Introduction: What Is Ontology?
What Is Metaontology?
Chapter Outline
1 Ontology …
2 … And metaontology
1
2
3 … And metaphysics
4 … And science, and common sense
5 The rest of the book
3
5
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1 Ontology …
Biology studies living things. Psychology studies mental functions. Astronomy deals
with celestial phenomena and mathematics deals with numbers. They all study
something, of course, but none of them studies everything. They do not address the
whole of reality, or all that there is. Ontology does.
This characterization of ontology can be traced back to Aristotle, who in Book
Four of his Metaphysics introduced the idea of a ‘science of being qua being’, or of
being as such. Yet Aristotle did not use (a Greek counterpart of) the word ‘ontology’
to name such a science, although the term comes from ón, the present participle of
eînai, the Greek verb for ‘to be’. The word is a more recent seventeenth-century
coinage (nor did Aristotle use a Greek counterpart of the word ‘metaphysics’ – we
will get back to this). After having been dismissed by much early analytic and neopositivistic philosophy, ontology made an impressive comeback in the second half of
the twentieth century. One initiator of the renaissance was Willard van Orman
Quine, who made mainstream the idea that the task of ontology is to write down
something like a complete catalogue of the furniture of the world. What we want
from ontology is a list of all there is, and ontology gets the list right insofar as it
misses nothing that is there, and includes nothing that isn’t there.
However, many still think that there is something perplexing about the study of
what there is, which sets it apart from the other above-mentioned disciplines. Laymen
have a rough understanding of what biology, psychology or mathematics are about,
and few doubt that living creatures, or the functioning of the mind or the realm of
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Ontology and Metaontology
numbers, are legitimate areas of rational investigation. But, first, what does it mean to
study being qua being, or what is? And, secondly, via which methods or procedures of
inquiry should such a study be carried out? While there are many excellent
introductions to ontology on the market, few deal extensively with these two
issues – questions to which professional philosophers give conflicting answers.
This provided our motivation for writing the book.
2 … And metaontology
As its title makes explicit, this book is an introduction to ontology as well as an
introduction to metaontology. And the term ‘metaontology’ is a very recent coinage:
as far as we know, it officially entered the philosophical landscape as the title of a
1998 essay by Peter van Inwagen, one of the greatest contemporary ontologists. Now,
van Inwagen understood metaontology as dealing precisely with the two issues just
mentioned: if the key question for ontology, as Quine told us, is ‘What is there?’,
then the (twofold) key question for metaontology is ‘What do we mean when we ask
“What is there?”’, and ‘What is the correct methodology of ontology?’. By using the
prefix ‘meta-’, van Inwagen meant to suggest a kind of higher level reflection: ‘meta-X’
as the inquiry on the central concepts and procedures of discipline X.
It is only natural that the reflection on the proper methodology of a discipline
historically comes after the discipline itself has flourished and developed its own
conceptual tools. Perhaps the main element of novelty in early twenty-first-century
ontological research is that many of its practitioners pay more and more attention to
metaontological issues. ‘Metaontology’, as Ross Cameron 2008: 1 said, ‘is the new
black’. This book aims to give a textbook presentation of the discipline in line with
such recent developments.
Now the metaontological turn has brought a rediscovery of some traditional and
pre-Quinean approaches to ontology. As for the first of those two meta-questions,
‘What do we mean when we ask “What is there?”’: the catalogue metaphor embedded
in the Quinean view has it that the goal of ontology is to write a list of everything that
falls under the notion being. But the original Aristotelian idea of a ‘science of being
qua being’ was concerned, first of all, with the very concept of being, that is, with the
meaning of the notion itself. Quine did have something important to say on the
meaning of being, as we will see in the first part of the book. Other recently developed
metaontological stances differ from the Quinean approach in their conceptualization
of being as such, and from this they derive different views of ontology’s tasks. Some
say that the primary goal of ontology is not to write a list of all there is, but (as also
Aristotle set out to do in the Metaphysics) to identify the most fundamental or basic
entities: those which ground all the rest, and on which everything (else) depends.
Introduction: What Is Ontology? What Is Metaontology?
Some claim, as Aristotle himself did, that being can mean different things – that there
are different ways of being – and that the primary goal of ontology is to identify these
meanings, or ways of being. Some even introduce a distinction between being and
what is there, and claim that some things should be included in the universal catalogue
because they are there, although they lack being.
As for the second meta-question, namely ‘What is the correct methodology of
ontology?’, the new methodological consciousness of twenty-first-century ontology
has revitalized deflationist perspectives on the goals and ambitions of ontology
itself. Quine’s methodology for ontology was naturalistic: he believed that we should
include in the universal catalogue the kinds of entities our best natural science
commits us to (he also had views on how such ‘ontological commitment’ ought to
be understood, as we will see). He thus denied that ontology has a special
philosophical autonomy, allowing it to float freely from the findings of natural
sciences. Contrary to the beliefs of his master Rudolf Carnap, Quine believed
ontological questions to generally make perfect sense and to allow substantive
replies. Nonetheless, other philosophers nowadays are much more Carnapian: they
think that ontological questions make sense only when appropriately restricted or
qualified. Some have a more strongly dismissive approach, and believe that most of
these questions are just shallow: they reduce – as some founding fathers of analytic
philosophy also thought – to confusions concerning the meanings of some
expressions of our everyday language.
3 … And metaphysics
Ontology entertains a complicated relationship with metaphysics, which is itself
one of the most traditional parts of philosophy. The border between ontology and
metaphysics in the works of contemporary philosophers is fuzzy. Some just use the
two terms interchangeably. Sometimes the relationship between metaphysics and
ontology is understood as of one between a discipline and one of its sub-disciplines.
As a first approximation, metaphysics is the branch of philosophy which asks what
reality is like – as opposed to such other branches as epistemology, which asks what
we can know about reality and how; or ethics, which asks how reality ought to be.
Textbook presentations often say that metaphysics is an investigation into the most
fundamental and general structures and features of reality (Crane and Farkas 2004;
Garrett 2006).
Just as the word ‘ontology’, so the word ‘metaphysics’ comes onstage later than the
Greek philosophers who can be considered the founding fathers of the discipline. It
has a tangled history too. When Aristotle’s works were ordered after his death, some
of them were put after his writings on physics. They belonged to a discipline Aristotle
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Ontology and Metaontology
called ‘first philosophy’, and which dealt with such fundamental topics as being,
causation, God and other issues. Such writings then got the label of ‘what comes after
the books on physics’, in Greek: tà metà tà physikà – hence, ‘metaphysics’. Physics was
taken as the study of the material world, subject to change, movement, generation
and corruption. ‘First philosophy’, as the discipline that studies the most general and
fundamental aspects of reality, was believed by Aristotle to transcend physics in
some sense. In order to fully understand the foundations of reality, for him and for
many others after him, one has to resort to incorporeal, nonphysical entities, such as
God. So the name ‘metaphysics’ also came to mean a study that goes ‘beyond physics’
in this sense: it deals with a realm that surpasses, or is anyway not reducible to, the
physical world.
Now when ontology is understood the Quinean way, that is as the quest for a
catalogue of all there is, it may then be seen as in some sense a preliminary to
metaphysics. One first writes down the complete inventory of reality – one says what
is there. Then one wonders about the nature, structure and fundamental features of
the kinds of things listed in the inventory.
Even if one agrees with the view of ontology as preliminary to metaphysics, the
border between the two remains fuzzy: as we will experience throughout this book,
ontological issues (so understood) naturally tend to shade into metaphysical ones (so
understood). Thinking about the relationship between ontology and metaphysics in
the aforementioned terms can help to understand the following pattern, often
recurring in contemporary philosophy: authors A and B can seriously disagree on
the metaphysical status of entities of kind F, which they nevertheless agree to include
in the ontological catalogue. Here’s one example that we will delve into in the third
part of the book. The notion of possible world is extremely useful in most branches of
contemporary philosophy. One starts by taking ‘possible world’ to stand for a way
reality as a whole could be or could have been. This quickly leads to the natural
twofold question: are there really possible worlds distinct from the actual one – that
is should we include them in the ontological catalogue? And if so, then what kind of
entities are they? Now philosophers A and B can agree on including possible worlds
in their ontologies: they both reply ‘yes’ to the first ontological question. However A
thinks that these things (possible worlds) are just like our actual world, but causally
and spatiotemporally isolated from it. In particular they are, as we may say, (mostly)
concrete material objects: things endowed with a mass, which occupy some space and
are subject to the flow of time. On the contrary, B thinks of them as abstract objects –
things more similar to numbers, functions and, perhaps, concepts, than to these
physical surroundings of ours. So A and B have diverging metaphysical views on
possible worlds.
It is fair to say that such characterization of the relation between ontology and
metaphysics, despite being widespread, is not uncontroversial. To begin with, it is
possible to accept the ontology-as-catalogue metaphor without taking ontology to be
Introduction: What Is Ontology? What Is Metaontology?
preliminary to metaphysics. If one thinks of metaphysics as an attempt at ‘writing the
book of the world’ (Sider 2011), then the ontological job will look like writing the
index of contents to the book of the world. And the index of contents is often written
when the book is close to completion. Some authors, for example, Bergmann 1967
and Grossmann 1992, believe that we just cannot decide whether some putative kind
of entities should be included in the ontological catalogue without first giving some
characterization of what the kind is like. These philosophers will tend to understand
‘ontology’ itself as meaning the study of the fundamental and most general structures
of reality. They will then tend to use ‘ontology’ just as a synonym of ‘metaphysics’, or
to blur any distinction between the two (for a comparison between this way of
understanding ontology and the one followed by us above, see the introduction to
van Inwagen 2001). Besides, the development of non-Quinean metaontologies, as we
will see, has brought even more pressure on the mainstream way of drawing the line:
for it presupposes the ‘Quinean catalogue’ view of ontology, which is questioned in
some alternative metaontological approaches. This quick overview should make
clear that this book, dealing with ontology and its methods, is perforce also, to some
extent, a metaphysical book.
4 … And science, and common sense
Let us stick again with the ‘catalogue’ or ‘index of contents’ metaphor for ontology.
