a set of possibilia bears to its individual members is certainly
not constituency. Freddy is no doubt in some sense a constituent of the set of all
possible pigs — ‘constituent’ is a very flexible word, and it is probably flexible
enough to permit that application —, but there is no conceivable sense in which
the set of all possible pigs is a constituent of Freddy.
Let this suffice for an account of “constituent ontology” and “relational
ontology.”13
I will now give some reasons for preferring a relational to a constituent
ontology — reasons for repudiating the idea of ontological structure. The austere
nominalists, of course, will want to remind me that we relational ontologians are
not the only ones to repudiate the idea of ontological structure. An austere
nominalist might remind me of this fact by a making a speech along these lines:
“The picture we austere nominalists have of concrete particulars is identical
with your picture of concrete particulars: we, like you, see them as what
Armstrong calls blobs.” And this reminder would be perfectly correct. But
in this essay, my target is constituent ontologies, not nominalism.14 I could
rephrase my description of my project this way: to put forward reasons for
repudiating the idea of ontological structure given that there are properties or
attributes.
My principal reason for repudiating the idea of ontological structure is a
reason I have for repudiating this idea, but it is not one that I can expect anyone
else to share. This reason is a very straightforward one: I do not understand
the idea of ontological structure or, indeed, any of the ideas with which one
finds it entwined in the various constituent ontologies. I do not understand the
words and phrases that are the typical items of the core vocabulary of any given
constituent ontology. ‘Immanent universal’, ‘trope’, ‘exist wholly in’, ‘wholly
present wherever it is instantiated,’ ‘constituent of’ (said of a universal and a
particular in that order): these are all mysteries to me. Perhaps the greatest of
all these mysteries — the one most opaque to my understanding — is the kind
of language that is used when the constituents of concrete particulars are said
to be physical quantities with numerical measures. The following passage from
On the Plurality of Worlds is a good example of such language. (In this passage
Lewis is expounding a theory that, although he stops short of endorsing it, is
for him a living option. He certainly does not think that the words in which he
expounds that theory are meaningless. Note that the “universals” referred to in
this passage are not “Ludovician properties”: they are immanent universals, not
sets of possible objects.)

[Consider] two particles each having unit positive charge. Each one contains
a non-spatiotemporal part corresponding to charge. [It is a universal and] the
same universal for both particles. One and the same universal recurs; it is multiply
located; it is wholly present in both particles, a shared common part whereby the
two particles overlap. Being alike by sharing a universal is ‘having something in
common’ in an absolutely literal sense. (p. 64)
394 / Peter van Inwagen

Such talk bewilders me to a degree I find it hard to covey. Perhaps I can “evoke
the appropriate sense of bewilderment” by quoting a passage from a referee’s
report I wrote a few years ago. (I should say that I was not recommending
that the editor reject the paper under review because I thought that the core
vocabulary of the author’s ontology was meaningless; I was rather trying to
convince the editor that the ideal referee for the paper was not someone who,
like me, thought that that vocabulary was meaningless.)

The author contends that the “features” of an electron (the electron’s mass,
charge, and spin are the examples of its features the author cites) are “con-
stituents” of the electron. I don’t care who says this — not even if it’s David Lewis
—, it just doesn’t make any sense. Consider the case of mass. Let Amber be a par-
ticular electron. Amber’s (rest) mass is 9.11 × 10 exp −31 kg. (I’ve rounded the
figure off to two decimal places; pretend I’ve written out the exact figure.) If ‘9.11
× 10 exp −31 kg’ is a name of something (if the ‘is’ of the previous sentence is the
‘is’ of identity), it’s a name of an abstract object. (And if ‘9.11 × 10 exp −31 kg’
isn’t a name of anything — if it is, as Quine liked to say, a syncategorematic
phrase —, or if it is a name of something but is not a name of Amber’s mass,
why would anyone suppose that ‘Amber’s mass’ is a name of anything? It looks
to me as if either ‘Amber’s mass’ and ‘9.11 × 10 exp −31 kg’ are two names for
one thing, or ‘Amber’s mass’ isn’t a name for anything: there just isn’t anything
for ‘Amber’s mass’ to name other than 9.11 × 10 exp −31 kg.15 ) You can perform
arithmetical operations on this object, for goodness’ sake. You can divide it by a
number, for example (if you divide it by 6, the result is 1.518 × 10 exp −31 kg),
and you can multiply it by another physical quantity (if you multiply it by 10
m/sec/sec, which is the magnitude of an acceleration, the result is 9.11 × 10
exp −30 kg-m/sec/sec). These “results” have other names. Other names for the
first result are ‘one-sixth the rest mass of an electron’ and ‘the amount Amber’s
mass would increase by if Amber were accelerated to half the speed of light from
rest’. Another name for the second result (if Amber is near the surface of the
earth) is ‘the magnitude of the gravitational force (in the direction of the center
of the earth) that the earth is exerting on Amber’—since 10 m/sec/sec is the
magnitude of the acceleration toward the center of the earth of a body (near the
surface of the earth and in free fall) that is due to the earth’s gravity.
Performing calculations like the ones I performed to get those results is
what solving the problems in physics textbooks largely consists in: applying
arithmetical operations like multiplication and division to items like masses,
charges, and spins.16 I can attach no sense to the idea that something one can
apply arithmetical operations to a “constituent” of might be of a physical thing.

