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Synthese Library 428
Studies in Epistemology, Logic, Methodology,
and Philosophy of Science

José Tomás Alvarado

A Metaphysics
of Platonic
Universals
and their
Instantiations
Shadow of Universals
Synthese Library

Studies in Epistemology, Logic, Methodology,

and Philosophy of Science
Volume 428

Editor-in-Chief
Otávio Bueno, Department of Philosophy, University of Miami,
Coral Gables, USA

Editorial Board Member

Berit Brogaard, University of Miami, Coral Gables, USA
Anjan Chakravartty, University of Notre Dame, Notre Dame, USA
Steven French, University of Leeds, Leeds, UK
Catarina Dutilh Novaes, VU Amsterdam, Amsterdam, The Netherlands
Darrell P. Rowbottom, Department of Philosophy, Lingnan University, Tuen Mun,
Hong Kong
Emma Ruttkamp, Department of Philosophy, University of South Africa, Pretoria,
South Africa
Kristie Miller, Department of Philosophy, Centre for Time, University of Sydney,
Sydney, Australia
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José Tomás Alvarado

A Metaphysics of Platonic
Universals and their
Instantiations
Shadow of Universals
José Tomás Alvarado
Instituto de Filosofía
Pontificia Universidad Católica de Chile
Macul – Santiago, Chile

ISSN 0166-6991 ISSN 2542-8292 (electronic)

Synthese Library
ISBN 978-3-030-53392-2 ISBN 978-3-030-53393-9 (eBook)
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Acknowledgments

This work was written during the execution of the research project Fondecyt
1160001 (2016–2019; Conicyt, Chile). It is, however, the fruit of more than
10 years’ work. The ideas presented here have been developed with the support of
the Fondecyt research projects 1070339 (2007–2008), 1090002 (2009–2011), and
1120015 (2012–2014). Many more people deserve my gratitude than I am able to
include here. In particular, I must mention the Colloquia of Analytic Metaphysics
that, since its first version in the Argentine Society of Philosophical Analysis
(SADAF) in Buenos Aires in 2008, has continued to meet every 2 years. Many of
the theses that appear in this book found their first formulations in those colloquia. I
must thank Ezequiel Zerbudis, Gonzalo Rodriguez-Pereyra, Juan Larreta (requiescat
in pace) Guido Imaguire, Sebastián Briceño, Carlo Rossi, Robert Garcia, and
Horacio Banega for their comments, criticisms, and suggestions on those memorable
occasions. In October of 2017, Sebastián Briceño organized a seminar in the
Department of Philosophy of the University of Concepción that was dedicated to
the discussion of the first version of this book. I am very grateful to Sebastián
Briceño and Javier Vidal for their sharp observations that greatly helped to improve
this draft. Marcelo Boeri, Juan Manuel Garrido, and Matthew Tugby have kindly
read the manuscript and made me see several errors that I have been able to rectify.
An anonymous referee for Springer made many useful observations that have
improved the book in many parts. Finally, I thank my colleagues from the Institute
of Philosophy of the Pontificia Universidad Católica de Valparaíso and from the
Institute of Philosophy of the Pontificia Universidad Católica de Chile who have
created a stimulating environment for philosophical work; and I thank the genera-
tions of students who have been exposed—in one way or another—to the ideas
explored here.

v
Contents

1 Introduction [§ 1] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Properties, Universals, Tropes [§ 2] . . . . . . . . . . . . . . . . . . . . . 2
1.2 Possible Worlds, Grounding, Dependence [§ 3–4] . . . . . . . . . . . 8
1.3 Intrinsic and Extrinsic Properties, Mereology, Concrete
and Abstract [§ 5–7] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.4 Summary of What Is to Come and some Nomenclature [§ 8] . . . 15
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

Part I Universals
2 Theoretical Roles for Universals [§ 9] . . . . . . . . . . . . . . . . . . . . . . . 23
2.1 One Over Many [§ 10] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.2 Many Over One [§ 11] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.3 Objective Resemblances [§ 12] . . . . . . . . . . . . . . . . . . . . . . . . 27
2.4 Causality [§ 13] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.5 Natural Laws [§ 14] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.6 Inductive Practices [§ 15] . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3 The Superiority of Universals Over Resemblance
Nominalism [§ 16] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.1 Resemblance Nominalism [§ 17] . . . . . . . . . . . . . . . . . . . . . . . 48
3.2 Primitive Facts of Resemblance [§ 18] . . . . . . . . . . . . . . . . . . . 54
3.3 How Would We Have Epistemic Access to Such
Resemblance Facts? [§ 19] . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.4 Determinate and Determinable [§ 20] . . . . . . . . . . . . . . . . . . . . 61
3.5 Natural Laws and Inductions [§ 21] . . . . . . . . . . . . . . . . . . . . . 65
3.6 Causal Powers [§ 22] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
3.7 A Vicious Regress [§ 23] . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
3.8 Modal Consequences [§ 24] . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

vii
viii Contents

4 The Superiority of Universals Over Classes of Tropes [§ 25] . . . . . . 81

4.1 Primitive Resemblances [§ 26] . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.2 Imperfect Communities and Companionships [§ 27] . . . . . . . . . 91
4.2.1 Resemblance Classes of Modifier Tropes [§ 28] . . . . . . . 93
4.2.2 Resemblance Classes of Module Tropes [§ 29] . . . . . . . 95
4.3 Modal Consequences [§ 30] . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
4.4 Natural Classes of Tropes [§ 31] . . . . . . . . . . . . . . . . . . . . . . . 103
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
5 The Superiority of Universals over Theological
Nominalism [§ 32] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
5.1 Concepts and Mind of God [§ 33] . . . . . . . . . . . . . . . . . . . . . . 114
5.1.1 Concepts [§ 34] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
5.1.2 The Mind of God [§ 35] . . . . . . . . . . . . . . . . . . . . . . . . 117
5.2 A Vicious Regress, Again [§ 36] . . . . . . . . . . . . . . . . . . . . . . . 120
5.3 Divine Aseity [§ 37] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
5.4 Conclusive Summary of Part I [§ 38] . . . . . . . . . . . . . . . . . . . . 125
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

Part II Transcendent Universals

6 Transcendent Universals and Modal Metaphysics [§ 39] . . . . . . . . . 129
6.1 Arguments to Accept Transcendent Universals [§ 40] . . . . . . . . 132
6.2 The Function of Universals in Modal Metaphysics [§ 41] . . . . . 135
6.3 Modal Theories Based on Universals [§ 42] . . . . . . . . . . . . . . . 138
6.4 Combinatorial Modal Theories [§ 43] . . . . . . . . . . . . . . . . . . . . 145
6.5 Linguistic Theories of Modality [§ 44] . . . . . . . . . . . . . . . . . . . 151
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
7 Transcendent Universals and Natural Laws [§ 45] . . . . . . . . . . . . . 159
7.1 Tooley-Type Cases [§ 46] . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
7.2 Functional Laws [§ 47] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
7.3 Powers to the Rescue? [§ 48] . . . . . . . . . . . . . . . . . . . . . . . . . . 169
7.4 Generalized Tooley-Type Cases [§ 49] . . . . . . . . . . . . . . . . . . . 172
7.5 The Necessary ‘Nomic Network’ [§ 50] . . . . . . . . . . . . . . . . . . 176
7.5.1 Natural Laws Essential for Universals [§ 51] . . . . . . . . . 176
7.5.2 Necessary Laws [§ 52] . . . . . . . . . . . . . . . . . . . . . . . . . 183
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
8 Transcendent Universals and Ontological Priority [§ 53] . . . . . . . . 189
8.1 The Ontological Priority of Universals [§ 54] . . . . . . . . . . . . . . 189
8.1.1 Priority to Natures [§ 55] . . . . . . . . . . . . . . . . . . . . . . . 190
8.1.2 Priority to Resemblances [§ 56] . . . . . . . . . . . . . . . . . . 191
8.1.3 Priority to Natural Laws and Causality [§ 57] . . . . . . . . . 191
8.2 The Priority Profile of Immanent Universals [§ 58] . . . . . . . . . . 194
Contents ix

8.3 Immanent Universals, Similarities, Laws,

and Causality [§ 59] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198
Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
9 Objections Against Transcendent Universals [§ 60] . . . . . . . . . . . . . 201
9.1 The Eleatic Principle [§ 61] . . . . . . . . . . . . . . . . . . . . . . . . . . . 204
9.1.1 What Is a Causal Power? [§ 62] . . . . . . . . . . . . . . . . . . 206
9.1.2 Causal Powers and Combinatorial Modality [§ 63] . . . . . 213
9.1.3 Primitive Causal Powers [§ 64] . . . . . . . . . . . . . . . . . . . 217
9.1.4 Dispositions? [§ 65] . . . . . . . . . . . . . . . . . . . . . . . . . . . 220
9.1.5 Do Transcendent Universals Confer Causal
Powers? [§ 66] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221
9.2 Lack of Economy [§ 67] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224
9.2.1 Bradley’s Regress [§ 68] . . . . . . . . . . . . . . . . . . . . . . . 226
9.2.2 Tropes of Instantiation [§ 69] . . . . . . . . . . . . . . . . . . . . 229
9.2.3 Primitive States of Affairs [§ 70] . . . . . . . . . . . . . . . . . . 231
9.3 The Epistemological Problem [§ 71] . . . . . . . . . . . . . . . . . . . . . 233
9.3.1 Perceptual Beliefs [§ 72] . . . . . . . . . . . . . . . . . . . . . . . 235
9.3.2 A Priori Intuitions [§ 73] . . . . . . . . . . . . . . . . . . . . . . . 239
9.3.3 Universals Epistemologically Transcendent? [§ 74] . . . . 241
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
10 Identity Conditions for Transcendent Universals [§ 75] . . . . . . . . . . 247
10.1 Structuralism [§ 76] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250
10.2 The Problem of Regress of the Conditions of Identity [§ 77] . . . 254
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259

Part III Particulars

11 Substrata and Bundles [§ 78] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263
11.1 Substrata or Bundles? [§ 79] . . . . . . . . . . . . . . . . . . . . . . . . . . 266
11.2 Difficulties of Substratum Ontologies [§ 80] . . . . . . . . . . . . . . . 270
11.3 Difficulties of Bundle Ontologies [§ 81] . . . . . . . . . . . . . . . . . . 275
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285
12 The Nuclear Theory of Trope Bundles [§ 82] . . . . . . . . . . . . . . . . . 287
12.1 Saturation Structures [§ 83] . . . . . . . . . . . . . . . . . . . . . . . . . . . 290
12.2 Persistence in Time [§ 84] . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296
12.3 The Problem of Substantial Change [§ 85] . . . . . . . . . . . . . . . . 301
12.4 Problems of Ontological Dependence [§ 86] . . . . . . . . . . . . . . . 304
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309
13 The Reformed Nuclear Theory [§ 87] . . . . . . . . . . . . . . . . . . . . . . . 311
13.1 Essences [§ 88] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314
13.2 The Unique Nuclear Trope Is a substratum [§ 89] . . . . . . . . . . . 320
13.3 What Qualitative Character Does a Nuclear Trope
Possess? [§ 90] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324
x Contents

13.4 The Problem of Spatiotemporal Localization [§ 91] . . . . . . . . . . 327

13.5 Analogy of Being [§ 92] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329
13.6 Physical Structures [§ 93] . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332
13.7 Structural Bundles [§ 94] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344
14 By Way of Conclusion: (Neo) Platonism [§ 95] . . . . . . . . . . . . . . . . 347
14.1 Everything There Is [§ 96] . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349
14.2 Open Problems [§ 97] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353
Chapter 1
Introduction

Abstract This first chapter presents the main line of argumentation that is going to
be followed in the book for the defence of an ontology of Platonic universals and
their instantiations. Several important concepts and theses for that argumentation are
introduced, like ‘property’, ‘universal’, ‘trope’, ‘possible world’, ‘grounding’,
‘dependence’, ‘intrinsic/extrinsic property’, ‘mereological sum’ and ‘abstract/
concrete’.