Another natural preliminary question about writing the catalogue or index of
contents to the book of the world is: what is specifically philosophical – as opposed
to scientific, on the one hand, and plainly commonsensical, on the other – about
this task?
Sciences such as physics, chemistry, astronomy, biology, etc., already teach us a lot
about the makeup of reality. We can learn, for instance, that the surface area of Saturn,
measured in square kilometres, is 1.08 · 1012 (Liggins 2008a), that some biological
species are cross fertile, that spiders share some important anatomical features with
insects (van Inwagen 2004), that the event of a solar flare can release several billions
of joules of energy. Also, we share commonsensical knowledge on lots of things
constituting the furniture of the world. We know that fragility is a feature of crystal
glasses, that bananas are yellow when ripe, that a bikini is composed of a bra and a
slip, that Emmental cheese has holes in it and that the Clinton-Lewinsky affair was a
scandalous incident. Suppose we look at examples such as these and start writing
down the following list:
1 Planets, like Saturn
2 Insects
3 Bananas
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Ontology and Metaontology
4 Spiders
5 Bikinis
6 Holes, for example, in pieces of cheese
7 Numbers, like 1.08 · 1012
8 Properties, such as fragility, ripeness, and genetic features
9 Biological species
10 Events, like solar flares and the Clinton-Lewinsky affair
11 ...
Would a list of this kind tell us an ontologically satisfying story? One problem is that
it seems randomly constructed. It resembles the classification of animals in Borges’
The Analytical Language of John Wilkins:
Those that belong to the Emperor
Embalmed ones
Those that are trained
Suckling pigs
Mermaids
Fabulous ones
Stray dogs
Those included in the present classification
Those that tremble as if they were mad
Innumerable ones
Those drawn with a very fine camelhair brush
Others
Those that have just broken a flower-vase
Those that from a long way off look like flies
One would like to impose more order and structure to our inventory of the furniture
of the world: we want our list to be systematic, in some sense.
A related issue may be one of insufficient generality – though pinning down the
exact level of generality is no easy task. Ontological catalogues don’t typically stick
with such entries as bikini, insect or banana, but comprise much more general
categories. For instance, we may group planets like Saturn as well as insects, bananas,
bikinis and human beings like Clinton and Lewinsky into a single very broad category.
All things belonging to these kinds are, to retrieve a label we used above, concrete
material objects: they all have mass, they occupy a place in the physical world.
But what about the sixth item in the list? Should we include holes in our catalogue
of all there is? Holes being devoid of mass, they look quite unlike things belonging to
the first five items. Is a hole something like an absence of matter, or a kind of
nothingness? If so, how can holes exist? A parsimonious ontologist may deny that
holes should be included in our ontological catalogue: out there in the world, there
Introduction: What Is Ontology? What Is Metaontology?
really are no holes. But then we have a problem: ‘There are holes in pieces of Emmental
cheese’ is a truth of common sense, and for this truth to be true there must be holes
in pieces of Emmental cheese – thus, there must be holes.
How about our seventh item – numbers, like 1.08 · 1012? These also look very
different from concrete material objects. Saturn has a very large mass – so large that
it generates a gravitational field, which would attract you, should you get close
enough. In fact, the number 1.08 · 1012 is, so to speak, too light and thin to have any
attractive force on you. It doesn’t even make much sense to wonder about the thinness
of a number, as well as about its spatiotemporal location. Indeed, 1.08 · 1012 does
nothing physical to you: it is causally inert, as we may say.
But how can we know anything about things we cannot entertain causal
relationships with? Can we even be sure that they are there? Even if we were freed
from our contingent spatiotemporal limitations, we could never cross paths with
1.08 · 1012, for it’s nowhere to be found in the physical world. Some may find 1.08 ·
1012 and its peers to be too obnoxious to be admitted in our ontological list of the
components of the world. Numbers, sets and other mathematical entities must simply
not be included in our ontology, these parsimonious folks may claim. On the other
hand, refusing to include numbers in our ontological catalogue may also bring
problems. If there are no numbers, how could it be true that, as mathematics teaches
us, seven is a prime number? This can only be the case, as it seems, if there is a
number (seven), which has the feature of being prime – thus, if there are numbers.
How about properties, such as fragility or ripeness, and biological species, such as
spiders and insects – our candidate items no. 8 and no. 9? Considerations of
ontological parsimony may lead some not to include them in the catalogue either. Of
course there are material objects, some of which are ripe or fragile, some of which are
human beings. Yet, why should we admit fragility, ripeness or the species homo
sapiens, above and beyond the things which are fragile, ripe or human? Parsimonious
ontologists might have arguments similar to the ones against numbers (properties
and species are often grouped with mathematical objects under the broad label of
abstract objects, which we also used above, and opposed to concrete material beings).
We see, touch and interact causally with human beings, fragile glasses and ripe
bananas, but nobody has ever seen or touched fragility, ripeness or humanity. One
may object. We also directly speak of species: we claim that some of them are crossfertile; and this can only be true if there are cross-fertile species, thus, if there are
species. We also seem to know things about properties – for instance, we know that
fragility is a property of crystal glasses; and this demands that there be properties.
How about item 10 in the list? Events – things that happen – make for another
popular ontological category. Events seem ubiquitous in our daily life: Clinton’s affair
with Lewinsky was scandalous, but Kennedy’s killing by Oswald was tragic; the
French revolution was a momentous event, while Francesco’s watering his flowers
yesterday just passed unnoticed. And unlike abstract objects, we cannot easily dismiss
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Ontology and Metaontology
events on the ground of their being devoid of causal powers. On the contrary, they
seem to be the main actors of causal processes: we say that the throwing of a stone
caused the breaking of the window, that the Clinton-Lewinsky affair caused the
impeachment of the President, and that the latest solar flare caused the emission of
billions of joules of energy in the Solar System. Events also present problems of their
own, for instance, concerning the fine-grainedness of their individuation. Francesco
walks to the same office every working day; but is the event of Francesco’s walking to
his office one single general event, which recurs many times across the year? Or are
we talking of similar but distinct particular events, each with its own unique
spatiotemporal setting? We may also have issues with the identity of the particular
events themselves: is Oswald’s shooting the same as Kennedy’s killing?
Now notice that all of these concerns are not typical of disciplines like physics,
mathematics or biology. Mathematicians talk about prime numbers; biologists talk
about cross-fertile biological species; astrophysicists deal with solar flares. But, qua
scientists, they will not typically wonder whether there really are prime numbers,
species, properties or events – whether these things ought to be included in the
ontological catalogue. Nor will they wonder what it means to ask whether the world
really includes these entities or not. Nor will they typically wonder what they themselves
are ontologically involved with when they claim that there are infinitely many prime
numbers, or that genetic features are shared between spiders and insects.
Nor is common sense unqualifiedly helpful in all of these issues – even though, as
we will see throughout this book, some ontologists take the deliverances of common
sense, for example, as they show up in our ordinary talk, very seriously. Common
sense often delivers vague, imprecise, ungrounded or occasionally inconsistent
verdicts on the existence of various kinds of things. Here’s one example. It is
commonsensical to maintain that everyday objects have parts that constitute them.
Bananas have a peel and a pulp, normally endowed human beings have arms, legs and
a head. Also, according to common sense, scattered material objects may constitute
further objects. A slip and a bra for instance, can compose a further thing: a bikini.
Yet it is not commonsensical to think that this can always happen: intuitively, there’s
no object made up of Brad Pitt’s face and George Clooney’s body. So according to
common sense, two objects sometimes compose a further one and sometimes do not.
And there seems to be no commonsensical criterion to draw a principled line between
the case in which bunches of material objects compose a further object as its parts,
and the case in which they don’t. But we need such a criterion to build a well-motivated
ontological catalogue.
Here philosophy steps in again. As we will see in the third part of our book,
specifically in Chapter 12, philosophical considerations may lead ontology to sharply
depart from common sense on the question: ‘When does the inclusion of two material
objects in our inventory force us to include also one further object, composed exactly
of them?’. A parsimonious ontologist may plainly deny the existence of bikinis by
Introduction: What Is Ontology? What Is Metaontology?
claiming that what actually exists are just slips and bras. A bikini is nothing but a slip
plus a bra: once we have counted the slip and a bra, there is no reason to countenance
a further object, the bikini. But then, an even more parsimonious ontologist may
claim, slips and bras are nothing but bunches of atoms and molecules arranged in a
certain way. Once we have countenanced the (properly arranged) atoms and
molecules, there is no reason to further countenance slips and bras. Worse:
countenancing them may bring lots of troubles concerning their persistence across
time and change and their spatial boundaries. It’s better to say that there really are no
such things (we now see that, although ontologists look for the most general kinds of
being, this does not prevent them from expressing their disagreements more
concretely: ‘Unlike van Inwagen, I include bananas in my ontology’ – not just
subatomic particles arranged banana-wise: van Inwagen 2001: 3).
There seems to be room for philosophical work, then – at least, if we are sensitive
to issues like the ones just explored, for which physics and the special sciences, but
also commonsensical shared beliefs, often deliver no clear verdicts. We may want to
know whether apparently problematic entities like numbers, holes and properties
can be admitted in our catalogue of the furniture of the world. If we don’t include
them, we need to make sense of facts, truths and bits of knowledge apparently
involving them. If we do include them, we need to answer objections of various kinds
to their ontological respectability.
5 The rest of the book
The book is neatly divided into two halves. Parts 1 and 2, making for the first half,
focus on metaontology. There is a mainstream metaontological view among analytic
philosophers: this is dealt with in Part 1. Its origins are traced back to Russell’s On
Denoting (Chapter 1), which provided the methodological paradigm of philosophical
analysis for much of twentieth-century philosophy.
The mainstream view, though, is usually labelled as ‘Quinean’, for it is most clearly
stated in such famous Quinean papers as On What There Is. Chapter 2 explains the
pivotal theses of Quine’s metaontology: that ontology’s key question is: ‘What is
there?’; that in some sense the question can be answered in one word, ‘Everything’,
for it is trivially true that everything exists, but in another sense it is not trivial at all;
that it is inconsistent to make certain claims while holding that things of a certain
kind do not exist (what is known as Quine’s ‘criterion of ontological commitment’);
that there is a principled way to settle debates about the existence of things like
numbers, propositions, properties, etc.