And, I contend, what goes for “quantitative” immanent universals like mass and
charge goes for “non-quantitative” immanent universals like color universals and
shape universals. Since these universals are non-quantitative, I cannot, in trying
to describe the bewilderment I experience when I try to understand what their
proponents have said about them, complain that they are objects that one can
apply arithmetical operations to. The bewilderment I experience arises when I
 Relational vs. Constituent Ontologies / 395

try to form some conception of what immanent universals could be. I can see
that they are not what I call properties — not things that stand to one-place
open sentences as propositions stand to closed sentences. Not things that are
like propositions in that the concepts “truth” and “falsity” apply to them, and
unlike propositions in that they are not true or false simpliciter but are rather
true of false of things — true, perhaps, of this thing and not of that thing. I
can see that they can’t be properties (what I call properties) because, if for no
other reason, they are supposed to have some sort of presence in the physical
world: they can be constituents of physical things and can be located in space
(albeit their spatial features are strikingly different from those of the paradigmatic
space-occupiers, concrete physical particulars). But if not properties, what? The
features attributed to immanent universals by those who believe in them seem to
me be an impossible amalgam of the features of substances and the features of
attributes. I must make it clear that when I say these things, I do not pretend to
be presenting an argument. What I am presenting is rather a confession. Just as
a confession of faith — someone’s recitation of the Nicene Creed, for example —
is not a presentation of an argument for the thesis that anyone other than the
speaker should accept the propositions the confession comprises, a confession
of bewilderment is not a presentation of an argument for the thesis that anyone
else should be bewildered by whatever it is that the speaker finds bewildering.
What goes for immanent universals goes for tropes. I don’t understand what
people can be talking about when they talk about those alleged items. I will
attempt, once more, to evoke the appropriate sense of bewilderment.
Consider two balls that are perfect duplicates of each other. Among their
other features, each is 10 centimeters in diameter and the color of each is a certain
rather distressing variant on lime green. Apparently, some people understand
what it means to say that each of the balls has its own color — albeit the color
of either is a perfect duplicate of the color of the other. I wonder whether anyone
would understand me if I said that each ball had its own diameter — albeit the
diameter of one was a perfect duplicate of the diameter of the other. I doubt it.
But one statement makes about as much sense to me as the other — for just as
the diameter of one of the balls is the diameter of the other (10 centimeters), the
color of one of the balls is the color of the other (that “rather distressing variant
on lime green”).
On that point, the friends of immanent universals — those who are not also
friends of tropes — will agree with me. Setting to one side the fact that it is
difficult to suppose that they and I mean the same thing by ‘property’, they and
I agree that one property, such as greenness or the color green (as far as I can
see, ‘greenness’ and ‘the color green’ are two names for one thing), may be a
property of two particular things, such as two balls; they and I disagree about
what it is for a property to be a property of a given particular. The friends of
immanent universals spell this out in terms of constituency, and I don’t spell it
out at all — nor do I have any sense of what it would be to spell out what it is
for a given property to belong to a given object or objects. Those of you who are
396 / Peter van Inwagen