§ 1. If we consider everything in the broadest possible sense, we may say that certain
entities are grounded on others (cf. § 4), while some entities are fundamental because
they are ungrounded. The central thesis of this work is that everything on the
fundamental level is either a transcendent universal or a trope. Many other categories
of entities can be admitted, such as sets, mereological fusions, states of affairs,
events, concrete structures, and—especially—particular objects; but they are onto-
logically derivative. This thesis has never enjoyed great acceptance, and a long and
relatively intricate journey will be undertaken to defend it here. The strategy to
justify this central thesis can be summarized in the following sub-theses:
(A) There are universals
(B) Every universal is independent of its instantiations
(C) There are particular objects
(D) Every particular object is a bundle of tropes
Sub-theses (A) and (B) can be taken relatively independently of sub-theses
(C) and (D). The defence of (A) and (B) will be made in Parts I and II of this
work (Chaps. 2, 3, 4, 5, 6, 7, 8, 9, and 10, §§ 9–77). The defence of (C) and (D) will
be made in Part III (Chaps. 11, 12, and 13, §§ 78–94). That is, the thesis to be
defended is that there are universal properties (sub-thesis (A)), but that—contrary
to what many of its defenders have assumed—these universal properties do not need
to be instantiated to exist (sub-thesis (B)). Much of this work will be dedicated to
justifying, then, that there are universals that are not instantiated. When it comes to
an understanding of the nature of particular objects, on the other hand, I will argue
that these should be understood as complexes of the instantiations of transcendent

© The Editor(s) (if applicable) and The Author(s), under exclusive license to 1
Springer Nature Switzerland AG 2020
J. T. Alvarado, A Metaphysics of Platonic Universals and their Instantiations,
Synthese Library 428, https://doi.org/10.1007/978-3-030-53393-9_1
2 1 Introduction

universals (sub-thesis (D); sub-thesis (C) does not require a justification). These
‘instantiations’ are tropes or particular properties. This ontology of tropes will be
explained in Part III. When considering the nature of particular objects it has been
usual to argue that there are two mutually exclusive alternatives: they are understood
either as being made up of a substratum that has properties, or as a cluster or bundle
of properties without a substratum. I will here advance the claim that there is no such
opposition and, moreover, will defend an ontology that understands particular
objects as tropes, but at the same time as having a substratum (see §89).
The central thesis to be defended in this work is that, at the fundamental level,
everything that exists is a universal or an instantiation of a universal. The ordinary
world of objects and events that happen to these objects is, in some sense, a world of
‘shadows’ of the universals of which the particular properties or tropes are essen-
tially an instantiation. Talk about ‘shadows of universals’ has Platonic resonances, of
course (cf. Plato (1982), VII, 514a-521b), but it is not used here except as a suitable
metaphor. It is not intended here to argue, for example, that the existence of concrete
objects and the particular properties that make them is an ‘illusion’, or that ‘really’
these objects do not exist, or that their existence is of a ‘minor degree’. Rather, the
metaphor is used here in the key sense that a shadow projects information about what
causes it. The particular objects are instantiations of universals. The reality of the
world of particular objects also ‘projects’ information from a different realm: a realm
of universals.
In this introductory chapter, along with a global presentation of the central
defence strategy to be employed, some notions of importance will be presented,
such as ‘property’, ‘universal’, ‘trope’, ‘possible world’, or ‘part’.

1.1 Properties, Universals, Tropes

§ 2. We ordinarily attribute characteristics, features, or determinations to the objects

with which we have regular contact. We can correctly say of an apple that it is red
and of a banana that it is yellow.1 Things are qualified by their form, by their mass,
by their location concerning other things, and so on. In this work, we will talk about
the ‘character,’ ‘trait’, or ‘nature’ of an object to designate the fact that it is square, or
green, or has a height of one metre. A ‘nature,’ ‘trait’, or ‘character’ is not a ‘thing’,
therefore, over which to quantify. If it is right to say that x is F then x is F or—which
is taken here as merely a paraphrase of this fact—x has the nature of being F. All
positions in the metaphysics of properties agree that objects have different traits,
characters, or natures. The differences between these positions appear when one

1
Although these are not very good examples, as will be explained below. There is probably no
unique real property of ‘being red’ or of ‘being yellow’. The closest thing to such a property would
be infinite pluralities of determined colour properties, i.e. of maximally specific colour tones. These
pluralities are vague, as there will be certain determined colour tones that will not clearly be red
tones or non-red tones. It is doubtful, then, that there are such pluralities.
1.1 Properties, Universals, Tropes 3

considers what it is that grounds such natures—if there is anything on which they are
grounded. In the following, a characteristic, feature, or determination of an object
that is supposed to be numerically different from the object that possesses it will be
called a ‘property’. The connection between a property and the object that owns it
will be designated as its “instantiation”, however such a ‘connection’ is finally
understood.2 An ontology that postulates properties, therefore, postulates that the
objects that are usually presented to us have a specific ontological structure—at least
in the sense in which the expression “property” is used here. What is presented to us
usually must be a ‘complex’ that must include properties that are numerically
different from the object that has them. Not all philosophers use this terminology
to designate a ‘property’. David Lewis (cf. 1983, 10) and Gonzalo Rodriguez-
Pereyra (cf. 2002, 15–17), for example, use “property” to designate whatever it is
that satisfies the theoretical functions usually attributed to universals. The theories
that they have proposed, then, are presented as theories about the nature of ‘prop-
erties’, even though according to the terminology employed here neither Lewis nor
Rodriguez-Pereyra postulates the existence of properties. For simplicity, it is
assumed that the properties in question will be monadic, but everything that is said
should be considered applicable mutatis mutandis for relations, that is, for dyadic
properties or properties with a larger number of arguments (or ‘adicity’). When the
distinction between monadic properties and relationships is relevant, the distinction
will be made explicitly.
A theory that rejects the existence of properties in the indicated sense is a form of
nominalism. Here, too, there is considerable terminological variability. In the phi-
losophy of mathematics, any theory that rejects the existence of abstract entities,
such as sets or classes (see, for example, Goodman and Quine 1947) has been called
“nominalist”. A traditional nominalist strategy to eliminate universals is to propose
classes of objects or natural classes of objects that can fulfil their functions. A class is
an abstract entity, however, of those that the ‘nominalists’ in the philosophy of
mathematics reject. Any theory that rejects the existence of universals has also been
called “nominalist” (see, for example, Armstrong 1978a, 138). According to the
terminology that is followed here, however, one can defend the existence of prop-
erties that are not universal.
Properties can be conceived as having a universal or a particular nature. A
universal property is a property that can be instantiated in a plurality of exemplifi-
cations at the same time. A universal can be shared by many objects. Unlike a
universal, a trope is a property of particular and not universal character. The
terminology here has also been very variable: they have been called “modes”,
“moments”, “abstract particulars”, “perfect particulars”, “concrete properties”, or
“instances of property”. From now on, they will be designated as “tropes”. A trope
cannot be shared by several objects. For a defender of universals, for example, the
mass of an electron is numerically the same property as the mass of another. For a

2
Later on (see § 79), other additional distinctions required for an adequate understanding of
particular objects will be introduced.
4 1 Introduction

defender of tropes, on the other hand, the mass of an electron is numerically different
from the mass of another electron, if these electrons are numerically different.3
Tropes can be perfectly similar to each other, but this is another matter.
There are two ways in which universals can be understood: as immanent or
‘Aristotelian’ universals, or as transcendent or ‘Platonic’ universals. The denomina-
tions “Aristotelian” or “Platonic” should not be taken too seriously here. One cannot
confidently ascribe to Aristotle the postulation of immanent universals.4 Neither can
one confidently attribute to Plato the postulation of transcendent universals (for a
general presentation, see Ross 1953), as those universals have been conceived in the
recent discussion—and indeed, the acceptance of a theory like the one that will be
defended here could not be attributed to Plato. An immanent universal is a universal
that exists only if it has instantiations. A transcendent universal is a universal that
does not require instantiations to exist. In other words, the difference between one
and another conception of universals has to do with the acceptance or rejection of
this principle (see Armstrong 1978a, 113):
[Principle of Instantiation] It is necessary for all n-adic universal U that
necessarily at least n objects instantiate U.5
The defenders of immanent universals accept this Principle of Instantiation, while
the defenders of transcendent universals reject it. Immanent universals are, therefore,
ordinarily contingent entities. Except for the case of essential properties for an
object, the fact that an object instantiates a property is a contingent fact. Still,
however, if it were an essential property for an object, if the object in question
were a contingent and not a necessary entity, then the property would also be
contingent and not necessary. In effect, as an immanent universal U exists only in
the possible worlds6 where it is instantiated, even if it is an essential property of an
object, in the worlds where that object does not exist, U will not either—assuming
that no other objects in those worlds instantiate U. For a defender of immanent
universals, the only cases of necessary universals would be the cases of essential
properties of necessary objects that invariably exist in all possible worlds. Necessary
universals could be got, perhaps, in the case of essential properties of mathematical
objects, if any, and the essential properties of God.
The situation is very different when it comes to transcendent universals. It would
not be inconsistent to suppose that these universals are contingent entities. All that is

3
An assumption that should always be taken with extreme caution when dealing with entities at the
quantum level. Cf. French and Krause 2006, 84–197.
4
Indeed, it has been the subject of discussion whether Aristotle admits universal or particular forms
in Metaphysics, especially about Z 13. Cf. for general presentations, Wedin 2000; Lewis 2013.
5
Armstrong’s original formulation (see 1978a, 113) does not include modal operators, but clearly,
he does not propose the principle as a happy contingent coincidence affecting all actually existing
universals. The principle obtains for the defender of an Aristotelian conception of universals due to
the essential nature of universals, i. e. as a matter of metaphysical necessity. The insertion of modal
operators in the principle above makes explicit this modal character.
6
On the concept of ‘possible world’, cf. § 3 below.
1.1 Properties, Universals, Tropes 5

required for a defender of transcendent universals is the rejection of the Principle of

Instantiation; that is, to suppose that it is possible that there is a non-instantiated
universal. A universal can exist non-instantiated in some possible worlds and not
exist in others. Positions of this type have been defended on the grounds of economy
(see Tooley 1987, 113–120), since postulating contingent universals would be less
‘costly’ ontologically than postulating necessary universals. However, reasons of
simplicity and economy militate against this hypothesis. The most sensible thing is
to suppose that transcendent universals, if they exist, must be necessary entities,
invariant between different possible worlds. Indeed, we might ask, if they were
indeed contingent, for what reason would they exist or fail to exist in one possible
world rather than in another? Whoever holds such a position ought to give a reason
why these variations can occur. It is not possible here to appeal to an instantiation
that a universal might have in one possible world and not have in others, because a
transcendent universal does not depend ontologically on having an instance. And
there do not seem to be any other reasons to suppose such differences. The most
economical thing, therefore, is to suppose that there are no such variations between
different possible worlds when it comes to transcendent universals.
There are also significant differences between immanent and transcendent uni-
versals concerning their space-time location. For transcendent universals, it does not
seem to make sense to attribute a location to them in space and time. For the
immanent universals, however, it does not seem inappropriate to attribute a spatio-
temporal location to their instantiations. Unlike a particular object, an immanent
universal will be located entirely in each of the regions in which the objects that
instantiate it are located. It has to be multi-located. A particular object, on the other
hand, is located in a region of space because it has different parts that are located in
the different sub-regions of that space. For temporal localization, however, the
contrast between universals and particular objects is more difficult to pin down.
Traditionally, it has been argued that particular objects persist in time, i.e. are
identical in different instants of time; or exist entirely in each of those instants,
i.e. are ‘simple’ but extended entities. In recent years, however, a different concep-
tion has become popular in which the persistence of an object in time is understood
analogously to the location of an object in space, that is, by the possession of
different temporal parts in each of the different moments of persistence. If the second
mode of temporal persistence is adopted, there is a marked contrast between the form
of the temporal location of a universal and the form of the temporal location of a
particular object, as happens with spatial localization. If one takes the first mode of
persistence, however, individuals are located in time, as are universals: they exist all
and entirely at every moment when they exist.7