Chapter 3 delves into the details of the standard metaontological view, as
developed, for example, in Peter van Inwagen’s essays: being is not a (non-trivial)
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1
Introduction
I look around my office and seem to see a table, a lamp, some books, and a variety
of other objects. I look out the window and seem to see a dog, a fence, a tree, and
of course the various things that together compose the tree: the trunk, the
branches, the leaves, and the partially visible roots. And when I think about
which other things out there together make up a single object, it seems that there
is nothing at all composed of the trunk and the dog—no one object that’s right
where they are, and that’s partly furry and partly wooden.
My aim in this book is to defend the view that, when it comes to which highly
visible objects there are right before our eyes, things are more or less the way they
seem. There are tables, trees, trunks, dogs, and all manner of other ordinary
objects, and there are no dog–trunk composites or other such extraordinary
objects. I call this a conservative view about which objects there are.
Outsiders to the debates over the metaphysics of material objects will likely
find my view so obvious as to hardly be worth stating. Let alone defending. Let
alone spending a whole book defending. Insiders, though, will likely find it
astounding and almost certainly indefensible. These insiders tend to fall into
INTRODUCTION
one of two broad categories. First, there are the eliminativists, who deny the
existence of wide swathes of ordinary objects: there are no tables or stones, and
perhaps no trees or dogs either. Next, there are the permissivists, according to
whom there are countless highly visible macroscopic objects that are right before
our eyes but nevertheless escape our notice. For instance, they will say that there
is a trog in my yard, an object composed of the dog and the tree trunk.
Here is what it’s going to take to change their minds. First, they need to be
convinced that eliminativism and permissivism are at odds with our ordinary
beliefs and intuitions about which objects there are, something that (you may be
surprised to hear) is widely denied. Second, they need to be convinced that it is
not simply a biological or cultural accident that we wind up dividing up the world
into objects the way we do. Third, they need to be shown how to resist the
arguments for eliminativism and permissivism—chief among them, arguments
that our way of dividing up the world into objects is objectionably arbitrary. And
this is what I propose to do.
The book is arranged into roughly three parts. The first is a guided tour of the
positions and arguments that define material-object metaphysics. In chapter 2,
I present the arguments that have driven so many philosophers away from
conservatism and towards eliminativism and permissivism. In chapter 3,
I survey the different forms that eliminativism, permissivism, and conservatism
can take, and I clarify the sort of conservative view that I plan to defend.
In the second part, I articulate and defend my main argument against
revisionary views like permissivism and eliminativism: an argument from
counterexamples. Eliminativist views entail that there aren’t any tables. But
there are. Counterexample. Permissivist views entail that there is something
composed of the dog and the trunk in my yard. But there isn’t. Counterexample.
In chapter 4, I explain why the premises of these arguments are at least prima
facie justified, and I address the complaint that the arguments are questionbegging. I then turn to the various reasons that revisionists have given for being
untroubled by the alleged counterexamples. Some are untroubled because they
think that the revisionary views are actually entirely compatible with ordinary
belief (and that ‘revisionary’ is a misnomer). In chapter 5, I argue that they are
genuinely incompatible. Others are untroubled because they take themselves to
have adopted a new way of talking—a “language of ontology room”—in which
revisionary-sounding claims like ‘there are no tables’ can be uttered without fear
of running afoul of ordinary belief. In chapter 6, I argue that we (and they) have
no way of telling what is and isn’t true in this newfangled language and,
accordingly, we all ought to take a skeptical attitude towards the claims being
uttered in that language. Still others are untroubled because they take themselves
INTRODUCTION
to have “debunked” our ordinary beliefs about which objects there are by
showing them to have a dubious source. In chapter 7, I show how conservatives
can answer these debunking arguments, and I argue that permissivists are in no
position to be advancing these debunking arguments.
In the third part, I turn to the arguments against conservatism. In chapter 8,
I examine a range of arbitrariness arguments, according to which there is no
ontologically significant difference between the ordinary objects that conservatives let into their ontology and certain of the extraordinary objects to which
they refuse entry. In chapter 9, I address the argument from vagueness, which
purports to show that the sort of restriction that conservatives want to impose on
which composites there are is bound to give rise to vagueness about what exists,
something that is ruled out by widely accepted theories of vagueness. Finally, in
chapters 10–12, I address the overdetermination argument, the argument from
material constitution, and the problem of the many, all of which are meant to
motivate eliminativism by showing that accepting ordinary objects commits one
to one or another absurdity.
The chapters are largely self-standing, so readers familiar with these debates
can skip around freely to whichever chapters strike their interest. Those unfamiliar with the debates should probably start with chapters 2 and 3.
My own view is that there are very serious threats to conservatism, particularly
the aforementioned debunking arguments, which threaten to undermine the only
reasons one might have for being a conservative in the first place, and the
arbitrariness arguments, which make the conservative ontology look intolerably
arbitrary (or, at least, embarrassingly messy). At the same time, I think this is a
battle worth fighting. Ontologists have been too quick to abandon the natural,
conservative account in the face of these problems, and rumors of its untenability
have been greatly exaggerated. Or so I hope to show.
2
The Arguments
Let’s begin with an overview of the arguments that have led so many to reject
conservatism in favor of one or another revisionary thesis. This will help us to see
what’s at stake in these debates.
1. Debunking Arguments
Conservatism is often claimed to be objectionably anthropocentric, on the
grounds that our beliefs about which objects exist are largely the result of
arbitrary biological and cultural influences. We are naturally inclined to believe
that there are trees rather than trogs because prevailing conventions in the
communities we were born into generally prohibit treating some things as the
parts of a single object unless they are connected or in some other way unified.
These conventions themselves likely trace back to an innate tendency to
THE ARGUMENTS
perceive some arrays of qualities but not others as being coinstantiated by a
single object and to its being adaptive for creatures like us to so perceive
the world (e.g., because it is too cognitively taxing to track objects under the
sortal trog).
One way of putting the upshot here is that there is no appropriate explanatory
connection between our beliefs about which objects there are and the facts about
which objects there are. This, in turn, serves as the key premise of a debunking
argument against our belief in such ordinary objects as trees:
(DK1)
(DK2)
(DK3)
There is no explanatory connection between our object beliefs and the
object facts.
If so, then we shouldn’t believe that there are trees.
So, we shouldn’t believe that there are trees.
DK2 can be motivated by the observation that if there truly is this sort of
disconnect between the object facts and the factors that lead us to our object
beliefs, then it could only be a lucky coincidence if those factors led us to beliefs
that lined up with the object facts; and since we have no rational grounds for
believing that we got lucky, we shouldn’t believe that we did, in which case we
should suspend our beliefs about which objects there are and, in particular, our
belief in the existence of trees.
These arguments fall short of establishing that eliminativism is correct, since
they purport to establish only that we ought to abandon our anti-eliminativist
beliefs, not that we should take up pro-eliminativist beliefs. They can, however,
serve as a powerful supplement to other arguments for eliminativism. For even
if there are ways of resisting those arguments, the debunking arguments
threaten to neutralize any reasons we might have for wanting to resist them.
There is always some bullet one can bite, but why bite it if our affection for
ordinary objects is a groundless prejudice, as the debunking arguments purport
to show?
The debunking arguments also provide indirect support for permissivism. For
permissivists appear to be in an especially good position to deny DK2. If
permissivism is true, then having accurate beliefs about which kinds of objects
there are is a trivial accomplishment (not a coincidence), since there are objects
answering to virtually every way that we might have perceptually and conceptually divided situations up into objects. So, the idea goes, anyone who wants to
resist the skeptical conclusion that we shouldn’t believe in trees ought to embrace
a permissivist ontology, which can make sense of the noncoincidental accuracy of
our object beliefs.
THE ARGUMENTS
2. Arbitrariness Arguments
Arguments from arbitrariness turn on the idea that there is no ontologically
significant difference between certain ordinary and extraordinary objects. That
is to say, there is no difference between them that can account for why there
would be things of the one kind but not the other.
Consider the incar. A full-sized incar is like a car in nearly all respects. The
main difference is that, unlike a car, it is impossible for an incar to leave a garage.
As a car pulls out of the garage, the incar begins to shrink at the threshold
of the garage, at which time an outcar springs into existence and begins growing.
What it looks like for an incar to shrink and gradually be replaced by an outcar is
exactly the same as what it looks like for a car to leave a garage. But an incar is
not a car that is inside a garage, since a car that is inside a garage can later be
outside the garage. Nor is the incar the part of a car that is inside a garage, because
that too will later be outside the garage. But the incar will never be outside the
garage.1
Here is an arbitrariness argument for the existence of incars:
(AR1)
(AR2)
(AR3)
(AR4)
There is no ontologically significant difference between islands and
incars.
If so, then: if there are islands then there are incars.
There are islands.
So, there are incars.2
The idea behind AR1 is that incars and islands are objects of broadly the same
kind, namely, objects that cease to exist when their constitutive matter undergoes
a certain sort of extrinsic change. Incars cease to exist when their constitutive
matter leaves the garage, and islands (the idea goes) cease to exist when their
constitutive matter is completely submerged at high tide. The idea behind AR2 is
that, if there truly are islands but no incars, then there would have to be
something in virtue of which it’s the case that there are things of the one kind
but not of the other. To think otherwise would be to take the facts about what
exists to be arbitrary in a way that they plausibly are not.
This is just one example of an arbitrariness argument. Permissivists might also
argue that there are scattered objects like trogs on the grounds that there is no
ontologically significant difference between them and ordinary scattered objects
like solar systems. And eliminativists can turn these arguments on their heads,
1
2
The example is due to Hirsch (1976: §2, 1982: 32).
See Hawthorne (2006: vii).
THE ARGUMENTS
arguing from the nonexistence of incars and trogs to the nonexistence of islands
and solar systems.
3. The Argument from Vagueness
According to conservatives, pluralities of objects sometimes compose a further
object and sometimes don’t. The argument from vagueness purports to show that
this isn’t so: either every plurality of objects composes something, or none do.3
(AV1)
(AV2)
(AV3)
(AV4)
(AV5)
If some pluralities of objects compose something and others do not,
then it is possible for there to be a sorites series for composition.