familiar with a controversy I had with David Lewis a long time ago will see that
we have wandered into the vicinity of what I once called ‘the Lewis-Heidegger
problem’.17 The Lewis-Heidegger problem may be framed as a question: ‘How
does a certain concrete object (a green ball, for example) reach out and take hold
of a certain proposition (the proposition that there is at least one green ball, for
example), an abstract object, and make it true?’ The question, ‘How does a
concrete object (like a green ball) reach out and take hold of a property (like the
color green), an abstract object, and make it had or exemplified or instantiated?’
is at least a very similar question. (It could be regarded as a generalization of
the former question — a generalization based on the fact that propositions are
true or false simpliciter and properties are true or false of things.) In my opinion,
these questions have no answers: no meaningful statement among all possible
meaningful statements counts as an answer to either of them.
I am experienced enough to know that there are philosophers who take
offence when you tell that what they are saying is meaningless or that they
are proposing answers to questions that have no answers. I’ll say what I have
said many times: in philosophy, and particularly in metaphysics, a charge
of meaninglessness should be no more offensive than a charge of falsity.
Meaninglessness is what we risk in metaphysics. It’s a rare metaphysical sentence
that does manage to express a proposition and expresses a false one — and
on those rare occasions on which a metaphysical sentence does do that (‘The
physical world has always existed’ might be an example), that is generally because
a metaphysician has encroached on someone else’s territory. If my metaphysical
writings contain meaningless sentences, and no doubt they contain a good many
of them, that is simply because I’m doing my job — trying to work out a
metaphysical position. If I weren’t willing to risk saying and writing things that
were, in Wolfgang Pauli’s immortal phrase, not even false, I’d take up the history
of philosophy.
Enough about my principal reason for rejecting constituent ontology in
all its forms. I’ll now say something about one of my ancillary reasons, a
reason that is epistemological or methodological or something in that area.
Bas van Fraassen, as many of you will know, is rather down on what he calls
analytic metaphysics.18 Most of the barbs he directs at “analytic metaphysics”
miss because they are based on misapprehensions or bad reasoning.19 But one of
them hits the mark squarely: I heartily applaud all that van Fraassen says against
those metaphysicians who ape the practice of scientists — or what they take to be
the practice of scientists — by appealing to “the method of inference to the best
explanation.” If I had ever thought that there was a method called “inference
to the best explanation” that could be used as an instrument of metaphysical
discovery (or which could be used to validate a metaphysical theory however
it had been discovered), van Fraassen would have convinced me otherwise. But
thank God I never have! I suspect, however, that use of this “method” is typical
of constituent ontologians, and I suspect that at least some relational ontologians
besides myself will find it as foreign to their way of thinking as I find it to mine.
 Relational vs. Constituent Ontologies / 397

Let me try to flesh these intuitions of mine out — these intuitions about what has
motivated the work that has led to the construction of constituent ontologies —
by giving an example. The example is fictional, but, like many fictions, it has got
some important bits of reality embedded in it.
A certain philosopher, Alice, sees or thinks she sees a certain metaphysical
problem. She calls it, perhaps, the problem of one over many: How can two or
more objects be in a perfectly good sense one, or in a perfectly good sense the same
(one in color or of the same color, for example)? This Granny Smith apple and
this copy of A Theory of Justice are both green. It follows that, in spite of the fact
that they are two distinct things, they are one in color. How can we account for
such facts? What metaphysical picture of the nature of ordinary particulars like
apples and books can explain how particulars that are not the same simpliciter
can nevertheless be the same in a certain respect? Obviously (Alice announces),
the way to proceed is to explain this phenomenon in terms of particulars’ having
certain structures, and to postulate some common item in the structures of the
members of every two-or-more-membered class of particulars that are the same
“in a certain respect.” Now the kind of structure that Alice proposes to appeal
to in giving an explanation of this sort obviously can’t be what I earlier called
mereological structure, for the apple and the book have no concrete particulars
as common parts — no atom or neutron or quark is common to them both.
The kind of structure that will do the explanatory job that Alice wants done
must therefore involve concrete particulars’ having constituents that belong to
some ontological category other than “concrete particular.” Alice therefore (let
us suppose) makes a proposal regarding a common constituent of — to revert to
our illustrative example — the apple and the book. She proposes, let us say, that
both the apple and the book have among their constituents a certain immanent
universal: an object that is wholly present wherever any of the concrete particulars
of which it is a constituent is present. She proposes, that is, that the common
feature of the book and the apple — what is ordinarily called greenness or
the color green — is a common constituent of the book and the apple. And why
should one believe in such a thing? Well (Alice contends), the theory that explains
best describes best: if the postulation of such a common constituent is both a
prima facie successful explanation of the sameness of color of numerically distinct
particulars and superior to all other prima facie successful explanations of that
explanandum (if there indeed are other prima facie successful explanations), that
will be sufficient to warrant our believing that that constituent really exists. (Cf.
the kind of warrant enjoyed by an early twentieth-century geneticist’s belief in
genes or in Einstein’s belief in the effect of the presence of mass on the local
metric of space-time.)
So Alice proceeds. Before we take leave of her, let us allow her to summarize
what she claims to achieved by proceeding in this way: “I have solved a
metaphysical problem — I have explained how objects that are not the same (that
are numerically distinct) can nevertheless be the same in a certain respect —,
and, in doing so, I have made a contribution to ontology: I have provided a
398 / Peter van Inwagen