7
There are other more exotic hypotheses discussed in the literature that will not be discussed here. It
has been argued, for example, that a particular object could also be multi-located entirely in
different regions of space because an object could travel in time to the past and occupy a different
region of space than it occupies at any given time (Ehring 2011, 27–30). It is not intended to argue
here that the differences between universals and individuals concerning their spatio-temporal
location are the way to analyse the difference between universal and particular.
6 1 Introduction

There has been a debate about how to analyse the distinction between universals
and particulars. Many criteria have been proposed, and many of them have been
unsatisfactory. One might think, for example, that the difference between a universal
and a particular consists in the fact that the universal—in the manner of a Fregean
function—is essentially incomplete and required to be saturated by an object.
Ramsey, however, showed that one could think analogously of objects as ‘incom-
plete’ and as ‘requiring saturation’ by one property or another (see Ramsey 1925).8
One might think, too, that the way to analyse the difference between universal and
particular is that individuals may enter into connections with an arbitrary number of
other objects and universals to form states of affairs. A universal, on the other hand,
seems to be able to enter into connection only with a fixed number of objects,
corresponding to its adicity, that instantiate it (cf. Armstrong 1997, 168; MacBride
2005, 571–572). It turns out, however, that one cannot exclude a priori the existence
of multigrade universals, that is, universals that can be instantiated in arbitrary
pluralities of objects. Suppose there were a universal of to surround—a hypothesis
not very plausible, but sufficient to clarify this point. It can be given the state of
affairs of being Peter, John, and James surrounding x, but also the state of affairs of
being Peter, John, James, and Andrew surrounding x, or the state of affairs of being
Peter and John surrounding x, etc. The same universal seems to be integrating states
of affairs with two, three, four, or n different objects. The fact that there is no way to
analyse the difference between universals and particulars, however, should not be
taken as a reason to argue that there is no difference between them. Not everything
can be analysed. The difference between universal and particular might be of such a
fundamental nature that there are no more basic conceptual resources from which it
could be made clear. It would not be strange if such a thing should happen. In the
following it is assumed that the distinction is simply primitive.9
A distinction has frequently been postulated between sparse and abundant prop-
erties, at least since it was presented in these terms by David Lewis (cf. 1983,
11–14). A traditional way of postulating universal properties has been to argue

8
Suppose that the proposition that Socrates is wise corresponds to a state of affairs. The semantic
components of the proposition correspond to the ontological components of the state of affairs. In
the proposition, we can distinguish a function x is wise in which the ‘x’ indicates the empty place of
the variable that requires saturation or to be bounded by a quantifier to generate a complete
proposition. Socrates seems to be ‘complete’. This contrast, however, seems excessively deter-
mined by the grammatical difference between predicates and names. Ramsey (1925) argued that
one could just as well represent Socrates as Socrates is F, where F is a variable that needs to be
saturated to form a complete proposition. If the ‘unsaturated’ character implies a certain ontological
precariousness and is not merely semantic, the same seems to happen with universals. Universals
cannot constitute states of affairs independently of objects—at least in the immanentist conception
of universals—nor can objects form states of affairs independently of universals.
9
Which does not rule out, of course, that some appropriate way of doing the analysis should appear.
For example, it has been proposed that the difference between universal and particular is given by
the fact that it is metaphysically impossible for universals to be perfectly similar to each other or
indiscernible among themselves (cf. Ehring 2011, 30–40). On the other hand, it is possible that there
are particulars which are indiscernible between themselves, whether they are objects or tropes.
1.1 Properties, Universals, Tropes 7

that they are the semantic value of the predicates of our language or that they are the
content of our concepts. Each possible predicate will be correlated with a ‘property’,
as well as each concept of a possible thinking subject. For a natural language like
English, which allows us to build denumerably infinite many10 different predicates
by the recursive application of compositional rules of grammatical construction,
there are infinite predicates that seem to select extremely heterogeneous things. For
example, there is a predicate like ‘being a cat and being examined before the year
3,000, or being a galaxy and being examined after the year 3,000’. In this conception
there is exactly one class of all the things that instantiate the ‘property’ which is the
meaning of the predicate in question. This class includes cats and galaxies. Examples
like this can be multiplied ad nauseam. There are certain theoretical functions that
properties specified in this way have been expected to satisfy. The discussion in this
work, however, will concentrate on the so-called ‘sparse properties’. These are
‘sparse’ because in comparison to the ‘abundant’ ones they form a minority. These
properties are those that are strictly necessary to ground the objective resemblances
and the causal powers of objects. The way in which we can determine if there is a
property in this sense is not through reflection on the contents of our thought and our
language, but rather through reflection on what are the objective resemblances
between the objects and what causal powers they have—according to our best
evidence regarding such objects, which will ordinarily be empirical. It is not the
task of the philosopher to determine, in general, what properties exist, but the task of
the natural scientist. In principle, ‘sparse’ properties should be the minimum basis
sufficient to fully characterize the world (see Lewis 1983, 12) or, in linguistic terms,
they should be what primitive predicates refer to in a language sufficient for a
complete description of everything. In the following, these sparse properties will
be referred to as “authentic properties”.11
Yet although it has been usual to maintain that it is natural science that determines
a posteriori, by empirical research, what properties exist, it should not be assumed
that the postulation of authentic properties is connected with some form of natural-
ism. Several advocates of theories of authentic properties, such as David
M. Armstrong (cf., for example, 1997, 5–10), are naturalists, that is, they hold that
everything that exists is the space-time system and the entities it contains that are
described by natural science. But there is no systematic connection between natu-
ralism and the postulation of authentic properties. The claim is simply that not every

10
An infinite plurality is said to be ‘denumerable’ if it can be put in bijection with the set of natural
numbers, as with the set of rational numbers or the set of integers. An infinite plurality is said to be
‘indenumerable’ if it cannot be put into bijection with the set of natural numbers, just as happens
with the set of real numbers.
11
This is not to deny, of course, that there is an important philosophical problem about what is the
content of our thinking, and what semantic values should be given to the expressions of our
languages. Nothing prevents, in particular, that operations from universals to universals should
allow the generation of such contents—as has been supposed by those who have defended
‘abundant’ properties—from a base constituted only by authentic properties, according to what is
indicated here. These, however, are further issues that will not be discussed in this work.
8 1 Introduction

term or predicate of our language must be correlated with some authentic property
that has to be its ‘meaning’, and that it is more reasonable to think that there are real
properties for which we do not have linguistic expressions that designate them.
Properties are not the mere correlates of our languages. Moreover, according to
everything we know, there could be properties of such a character that they will
evade our best efforts to discover or understand them. These properties could still be
the kinds of properties with which natural science deals. Something like this is what
we should suppose if everything that exists is of a physical nature, but it is not what
we should suppose if there are entities that transcend time and space. There could be
properties of a non-physical nature. There may be mental properties, for example,
that are not reducible to physical properties or not based on physical properties. If so,
such mental properties need to be entered into a complete characterization of the
world.

1.2 Possible Worlds, Grounding, Dependence

§ 3. The expression “possible world” will be used freely. As is well known, there is
controversy about what should be understood by this term (cf. for a general per-
spective, Divers 2002; Alvarado 2008). Despite the differences in perspective, there
is a minimum content that can be assigned to the expression, and which has utility
when it comes to considering modal facts—that is, facts about what might be the
case, or about what necessarily is the case, or about what is not necessarily the case,
etc. By ‘possible world’ we should understand a form in which all the things could
be. Anyone who believes that things could be different from how they actually are
believes that there are ways in which things could be that is not the way things are
(see Lewis 1973, 84). Accepting the existence of possible worlds, therefore, is little
more than accepting the existence of possibilities, which seems a matter of common
sense. No special assumption is made here about their nature.
Modal issues are considered in several sections of the work (see §§ 24, 30,
41–44). It will be seen that when it comes to an understanding of the nature of
worlds, an ‘actualist’ conception will be preferred, according to which there is only
one concrete world, the actual world. ‘Possible worlds’ are abstract constructions
that represent how things could be. For the moment, however, it will not be
necessary to assume anything more than that to speak of ‘possible worlds’ is simply
to speak of metaphysical possibilities considered globally.
§ 4. Much of the argumentation in this chapter will have to do with the aptitude or
inaptitude of certain postulated entities to ‘explain’ specific facts. The notion of
‘explanation’, however, has been the subject of much controversy throughout the
past century. An important tradition has connected it with the notion of ‘causality’.
This connection to causality makes its application in ontology difficult, since it is
doubtful, for example, that universals ‘cause’ the phenomena of one over many (cf. §
10). An ‘ontological’ explanation must have a different character from what is
expected of an explanation in the natural sciences. In a very general sense, one
1.2 Possible Worlds, Grounding, Dependence 9

could argue that universals allow us to answer in a satisfactory way—given certain

presuppositions—the question about why oneness is given in what is multiple (see §
10), why there are objective resemblances (see § 12), why objects have causal
powers (see § 13), and so on. These ontological ‘explanations’, however, require
special clarification.
Following a significant number of theorists, we here assume that the ontological
‘explanation’ is given by the highlighting of relations of ‘grounding’ or of ‘depen-
dence’. Grounding will be taken as a primitive, non-analysable, and multigrade
relationship that can occur between a plurality of grounding entities and the
grounded entity. It is usually assumed that the relata of grounding are ‘facts’, but
this restriction will not be imposed here.12 Entities of different categories can be with
each other in the grounding relationship. It is a strict order, that is, it is an irreflexive,
asymmetric, and transitive relationship.13 If x is grounded on y1, y2, . . ., yn then it is
assumed that y1, y2, . . ., yn are constitutively sufficient for the existence of x, given its
essence. The entities y1, y2, . . ., yn ‘determine’ the existence of x. For this reason, the
following link will be assumed:
[Grounding – Implication] If y1, y2, . . ., yn ground x, then it is necessary that: if y1
exists, y2 exists, . . . and yn exists, then x exists
However, the converse is not valid, because it could be the case that it is necessary
that if y1, y2, . . ., yn exist, then x exists, without x intuitively being grounded on y1, y2,
. . ., yn. For example, a strict conditional is true if its consequent is necessary, no
matter what is in the antecedent. The strict implication [□((I exist) ! (2 + 1 ¼ 3))] is
true, then, but it would be extravagant to think that I am the ground of the
mathematical truth that 3 is the sum of 2 and 1. Modal covariations do not discrim-
inate which entities are prior—the ground—and which are derivative—grounded
(cf. Rosen 2010; Correia and Schnieder 2012; Fine 2012; Alvarado 2013; among
many others).
Ontological dependence, on the other hand, is a primitive, irreflexive, asymmet-
ric, and transitive relationship, which implies a strict implication, but is not