Any such sorites series must contain either an exact cut-off or borderline cases of composition.
There cannot be exact cut-offs in such sorites series.
There cannot be borderline cases of composition.
So, either every plurality of objects composes something or none do.
AV1 is extremely plausible. A sorites series for composition is a series of cases
running from a case in which composition does not occur to a case in which it
does occur, where adjacent cases in the series are extremely similar in all respects
that would seem to be relevant to whether composition occurs (e.g., the spatial
and causal relations among the objects in question). As an illustration, consider
the assembly of a hammer from a handle and a head, and suppose that the
conservative is right that they do not compose anything at the beginning of the
assembly process and that they do compose something by the end. In that case,
the moment by moment series leading from the beginning to the end of the
assembly would be a sorites series for composition.
AV2 is trivial. Any such series must contain some transition from composition
not occurring to composition occurring, and in any given series there either will
or will not be an exact point at which that transition occurs.
AV3 is plausible. It just seems absurd to suppose that there is some exact
moment in the sorites series at which the handle and head go from not composing anything to composing something. Furthermore, if composition occurs in
one case but not in another, then surely there must be some explanation for why
that is; compositional facts are not brute. Yet the sorts of differences that one
finds among adjacent cases in a sorites series for composition—for instance, that
3
Some xs compose something just in case there is a y such that (i) each of the xs is part of y and
(ii) every part of y shares a part with at least one of the xs. I depart from van Inwagen (1990: 29) in
dropping a third condition that he places on composition: (iii) no two of the xs share a part.
THE ARGUMENTS
the handle and head are a fraction of a nanometer closer together in the one than
in the other—can’t plausibly explain why composition would occur in one case
but not in the other.
What is less obvious is why we should accept AV4. It seems just as obvious
that there can be borderline cases of composition (e.g., the loosely affixed
hammer head and handle) as that there can be borderline cases of redness
or baldness. But as we will see in chapter 9, there is reason to believe that
composition is importantly different. That’s because questions about when
composition occurs look to be intimately bound up with questions about which
things exist, in a way that questions about which things are red or which people
are bald are not. Compositional vagueness thus threatens to give rise to existential
indeterminacy, something that is ruled out by the widely accepted linguistic
theory of vagueness.
4. Overdetermination Arguments
Overdetermination arguments aim to establish that ordinary objects of various
kinds do not exist by way of showing that there is no explanatory work for them
to do that isn’t already being done by their microscopic parts. Here is one such
argument:
(OD1)
(OD2)
(OD3)
(OD4)
(OD5)
Every event caused by a baseball is caused by atoms arranged
baseballwise.
No event caused by atoms arranged baseballwise is caused by a baseball.
So, no events are caused by baseballs.
If no events are caused by baseballs, then baseballs do not exist.
So, baseballs do not exist.
‘Atoms’ can be understood here (and throughout) as a placeholder for whichever
microscopic objects or stuffs feature in the best microphysical explanations of
observable reality. These may turn out to include the composite atoms of
chemistry, or they may all be mereological simples (i.e., partless objects), or they
may even be a nonparticulate quantum froth.4
OD1 is plausible. To deny it, one would have to say that baseballs cause things
that their atoms don’t. Perhaps one could say that atoms arranged baseballwise
4
I follow Merricks (2001: 4) in using the xs are arranged K-wise to mean: the xs both have the
properties and also stand in the relations to microscopica upon which, if Ks existed, the xs’
composing a K would nontrivially supervene. See Brenner (forthcoming) for further discussion of
the ‘arranged K-wise’ locution.
THE ARGUMENTS
can’t collectively cause anything to happen so long as they’re parts of the baseball.
Or perhaps one could postulate a division of causal labor: baseballs cause events
involving macroscopic items like the shattering of windows, while their atoms
cause events involving microscopic items like the scatterings of atoms arranged
windowwise. But neither option is especially plausible.
OD2 can be defended by appeal to Ockham’s Razor: do not multiply entities
beyond necessity. Either postulate the baseball or postulate the atoms, but there is
no explanatory need to postulate both, systematically overdetermining each
other’s causal impacts. Some may feel that this is a misapplication of Ockham’s
Razor: given the intimate connection between baseballs and their atoms, this isn’t
an especially objectionable sort of overdetermination. More on this in
chapter 10.2.
OD4 can (again) be defended by appeal to Ockham’s Razor. If there is no
explanatory need to postulate baseballs—if they aren’t doing any causal work—
then we shouldn’t postulate them. Or it may be defended more directly by
invoking the controversial Eleatic Principle, according to which everything that
exists has causal powers.5 Together with the plausible assumption that if baseballs
don’t cause anything it’s because they can’t cause anything, the Eleatic Principle
delivers OD4.
5. The Problem of Material Constitution
Wooden tables are constituted by hunks of wood. Clay statues are constituted by
lumps of clay. Reflection on the relationship between constituted objects and the
objects that constitute them reveals a tension between our intuitions about the
persistence conditions of these objects and our intuitions about which objects are
identical to which. The tension can be resolved by simply eliminating the
ordinary objects that give rise to it in the first place.
Here is an argument from material constitution for the elimination of clay
statues. Let Athena be a clay statue, and let Piece be the piece of clay of which it’s
made.6
(MC1)
(MC2)
(MC3)
5
Athena (if it exists) has different properties from Piece.
If so, then Athena 6¼ Piece.
If so, then there exist distinct coincident objects.
The principle is controversial because numbers and other abstracta, if they exist, are plausibly
causally inert. For purposes of the argument, one could get by with the weaker principle that physical
objects exist only if they have causal powers. See Merricks (2001: 81).
6
I borrow the names from Paul (2006: 625).
THE ARGUMENTS
(MC4)
(MC5)
There cannot exist distinct coincident objects.
So, Athena does not exist.
MC1 can be motivated by appeal to modal differences between Athena and Piece:
Piece is able to survive being flattened and Athena isn’t. Or by sortal differences:
Athena, but not Piece, has the property of being a statue. And, depending on how
the details of the case are filled in, there may be other differences as well. If Piece
was just a ball of clay on Monday and was not made into a statue until Tuesday,
then they will have different temporal properties: Piece but not Athena has the
property of having existed on Monday. Additionally, Piece may be well made by
virtue of being made from high-quality clay, while Athena lacks the property of
being well made because it is a poor representation of the woman of whom it is
meant to be a statue.
MC2 follows from Leibniz’s Law: 8x8y(x=y ! 8P(Px $ Py)).7 In other words,
if x and y are identical, then they had better have all the same properties. After all,
if they are identical, then there is only one thing there to have or lack any given
property.
To say that objects coincide, or that they are coincident, is to say that they
share all of their parts. And Athena and Piece plausibly do coincide: each is
composed of precisely the same bits of clay. So, if indeed Athena 6¼ Piece, then
Athena and Piece are distinct coincident objects.8 Thus, we get MC3.
The idea behind MC4 is that, while it is plausible that some things can compose
one thing at one time and a distinct thing at a later time—as when some Lego bricks
first compose a castle and later compose a ship—it is hard to see how some things
can compose more than one thing at a single time. Moreover, those who say that
Athena is distinct from Piece face what is called the grounding problem: the
putative modal and sortal differences between Piece and Athena seem to stand
in need of explanation and yet there seems to be no further difference between
them that is poised to explain, or ground, these differences.
6. The Problem of the Many
The office appears to contain a single wooden desk. The desk is constituted by a
hunk of wood whose surface forms a sharp boundary with the environment,
without even a single cellulose molecule coming loose from the others. Call this
7
More cautiously, it follows from the contrapositive of Leibniz’s Law. Some (e.g., Parsons 1987:
9–11) deny that the two are equivalent. I will ignore this complication.
8
I use ‘distinct’ to mean ‘not numerically identical’. Others use it to mean something like ‘entirely
separate from’.
THE ARGUMENTS
hunk of wood Woodrow. Now consider the object consisting of all of Woodrow’s
parts except for a single cellulose molecule, Molly, making up part of Woodrow’s
surface. Call this ever so slightly smaller hunk of wood Woodrow-minus. The
problem of the many is that, as soon as we admit that there is a single desk in the
office (or cat on the mat, or lamp on the nightstand), we seem forced to conclude
that there are countless desks (cats, lamps) there. The problem can be framed as
an argument for the elimination of desks:
(PM1)
(PM2)
(PM3)
(PM4)
Woodrow is a desk iff Woodrow-minus is a desk.
If so, then it is not the case that there is exactly one desk in the office.
There is at most one desk in the office.
So, there is no desk in the office.
The idea behind PM1 is that Woodrow-minus seems to have everything it takes
to be a desk: it’s got a flat writing surface, it’s suitable for sitting at, and so on.
Accordingly, it would be arbitrary to suppose that Woodrow but not Woodrowminus is a desk. Moreover, if Molly were removed, Woodrow-minus would
plausibly then be a desk. But since Woodrow-minus doesn’t itself undergo any
interesting change when Molly is removed (after all, Molly isn’t even a part of
Woodrow-minus), it stands to reason that Woodrow-minus must likewise be a
desk even while Molly is attached to it.
PM2 is plausible. Given PM1, either both are desks, in which case there is more
than one desk, or neither is a desk, in which case there is fewer than one desk.
And PM3 is about as plausible a premise as one can expect from an argument
in metaphysics. If ever there were an office in which there is no more than one
desk, this is it.
A sneak peek at what’s to come. I deny DK1 of the debunking arguments: there is
an explanation of our object beliefs in terms of the object facts, which crucially
involves postulating a capacity for the apprehension of facts about composition
and kind-membership. I deny AR1 of the arbitrariness argument from islands to
incars, and I identify ontologically significant differences between numerous
other such pairs of ordinary and extraordinary objects. I respond to the argument
from vagueness by denying AV4, embracing existential indeterminacy, and
rejecting the linguistic theory of vagueness. I deny OD2 of the overdetermination
argument and affirm that events are systematically overdetermined by objects
and their parts. I deny MC4, grant that statues are distinct from the lumps of clay
that constitute them, and solve the grounding problem. And I deny PM2 of the
problem of the many: there is exactly one desk, and it is constituted by (but not
identical to) Woodrow.