good reason for supposing that a certain ontological category exists (that is,
has members, is non-empty). I have, moreover, demonstrated an important truth
about the way in which the members of this category — ‘immanent universal’ —
are related to the members of another category, ‘concrete particular’.”
I am happy to concede that the story of Alice — which was put forward
as a parabolic representation of the philosophical method that gives rise to
constituent ontologies — is not only fictional but a caricature. I could hardly
present anything other than a caricature of a philosophical method in such a
brief compass. But I do think it is a caricature that is not utterly divorced from
the actual practice of many metaphysicians. I don’t suppose that I shall succeed
in convincing anyone who is not already inclined to agree with me that Alice’s
use of “inference to the best explanation” is a bad method for metaphysics. In
my judgment, it can lead only to quasi-scientific theories that (supposing that the
words in which they are framed mean anything at all) fail to explain what they
were supposed to explain. (I distinguish quasi-science from pseudo-science. A
pseudo-scientific theory like astrology makes empirical claims; a quasi-scientific
theory does not.) When I say that a theory like Alice’s fails to explain what it
is supposed to explain, I do not mean that someone else may eventually devise
a theory that explains what Alice’s theory has failed to explain. I mean rather
that there’s nothing there to be explained, that no set of statements among all
possible sets of statements counts as an explanation of what it is for a particular
to have a property or for two distinct particulars to have the same property.20 (I
am, you see, what Armstrong would call an ostrich nominalist — or would be
but for the fact that I am not a nominalist. Perhaps I am an ostrich Platonist.)
And what does the Favored Ontology have to say about the common
properties of concrete particulars? I’ll answer this question by setting out what
I have to say about this matter, for I am the only proponent of the Favored
Ontology I am aware of.
I do believe that there is an object I call ‘the color green.’21 And, of course,
I think that the color green or the property greenness is exactly what all green
objects have in common, and I of course think that they share this thing that
they have in common with no non-green object. But I should never want to
say that the fact that greenness was a property of both the apple and the book
explained the fact that they were both green or the fact that they were both of
the same color. In my view that would be as absurd as saying that the fact that
the proposition that the book and the apple are both green is true explained the
fact that the book and the apple were both green. (“Daddy, why is the sky blue?”
“Well, sweetheart, that’s because the proposition that the sky is blue is true.” “Oh,
Daddy, how wise you are!”) I do think that there are such things as propositions,
and I do think that they have the properties truth and falsity, and I do think that
ascribing these properties to propositions plays an important and indispensable
role in our discourse. (For example: ‘No false proposition is logically deducible
from of a set of true propositions’ and ‘If q is logically deducible from a set of
statements that includes p and all of whose members other than p are true, then
the conditional whose antecedent is p and whose consequent is q is true’ are fairly
 Relational vs. Constituent Ontologies / 399