12
The reason why it has usually been assumed that grounding is a relationship that has as relata
‘facts’ is that many analyses have focused on the uses of the expression ‘–because–’ and the like,
that connect complete sentences. For this reason, it has also been proposed that it be treated as a
sentential connective (see Fine 2012). If someone has difficulties with the freedom with which the
relations of grounding between entities of any category will be treated here, one can replace the
expressions ‘x is grounded on y’ with ‘the fact that x exists is grounded in the fact that y exists’. Of
course, this is not the place to make a detailed discussion of this topic. For a recent defence of
‘entity’ grounding, see Wilhelm, 2019.
13
With a better understanding of the nature of grounding, other hypotheses have been explored with
infinite or cyclic structures of grounding in which there is nothing ‘fundamental’, not based on
anything (cf. for example, Bliss 2013, 2014). Although none of these hypotheses is inconsistent, it
is far from clear that there are cases in which it is reasonable to postulate such structures. Here we
are going to assume that both grounding and dependence are ‘well-founded’ relationships, so there
must be something fundamental, not grounded on anything, or independent, not dependent on
anything.
10 1 Introduction

analysable as a strict implication. If x depends ontologically on y, then it follows that

it is necessary that, if x exists, then y exists. A strict conditional by itself, however,
only registers some modal covariation. If it is about the propositions x exists and y
exists, the strict conditional will be: it is necessary that if x exists, then y exists. That
is, in all possible worlds, either x does not exist—so x exists is false—or y exists—
that is, in all possible worlds where x exists, y also does. Of course, this covariation
may be based on the fact that it is part of the essence of x that y exists, but it can also
be based on other circumstances. The strict conditional may be based on the fact that
y is a necessary entity, existing equally in all possible worlds. Trivially, then, in all
possible worlds in which x exists, y will exist also. It can also be based on the fact
that y necessarily results from the existence of x. For example, given the axioms of
set theory, in all possible worlds where x exists, there is also the singleton set {x}. It
is evident, however, that x does not depend ontologically on {x}. Ontological
dependence goes in the opposite direction. It turns out, therefore, that if x is
dependent on y1, y2, . . ., yn, then the entities y1, y2, . . ., yn are included in the essence
of x, so that it is necessary that if x exists, then y1, y2, . . ., yn exist. The following link
therefore results:
[Dependence – Implication] If x depends on y1, y2, . . ., yn, then it is necessary that:
if x exists, then y1 exists, y2 exists, . . ., and yn exists
The relations of grounding and dependence are strict orders, that is, they are
irreflexive, asymmetric and transitive relations. Nothing is grounded on itself or is
dependent on itself. Some attempts to challenge these formal characteristics of
dependence are discussed below (see § 86). We can also define weaker notions of
anti-symmetric grounding and dependence:
[Weak grounding] x is weakly grounded on y ¼ df x is grounded on y or x ¼ y

[Weak dependence] x depends weakly on y ¼ df x depends on y or x ¼ y

In both cases it is a reflexive, anti-symmetrical, and transitive relation, that is: (i) for
all x, x depends weakly on itself and x is weakly grounded on itself; (ii) for all x and
y, if x is weakly grounded on y, and y is weakly grounded on x, then x ¼ y; if
x depends weakly on y, and y depends weakly on x, then x ¼ y; (iii) for all x, y, z, if
x is weakly grounded on y, and y is weakly grounded on z, then x is weakly grounded
on z; if x depends weakly on y, and y depends weakly on z, then x depends weakly on
z. These weaker notions may have a formal interest, but the notions of ontological
importance are those that have to do with relations of ontological priority/posterior-
ity. Moreover, nothing is previous to or derivative on itself, so the notions of strict
grounding and strict dependence are relevant to what will be discussed here.
It follows from this that ‘ontological priority’ is said in many ways. The onto-
logical ‘priority’ is the converse relation of ontological ‘posteriority’ or ‘derivative-
ness’. An entity x can be said to be ‘posterior’ to y, either because x is grounded on y,
or because x is dependent on y. There are two different forms of priority, then, which
should be distinguished, and which can be analysed as follows:
1.3 Intrinsic and Extrinsic Properties, Mereology, Concrete and Abstract 11

[Grounding Priority] x is ontologically prior to y ¼ df y is grounded on x

[Dependence Priority] x is ontologically prior to y ¼ df y depends on x

Something can be prior in the first sense without being prior in the second, or vice
versa. We will say that an entity is ‘emergent’ if it is ungrounded, but is ontologically
dependent on something (cf. Barnes 2012). Analogously, we will say that an entity
that is independent, but grounded on x1, x2, . . ., xn, is ‘realized’ in x1, x2, . . ., xn.
Something like this would be a ‘multiply realizable’ entity, something that must be
grounded ontologically, but such that it need not be grounded on the specific entities
on which it depends.
For what follows, it will also be useful to consider another notion close to the
notion of grounding that has been described:
[Partial Grounding] x is partially grounded on y ¼ df there are z1, z2, . . ., zn such
that: z1, z2, . . ., zn, y ground x
Both grounding and dependence are non-monotonic relationships. That is, if y1, y2,
. . ., yn ground x, then there is no z, z 6¼ y1, z 6¼ y2, . . ., z 6¼ yn such that: z, y1, y2, . . ., yn
ground x. The ground of an entity is that which is constitutively sufficient for the
existence of such an entity and nothing else. Otherwise, it would be trivial that
everything that fully grounds something, also partially grounds something, because
if x is grounded on y, then x could be grounded also on y, z, for an arbitrary z. For
dependence, however, there is another notion of ‘generic dependence’ that has
proved useful and is opposed to ‘rigid dependence’. If x depends generically on an
F, then it is necessary that if x exists, then there is an F.
A notion close to that of ‘grounding’ is that of truthmaking or ‘making true’
(cf. Fine 2012, 43–46). The truthmaker of a proposition is that entity whose
existence grounds its truth. We will assume, furthermore, that for every true prop-
osition p, it is necessary that there is some entity e such that e grounds the truth of p.
From this, it follows that it is necessary that, if e exists, then p is true.

1.3 Intrinsic and Extrinsic Properties, Mereology, Concrete

and Abstract

§ 5. A distinction to which we will have several occasions to resort is that between

‘intrinsic properties’ and ‘extrinsic properties’, as well as the distinction between
‘internal’ and ‘external’ relations. It has been notoriously difficult to analyse the
difference between intrinsic and extrinsic properties. In some ways of effecting the
distinction, the intrinsic properties are those that persist after ‘enlargements’ or
‘reductions’ of the possible worlds in which an object possesses such a property.
In other ways of effecting the distinction, a property is intrinsic if it does not imply
the existence of other objects different from the object that possesses such a
property—assuming forms of ‘relevant’ implication. In other ways of effecting the
12 1 Introduction

distinction, intrinsic properties are those that are not relational. None of these
strategies has been entirely satisfactory (see Weatherson and Marshall 2012). Of
course, it is not possible to adjudicate this question here. Probably, there is no single
precise concept of ‘intrinsic property’. There are certain relatively vague intuitions
about properties that determine an object regardless of what other objects exist and
what relationships exist with them, but these intuitions are consistent with different
and incompatible ways of making them precise. It seems more prudent, for these
reasons, to define two different concepts of ‘intrinsic property’ according to two
different criteria. The first is the one that corresponds to combinatorial modal
intuitions:
[Combinatorially Intrinsic] P is combinatorially intrinsic ¼ df the fact that
x instantiates P is independent of whether x is alone
or accompanied
Of course, a ‘combinatorially extrinsic’ property is one that is not ‘combinatorially
intrinsic’. This formulation comes from Lewis and Langton (1998).14 An object x is
alone in the possible world w if and only if there is no other object than x in w. An
object x is accompanied in w if and only if it is not alone in w. According to this first
way of characterizing what an intrinsic property is, it is one whose instantiations do
not vary if the possible world in question includes more or less different objects. If
something has 5 gr of mass, for example, its mass does not vary if there is another
object or not. On the contrary, the property of being 5 metres from a cube is not
intrinsic because nothing will instantiate it in possible worlds in which there is no
cube. Adding or removing a cube makes a difference to whether something has the
property of being 5 metres from a cube. Note that if there are objects of necessary
existence, these will not vary between different possible worlds, because no world
lacks them. If the number 3 is a necessary object, then the property of being
accompanied by the number 3 will be combinatorially intrinsic to every object,
since the fact that an object is accompanied by the number 3 is invariant concerning
worlds in which that object is or is not accompanied by others. For this property to be
combinatorially extrinsic, there must be possible worlds in which adding or remov-
ing an object to a possible world determines that something is no longer accompa-
nied by the number 3 or that it becomes accompanied by the number 3. However, as
the number 3 is—ex hypothesi—modally invariant, nothing that is added or removed
modally produces a difference.

14
There are sophistications introduced in the analysis of Lewis and Langton that are not important
here. These sophistications are motivated by the possibility of disjunctive properties. The proposed
analysis ultimately depends on a primitive distinction between ‘natural’ properties and those that are
not (see Lewis and Langton 1998, 118–121). A property is said to be basic intrinsic if and only if:
(i) the fact that an object instantiates it is independent of whether the object is alone or accompanied
(as indicated above), (ii) it is not the disjunction of other natural properties, and (iii) it is not the
negation of a natural disjunctive property. Two objects are duplicates if and only if they have the
same ‘basic’ intrinsic properties. Now, a property is intrinsic if and only if it cannot differ between
duplicates.
1.3 Intrinsic and Extrinsic Properties, Mereology, Concrete and Abstract 13

Another way of analysing the notion of ‘intrinsic’ property is that proposed by

Rosen (2010, 112) and depends on the concept of ‘grounding’ already explained.
F is an intrinsic property if and only if, necessarily for all x: (i) if x is F in virtue of a
fact involving y, then y is an improper part of x; and (ii) if x is not F in virtue of a fact
involving y, then y is an improper part of x. The following alternative analysis can be
given:
[Grounding Intrinsic] P is grounding intrinsic ¼ df the fact that an object x does or
does not instantiate P must be grounded on an improper
part of x if it is grounded
Of course, a property is ‘grounding extrinsic’ if and only if it is not grounding
intrinsic. This concept is substantially stronger than that of being ‘combinatorially
intrinsic’. According to this alternative analysis, it is not enough that the instantiation
of the property in question by an object is invariant in possible worlds in which there
are or not other objects The instantiation—or the non-instantiation—must be
grounded on the object that instantiates the property or on its parts. In this way,
although the property of being accompanied by the number 5 turns out to be
combinatorially intrinsic—assuming that the number 5 is a necessary object—it is
not grounding intrinsic, since the existence of the number 5 is not grounded on the
existence of any other concrete object. In the following, it will be assumed as a
general rule that the ‘intrinsic’ properties are grounding intrinsic, and the ‘extrinsic’
properties are grounding extrinsic. In some cases, the alternative notions of being
‘combinatorially intrinsic’ or ‘combinatorially extrinsic’ may be relevant, but when
this is so it will be expressly indicated.
Given the concept of ‘intrinsic property’, the notion of an ‘internal relation’ can
be analysed. A relation R is internal if and only if the fact that x1, x2, . . ., xn are in the
relation R is grounded on the intrinsic natures of x1, of x2, . . . and of xn. The intrinsic
nature of x is the totality of the intrinsic properties instantiated by x. For example, if
x1 is 1 metre and x2 is 2 metres, then it follows that x1 is in the relation of being
smaller than with respect to x2. The relationship in question is not an ‘ontological
addition’ over the intrinsic properties possessed by the relata. A relationship is said
to be ‘external’ if and only if it is not internal.15 Of course, if one conceives intrinsic
properties as combinatorially intrinsic, internal relationships will be ‘combinatorially
internal’. If one conceives of intrinsic properties as grounding intrinsic, internal
relationships will be ‘grounding internal’. As it is generally assumed that intrinsic
properties are grounding intrinsic, as explained above, internal relationships will be
understood—correlatively—as grounding internal, unless there is an explicit
prevention.16

15
Although cf. Lewis 1983, 26, note 16; Lewis calls ‘external’ the dyadic relations that are
supervening on the pair of relata considered together, although they are not supervening on the
intrinsic natures of these relata.
16
The expression ‘internal relationship’ has also been used to designate a relationship that is
essential to their relata. That is, if R is an internal relation for x1, x2, . . ., xn, then none of those
objects would exist if it were not in the relation R with the rest. The designation ‘internal’ has also
14 1 Introduction