THE ARGUMENTS
No other arguments have been as influential as these six in driving people away
from conservatism. That said, these are not the only arguments against conservatism. For instance, there are sorites arguments that purport to show that there
are no tables, turning on the premise that the removal of a single atom can never
turn a table into a nontable.9 I set these aside, not because I think they are
unimportant or that they have some obvious flaw, but because I have nothing to
add to the sprawling literature on the sorites. The correct response to the sorites
argument against tables will almost certainly be the same as the correct response
to the sorites arguments that everyone is bald or that nothing is red. Whatever
that is.10 My inclination is to say that, in some cases, there is just no fact of the
matter whether something is bald, or red, or a table. But that is only the beginning
of a response to the paradox, and a proper response would take us far beyond the
scope of this book.11
9
Arguments of this sort have been advanced by Unger (1979a, 1979b), Wheeler (1979: §3), and
Horgan and Potrč (2008: §2.4).
10
Cf. Sider (2001a: 188): “If paradoxical conclusions emerge in the area, it is hard to justify
attributing them to the postulation of ordinary objects . . . rather than to an inadequate understanding of vagueness.”
11
I also do not discuss arguments from the impossibility of indeterminate identity: if there were
tables, then there could be cases in which it is indeterminate which is identical to which, which is
impossible. Such arguments have been advanced by van Inwagen (1990: 128–35), Hoffman and
Rosenkrantz (1997: §5.4), and Hossack (2000: 428). I am attracted to Lowe’s (2011: 20–32) response
to the arguments against indeterminate identity. See my (2011) for some discussion of sorites
arguments and arguments from indeterminate identity.
3
The Positions
The arguments in chapter 2 have led droves of metaphysicians to abandon
conservatism in favor of one or another form of eliminativism or permissivism.
In this chapter, I’ll discuss the different varieties of eliminativism and permissivism and then say a bit about the sort of conservative view that I will be defending
in the remainder of the book.
1. Permissivism
Permissive views are those according to which there are wide swathes of highly
visible extraordinary objects, right before our eyes, that ordinarily escape our
notice. I won’t try to give a more precise characterization of permissivism that
THE POSITIONS
encompasses all and only those views that should naturally be counted as
permissive. However, my two main permissivist targets, universalism and plenitude, can be characterized quite clearly.
1.1 Universalism
Universalism is the thesis that composition is unrestricted: for any objects, there
is a single object that is composed of those objects.1 Whenever there are some
atoms arranged dogwise, there is an object composed of them. Whenever there is
a dog and a trunk, there is an object composed of them.
What universalism does not tell us is which kinds of objects there are.
Whenever there are some atoms arranged tablewise, universalism entails that
there is some object that they compose. But it remains open to universalists to
deny that this composite is a table. And some do (more on this in §2.1).
Accordingly, even together with the assumption that there are atoms arranged
dogwise and atoms arranged treetrunkwise, universalism does not entail that
trogs exist, since it does not entail that there are dogs and trunks. But supposing
that there are both dogs and trunks, universalism is going to deliver trogs as well.
Universalism can be motivated by the arbitrariness arguments we considered
in chapter 2.2. If the arbitrariness argument from solar systems to trogs is
effective, then an argument from solar systems to any of the universalist’s strange
fusions will likely be equally effective. Thus, it is a short step from this argument
to universalism.
The argument from vagueness provides another motivation for universalism.
In chapter 2.3, I framed the argument from vagueness as an argument for the
conclusion that either every plurality of objects composes something or none do.
Supplemented with the premise that at least some pluralities of objects compose
something, this leads to the conclusion that composition is unrestricted: universalism is true.
The supplementary premise that there are some composites is sometimes
defended with an argument from the possibility of atomless gunk, that is,
composites all of whose parts have proper parts. The argument from gunk against
the nihilist thesis that composition never occurs runs as follows:
1
Proponents of universalism include Leśniewski (1916/1922), McTaggart (1921/1968: 140–1),
Leonard and Goodman (1940), Goodman and Quine (1947), Cartwright (1975), Quine (1981a: 10),
Thomson (1983: 216–17), Lewis (1986: 212–13, 1991: §1.3), Van Cleve (1986, 2008), Heller (1990:
§2.9), Armstrong (1997: 13), Sider (1997: §3.1, 2001a: §4.9), Rea (1998), Fine (1999: 73), Hudson
(2000, 2001: §3.8), Varzi (2003), Bigelow and Pargetter (2006), Braddon-Mitchell and Miller (2006),
Baker (2007: 191–3), Schaffer (2009b: 358 n. 11), and Sattig (2015: 13–14). As indicated in
chapter 2.3, I say that some xs compose y iffdef the xs are parts of y and every part of y shares a
part with at least one of the xs.
THE POSITIONS
(AG1)
(AG2)
(AG3)
(AG4)
It is possible for there to be gunk.
If gunk is possible, then nihilism isn’t necessarily true.
If nihilism isn’t necessarily true, then nihilism isn’t actually true.
So, nihilism is false.2
AG1 is plausible: it is easy enough to imagine objects dividing into parts, which
in turn divide into parts, all the way down. AG2 is trivial: if there is gunk in world
w, then there is something with proper parts in w, in which case there are
composites in w and nihilism is false in w. The idea behind AG3 is that nihilism
is a metaphysical principle, and metaphysical principles are not the sorts of things
that vary from one world to the next. Moreover, the actual world contains what
would seem to be paradigm cases of composites (trees, etc.). So if composition
occurs anywhere, it surely occurs here.
Finally, universalism draws indirect support from the debunking arguments in
chapter 2.1. By postulating objects answering to every way of dividing the world
into composites, universalists look to be well positioned to explain the accuracy
of our judgments about which objects there are, even on the assumption that
these judgments are largely determined by arbitrary biological and cultural
contingencies.
1.2 Is Universalism Trivially True?
One might wonder why we even need an argument for universalism. For one
might think that universalism is in some sense trivial, that it is trivial that trogs
and other such arbitrary fusions exist. I’ll consider three ways that one might be
led to this conclusion.
First, one might wonder how anyone can deny that there are trogs, given that
I defined ‘trog’ by saying that there is a trog whenever there is a dog and a trunk.
But I did no such thing. What I said was only that there is a trog whenever there is
an object composed of a dog and a trunk. So one can deny that there are trogs,
while agreeing that there are dogs and trunks, by denying that a dog and trunk
ever compose anything.
Second, universalism seems to be a trivial consequence of the composition as
identity (CAI) thesis: if O is composed of o1 . . . on, then O is identical to o1 . . . on.3
2
The argument is due to Sider (1993). See Dorr (2002: §2.4), Sider (2003b: 724–5, 2013: §10),
Williams (2006b), Cameron (2007: 101–2), Van Cleve (2008: 325), and Effingham (2011) for
discussion.
3
This should be read as saying that the composite is identical to its parts taken collectively, not to
each taken individually. See Wallace (2011a, 2011b) for general discussion of CAI, and see Harte
(2002: 114), Merricks (2005: 629–31), Sider (2007b: 61–2), McDaniel (2010), and Cameron (2012)
on whether CAI entails universalism.
THE POSITIONS
Given CAI, all that the universalist is committed to in affirming that there is a
trog is that there is a trunk and a dog. In that case, in saying that there are trunks
and dogs, conservatives already acknowledge the existence of everything that the
universalist is committed to in saying that there are trogs.
But CAI is highly controversial (and almost universally rejected) because of
Leibniz’s Law arguments like the following. Take a tree and its parts: the leaves, the
branches, the trunk, and the roots. If the leaves are all instantly annihilated but the
other parts are left intact, the tree will still exist. But it will no longer be the case that
the leaves, branches, trunk, and roots still exist: if the leaves don’t exist then it can’t
very well be that these other things and the leaves still exist. So, by Leibniz’s Law, the
tree is not identical to its parts. Not everyone will be convinced by such arguments.4
But they do show that CAI is not trivial, and so the (putative) fact that it entails
universalism does not render universalism itself trivial.
Third, universalism may seem to be a trivial consequence of our commitment
to such things as assortments and pairs.5 There is an assortment of objects
scattered across my desk at the moment. Each is part of the assortment. Thus,
it would seem to follow that there is a single object—an assortment—that each of
these objects is part of. And it seems no less natural to talk about even more
arbitrary assortments. For instance, here is an assortment of objects that seem to
have nothing to do with one another: the planet Neptune, Joan Jett’s favorite
guitar, and Barack Obama’s nose. Each is part of that assortment. Indeed, for any
entities, it seems perfectly natural to refer to them as an assortment (collection,
variety, array, plurality, bunch)—unless there are only two of them, in which case
we naturally refer to them as a pair. This suggests the following argument from
assortments:
(AS1) For any objects, there is an assortment or pair that has them as its parts.
(AS2) If so, then for any objects, there is a single object composed of them.
(AS3) If so, then universalism is true.
(AS4) So, universalism is true.
I deny AS2. An assortment of things is not a single object. Nor is it a single
anything. It is several things. ‘The assortment’ behaves grammatically like a
4
Friends of CAI might complain, for instance, that I beg the question against them in supposing
that ‘the leaves, the branches, the trunk, and the roots’ successfully refers. See Wallace (2011b: §3)
and Sider (2014a) for further discussion of Leibniz’s Law arguments against CAI. Thanks to
Cameron Gibbs for helpful discussion here.
5
See, e.g., Lewis (1983b: 44): “Consider the twin brothers Dee and Dum. Together they comprise
a pair. In this easy case, we may take the pair simply as a mereological sum.” Cf. Schaffer (2009b: 358
n. 11) for another argument in the vicinity. Thanks to Dave Barnett and Mark Moyer for getting me
thinking about these arguments.
THE POSITIONS
singular term, but it is referentially plural. Like ‘Alice, Bob, and Carol’ or ‘the
students’, it refers to some things, not one thing. Which, of course, is not to say
that it refers to each of them; rather, it refers collectively to all of them.6
AS1 is somewhat misleading as well. I do think that ‘the mug is part of the
assortment’ is true, but I don’t think that ‘part’ expresses the same relation here as
it does in ‘the seat is part of the bicycle’ or ‘the leg is part of the table’. Rather, it
picks out the amongness relation. What ‘the mug is part of the assortment’ means
is that the mug is among them—it is one of them—where the them in question is
the things on my desk. To help see that ‘part’ has multiple senses, suppose that
someone steals a bolt from a collection of antique bolts and uses it in his ship.