important logical principles.) But the concept of the truth of a proposition can
have only a “logical” role in an explanation of why some state of affairs obtains:
the concept of truth can figure in an explanation only in the way in which
concepts like logical deducibility and universal instantiation and transitivity can
figure in an explanation. And the same point holds, mutatis mutandis, for the
concept of the instantiation of a property.
“Well, then,” the interlocutor asks, “what method do you recommend
in ontology if not the method of constructing theories to explain observed
phenomena? And what has this method you would recommend got to do with
your adherence to a relational ontology?”
The answer to the first part of this question is complex, but fortunately I
have presented it elsewhere — and in some detail. (See, for example, the essay “A
Theory of Properties,” cited in note 10.) Stripped to the bare bones, the method
is this:
Look at all the things that you, the ontologian, believe “outside” ontology —
the beliefs that, as it were, you bring to ontology. Subject them to quantificational
analysis à la Quine. This will provide you with a large class of one-place open
sentences that you believe are satisfied. Try to give a coherent account of the
“satisfiers” of those sentences, a project that will, in some cases, involve fitting
them into a system of ontological categories. See whether the resulting system
of categories satisfies you intellectually. Subject it to all the dialectical pressures
you can muster — and attend to the dialectical pressures those who disagree
with you bring against it. As you are carrying out these tasks, keep the following
methodological rules of thumb in mind (and remember that they are only rules
of thumb, not infallible guides to the truth):

• Suppose you contend that certain objects (which you have somehow
specified) form or make up or constitute an ontological category — call it
“category X”; remember that every object has, for every property, either
that property or its complement: everything has a complete and consistent
set of properties; and that obvious truth must apply to the members of X;
if what you have said about X leaves it an open question whether certain
specifiable members of X have the property F, you have not said enough
about X.
• Suppose you contend that certain objects (which you have somehow
specified) constitute an ontological category — call it “category X”;
suppose that what you have said about X implies that each of the two
putative denoting phrases A and B denotes a member of X; ask yourself
whether A and B denote the same member of X; if what you have said
about X leaves this an open question, you have not said enough about X.
• Do not multiply categories beyond dire necessity.
• Try to tie all your terms of art to ordinary language by some sort of thread
that can be followed; for a good guide in this matter, look at any reputable
400 / Peter van Inwagen

introductory physics text, and learn from the way in which, starting with
ordinary language, the author introduces technical terms like ‘mass’ and
‘force’ and ‘energy’ and ‘momentum’.

And, finally, don’t be seduced by anything like “the Quine-Putnam indispens-

ability argument.” (This imperative doesn’t get a bullet point because it’s not a
rule of thumb. This imperative is an injunction.) If, for example, your analysis
of scientific discourse convinces you that quantification over — say — the real
numbers is an indispensable component of the practice of scientists, don’t go
on to maintain that the undoubted fact that science has been “successful” is
best explained by postulating the existence of the real numbers. Stay out of the
explanation business. Here endeth the lesson.

As to the second part of the interlocutor’s question (“What has the method
you recommend got to do with your adherence to a relational ontology?”), I have
no good answer. I can do no more than record my conviction that if you follow the
method I recommend, you will end up with neither a monocategorial ontology
(like austere nominalism) nor a constituent ontology. I think you will end up with
a relational ontology (if you end up with anything at all; perhaps you will confess
failure). But I should not regard it as a tragedy if someone were to demonstrate
that this conviction was wrong. If some philosopher showed me how to eliminate
quantification over abstract objects from our discourse — an achievement
that would in my view make the world safe for austere nominalism —,
I’d be delighted, for I’d really like to be an austere nominalist. And if a
philosopher adopted my proposed method and ended up with a constituent
ontology — well, if I didn’t find that outcome delightful, I’m sure I should find
it instructive: I should almost certainly learn something valuable by retracing the
intellectual steps that had led that philosopher to a constituent ontology. In any
case, whatever you end up with, it won’t be an explanatory theory. Explanatory
theories belong to everyday empirical investigation (the investigations of police
detectives, for example) and to the empirical sciences. What you can hope to end
up with is a system of ontological categories that it is plausible to suppose is the
system that we tacitly appeal to in our everyday and our scientific discourse.
I will close by turning briefly to a different topic, a possible objection to the
classification of ontologies that I have proposed.
I have said that constituent ontologies are a species of the genus “poly-
categorial ontology.” But at least two monocategorial ontologies — the New
Bundle Theory and L. A. Paul’s ontology — pose a problem for my scheme
of classification, for there is considerable intuitive plausibility to the thesis that
they and the constituent ontologies together constitute a natural class and that
a perspicuous taxonomy of ontologies should recognize this fact by placing
those two monocategorial ontologies and the relational ontologies in the same
genus. One might plausibly contend that the primary division in a taxonomy of
ontologies should not be twofold (“monocategorial” and “polycategorial”) but
threefold; something like this:
 Relational vs. Constituent Ontologies / 401