§ 6. It was mentioned in § 5 above that an object can be part of another. The

notion of ‘part’ will be understood according to standard extensional mereology.
Mereology is a theory that formalizes the relationships between wholes and parts. It
can be characterized by the following axioms:
(a) if x is a proper part of y, and y is a proper part of z, then x is a proper part of
z [Transitivity of the relation of ‘being a part of’]
(b) if x is a proper part of y, then y is not a proper part of x [Asymmetry of the
relation of ‘being a part of’]
(c) if x is a proper part of y, then there is a z such that: z is a proper part of y and z is
disjoint from x [Principle of supplementation]
(d) if there is any F, then there is a unique object x such that: something overlaps
with x if and only if it is overlapped with an F [Principle of unrestricted sums]
The notion of ‘being a part of’ has been used here as a primitive. It corresponds to
our ordinary intuition about a part that has to be ‘smaller’ than the whole of which it
is a part. A part that may be ‘smaller’ or possibly identical to the whole of which it is
a part is designated an ‘improper part’. The relation of ‘being an improper part of’ is
therefore reflexive and antisymmetric. Two objects are ‘overlapping’ if and only if
they have some (improper) part in common. Two objects are ‘disjoint’ if and only if
they do not overlap each other (cf. Simons 1987, 1–45). In standard extensional
mereology, it is automatic that for any objects—no matter how far apart they may be
spatially or temporally, or how heterogeneous they are—there is the mereological
sum of precisely those objects. It is also characteristic of standard extensional
mereology that the only thing that is relevant for the conditions of identity of a
mereological sum is what its parts are. It does not matter what kind of ‘structure’
such parts have or do not have.
§ 7. We will assume that entities can be ‘concrete’ or ‘abstract’. However, as in so
many other areas, this distinction has been mired in controversy (for a general
presentation, see Cowling 2017, 69–105). In the present work, it will be assumed
that universals are paradigmatic cases of abstract entities, whereas particular objects
are paradigmatic cases of concrete entities. It will not be necessary to consider
whether one or another analysis is the most pertinent to specify the distinction.17 It

been used for a relationship that has a plurality of objects that are not entirely independent of each
other. These notions will not be considered in this work.
17
The most important difficulties that have arisen for these proposals of analysis have to do with the
status that should be granted to entities that have as ‘constituent’ something that is clearly concrete.
Attempts have been made to distinguish between the concrete and the abstract through, for example,
the distinction between what has spatio-temporal location and what does not, what can enter into
causal interactions and what cannot, what is necessary and what is contingent, and also in relation to
features of categories of entities. Thus, Hoffman and Rosenkrantz (1994, 182–187) argue that
something is concrete if and only if it instantiates a category C such that C possibly has at least one
instance with spatial or temporal parts. Assume the particular object b, which is a clear case of a
concrete entity. It is, in effect, localized spatio-temporarily, it can enter into causal interactions, it is
contingent, and it belongs to a general category of entities that possibly possess instances with
spatial or temporal parts. Consider now the set {b}. Is it located where b is located? Does it
1.4 Summary of What Is to Come and some Nomenclature 15

will also be assumed that the distinction satisfies certain theoretical restrictions
(cf. Cowling 2017, 70–71): (i) something is concrete if and only if it is not abstract,
and is abstract if and only if it is not concrete (although cf. Williamson 2013, 7);
(ii) everything is either concrete or abstract; (iii) if something is concrete, then it is
necessarily concrete, and if something is abstract, then it is necessarily abstract; (iv) a
mereological sum, one of whose parts is concrete, is a concrete entity.

1.4 Summary of What Is to Come and some Nomenclature

§ 8 The central thesis defended in this work is that, at the fundamental level, all that
there is are universals and their instantiations. To defend this thesis, it is necessary to
justify, in the first place, the claim that there are universals. This is done in Part I
(Chaps. 2, 3, 4, and 5, §§ 9–38). As is well known, the philosophical discussion
around universals has undergone a profound transformation in the last fifty years,
especially since the work of Armstrong (1978a, b, 1983, 1989, 1997). It had been
traditional to approach the question about the existence of universals as a problem
about the ontological commitments to which our everyday communicative practices
compel us, in which it seems that we quantify over universals, or reference is made to
universals (see on this approach, Jackson 1977). After Armstrong’s contributions,
however, the postulation of universals has come to be seen as having more to do with
the roles that must be fulfilled for the explanation of objective resemblances—as
these are described in our best scientific theories—as well as causal connections and
natural laws. This is the approach followed here. If the reasons for the postulation of
universals as part of our ontology have to do with specific theoretical roles that
cannot be satisfied by other entities, then it will be essential to pay some attention to
the nature of such ‘roles’. It will also be essential to carefully consider whether
universals systematically fulfil these roles better than their alternatives. Chap. 2 (§§
9–15) explains the theoretical roles usually attributed to universal properties or their
systematic alternatives. In Chaps. 3, 4, and 5 (§§ 16–38), a comparative evaluation is
made between universals and those alternatives. As will be explained later, this
relative weighting will not be carried out with respect to all the conceptually possible
alternatives but only with respect to the conceptions that seem more relevant, at least
for me. These are: resemblance nominalism (Chap. 3, §§ 16–24), the theories of
tropes (Chap. 4, §§ 25–31), and theological nominalism (Chap. 5, §§ 32–38). The
question that will be considered in Part I, then, is whether there are universals rather
than resemblance classes of objects, resemblance classes of tropes, or concepts in the
mind of God.

intervene in the causal relationships in which b intervenes? Since, in general, a set depends on its
elements, the singleton set {b} is contingent, since it does not exist if b does not. It is not obvious if
{b} should count as ‘concrete’ after all. Similar considerations could be made regarding the
proposition b exists, and of the property of being identical to b.
16 1 Introduction

The justification of the claim that there are universals, however, leaves open
whether universals are immanent or transcendent. This is discussed in Part II
(Chaps. 6, 7, 8, 9, and 10, §§ 39–77). Traditionally, those who have postulated the
existence of transcendent universals have basically done so through considering the
functions that universals would have as the content of thought and language. Since
here it is assumed that the properties are those that are required to fulfil the
theoretical roles indicated in Chap. 2, it cannot be assumed that for each concept
that is the content of our judgments there must be a correlative property. The way in
which the existence of transcendent universals will be justified—or, more precisely,
the conditional according to which, if something is a universal, it must be a
transcendent universal—will be through considering the theoretical functions of
universals in three areas: modal metaphysics (Chap. 6, §§ 39–44), the metaphysics
of natural laws (Chap. 7, §§ 45–52), and the profile of ontological priority that a
universal must have (Chap. 8, §§ 53–59). In each of these cases, it will be shown that
the only alternative coherent with the functions attributed to a universal is to suppose
that it is a universal whose existence does not depend on having any instantiation.
For many, however, these arguments will not be persuasive if the difficulties usually
directed against them are not addressed. In Chap. 9 (§§ 60–74), then, such difficul-
ties are considered, and I show that none of them is a reason to reject transcendent
universals. Attention will be focused on three principal objections: the assumption
that a transcendent universal would have no causal power, nor would make any
difference in the causal powers of something; the criticism that the postulation of
transcendent universals would be less economical ontologically than the postulation
of immanent universals; and the epistemological objection that transcendent univer-
sals would not be cognizable by our ordinary cognitive capacities. Part II includes a
chapter devoted to considering the question of what are the conditions of identity for
transcendent universals (Chap. 10, §§ 75–77). It goes on to show that, contrary to
what might have been assumed, transcendent universals make up a unitary structure
of necessary existence. The universals are the nodes of such a structure.
The postulation of transcendent universals leaves unaddressed the question about
how particular objects should be understood. This is dealt with in Part III (Chaps. 11,
12, and 13, §§ 78–94). Given what has been argued, especially in §§ 67–70, the
ontology of particular objects must include tropes that are essentially the particular
instantiation of a transcendent universal. In the abstract, it would be consistent with
the postulation of tropes with these characteristics to understand particular objects
with a substratum that is characterized by tropes but also to understand particular
objects as trope bundles. In Chap. 11 (§§ 78–81), these theoretical alternatives will
be presented, along with the traditional difficulties directed against ontologies of
substrata and ontologies of bundles. One of the alternatives seems especially
appropriate for solving the problems discussed in Chap. 11: the so-called ‘nuclear
theory of bundles of tropes’ (Chap. 12, §§ 82–86). This is a form of a theory of trope
bundles, but with two important features that distinguish it from theories of tradi-
tional trope bundles. In this conception, the unity of an object is grounded on
ontological dependence relations, and there is a distinction between essential and
accidental properties for an object. This is achieved with the distinction between two
1.4 Summary of What Is to Come and some Nomenclature 17

different ontological strata in a particular object, called the “core” or “nucleus” and
the “periphery”. Despite the advantages offered by the traditional theory of nuclear
trope bundles, it has serious problems that have to do crucially with how the relation
of ontological dependence must be understood (especially § 86). This makes it
convenient to propose a ‘reformed’ nuclear theory (Chap. 13, §§ 87–94) that evades
these difficulties by postulating a nucleus consisting of a single trope. The reformed
nuclear theory retains the advantages of the traditional nuclear theory, but also
achieves the unification of the ontologies of properties and substrata, customarily
considered as incompatible with each other. The only nuclear trope is, in effect, a
substratum (see § 89). The reformed nuclear theory is a theory that conceives
particular objects, at the same time, as bundles of tropes and as constituted by a
substratum. We also consider how the reformed nuclear theory can make intelligible
sense of structures formed from beginning to end only by relations, without relata
(cf. §§ 93–94). Ontologies of this type have been of interest to conceive a multitude
of different types of physical entities, both at the quantum level and for the grand
scales of the universe. The reformed nuclear theory has enough flexibility to give an
adequate treatment of these structures.
I have tried to offer in this book a comprehensive defence of a Platonistic
ontology of universals that presents the advantages and discusses its counter-
intuitive consequences. In effect, for an adequate assessment of the feasibility of
such an ontology it is necessary to have a synoptic perspective of those theoretical
advantages and disadvantages. I do not intend, then, to convince the reader just with
some short argument, but with a much more arduous revision of most of the reasons
that have been put forward in decades of philosophical discussion –in some cases,
centuries of philosophical discussion. So, it has been convenient to include here the
exposition of many ideas that for most specialists are hardly new, to gain a broader
perspective appropriate for a correct theoretical assessment. Besides, a more com-
prehensive presentation of the range of questions that involve universals has the
additional advantage that the book results more accessible to non-specialist readers
that want to be introduced to the ontological debates that is both informative and
‘opinionated’.
Throughout this work, reference will be made to predicates (that is, sequences of
phonemes or graphemes of some language), concepts (that is, the content of mental
states in which we judge or consider something), and universal properties. To avoid
confusion, predicates will be presented in double quotes, as usual. Concepts, on the
other hand, will be presented in single quotes. A universal property, however, will be
presented in italics. In this way, “__ is a cube” is the predicate that is truthfully
attributed to something that is a cube; ‘being a cube’ is the concept that a rational
subject truly judges of something that is a cube; being a cube, on the other hand, is
the universal property that all objects that are cubes instantiate. Analogously, the
propositions—that is, the content of what is stated by whoever states a complete
18 1 Introduction

sentence—will also be presented in cursive letters. The proposition that is stated