‘The bolt is part of the collection and the ship’ sounds strained (“zeugmatic”), in
just the way one would expect if there were multiple senses of ‘part’.7
I will have more to say about such disguised plurals and associated uses of
‘part’ in chapter 8.3.1.
1.3 The Doctrine of Plenitude
Even more permissive than universalism is the doctrine of plenitude: for any
function from worlds to filled regions of spacetime in those worlds, there is an
object that exists at just those worlds and that occupies exactly those regions at
those worlds.8
Plenitude entails universalism. There is an object (indeed: countless objects)
composed of the entire plurality of atoms arranged dogwise and atoms arranged
trunkwise in my yard. But, in addition to delivering objects with extraordinary
mereological profiles, plenitude delivers objects with extraordinary temporal and
modal profiles. We have already seen one example: incars. Here is another. Let a
snowdiscall be an object that is made of snow, that has any shape between being
round and being disc-shaped, and that has the following strange persistence
conditions: it can survive taking on all and only shapes in that range.9 A round
snowdiscall can therefore survive being flattened into a disc but cannot survive
6
Cf. Simons (1987: 142–3).
The zeugmatic effect isn’t as strong here as it is in other cases, where the different senses are
entirely unconnected (as in: ‘the fire lit his way and his cigarette’). Rather, we get the sort of weak
zeugmatic effect one would expect from polysemous expressions, as in ‘exercise and broccoli are
healthy’. See chapter 11.2 for more on zeugmatic effect. Thanks to Meg Wallace, Peter Finocchiaro,
and Chad Carmichael for discussion.
8
Advocates of plenitude, or at least something in the vicinity, include Fine (1982: 100, 1999: 73), Sosa
(1987: 178–9, 1999: 142–3), Yablo (1987: 307), Hawley (2001: 6–7), Sider (2001a: §4.9.3), Bennett
(2004: §4), Hawthorne (2006: vii–viii), Johnston (2006: §17), Thomasson (2007: §10.3), Eklund
(2008b: §4), Inman (2014), and Sattig (2015: 25). This formulation is drawn from Hawthorne (2006: 53).
9
See Sosa (1987: 178–9).
7
THE POSITIONS
being packed into the shape of a brick. It is not just that something that was once
a snowdiscall ceases to qualify as a snowdiscall when the snow comes to be brickshaped. Rather the object that was once a snowdiscall ceases to exist altogether.
These are some of the tamer deliverances of plenitude. It also delivers an object
that coincides with your kitchen table for its entire existence, but which in some
other world is composed of a dog and trunk for half the time it exists and
composed of a pair of helium atoms for the other half, and which in every
other world is composed of everything in the universe for its entire existence.
Like universalism, the doctrine of plenitude can be motivated by the arbitrariness arguments and the argument from vagueness. In chapter 2.2, we saw how
arbitrariness arguments can be used to establish that there are incars and trogs,
and in chapter 8.4.4 we’ll see an arbitrariness argument for snowdiscalls as well.
And once you accept that all of these things exist, you are already on the slippery
slope to full-blown plenitude.
To see how the argument from vagueness can be adapted as an argument for
plenitude, it will be useful to have a somewhat different formulation of plenitude.
Let a D-assignment be a function from times to nonempty sets of objects. An
object O is a D-fusion of D-assignment f just in case, at each time t in the domain
of f, O is composed of the members of f(t). O is a minimal D-fusion of f just in
case O is a D-fusion of f and O exists only at the times in the domain of f. Now, let
an M-assignment be a function from worlds to D-assignments. O is an M-fusion
of M-assignment f just in case, in each world w in the domain of f, O is a minimal
D-fusion of f(w). O is a minimal M-fusion of M-assignment f just in case O is an
M-fusion of f and O exists only in the worlds in f ’s domain. Plenitude may then
be understood as the thesis that every M-assignment has a minimal M-fusion.
Here, then, is the argument from vagueness for plenitude:10
(VP1)
(VP2)
(VP3)
(VP4)
(VP5)
(VP6)
10
If some but not all M-assignments have a minimal M-fusion, then it is
possible for there to be a sorites series for minimal M-fusions.
Any such sorites series must contain either an exact cut-off or borderline cases of composition.
There cannot be exact cut-offs in such sorites series.
There cannot be borderline cases of having a minimal M-fusion.
So, either every M-assignment has a minimal M-fusion or none do.
Some M-assignments have minimal M-fusions.
This is an adaptation of Sider’s (2001a: §4.9.3) argument for diachronic universalism, which is
weaker than plenitude, but delivers many of the same strange objects. See Markosian (2004: §2),
Balashov (2005, 2007), Miller (2005: 321–2), and Magidor (forthcoming) for critical discussion. See
Wallace (2014) for a related modalized version of the vagueness argument.
THE POSITIONS
(VP7)
So, every M-assignment has a minimal M-fusion.
The reasoning is going to be much the same as the reasoning behind the original
argument from vagueness. VP3 is motivated by the thought that any such cut-off
would be metaphysically arbitrary. VP4 is motivated by the thought that having
borderline cases of this sort would give rise to existential indeterminacy, which is
ruled out by the linguistic theory of vagueness. And VP6 is just the innocuous
claim that there are some objects with modal profiles.
Finally, as with universalism, the debunking arguments lend indirect support
to plenitude, insofar as proponents of plenitude are well positioned—even more
so than mere universalists—to resist those arguments.
2. Eliminativism
Eliminativist views are those that eliminate some wide range of ordinary objects.
All of the arguments considered in chapter 2 can be seen as supporting
eliminativism, and together they make a strong cumulative case for the position.
By eliminating ordinary objects, one escapes commitment to arbitrariness, coincident objects, overdetermination, overpopulation, and so on, in one fell swoop.
No objects, no problems.
2.1 Varieties of Eliminativism
Eliminativist views come in two varieties: nihilistic and nonnihilistic. Nihilism
(which we already encountered in §1.1) is the thesis that there are no composite
objects: every object is mereologically simple. So what is there according to
nihilists? Nihilists typically accept countless microscopic simples, that is, partless
objects. Some are arranged treewise, some are arranged tablewise, but none of these
pluralities compose anything. But it is also open to nihilists to accept existence
monism, the thesis that there is only one object, the cosmos, which despite
appearances has no parts. Either way, assuming that ordinary objects like tables
would have to be composite objects, nihilism entails that there are no such things.11
I say assuming because nihilists may in principle accept a nonstandard view on
which, just as ‘the assortment’ refers plurally to the assorted items (see §1.2), ‘the
11
Hossack (2000) and Dorr (2002, 2005) defend the microphysicalist version of nihilism. Horgan
and Potrč (2000, 2008: ch. 7) and Rea (2001) defend existence monism. Turner (2011) and Le Bihan
(forthcoming) explore the extreme nihilist view that there are no objects; cf. Cowling (2014). See
Siderits (2003: ch. 4) for discussion of nihilism in the Buddhist tradition. Cameron (2008a: §2,
2010a) and Sider (2013) embrace what I call deep nihilism (see chapter 6.2), and as we’ll see it’s a
delicate question whether they are thereby committed to the nihilist thesis stated above.
THE POSITIONS
table’ refers plurally to the simples arranged tablewise. In that case, there is a
table, but the table is not an individual composite object; it is many objects.12 It is
also open to nihilists to insist that there are tables but that, despite appearances and despite being spatially extended, each table is itself a simple.13 So,
just as one can in principle be a universalist while denying that there are
tables, one can in principle be a nihilist without denying that there are tables.
Nihilism draws support from the argument from vagueness, which, supplemented with the plausible premise that not every plurality of objects composes
something, entails that there are no composites. It also draws support from the
overdetermination argument: composites ought to be eliminated because, were
there such things, they would be in causal competition with their atomic parts
and would therefore be causally redundant.14
Other arguments for eliminativism fall short of establishing nihilism. The
argument from material constitution, for instance, purports to establish that
there are no statues, but not that there are no composites whatsoever. One can
happily affirm the existence of the composite lump of clay without any fear of
commitment to coincident objects so long as one denies that there is a statue
where it is. Likewise, the problem of the many is a problem about the proliferation of ordinary objects. There is nothing so terrible about there being a
multitude of overlapping aggregates of cellulose molecules in my office (one
with Molly as a part, one without). To escape the problem of the many, it is
enough to deny that there are composites belonging to such familiar kinds as desk
or cat. One need not deny that there are any composites at all.
So it is open to eliminativists—and entirely compatible with at least some of
the motivations for eliminativism—to reject nihilism. And many do.15 Peter
Unger, for instance, denies that there are tables but does not deny that there
are composite hunks of wood where we ordinarily take tables to be:
There is nothing in these arguments [for eliminativism] to deny the idea, common
enough, that there are physical objects with a diameter greater than four feet and less
than five. Indeed, the exhibited [arguments] allow us still to maintain that there are
physical objects of a variety of shapes and sizes, and with various particular spatial
12
Liggins (2008) and Contessa (2014) defend this view, and it is possible that Hossack (2000:
427–8) does too.
13
See Williams (2006b: §5) for discussion. See Goldwater (forthcoming) for yet another strategy
for reconciling nihilism with the existence of ordinary objects.
14
Though see Merricks (2001: ch. 4) for an argument that at least some composites would not be
causally redundant.
15
Nonnihilistic eliminativists include Unger (1979a, 1979b, 1980), Heller (1990: §§2.4–2.5), van
Inwagen (1990: ch. 9), Hoffman and Rosenkrantz (1997: ch. 5), Merricks (2001: §4.6), Olson (2007:
§§9.4–9.5), and Van Cleve (2008: §2).