(1) austere nominalism

(2) relational ontologies
(3) the New Bundle Theory; the “Pauline” ontology; constituent ontolo-
gies.22

The lines of division drawn by this alternative taxonomy, it will be observed, cut
across the lines my taxonomy draws: my genus “monocategorial ontology” is
composed of the member of (1) and some of the members of (3), and my genus
“polycategorial ontology” is composed of the members of (2) and the remaining
members of (3).
What can be said in favor of this alternative scheme of classification? Why
does it seem that the ontologies grouped together in (3) form, as I put it, a natural
class? Is there a common characteristic of the members of the third division that
argues for their being grouped together? If there is such a common characteristic,
is it of sufficient importance to outweigh the fact that some of the ontologies
that share it are monocategorial and some of them polycategorial?
I can think of one characteristic common to the members of (3) that might
provide an interesting answer to these questions. I have had a very instructive
conversation with Professor Paul concerning the very different ways in which she
and I conceive of properties. When I thought about what she had said in this
conversation, it became clear to me that her conception of properties and the
constituent ontologians’ conception of properties were, if not identical, then at
least very similar, and very similar despite the fact that she and they disagree
about the mode in which properties, so conceived, function as constituents of
things.23 I base this judgment on a supposed feature of properties — and a
very significant feature it is — that is certainly common to Paul’s conception
of properties and the constituent ontologians’ conception of properties. This
common feature is nicely laid out in the following quotation from Jonathan
Lowe’s The Four-category Ontology:

Perception. .. involves a causal relationship between the perceiver and the object
perceived and we perceive an object by perceiving at least some of its properties.
We perceive, for instance, a flower’s colour and smell.24

This passage occurs in the course of an argument for the conclusion that some
properties must be accidents or tropes (Lowe’s term is “modes”) — for, in
Lowe’s view, universals cannot enter into causal relations and therefore cannot be
perceived. Unlike Lowe, Paul does think that some universals can be perceived.
But Lowe and Paul agree that some properties can be perceived. Lowe is a
constituent ontologian, and I think that all his fellow constituent ontologians
would agree with him and Paul on this point — and that New Bundle Theorists,
if there ever are any, should agree with him and Paul on this point.25 And this,
I suggest, is the “common characteristic” in virtue of which it is natural and
402 / Peter van Inwagen

intuitive for the taxonomist of ontologies to assign Paul’s ontology and the New
Bundle Theory and the constituent ontologies to the same genus.
I have no space to develop this suggestion in detail, but I would suggest
that anyone who thinks that my twofold taxonomy of ontologies is objectionable
because it places the Pauline ontology and the New Bundle Theory in a different
genus from the genus that contains the constituent ontologies should consider
the following proposal: that the primary division of ontologies should be into

— those for which the only primary ontological category is “concrete

particular” or “individual” or “ordinary object” or “substance” and
which therefore deny the existence of properties or attributes. (This genus
may have only one member, austere nominalism. Or it may turn out
that “austere nominalism” is a species, a species whose members are
individuated by their differing specifications of the one primary category.)
— those that affirm the existence of properties or attributes and treat
properties as wholly abstract things to which the concepts of location and
causation have no application (and which therefore cannot be objects of
perception).
— those that affirm the existence of properties and affirm further that
at least some properties are perceivable (and therefore have some sort of
spatial location and are capable of entering into causal relations).

Notes

1. To appear in Daniel Novotny (ed.) Metaphysical Disputations: Contemporary

Neo-Aristotelian Perspectives — despite the fact that the “perspective” from
which that essay is written was very far from being neo-Aristotelian.
2. Or, if you like, we may distinguish a strong and a weak sense of “an ontology”
and say that a strong-sense ontology is an attempt to answer the ontological
question in terms of a system of ontological categories. A weak-sense ontology
will then be an attempt to answer the ontological question in a way that does
not involve an appeal to a system of ontological categories. When Quine himself
uses the word ‘ontology’ as a count-noun, he presumably uses it in only the weak
sense; no doubt he would have vehemently rejected any proposal to introduce
the concept “ontological category” into philosophy.
3. In this essay, I will assume, for the sake of simplicity, that everything is a member
of at least one ontological category — that there are no “categorially homeless”
things. The question whether there are or could be categorially homeless things is
an important meta-ontological question, but it is a question not closely connected
to any of the issues that will be considered in this essay
4. A monocategorial ontology implies, contra Aristotle, that the universal class
possesses sufficient internal ontological unity or uniformity to count as a
natural class (it contains only concrete particulars, for example, or it con-
tains only properties). In contrast, a polycategorial ontology — such as
 Relational vs. Constituent Ontologies / 403