when it is stated that there is a cat is there is a cat.18

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18
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lations, without Barcan’s Formula or the Converse Barcan’s Formula.
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Another random document with
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accurate. A glaring instance of inaccuracy is abundantly apparent in
his account of this very journey over the ice, from the demolished
blockhouse to York, the capital of Upper Canada. He asserts that
this journey was performed from the coast of Lake Huron, across
Lake Michigan, to the town of York—an exploit which any one, by
slightly inspecting a map of North America, will instantly see is
impossible to be accomplished.
After Sir Edward Owen was appointed to the command of the
British naval force upon the Canadian lakes, he gave Clapperton an
acting order as a lieutenant, and appointed him to the command of
the Confiance schooner. This was a situation, which, as it implied
more responsibility than any he had hitherto held, likewise allowed
him a greater degree of liberty than he could have enjoyed, had he
been assigned a birth on board of a vessel commanded by a
superior officer. When, therefore, he had the command of the
Confiance, he was in the habit of making excursions into the forests
on the coast, both of lake Huron and lake Erie, for the purpose of
shooting game. While engaged in these excursions, he cultivated an
acquaintance with several of the Indian tribes. The romantic turn of
his mind led him not only to delight to associate with those aboriginal
inhabitants of America, but also to adopt their manners and customs,
and even to acquire their language. He became a great favourite
among them; for he sometimes treated them with feasts, and on
these occasions they used to fire a feu de joie in honour of him as
their benefactor. At one time, indeed, he entertained serious
intentions of uniting himself to the Indians, marrying a princess, and
thereby becoming a chief among them; and actually assumed the
distinctive badge of the Huron nation. This romantic and foolish
design was, however, soon relinquished; but the feasts which he had
given to the chiefs led to deficiency in his accounts to the victualling
department; and this deficiency was afterwards deducted from his
half pay, and was the means of involving him in pecuniary difficulties,
from which he was not altogether relieved till after his return from his
first expedition from Africa.
But notwithstanding this fact, he was a most active, diligent, and
efficient officer, while he served upon the lakes; so that it was the
wish of Sir Edward Owen that the acting order which he had given
him should be confirmed by the Board of Admiralty; and for this end
Clapperton sent it to his uncle in London; but as the Board of
Admiralty had just promoted a great number of naval officers, they
refused to confirm his commission at that time. It was the feeling of
disappointment arising from this refusal which made him form the
design of permanently connecting himself with the Indians. When he
went on shore to visit his friends among these tribes, he did not
always order a boat to be in attendance upon him to bring him on
board; but when he regarded it as time to return, he used to plunge
into the water with his clothes on, swim along side of the schooner,
and hail the people on board to take him up. This rash mode of
proceeding, however, nearly cost him his life; for on one occasion he
encountered a strong current which bore him away from his own
schooner, the Confiance; and it was with difficulty he could make
himself be heard, as in distress, and unable to bear up against the
stream, by the men on board the schooner commanded by
Lieutenant Adam Gordon, who sent a boat to fetch him on board.
This adventure put an end to the exploits of swimming to and from
the vessel, when he had occasion to be on shore. While he served
on the lakes, he was distinguished by another singular practice. In
the midst of winter he was in the habit of causing the ice to be
broken daily for the purpose of making an opening in which he might
bathe. He used to say, he felt a shock when he first plunged into the
cold water, but that this was followed by a pleasant glow. The place
which was broken in the ice, for the indulgence of this luxury, was
with great propriety designated “Clapperton’s bath,” as no one else
chose to participate with him in this species of pleasure. Yet amidst
all these singularities he never neglected his duty as an officer; he
loved to keep the sailors upon the alert; and when he rowed guard,
he delighted to surprise the sentinels.
Like most other Scotsmen, when at a distance from their native
land, he displayed a strong feeling of amor patriæ, and was
particularly attentive to any of his countrymen he happened to meet
with abroad, a fact which perhaps laid the foundation of his
attachment to Mackenzie. At any rate, when he was on the lakes,
there happened to be some species of merry-making among the
officers, when he met, for the first time, a gentleman from Edinburgh,
belonging to the medical department. As he had a very youthful
appearance, Clapperton supposed that he must be inexperienced,
and from a sincere desire to be serviceable to him, he took him aside
and advised him always to maintain his rights, gave him some sage
advice about his dress, and decorated his right thigh with a brilliant,
scarlet-coloured watch ribbon. This gentleman took all in good part,
assumed the aspect of the greenhorn which Clapperton supposed
him to be, and allowed him both to direct and decorate him as he
pleased. But when he understood that he was of considerable
standing in the service, he came to him and apologized for his
mistake—a thing which was of course accepted, and the curious
incident proved the commencement of a sincere and firm friendship
on both sides.

Sect. VII.—HIS SECOND STEP OF PROMOTION, AND HIS CONDUCT

WHILE AN OFFICER ON HALF-PAY.

When Sir Edward Owen returned to England towards the end of

1816, he got Clapperton’s commission confirmed. Previous to this he
had been examined as to his knowledge of naval tactics, and the
information which he had displayed both as a theoretical and
practical seaman was highly satisfactory to his examinators. The
manner especially in which he had kept his log-book, was the cause
of procuring for him the greatest encomiums. It is the practice of the
officers of his majesty’s ships to note down at noon, in their log-
books, what sails the ships to which they respectively belong, then
carry. And as Clapperton had a natural talent for drawing, which he
had cultivated with care, instead of doing this in the ordinary way, he
represented the state of his ship’s canvass, at the hour required, by
a spirited sketch. He likewise shewed, by the ingenious efforts of his
pencil, the different headlands and the peculiar appearance of the
coasts, together with their harbours, noting at the same time their
soundings, and the mode of approaching them. This log-book was
so highly approved by his examinators, that they asked him to allow
them to transmit it to the Admiralty—a request which being readily
granted, it was sent there, where it still remains. As Great Britain was
now at peace with the whole world, Lieutenant Clapperton like many
others was put on half pay, and soon afterwards returned to
Edinburgh in 1817.
He had not been long in Edinburgh after his return from the
Lakes, till he was surprised to hear himself inquired after by the
attendants of an elegant equipage, which had stopped at his
lodgings. This equipage proved to be that of Lady Seaforth, the
mother of his respected friend Mackenzie, whom he had met in
India. This lady, prompted by the feelings of gratitude with which she
had been inspired by the account which her beloved son had given
her with his dying breath, of the unremitting kindness and attention
which he had experienced from Clapperton during his illness in India,
had been very anxious to have a personal interview with him, that
she might have an opportunity of expressing to him the obligations
which his friendship for her son had laid upon her. For this end she
had made many inquiries respecting him even at the Admiralty, and
at length she discovered where he was to be found through means
of her relative, Lieutenant Proby, and had come to call upon him.
The name of Lady Seaforth speedily brought to his recollection the
imputation of the interested motives to which his friendship for her
son had been attributed, and at first he refused to see her. He
however, at that time lived with a gentleman—the same he had been
so anxious should cut a respectable appearance among the officers
on the Lakes—who represented to him the ill breeding and absurdity
of refusing to see her ladyship, when she had done him the honour
of waiting upon him. He then went into her ladyship’s presence, who
being overpowered by her feelings, almost overwhelmed him with
her kindness. After the occurrence of this scene, Clapperton was
persuaded by the same gentleman, to accept of Lady Seaforth’s
invitations to visit her at her own house. And from that period, during
all the time he was in Edinburgh, he was a frequent guest and
inmate there, and was uniformly treated with the greatest kindness,
but he steadily and even resolutely refused to be in any way
indebted to her ladyship beyond the common forms of hospitality. It
was needless for the grateful lady to offer to exert her influence in his
behalf in reference to promotion in his profession. Clapperton would
not hear of such a thing. It was in vain that both she and her
daughters urged him to accept of a gold watch, chain, and seals, to
be worn by him as a token of the sense they entertained of his
kindness towards the son and the brother of whom they had been
bereaved. Our hero positively declined their generous offer,
declaring that he had already a most capital watch, and had no
occasion for another. Sometime afterwards her ladyship sent him a
large package of books, chiefly on religious subjects; these likewise
he was determined to return, till it was represented to him that he
must not only retain the books, but thank Lady Seaforth for sending
them, with a promise to peruse them diligently, otherwise he would
be regarded by her and her family as a downright heathen. The only
other thing which he would accept from Lady Seaforth, was a lock of
her son’s hair, which he received as a token of affection, and ever
after wore in a locket about his person. He always declared that he
had a sincere regard for Lady Seaforth, and was very much affected
with her kindness, but such was the morbid sensitiveness of his
nature on this point, cherished by the rankling recollection of what
his messmates had unjustly said of him, that he was of opinion he
could accept of nothing either from herself, or procured through her
interest, without compromising his principles of honour and
independence. How different is all this from the common ways of the
world!
During the greater part of the year 1818, and part of 1819,
Clapperton lived with an aunt in Lochmaben, Dumfries-shire. While
domesticated with his aunt, who was a sister of his mother’s, and of
whom, in his letters to his friends, he speaks with much affection, he
applied himself to the study of the French language; his open and
frank manners likewise procured him many friendships, and many
curious anecdotes are told of his sailor-like conduct, in paying little
regard to the ordinary etiquette of social intercourse. Like other
sailors on shore, he seemed to be of opinion that nothing should
obstruct the gratification of his whims and oddities. Hence he was
sometimes disposed to pay unseasonable visits to his friends, and
not to be particularly ceremonious as to the mode in which he
entered the houses of those with whom he lived in terms of intimacy;
but he was much beloved while he resided in Dumfries-shire, by all
to whom he was known.
 Clapperton, however, soon tired of the dullness of a country life;
and so returned to Edinburgh, and went to live with the gentleman
with whom he had resided when he was so much embarrassed by
the kindness of Lady Seaforth. Here, being an entirely idle man, fond
of adventures withal, and in a place where they might easily be
found, he soon had a hand in some curious scenes. Having little idea
of economy, and not being well acquainted with the value of money,
and indeed caring nothing for it whatever, provided he got enough to
serve his purposes at the time when it was wanted, the quarterly
items of his half pay did not last him long. Indeed, he entertained
some singular notions on the subject of borrowing money, and when
he had recourse to his friends for a supply, he gave them to
understand that he was doing them a favour by becoming their
debtor. As an instance of the careless way in which he parted with
his money when in Edinburgh, we may mention the following
incident. At this time a young man, the son of a staunch anti-
patronist, was figuring away in this town as a popular preacher, in
which capacity he became so notorious, that week after week he
was puffed in the newspapers, and was attended by vast crowds on
Sunday, when he held forth in a well known chapel of ease. This
person happened to meet Clapperton one day just after he had
drawn his quarter’s pay; and he immediately laid a plan, and
forthwith commenced the putting of it in practice, for the purpose of
getting possession of a considerable share of it. He said to
Clapperton that he had that day met with a great disappointment, in
not getting from his friends a remittance of money which he had
expected; that now he would not get it before Monday; nor would he
have cared for the delay of a day or two, had he not promised to pay
his tailor’s account, and regretted exceedingly that he should not be
able to do it, as he was a lover of punctuality, and was anxious
above every thing to keep his word. At the end of this fair speech,
Clapperton asked his reverend friend how much money would serve
his purpose, and was told that ten pounds would do all he wanted, till
he heard from his friends on Monday. Clapperton, believing the man
to be honest, gave him the sum specified, when the reverend
gentleman asked him to go to Barclay’s hotel and he would treat him
to his dinner. Away they went. An excellent dinner was set upon the
table and discussed. Madeira, champaign, and other expensive
wines were called for, and the two got cheerful, joyous, happy,
glorious. At length the swindler, as he proved to be, made some
pretence for going out for a little. He went, but never returned, and
Clapperton, in addition to the ten pounds which he had given him,
never to see again, had a bill of between two and three pounds more
to pay before he could leave the house.
Barclay’s was the place where Clapperton and his friends
generally met for enjeuement; and though, with the exception of a
single individual, none of them were addicted to intemperance,
sometimes very curious scenes occurred, of which a specimen or
two may serve both to amuse our readers and to develope our
hero’s character. He was told of a swaggering fellow, who generally
sat at the bar, and boasted of his extraordinary strength, and his
profound knowledge of the fancy science; Clapperton walked up to
him one night, and said in a loud determined tone, “Sir, I am told you
are a bully; I should like to try a round or two with you.” The poor
man was so much terrified that he walked off, and never returned to
the house again. One night, as he was going home, with another of
his friends, and the individual, who was apt to take a cup too much,
and whom, perhaps from the circumstance that he was too
frequently in a state of imbecility, they were accustomed, by the rule
of contraries, to call Able; the difficulty they found in keeping Able
steady threw the other gentleman into a fit of laughter which he could
not restrain. Clapperton, thinking it was cruel to laugh at poor Able’s
infirmity, placed him against the railing, in front of the College, and
fairly knocked the laugher down, and then apologized to him for what
he had done. On the same occasion, when he had Able in tow, the
latter fell down on the curb stone of the pavement, and Clapperton
found that he could not raise him up again, and so, though it was
eleven o’clock at night, he said, “My dear fellow, I cannot set you on
your feet again, but I shall do all that man can do, I shall sit down
beside you,” and so fairly sat down beside him till more assistance
was procured. But the most amusing of his frolics, of which we have
heard any account, was the method he took to get into his lodgings
one night when he happened to be rather late out. He had rung the
door bell several times without being answered; so he went and
brought a long heavy ladder, belonging to a house painter, and
reared it in front of the house in which he lodged. Then he mounted
it, opened the window of his own room, went in, and then hurled the
ladder down, the rubbing of which on the wall made a loud and
uncommon noise which disturbed the neighbourhood. This latter part
of our hero’s proceeding was observed by the watchman, who called
some of his companions, and came to reconnoitre. On seeing the
ladder lying on the pavement, they naturally imagined that it was the
instrument by which thieves had broken into some of the upper flats.
Immediately a tremendous ringing commenced at the door of the
house into which Clapperton a few minutes before had entered by
the window. The door was opened, and in came the policemen, who
insisted that they had seen some person enter the house through a
window, with the aid of a ladder, which was still lying below. By this
time Clapperton was in bed, and had found means to request the
people in the house not to betray him. But the policemen were not to
be satisfied with the assurance that there was no person in the
house but such as belonged to it. They searched every hole and
corner, and at length they found wet clothes; and as the night was
rainy, they naturally conjectured that they must belong to the man
who had come in by the window. On this Clapperton, laughing
heartily, raised himself up in his bed, and told the vigilant policemen
how the matter stood, and on giving them his name, and his promise
to pay any expenses which might be incurred by this frolic, they
departed. The ladder was carried to the police office, and was with
difficulty conveyed thither by three stout men. At the police office, the
whole was viewed as a piece of sailor-like humour, and Clapperton
got off on paying a trifling sum, and the house painter was ordered to
chain his ladder to his premises in future.