THE POSITIONS
relations and velocities with respect to each other. It is simply that no such objects will be
ordinary things; none are stones or planets or pieces of furniture.16
Indeed, eliminativists can even accept universalism. Van Cleve, for instance,
accepts universalism on the basis of the argument from vagueness, supplemented
with an argument from gunk against nihilism (see §1.1).17 But he denies that there
are statues—that is, he denies that any of the universalist’s composites belong to the
kind statue—on the basis of an argument from material constitution. He is both an
eliminativist and a permissivist; the categories are not mutually exclusive.
Eliminativists also sometimes make an exception for humans and other organisms. One prominent example is Peter van Inwagen who accepts the organicist
thesis that there are composite organisms but no other composite objects. This
leads to a somewhat less severe restriction on composition than nihilism, one
which excludes mountains but permits mountain lions.18
Finally, I want to warn against characterizing eliminativism as the view that
fundamentally speaking there are no ordinary objects. This could mean a variety
of different things, for instance that ordinary objects are not fundamental objects,
or that they are not in the domain of the most fundamental quantifiers. It may be
that such views also deserve the label ‘eliminativism’—maybe ‘deep eliminativism’—but they are not versions of the eliminativist thesis articulated above, for
they carry no commitment to denying that any ordinary objects exist. I do think it
is an interesting question whether the most fundamental quantifiers range over
ordinary composites, and I have a good deal to say on the topic in chapter 6. But,
since deep eliminativism seems to be entirely compatible with conservatism, I am
not too concerned with challenging it here. My target is eliminativism.
2.2 Is Eliminativism Trivially False?
Eliminativists will typically deny that there are tables while at the same time
affirming that there are atoms arranged tablewise. This may strike some as
trivially false or even incoherent. After all, the idea goes, that is just what it is
for there to be a table.
There are a couple different ways of taking the claim that what it is for there to
be a table is for there to be atoms arranged tablewise. On the first, the idea is that
tables are identical to atoms arranged tablewise. But this relies on the highly
16
17
Unger (1979b: 150).
Van Cleve (2008).
See van Inwagen (1990: ch. 9). Others who make an exception for (at least some) organisms,
but who do not endorse organicism, include Hoffman and Rosenkrantz (1997), Merricks (2001:
§4.6), and Olson (2007: §§9.4–9.5).
18
THE POSITIONS
controversial CAI thesis discussed in §1.2—controversial because, among other
things, the atoms don’t seem to have the right sort of modal profile to be a table.
The atoms, but not the table, will still exist after the table has been sent through
the wood-chipper. (And don’t say: “Yes, the atoms will exist, but the atoms
arranged tablewise won’t.” Those atoms now arranged tablewise will still exist.
They won’t be atoms arranged tablewise anymore, but they will still exist.) Since
it is not trivial that the table is identical to its atomic parts, it is not trivially false
or otherwise incoherent to affirm the existence of the latter but not the former.
Furthermore, even advocates of CAI should concede that eliminativism is a
coherent view, just as someone who is convinced that William Shakespeare is
Francis Bacon should concede that one can coherently deny, and even have
compelling reasons for denying, that Shakespeare is Bacon.
On the other way of understanding the claim that there being atoms arranged
tablewise is just what it is for there to be a table, the idea is that atoms arranged
tablewise bear some very intimate relationship to tables other than identity. For
instance, one might hold that eliminativism is trivially false because if there are
atoms arranged tablewise then there are tables is an a priori necessary truth.
I agree that this is an a priori necessity. Still, it is hard to see why this is supposed to
show that eliminativism is trivially false. Virtually every time two philosophers
disagree about what follows from what, one is denying what the other takes to be an
a priori necessity. Consider the free will compatibilist who insists that we are free
while conceding that our actions are entirely determined. The incompatibilist
doesn’t regard compatibilism as incoherent or trivially false, even if she thinks
that it is a necessary a priori truth that free actions cannot be determined. That’s
because she recognizes that there are reasons for denying that determinism is
incompatible with freedom, albeit without finding those reasons convincing.
Similarly, the eliminativist contends that it is not true, let alone true necessarily
and a priori, that there are tables if there are atoms arranged tablewise. And her
reasons for saying this are perfectly intelligible (see chapter 2).19
Perhaps those tempted to say that eliminativism is trivially false really just
mean that it is obvious that tables and other such ordinary objects exist. Here
I have to agree: it is obvious (to me, anyway) that tables exist. Even so, it’s not
always obvious where the arguments for the elimination of tables go wrong.
So we still have our work cut out for us. Furthermore, some eliminativists will
insist that the obvious truth expressed by an ordinary utterance of ‘there are
19
Similar remarks apply to the suggestion that if there are atoms arranged tablewise then there
are tables is analytic, as Thomasson (2007) thinks. See chapter 4.4.2 for discussion of her view. See
Merricks (2001: ch. 1) for more on the complaint that eliminativism is incoherent or trivially false.
THE POSITIONS
tables’ is actually compatible with what eliminativists are saying when they say
‘there are no tables’. More on this in chapter 5.
3. Conservatism
Conservative views are views on which there are such ordinary objects as tables,
dogs, and tree trunks but no such extraordinary objects as trogs, incars, and
snowdiscalls.20 Accordingly, conservatism is a view (only) about which objects
there are and aren’t and is neutral on a wide variety of other questions about
objects. It will be useful to flag a few such questions.
First, conservatism is compatible with different accounts of the persistence
conditions of ordinary objects and the way in which they persist. For instance,
conservatives can accept either endurantism, according to which objects are
wholly present at every moment of their existence, or perdurantism, according
to which objects persist by having different temporal parts at different times.21
Conservatives can also endorse mereological essentialism, the thesis that no
object can survive the loss of any of its parts. I myself reject mereological
essentialism, not because I am a conservative, but because it is open to counterexamples: a tree, for instance, can survive the loss of its leaves. But conservatives can, in principle, accept all manner of counterintuitive views about the
natures and features of ordinary objects. Those who accept conservatism aren’t
ipso facto “common sense ontologists.”
Second, conservatism is compatible with different views about whether and to
what extent objects are mind-dependent. For instance, it is open to conservatives
to accept the anti-realist thesis that all ordinary objects are mind-dependent: they
exist only because people take them to exist. This sort of anti-realism must be
sharply distinguished from the view that ordinary objects are “mere projections,”
which we take to exist but which do not in fact exist. The latter is an eliminativist
view, and as such is incompatible with conservatism.22
Anti-realism has its perks, particularly when it comes to addressing the
debunking arguments (chapter 7) and the arbitrariness arguments (chapter 8).
But I, for one, can’t bring myself to believe that there were no trees or stones
20
Conservatives include Sanford (1993), Markosian (1998, 2008, 2014), Hirsch (2002a), Elder
(2004, 2011), Lowe (2007), Koslicki (2008), Kriegel (2011), Carmichael (forthcoming), and myself.
21
What they can’t accept are permissive varieties of perdurantism, according to which there are
arbitrary fusions of temporal parts. See Heller (1993: §3) on liberal and conservative varieties of
four-dimensionalism.
22
Some, I have found, claim not to see the difference between the view that trees are nonexistent
and the view that trees are mind-dependent existents. I really don’t know what to say to such people.
Sometimes all you can do is smile politely and wave as your interlocutors float away from the shore.
THE POSITIONS
before we came along and began to believe in trees and stones. So I will try to
answer these arguments without the help of anti-realism in what follows.23 I do,
however, think that artifacts are to some extent mind-dependent. When some
clay is sculpted into the shape of a statue by an artist who intends to make a
statue, a new object comes into existence belonging to the kind statue and having
the modal profile it does partly in virtue of those creative intentions. But this is
not to say that artifacts depend on us for their continued existence.24 If all sentient
creatures were suddenly to be annihilated, there would still be statues and tables
and other artifacts. More on this in chapter 8.4.
Third, while conservatives are united in their commitment to rejecting sweeping eliminativist and permissivist views—like nihilism and universalism—there is
still a great deal of room for variation concerning which objects exist. For instance,
conservatives may disagree among themselves about whether there really are such
scattered objects as disassembled pipes, or whether there are arbitrary undetached
parts like leg-complements (composed of all of your body except one of your legs).
Some may worry that, by leaving these sorts of questions open, my characterization of conservatism is too impoverished to serve as a suitable starting point for an
inquiry into its viability. I address such concerns by simply forging ahead and
showing how much progress can be made even without having in hand any
precise conservative thesis.
Fourth, conservatism is compatible with different ways of understanding the
status of debates about objects. For instance, conservatives can accept a deflationary view according to which, while it’s mind-independently true that there
are trees and no trogs, our way of dividing up the world into objects is (in some
sense) just one of many equally good ways of dividing up the world into objects.25
I don’t myself accept any such form of deflationism, but I’m also not concerned
to argue against it here. I’ll take my allies where I can find them.
Fifth, conservatism is compatible with a variety of methodological outlooks.
I don’t myself have any overarching methodology that I am bringing to bear on
these issues. I don’t assume a particularist methodology, on which our intuitive
judgments about concrete cases are always or even normally to be favored over
intuitive judgments about general principles.26 Nor do I endorse a Moorean view
23
Anti-realists include Goodman (1978) and Einheuser (2006). See Bennett (2004: §3), Elder
(2004: ch. 1), and Boghossian (2006: ch. 3) for criticism.
24
Cf. Thomasson (2003).
25
See Carnap (1950), Putnam (1987), Cortens (2002), and Hirsch (2002b) for some ways of
filling in the details. See Blackburn (1994) and Sider (2011: ch. 9) for criticism.
26
This is a departure from my (2010b). See Hirsch (2002a: 113–14), Bealer (2004: 14–15), and
Comesaña (2008: 34) in support of particularism; cf. Chisholm (1982: ch. 5).
THE POSITIONS
on which commonsense beliefs are somehow nonnegotiable.27 Nor do I take
myself to be trying to vindicate the beliefs and intuitions of nonphilosophers
(“the folk”).28 Nor do I take myself to be engaging in what Strawson calls
“descriptive metaphysics,” the aim of which is “to describe the actual structure
of our thought about the world.”29 My target of inquiry is the way the world is,
not our way of thinking about the world.