Aristotle’s — implies that the universal class possesses insufficient internal

ontological unity to count as a natural class.
5. A non-austere or luxuriant nominalism is a nominalism that admits the existence
of tropes or individual accidents or particularized properties: the referents of
phrases like ‘the wisdom of Solomon’, ‘the rectangularity of central park’, and
‘the aridity of Arizona’ — phrases that denote properties of Solomon, Central
Park, and Arizona, respectively, and which do not denote properties of the Twin
Earth counterparts of these objects. Luxuriant nominalism lays claim to the title
‘nominalism’ on the ground that it denies the existence of universals.
6. James Van Cleve, “Three Versions of the Bundle Theory,” Philosophical Studies
47 (1985), pp. 95–107.
7. The earliest statement of Paul’s ontology was in “Logical Parts” Noûs 36 (2002),
pp. 578–96. (Reprinted in Michael Rea (ed.), Critical Concepts in Philosophy:
Metaphysics, Vol. V (London and New York: Routledge, 2008).) More recent
statements of the ontology can be found in “A One Category Ontology,”
forthcoming, and “Building the World from Fundamental Constituents,” forth-
coming in Philosophical Studies. There are useful summaries of the ontology
in “Coincidence as Overlap,” Noûs 40 (2006), pp. 623–59 and “In Defense of
Essentialism” in John Hawthorne (ed.) Philosophical Perspectives, Vol. 20 (2006)
Metaphysics, pp. 333–72.
8. For the origin of this terminology, see Nicholas Wolterstorff, “Bergmann’s
Constituent Ontology,” Noûs 4 (1970), pp.109–34, and Michael Loux, “Aris-
totle’s Constituent Ontology,” in Dean W. Zimmerman (ed.) Oxford Studies in
Metaphysics, Vol. 2 (Oxford: Oxford University Press, 2006), pp. 207–49.
9. Unless, perchance, the relational ontologian — the term I prefer for a practitioner
of ontology — thinks that some concrete particulars are “extended simples”;
someone who holds this view may want to say that extended concrete simples
have no mereological structure but do have a spatial or spatiotemporal structure.
10. My “favored ontology” is not the ontology of material things that was set out
in my book Material Beings. It is, rather, the much more abstract and general
ontology I described in “A Theory of Properties,” in Dean W. Zimmerman (ed.)
Oxford Studies in Metaphysics, Vol. 1 (Oxford: Oxford University Press, 2006)
pp. 107–38. I concede that in that essay I did not explicitly state that properties
(or, more generally, relations) constitute an ontological category, for my primary
concern was with the question whether there were properties and relations.
But the idea that “substance” and “relation” were the two primary ontological
categories is certainly tacitly present throughout “A Theory of Properties.”
11. My use of this term (in the essay cited in the previous note) has caused
some confusion. Observing, correctly, that I have borrowed it from Frege (the
German word is ungesättigt), some of the readers of that essay have inferred,
incorrectly, that my use of the term implies that I accept something resembling
Frege’s concept/object distinction: a property/object distinction modeled on the
concept/object distinction. Far from it, however, for I do not understand the
concept/object distinction. The objects I call properties are just that: objects.
More exactly, they are objects in the very general sense that this word has in
logic and mathematics: a property can be the referent of a noun or a noun-phrase
(‘wisdom’; ‘Solomon’s most famous property’; ‘the property of being an x such
that x is wise’) and properties can be “quantified over” (‘Some properties are
404 / Peter van Inwagen