Sect. VIII.—HIS FIRST EXPEDITION TO AFRICA.

By this time our hero had become acquainted with Dr. Oudney, at
whose house we have had the pleasure of occasionally meeting him;
and when the Doctor was appointed to his exploratory expedition to
Africa, he expressed, through the medium of the common friend of
both, and to whose information we have been much indebted in
drawing up our memoir of their lives, his desire to be attached to the
mission. Clapperton could not boast the possession of much either
of the literary or the scientific knowledge requisite to constitute the
intelligent traveller; but he was distinguished for other qualities fitted
to render him a valuable acquisition to any mission similar to that to
the accomplishment of which Dr. Oudney had been appointed. The
portrait prefixed to the “Journal of his second Expedition,” shows that
his figure was tall, strong, and manly. He had a fine bust, and his
whole frame combined length of arm, great strength, weight, and
agility—circumstances which the portrait does not sufficiently
represent, and is also deficient in expressing his fine lion-like
forehead and eye. We have seen that he was endowed with a
constitution of almost invincible strength, that he possessed a most
enterprising disposition of mind, great conscientiousness in the
discharge of duty, and a heart alive to the kindly impressions of
compassion, and capable of strong and steady friendship. Such a
travelling companion was likely to be a treasure to a man like Dr.
Oudney; and he had the pleasure to be informed that his application
to have Clapperton attached to the mission was granted.
Accordingly, in the autumn of 1821, the travellers left Scotland for
London, with the view of then commencing their expedition to the
interior of Africa. In a letter to a friend dated London, September 1,
1821, Clapperton says, he had been supplied with arms, and had got
instruments of his own choosing, and mentions the sextant as the
most complete he had ever seen; he states to his friend that he had
had several agreeable interviews with his uncle; and adds, that he
was just on the eve of setting off for Falmouth. His next letter to the
same gentleman was written at Mourzuk, May 20, 1822, in which he
tells his friend that his health had continued vigorous, although the
heat was 106 degrees of Fahrenheit, in the shade; and says, that
Oudney was much admired by the ladies for the blackness of his
beard, and himself for the strength of his mustachoes. Oudney in a
postscript on the same sheet, says, “Clapperton is just the old man.
He is a strange-looking figure with his long sandy coloured beard
and mustachoes. You would smile were you to see him smoking his
pipe, and calling to his servant, Waddy ama simpri, or fill my pipe.” In
a subsequent letter from the same place, to the same
correspondent, Clapperton speaks in praise of the Tuaricks, whom
by this time, (Sept. 1822) he had visited. He says they are a fine
warlike race, who fear nothing but the devil and his agents, that they
offered to convey both him and Oudney to Timbuctoo; and adds,
“They wished me much to take a wife amongst them, but I said she
would have to go to Bournou and England with me, which got me out
of the scrape with a good grace, as their women never leave their
country, and those who marry them must stay with them.” And the
fact is that our hero very soon found himself as much at home
among the wild Tauricks, who traverse the sandy deserts of
Sahaara, as he had formerly done among the Indians who dwell in
the midst of the forests of Canada.
It would seem that Clapperton did not regard it as any part of his
duty to keep a separate journal while Oudney lived; nor was it
necessary, as they were generally together in all the excursions
which they made in Fezzan, and their joint observations were
combined by the Doctor into the same narrative, to which he put his
own name. But the case was greatly altered after the arrival of the
travellers in Bournou, where Oudney was seized with the illness
which terminated in death, upon the 12th of January, 1824. After this
mournful event, Clapperton, sick and sorrowful as he was,
proceeded onward to Kano, with the view of visiting Sackatoo, as
was originally intended. He reached this city, (as may be seen in his
printed journal) upon the 16th of March, and had many interviews
and long conversations with the sultan, Bello. He remained at
Sackatoo till the 4th of May, when he began to retrace his steps,—
again reached Kuka upon the 8th of July, and arrived in London in
the summer of 1825. Clapperton and Denham came from Tripoli to
Leghorn, sent the animals and baggage home by sea, under the
charge of Hillman, their only surviving companion, while they
themselves crossed the Alps, and on the 1st of June, 1825, they
reported their arrival in England to Earl Bathurst, under whose
auspices the mission had been sent to Africa.

Sect. IX.—HIS SECOND EXPEDITION TO AFRICA.