To the extent that I have a methodology, it is something like serving as legal
counsel for conservatism. I have taken up its case, because I think that it is worth
defending. I examine the best reasons for it, and I challenge attempts to impugn
those reasons. I examine the best arguments against it, and I show that they can
be resisted. What I do not have is any methodology, or any argument for a
methodology, that dictates that you must accept conservatism once you see that
the reasons for accepting it survive scrutiny and that the arguments against it can
be resisted. At that point, though, I honestly don’t see why you wouldn’t.
Let me close this chapter with a word about my use of ‘object’. I say that a
trog is an object that is composed of a dog and a trunk, and I characterize the
conservative as denying that there is any such object. I don’t thereby mean to
be taking a stand on whether there are sets or properties that are composed of a
dog and a trunk (e.g., {that dog, that trunk} or being that dog or that trunk).
Nor, when I deny that any object in my backyard has the dog and trunk as
parts, do I mean to deny that there are events occurring in my backyard that
have a dog and a trunk as parts. By ‘objects’, I mean material objects, that is,
entities that are made of stuff, have locations, and can move through space.30
When I need a term with wider scope, covering both objects and nonobjects,
I will use ‘entity’. Everything is an entity; not everything is an object.
Finally, it is not quite right to characterize the conservative view as one according
to which “trogs are not objects.” This misleadingly suggests that conservatives agree
that there are entities that are partly furry and partly wooden, but withhold the label
‘object’ from such entities, perhaps because they are reserving it for more “unified”
entities. I would say that trogs are objects, just as I would say that unicorns are
animals, even though I believe in neither. If there were trogs, they’d be just as
deserving of the label ‘object’ as the dogs and tree trunks that compose them. The
conservative attitude toward trogs is best captured not by saying what trogs aren’t
but rather by saying that they aren’t. There are no trogs. That is what conservatives
think.
27
28
29
See Kelly (2008) and Sattig (2015: 67–74) for a Moorean approach.
This is a departure from my (2009). More on the folk in chapter 5.6.
30
Strawson (1959: 9).
Cf. van Inwagen (1990: 17).
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Stanford Encyclopedia of Philosophy
Platonism in Metaphysics
First published Wed May 12, 2004; substantive revision Wed Mar 9, 2016
Platonism is the view that there exist such things as abstract objects — where an abstract object is an object
that does not exist in space or time and which is therefore entirely non-physical and non-mental. Platonism in
this sense is a contemporary view. It is obviously related to the views of Plato in important ways, but it is not
entirely clear that Plato endorsed this view, as it is defined here. In order to remain neutral on this question,
the term ‘platonism’ is spelled with a lower-case ‘p’. (See entry on Plato.) The most important figure in the
development of modern platonism is Gottlob Frege (1884, 1892, 1893–1903, 1919). The view has also been
endorsed by many others, including Kurt Gödel (1964), Bertrand Russell (1912), and W.V.O. Quine (1948,
1951).
Section 1 will describe the contemporary platonist view in detail. Section 2 will describe the alternatives to
platonism — namely, conceptualism, nominalism, immanent realism, and Meinongianism. Section 3 will
develop and assess the first important argument in favor of platonism, namely, the One Over Many argument.
Section 4 will develop and assess a second argument for platonism, namely, the Singular Term argument.
This argument emerged much later than the One Over Many argument, but as we will see, it is widely
thought to be more powerful. Finally, section 5 will develop and assess the most important argument against
platonism, namely, the epistemological argument.
!"1. What is Platonism?
!"2. A Taxonomy of Positions
!"3. The One Over Many Argument
!"4. The Singular Term Argument
#"4.1 Mathematical Objects
#"4.2 Propositions
#"4.3 Properties and Relations
#"4.4 Sentence Types
#"4.5 Possible Worlds
#"4.6 Logical Objects
#"4.7 Fictional Objects
!"5. The Epistemological Argument Against Platonism
!"Bibliography
!"Academic Tools
!"Other Internet Resources
!"Related Entries
1. What is Platonism?
Platonism is the view that there exist abstract (that is, non-spatial, non-temporal) objects (see the entry on
abstract objects). Because abstract objects are wholly non-spatiotemporal, it follows that they are also entirely
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non-physical (they do not exist in the physical world and are not made of physical stuff) and non-mental
(they are not minds or ideas in minds; they are not disembodied souls, or Gods, or anything else along these
lines). In addition, they are unchanging and entirely causally inert — that is, they cannot be involved in
cause-and-effect relationships with other objects.[1] All of this might be somewhat perplexing; for with all of
these statements about what abstract objects are not, it might be unclear what they are. We can clarify things,
however, by looking at some examples.
Consider the sentence ‘3 is prime’. This sentence seems to say something about a particular object, namely,
the number 3. Just as the sentence ‘The moon is round’ says something about the moon, so too ‘3 is prime’
seems to say something about the number 3. But what is the number 3? There are a few different views that
one might endorse here, but the platonist view is that 3 is an abstract object. On this view, 3 is a real and
objective thing that, like the moon, exists independently of us and our thinking (i.e., it is not just an idea in
our heads). But according to platonism, 3 is different from the moon in that it is not a physical object; it is
wholly non-physical, non-mental, and causally inert, and it does not exist in space or time. One might put this
metaphorically by saying that on the platonist view, numbers exist “in platonic heaven”. But we should not
infer from this that according to platonism, numbers exist in a place; they do not, for the concept of a place is
a physical, spatial concept. It is more accurate to say that on the platonist view, numbers exist (independently
of us and our thoughts) but do not exist in space and time.
Similarly, many philosophers take a platonistic view of properties. Consider, for instance, the property of
being red. According to the platonist view of properties, the property of redness exists independently of any
red thing. There are red balls and red houses and red shirts, and these all exist in the physical world. But
platonists about properties believe that in addition to these things, redness — the property itself — also
exists, and according to platonists, this property is an abstract object. Ordinary red objects are said to
exemplify or instantiate redness. Plato said that they participate in redness, but this suggests a causal
relationship between red objects and redness, and again, contemporary platonists would reject this.
Platonists of this sort say the same thing about other properties as well: in addition to all the beautiful things,
there is also beauty; and in addition to all the tigers, there is also the property of being a tiger. Indeed, even
when there are no instances of a property in reality, platonists will typically maintain that the property itself
exists. This isn't to say that platonists are committed to the thesis that there is a property corresponding to
every predicate in the English language. The point is simply that in typical cases, there will be a property. For
instance, according to this sort of platonism, there exists a property of being a four-hundred-story building,
even though there are no such things as four-hundred-story buildings. This property exists outside of space
and time along with redness. The only difference is that in our physical world, the one property happens to be
instantiated whereas the other does not.
In fact, platonists extend the position here even further, for on their view, properties are just a special case of
a much broader category, namely, the category of universals. It's easy to see why one might think of a
property like redness as a universal. A red ball that sits in a garage in Buffalo is a particular thing. But
redness is something that is exemplified by many, many objects; it's something that all red objects share, or
have in common. This is why platonists think of redness as a universal and of specific red objects — such as
balls in Buffalo, or cars in Cleveland — as particulars.
But according to this sort of platonism, properties are not the only universals; there are other kinds of
universals as well, most notably, relations. Consider, for instance, the relation to the north of; this relation is
instantiated by many pairs of objects (or more accurately, by ordered pairs of objects, since order matters here
— e.g., to the north of is instantiated by , and , but not
by , or ). So according to platonism, the relation to the
north of is a two-place universal, whereas a property like redness is a one-place universal. There are also
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three-place relations (which are three-place universals), four-place relations, and so on. An example of a
three-place relation is the gave relation, which admits of a giver, a givee, and a given — as in ‘Jane gave a
CD to Tim’.
Finally, some philosophers claim that propositions are abstract objects. One way to think of a proposition is
as the meaning of a sentence. Alternatively, we can say that a proposition is that which is expressed by a
sentence on a particular occasion of use. Either way, we can say that, e.g., the English sentence ‘Snow is
white’ and the German sentence ‘Schnee ist weiss’ express the same proposition, namely, the proposition that
snow is white.
There are many different platonistic conceptions of propositions. For instance, Frege (1892, 1919) held that
propositions are composed of senses of words (e.g., on this view, the proposition that snow is white is
composed of the senses of ‘snow’ and ‘is white’), whereas Russell at one point (1905, 1910–11) held that
propositions are composed of properties, relations, and objects (e.g., on this view, the proposition that Mars is
red is composed of Mars (the planet itself) and the property of redness). Others hold that propositions do not
have significant internal structure. The differences between these views will not matter for our purposes. For
more detail, see the entry on propositions.
(It might seem odd to say that Russellian propositions are abstract objects. Consider, e.g., the Russellian
proposition that Mars is red. This is an odd sort of hybrid object. It has two components, namely, Mars (the
planet itself) and the property of redness. One of these components (namely, Mars) is a concrete object
(where a concrete object is just a spatiotemporal object). Thus, even if redness is an abstract object, it does
not seem that the Russellian proposition is completely non-spatiotemporal. Nonetheless, philosophers
typically lump these objects together with abstract objects. And it's not just Russellian propositions; similar
remarks can be made about various other kinds of objects. Think, for instance, of impure sets--e.g., the set
containing Mars and Jupiter. This seems to be a hybrid object of some kind as well, because while it has
concrete objects as members, it's still a set, and on the standard view, sets are abstract objects. If we wanted to
be really precise, it would probably be best to have another term for such objects--e.g., ‘hybrid object’, or
‘impure abstract object’--but, again, this isn't how philosophers typically talk; they usually just treat these
things as abstract objects. None of this will matter very much in what follows, however, because this essay is
almost entirely concerned with what might be called pure abstract objects--i.e., abstract objects that are
completely non-spatiotemporal.)
Numbers, propositions, and universals (i.e., properties and relations) are not the only things that people have
taken to be abstract objects. As we will see below, people have also endorsed platonistic views in connection
with linguistic objects (most notably, sentences), possible worlds, logical objects, and fictional characters
(e.g., Sherlock Holmes). And it is important to note here that one can be a platonist about some of these
things without being a platonist about the others — e.g., one might be a platonist about numbers and
propositions but not properties or fictional characters.
Of course, platonism about any of these kinds of objects is controversial. Many philosophers do not believe
in abstract objects at all. The alternatives to platonism will be discussed in section 2, but it is worth noting
here that the primary argument that platonists give for their view...
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