uninstantiated’; ‘An impossible property entails every property’); and when we

quantify over properties we use the same logical machinery that we use when we
quantify over shoes and ships and bits of sealing wax.
12. See David Lewis, On the Plurality of Worlds (Oxford: Blackwell, 1986),
Section 1.5 “Modal Realism at Work: Properties,” pp. 50–69.
13. Consider the thesis (“Platonism”) that properties can exist uninstantiated,
and the thesis (“Aristotelianism”) that properties cannot exist uninstantiated.
Relational ontologians tend to be Platonists, and constituent ontologians tend
to be Aristotelians. But it is at least possible consistently to be a relational
ontologian and an Aristotelian, and it may even be possible consistently to be
a constituent ontologian and a Platonist. For that reason, I decline to regard
Aristotelianism as essential to the idea of a constituent ontology, and I decline
to regard Platonism as essential to the idea of a relational ontology. Similar
remarks apply to the question whether properties are “sparse” or “abundant.”
Relational ontologians tend to hold that most open sentences (all of them but
a few Russellian monsters) express properties, and constituent ontologians tend
to hold that very few open sentences express properties. But I think that these
tendencies are only tendencies, that both can be resisted without contradiction.
14. For my reasons for rejecting nominalism, see “A Theory of Properties” (cited in
note 10).
15. This parenthesis is one illustration among many possible illustrations of a
very general point about the semantics of physical-quantity terms. Consider,
for example, what is perhaps the simplest case of a physical quantity: distance
(or length or displacement). The two putative denoting phrases ‘the equatorial
diameter of the earth’ and ‘1.276 × 10 exp 7 m’ are either both real denoting
phrases and denote the same thing or are both syncategorematic.
16. Or one might want to say that applying arithmetical operations like multipli-
cation and division to items like masses, charges, and spins is the typical final
stage of finding the solution to a physics problem. (In the earlier stages, one
generally has to engage in some mathematical reasoning that involves techniques
rather more “advanced” than multiplication and division; the purpose of this
reasoning is to reach the point at which one can find the answer to the problem
by applying simple arithmetical operations to the particular physical quantities
that were specified in the statement of the problem.)
17. In “Two Concepts of Possible Worlds,” Midwest Studies in Philosophy 11 (1986)
pp. 185–213. See p. 204 ff .
18. See his The Empirical Stance (New Haven and London: Yale University Press:
2000), particularly Lecture 1, “Against Analytic Metaphysics,” pp. 1–30.
19. So I say, at any rate. See my essay, “Impotence and Collateral Damage: One
Charge in Van Fraassen’s Indictment of Analytical Metaphysics,” Philosophical
Topics 35 (2007), pp. 67–82, and my A.P.A. Central Division Presidential
Address, “The New Anti-Metaphysicians,” Proceedings and Addresses of the
American Philosophical Association, Vol. 83 no. 2 (2009), pp. 45–61.
20. That is, no possible set of statements could be an explanation of these things
that is of the kind that constituent ontologians claim to provide. I don’t mean
to say that the fact that the book and the apple are both green could not have
explanations of other kinds. It is no doubt possible to construct a causal narrative
 Relational vs. Constituent Ontologies / 405

that explains how the book got to be green and no doubt possible to construct
a causal narrative that explains how the apple got to be green. (And those two
narratives, taken together, would, in one sense, explain the common greenness of
the book and the apple.) And it may well be possible to identify certain physical
features of the surfaces of objects of a certain sort, a “sort” that contains things
like apples and books, such that for a thing of that sort to be green is for it
have a surface with those features — and identify a corresponding set of surface-
features of objects of the book-apple sort for each color-property. (And if that
were accomplished, one could, in one sense, give an account what it is for distinct
objects to be of the same color.)
21. At any rate I think that there are attributes or properties, and I’m willing to
suppose for the sake of the present example that greenness or the color green
is one of them; but the physics and physiology of color are subtle and difficult,
and the metaphysics of color must take account of the subtleties and difficulties
that the special sciences have discovered.
22. Perhaps the ingenuity of metaphysicians will in the course of time produce
additional monocategorial ontologies that should be assigned to the third genus.
After all, the New Bundle Theory and the “Pauline” ontology are both recent
arrivals on the philosophical scene.
23. Since adherents of the New Bundle Theory exist only as creatures of fiction,
and since the author of the fiction, Professor Van Cleve, has not filled in that
part of the fiction, there is no definitive, textual answer to the question whether
they conceive of properties as Paul and the constituent ontologians do. But
if there were any actual New Bundle Theorists they certainly would not —
could not — conceive of properties as relational ontologians do: as necessarily
existent abstract objects to which the concepts of location and causation have
no application.
24. E. J. Lowe, The Four-Category Ontology: A Metaphysical Foundation for Natural
Science, (Oxford: Oxford University Press, 2006). The quoted passage occurs on
p. 15.
25. There is, of course, the fact to be considered that, according to the New Bundle
Theory, there are no perceivers.