 The result of the expedition was upon the whole favourable, and
afforded encouragement to make farther researches in the interior of
Africa; and especially a letter from Bello, the sultan of the Fellatahs,
addressed to our King, George IV. and brought to England by
Clapperton, was the occasion of his second expedition. In that letter
Sultan Bello proposed “The establishment of a friendly intercourse
between the two nations, by means of a consul who was to reside at
the seaport of Raka;—the delivery of certain presents described, at
the port of Funda, (supposed to be somewhere near Whidah);—and
the prohibition of the exportation of slaves by any of the Houssa
merchants, to Atagher, Dahomy, or Ashantee.” These proposals of
the Fallatah sultan led to the resolution forthwith to send out a
second expedition to Africa, and our hero, now Captain Clapperton,
immediately volunteered his services on the occasion, with whom
were associated in the same hazardous enterprise, Captain Pearce,
Dr. Morrison, and Dr. Dickson, with their respective attendants.
Soon after Clapperton’s return to London from his first expedition
to Africa, he wrote to the friend with whom he had lived during his
residence in Edinburgh, expressing the pleasure which he felt in
being again in Britain, and informing him, that since his arrival in
London, he had been so busily employed in making out reports to
government, that he had not a moment’s leisure to attend either to
pleasure or friendship. In a subsequent letter, he told him, that along
with his other duties and avocations, he had to prepare his part of
the “journal of the expedition,” that it might be ready for publication
before his departure on the second mission. “I have got,” says he,
“no sinecure in this new appointment. I have to see the whole of the
presents sent off without any one to assist me. My Journal will
scarce be complete before I go, and the necessary attendance at the
public offices is truly harassing.” In a letter of a later date, he says
“You cannot have any idea of the infinite trouble and anxiety I have
had since I have been in London. If I receive honour and praise, they
are assuredly earned with labour and pain. The whole of the
arrangements for the new mission have fallen upon me. To give you
an outline of what I am to do, or where I am to go, is at present
impossible, but when I get to sea I shall write to you more fully.”
From Portsmouth, 27th August, 1825, he tells the same
correspondent, “We leave England this morning; and as far as I am
concerned, I have experienced nothing but misery and trouble since
my arrival, and look forward to our voyage for peace and rest.” In this
letter, he mentions that Mr. Brown of the Linnæan Society had called
one of the plants in Dr. Oudney’s collection by the name of that
lamented gentleman, and after sending compliments and
remembrances to several of his intimate acquaintances, he bids an
affecting, and, as it proved, a final farewell to his “dear friend.”
On the 27th of August 1825, Captain Clapperton and his
associates of this second expedition, with their servants, embarked
in his Majesty’s ship Brazen, at Portsmouth, and arrived off Whidah
on the 26th of November thereafter. Here Dr. Dickson landed for the
purpose of proceeding into the interior, along with a Portuguese
named De Seusa. The design of their journey is not unfolded in any
of the journals which have been published by the travellers; but the
agreement between Dr. Dickson and Captain Clapperton was, that
after the former had traversed the kingdom of Dahomy and the
adjacent countries, he should rejoin his friend, the Captain, at
Jennah. Lander, in his recently published “Records of Captain
Clapperton,” says the parting between the friends was tender and
affecting, and seemed to intimate that they should meet again no
more. “Study the natives well,” said the Captain to the Doctor,
“respect their institutions, and be kind to them on all occasions; for it
is on paying proper respect to these rules, and these only, that you
must ground your hope of being successful in your progress through
the country; and the conduct of the people to you will be guided by
your behaviour towards them. Set a guard upon your temper, my
dear Dickson, and never, let it lead you into error.” “We meet at
Jennah, then,” said the Doctor, with an inquiring eye, and anxious
half doubting look. “We meet at Jennah,” answered Captain
Clapperton, solemnly. “Once more adieu, my dear Dickson, and may
God bless and protect you.” Lander adds, that it was reported that
Dr. Dickson was slain in a quarrel with the natives, about two days’
journey from Shar; and so was the first of the mission who fell a
victim to African research.
 The Brazen proceeded with the other members of the mission to
the river Benin or Formosa; and on the advice of Mr. Houtson, an
English merchant whom they met there, they relinquished the plan of
ascending that river, and went into the interior from Badagry. They
could hear no tidings at Whidah either of Sultan Bello or of his
messengers, and as for Funda and Raka, such towns were wholly
unknown at that place.
Besides the gentlemen of the mission, whose names have been
already mentioned, there were in the capacity of servants,
Columbus, a West Indian mulatto, who had accompanied Major
Denham in the previous journey; Pasko, a black native of Houssa,
who had served on board an English man-of-war, and though a great
scoundrel, was useful as an interpreter; George Dawson, an English
sailor, engaged at Badagry, as servant to Dr. Morrison; and Richard
Lander, Captain Clapperton’s own confidential servant. This man
had been a wanderer from his youth. When only eleven years of
age, he accompanied a mercantile gentleman to the West Indies. He
was absent three years; and on his return went to France and other
places on the continent, as a gentleman’s servant, and continued
abroad in that capacity till his nineteenth year. On his return home,
he did not stay long in his native country, but went to South Africa
with Major Colebrook, and traversed, along with that gentleman, the
whole of the Cape colony, from one extremity to the other. The
reason why he left Major Colebrook has not been made public, but,
on his return to England in 1824, he heard of Captain Clapperton’s
second expedition to the interior of Africa, and regarding the
adventure as something peculiarly suited to his roving disposition, he
went to the Captain and tendered his services, which were accepted.
His own account of the matter is as follows:—“The Captain listened
to me with attention, and after I had answered a few interrogations,
willingly engaged me to be his confidential servant. In this interview
the keen penetrating eye of the African traveller did not escape my
observation, and by its fire, energy, and quickness, depicted, in my
own opinion at least, the very soul of enterprise and adventure.” This
man continued faithful and attached to Clapperton to the last; and to
him we are indebted for the preservation of his beloved master’s
journal, from which, in connexion with his own recently published
“Records” of the Expedition, we derive all that can now be known of
the last stage of Captain Clapperton’s short but eventful career.[11]
Clapperton and his associates commenced their journey from
Badagry upon the 7th of December 1825; and, regardless of what
they could not but know either from the information of others, or—as
was the case with some of them at least—from their own personal
experience, that an African climate was most unfriendly to European
constitutions, they were guilty of the great imprudence of sleeping
the first night of their journey upon the low and swampy banks of the
river, or rather creek, named Bawie, under the open canopy of
heaven. Lander says they had previously been drinking; and adds,
that next morning they found themselves wet to the skin with the
heavy dew which had fallen during the night. And, as he remarks,
after the Quarterly Review, “in all probability were thus sown the
seeds of those disorders which subsequently broke out with such
fatal virulence, and produced suffering, disease, and death to almost
the whole of the little party.” The second night after that was likewise
spent in the open air, and, in the morning, the clothes of the party
were saturated with dew. This exceedingly imprudent conduct was
speedily followed by its natural consequences. On the 10th
Clapperton was seized with ague, from which it would appear he
never perfectly recovered. Dr. Morrison and Captain Pearce soon
after became very unwell, and died before they had proceeded far
on their journey. About the same time one of the servants died, and
Lander was so ill that no hopes were entertained of his recovery. The
loss of Captain Pearce is thus bewailed by his friend and companion
in danger, Captain Clapperton: “The death of Captain Pearce has
caused me much concern; for, independently of his amiable qualities
as a friend and companion, he was eminently fitted, by his talents,
his perseverance, and his fortitude, to be of singular service to the
mission, and on these accounts I deplore his loss as the greatest I
could have sustained, both as regards my private feelings and the
public service.” One day about this time, when our traveller was sick
and sorrowful, as he reposed under the shade of trees which skirted
the way, unable to proceed, a native, on horseback, moved by the
kindness of a generous nature, quickly dismounted, and offered the
invalid the use of his horse—a proffer which was gratefully accepted.
Both Clapperton and Lander speak with rapture respecting the
beauty and fertility of the country through which they passed, from
the western coast to the City of Sackatoo, where their journey and
the life of the former were unhappily terminated. The country is
represented by them as extremely populous, and the inhabitants,
unless when selfish feelings intervened, as possessing very kind,
and even generous dispositions. Our traveller did all in his power to
recover the books, papers, and other property, which might have
been left by the unfortunate and lamented Mungo Park, as well as to
ascertain an accurate account of the manner of his death, but with
little success. The chiefs in the neighbourhood of Boussa, where the
event occurred, were anxious to avoid all communication on the
subject; and some of them were greatly embarrassed when they
were questioned respecting it. He received the following account of
the death of that unfortunate traveller from an eye-witness:—“He
said, that when the boat came down the river, it happened
unfortunately just at the time that the Fellatahs first rose in arms, and
were ravaging Goobur and Zamfra; that the Sultan of Boussa, on
hearing that the persons in the boat were white men, and that the
boat was different from any that had ever been seen before, as she
had a house at one end, called his people together from the
neighbouring towns, attacked and killed them, not doubting that they
were the advance guard of the Fellatah army then ravaging Soudan,
under the command of Malem Danfodio, the father of the present
Bello; that one of the white men was a tall man, with long hair; that
they fought for three days before they were killed; that the people in
the neighbourhood were very much alarmed, and great numbers fled
to Niffé and other countries, thinking that the Fellatahs were certainly
among them. The number of persons in the boat was only four, two
white men and two blacks; that they found great treasure in the boat;
but that the people had all died who eat of the meat that was found
in her.” “This account,” Clapperton adds, “I believe to be the most
correct of all that I have yet got; and was told to me without my
putting any questions, or showing any eagerness for him to go on
with his story.”
 At Wawa, or according to Lander’s orthography of the town, Waw
Waw, Clapperton had a singular adventure with a rich widow of
Arabian extraction. This lady was between 30 and 40 years of age,
and being fairer than the natives of the city of her residence, was
anxious to be regarded as a white woman. She was the richest
person in Wawa, having the best house in town, and a thousand
slaves; and was withal a “perfect Turkish beauty—just like a walking
water-butt.” Her great riches, and her intriguing disposition, had
prompted her oftener than once to rise in rebellion against her
rightful sovereign, who always had the gallantry generously to
pardon her on her submission. Though it might have been supposed
that the age of the tender passions was over with the widow, yet she
fell violently in love with Lander, and tried all the female arts and
winning ways her ingenuity could suggest to induce him to visit her
at her own house, but without success. She, however, visited him;
and on these occasions Clapperton humoured the joke, and fanned
the love-sick widow’s flame by sounding the praises of his servant.
He sat with as much non challance as if he had been at home in a
Scottish cottage, with his arms folded, rolling out great volumes of
smoke from his pipe, enjoying this singular scene of African
courtship, and saying at intervals, to induce the widow to persevere
in her suit, “See what beautiful eyes he has,—if you were to search
from Badagry to Wawa, and from Wawa to Badagry, you would not
find such eyes.” While all the time poor Lander was embarrassed
with the amorous attentions of the widow, and was afraid lest he
should be squeezed to death by the closeness of her tender
embraces. At length he mustered courage fairly to tell her that he
could not return her passion; and though she afterwards ceased to
persecute him farther, she was not, as many of her sex in similar
circumstances would have been, actuated by the least feeling of
revenge. On the contrary, she continued to regard him with kindness
to the last, but forthwith transferred her love to Clapperton.
To ingratiate herself with him, she sent him rich and abundant
store of provisions ready cooked, and endeavoured to gain his black
rascal of a servant, Pasko, to her interests, by bribing him with a
handsome female slave for a wife. She invited the captain to pay her
a visit, which he accepted, and has given us, in his journal, the
following graphic account of his entertainment:—
“Not being much afraid of myself, and wishing to see the interior
arrangement of her house, I went and visited her. I found her house
large, and full of male and female slaves; the males lying about the
outer huts, the females more in the interior. In the centre of the huts
was a square one of large dimensions, surrounded by verandahs,
with screens of matting all around, except in one place, where there
was hung a tanned bullock’s hide; to this spot I was led up, and, on
its being drawn to one side, I saw the lady sitting cross-legged on a
small Turkey carpet, like one of our hearth-rugs, a large leather
cushion under her left knee; her goora-pot, which was a large old-
fashioned pewter mug, by her side, and a calebash of water to wash
her mouth out, as she alternately kept eating goora, and chewing
tobacco snuff, the custom with all ranks, male or female, who can
procure them; on her right side lay a whip. At a little distance,
squatted on the ground, sat a dwarfish hump-backed female slave,
with a wide mouth, but good eyes; she had on no clothing, if I except
a profusion of strings of beads and coral round her neck and waist.
This personage served the purposes of a bell in our country, and
what, I suppose, would in old times have been called a page. The
lady herself was dressed in a white clean muslin turban; her neck
profusely decorated with necklaces of coral and gold chains,
amongst which was one of rubies and gold beads; her eyebrows and
eyelashes black, her hair dyed with indigo, and her hands and feet
with henna; around her body she had a fine striped silk and cotton
country cloth, which came as high as her tremendous breasts, and
reached as low as her ankles; in her right hand she held a fan made
of stained grass, of a square form. She desired me to sit down on
the carpet beside her, which I did, and she began fanning me, and
sent hump-back to bring out her finery for me to look at; which
consisted of four gold bracelets, two large paper dressing-cases,
with looking-glasses, and several strings of coral, silver rings, and
bracelets, with a number of other trifling articles. After a number of
compliments, and giving me an account of all her wealth, I was led
through one apartment into another, cool, clean, and ornamented
with pewter dishes and bright brass pans. She now told me her
husband had been dead these ten years, that she had only one son
and he was darker than herself; that she loved white men, and would
go to Boussa with me. I thought this was carrying the joke a little too
far, and began to look very serious, on which she sent for the
looking-glass, and looking at herself, then offering it to me, said, to
be sure she was rather older than I was, but very little, and what of
that? This was too much, and I made my retreat as soon as I could,
determined never to come to such close quarters with her again.”
A short time after this interview with the beautiful and amorous
widow Zuma, Clapperton went to Boussa, leaving Lander and his
baggage in Wawa; and though the widow did not actually
accompany him in his journey thither, as she had intimated her
intention of doing; yet she followed very speedily after him. On this
occasion, Lander informs us, she was dressed in a mantle of scarlet
silk and gold, and loose trowsers of scarlet silk, with red morocco
boots, and an ample white turban on her head; she rode astride on a
noble horse decorated with brass plates and bells, with a profusion
of charms or amulets in green, red, and yellow leather. Her saddle-
cloth was of scarlet, and both widow and horse were singularly
imposing. In her train were many spearmen and bowmen on
horseback, with a band of musicians furnished with drums, fiddles,
guitars, and flutes.
The romantic intention of Zuma was to accompany Clapperton
wherever he went. The Sultan, however, was anxious, for the sake of
his revenue and the security of his throne, to counteract the widow’s
designs; and his first step for that end was to put an embargo on
Lander and Clapperton’s baggage, and his next was to despatch a
strong party in pursuit of the fugitive widow, with strict injunctions to
bring her back. This was accomplished, and, on her submission, she
was pardoned. The travellers saw the widow no more, and the
serious consequences by which this singular adventure was likely to
be followed, made them resolve to be more cautious in future in
giving encouragement to the advances of the African ladies. But
Zuma was not the only belle of distinction who wished to attach
herself to Clapperton. He was, while at Wawa, haunted even to
annoyance by another lady of high rank. “I was pestered,” he says,
“for three or four days by the governor’s daughter, who used to come
several times in the day, painted and bedizened in the highest style
of Wawa fashion, but always half tipsy; I could only get rid of her by
telling her that I prayed and looked at the stars all night, never drank
any thing stronger than roa in zafir, which they call my tea—literally
hot water: She always departed in a flood of tears.”
As Clapperton and Lander proceeded on their journey towards
Sackatoo, the latter was seized with dysentery, and while he
continued ill and weak, he experienced the kindness of his generous
master in a very marked manner. Though his own strength was fast
declining, Lander says of him, “whenever we came to a stream
which was too deep to ford, and unfurnished with a ferry-boat, being
too weak myself to swim, my generous master used to take me on
his shoulders, and often times at the imminent risk of his own life,
carry me in safety to the opposite bank.”
On their arrival at Kano, Lander was left in that town while
Clapperton proceeded to Sackatoo, the capital of Bello, Sultan of the
Felathas, on whose account chiefly this second mission had been
undertaken. Bello at this time happened to be at war, and with his
army encamped before Coonia, the capital of Goobur. Clapperton
went there to join him, was most kindly received by him, and had an
opportunity of witnessing the African mode of fighting in a furious
assault which was made upon the city of Coonia the day after his
arrival in the camp. Soon after this event he reached Soccatoo,
where for about six months he inhabited the same house which he
had occupied during his first visit to that city. The Sultan sent to Kano
and brought Lander and the baggage to his capital, and on their
arrival the baggage was seized, under pretence that Clapperton was
conveying guns and warlike stores to the Sheik of Bornou, with
whom Bello was then at war. He was next ordered to deliver up Lord
Bathurst’s letter to the Shiek, and indeed every thing which was
supposed to form a part of the intended present to him was seized
upon. Clapperton remonstrated against these nefarious proceedings
with the utmost earnestness, but without effect. He was stript of
every thing, and detained himself as a prisoner. The effect of this
treatment upon his spirits was so great, that Lander declares he
never saw him smile afterwards.
He was strongly impressed with the idea that the Arabs had
stirred up the Africans against him and his companions. By their
insinuations against them in the hearing of Bello, they succeeded in
undermining their reputation with that monarch. Clapperton had not
been perfectly well from the day of his arrival in Africa, and the entire
failure of his mission, and the ungenerous treatment he had
experienced at Soccatoo, were the means of bringing on his last
illness and hastening his death.
As long as he was able, while at Soccatoo, he was in the habit of
spending whole days in shooting, dressed in the costume of the
country; his beard was long and flowing, and he lived in a clay hut
like an enormous bee hive. At night he and Lander used frequently
to smoke cigars for an hour or two together; but in every other
respect they lived like the Africans. Sometimes they sung, and
Clapperton was delighted to listen while Lander sung, “My Native
Highland Home.”