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Metaphysics
Metaphysics: An Introduction combines comprehensive coverage of the
core elements of metaphysics with contemporary and lively debates within
the subject. It provides a rigorous and yet accessible overview of a rich
array of topics, connecting the abstract nature of metaphysics with the real
world. Topics covered include:
■ Basic logic for metaphysics
■ An introduction to ontology
■ Abstract objects
■ Material objects
■ Critiques of metaphysics
■ Free will
■ Time
■ Modality
■ Persistence
■ Causation
■ Social ontology: the metaphysics of race.
This outstanding book not only equips the reader with a thorough knowl-
edge of the fundamentals of metaphysics but provides a valuable guide to
contemporary metaphysics and metaphysicians.
Additional features such as exercises, annotated further reading, a
glossary, and a companion website at www.routledge.com/cw/ney will help
students find their way around this subject and assist teachers in the
classroom.
A
Al
ly
ys
ss
sa
a N
Ne
ey
y is Associate Professor of Philosophy at the University of
Rochester, USA. She is editor (with David Albert) of The Wave Function:
Essays in the Metaphysics of Quantum Mechanics (2013).

“An up-to-date, well-written text that is both challenging and accessible. I think that
the greatest strengths of the book are its science-friendliness and the interweaving
of under-represented issues, such as social construction, race, and numbers, with
traditionally-favoured topics.”
Matthew Slater, Associate Professor of Philosophy, Bucknell University, USA
“I find the text accessible while maintaining an appropriately high level of difficulty.”
Tom Roberts, Department of Sociology, Philosophy,
and Anthropology; University of Exeter, UK
“Exemplary clarity and concision . . . The author has presented some difficult mate-
rial in a light, brisk and appealing style”
Barry Lee, Department of Philosophy, University of York, UK
“An excellent introduction . . . some very complicated and important work is made
accessible to students, without either assuming background knowledge or over-
simplifying.”
Carrie Ichikawa Jenkins, Department of Philosophy,
University of British Columbia, Canada
“This book will serve as an excellent introduction to contemporary metaphysics.
The issues and arguments are well chosen and explained with a carefulness and
rigor ideal for beginning students. The teaching-oriented materials, which include
a helpful overview of elementary logic, are useful additions to Ney’s expert dis-
cussion.”
Sam Cowling, Philosophy Department, Denison University, USA
“Over the last several decades, metaphysics has been a particularly active and
productive area of philosophy. Alyssa Ney’s Metaphysics: An Introduction offers a
superb introduction to this exciting field, covering the issues, claims, and arguments
on fundamental topics, such as existence and persistence, material object, cau-
sation, modality, and the nature of metaphysics. While the presentation is admirable
in its clarity and accessibility, Ney does not shy away from sophisticated problems
and theories, many of them from recent developments in the field, and she succeeds
in infusing them with immediacy and relevance. The reader has a sense of being a
fellow companion on Ney’s journey of exploration into some fascinating meta-
physical territories. This is the best introduction to contemporary metaphysics that
I know.”
Jaegwon Kim, Professor of Philosophy, Brown University, USA
“This is a terrific text. In a remarkably short space Alyssa Ney manages to be simul-
taneously comprehensive, authoritative and deep. She gives a cutting-edge account
of all the standard topics, and for good measure adds an illuminating discussion of
the metaphysics of race. This will be not only be a boon to students, but also a
valuable resource for more experienced philosophers.”
David Papineau, Professor of Philosophy, King’s College London, UK
“One of the best introductions to metaphysics available. It covers a wide range of
contemporary topics in metaphysics, giving a clear, accessible yet substantive
account of the key questions and issues and providing an up to date account of the
current debate. It’s the text I’d choose for my own course on the subject.”
L.A. Paul, Professor of Philosophy University of North Carolina, Chapel Hill, USA

Metaphysics
An Introduction
ALYSSA NEY
Routledge
ROUTLEDGE
Taylor & Francis Group
LONDON AND NEW YORK

First published 2014
by Routledge
2 Park Square, Milton Park, Abingdon, Oxon OX14 4RN
and by Routledge
711 Third Avenue, New York, NY 10017
Routledge is an imprint of the Taylor & Francis Group, an informa business
© 2014 Alyssa Ney
The right of Alyssa Ney to be identiﬁed as author of this work has been
asserted by her in accordance with sections 77 and 78 of the Copyright,
Designs and Patents Act 1988.
All rights reserved. No part of this book may be reprinted or reproduced
or utilized in any form or by any electronic, mechanical, or other means,
now known or hereafter invented, including photocopying and recording,
or in any information storage or retrieval system, without permission in
writing from the publishers.
Trademark notice: Product or corporate names may be trademarks or
registered trademarks, and are used only for identiﬁcation and explanation
without intent to infringe.
British Library Cataloguing in Publication Data
A catalogue record for this book is available from the British Library
Library of Congress Cataloging in Publication Data
Ney, Alyssa.
Metaphysics : an introduction / Alyssa Ney. — 1st [edition].
pages cm
Includes bibliographical references.
1. Metaphysics. I. Title.
BD111.N49 2014
110—dc23 2014002666
ISBN: 978-0-415-64074-9 (hbk)
ISBN: 978-0-415-64075-6 (pbk)
ISBN: 978-1-315-77175-5 (ebk)
Typeset in Akzidenz Grotesk and Eurostile
by Keystroke, Station Road, Codsall, Wolverhampton

This book is dedicated to the memory of my father, Garrett William Ney.

This page intentionally left blank

Contents
List of Figures and Tables xi
Preface xiii
Acknowledgments xv
Visual Tour of Metaphysics: An Introduction xvii
Preparatory Background: Logic for Metaphysics 1
Arguments 1
Validity 3
Soundness 7
Criticizing Arguments 9
The Principle of Charity and Enthymemes 11
Propositional Logic 13
First-Order Predicate Logic 18
Suggestions for Further Reading 28
Notes 28
Chapter 1 An Introduction to Ontology 30
Ontology: A Central Subﬁeld of Metaphysics 30
The Puzzle of Nonexistent Objects 31
Finding One’s Ontological Commitments: Quine’s
Method 37
The Method of Paraphrase 42
Ockham’s Razor 48
Where Should Metaphysical Inquiry Begin? Some
Starting Points 50
Fundamental Metaphysics and Ontological
Dependence 53
Notes 58
Chapter 2 Abstract Entities 60
More than a Material World? 60
The Abstract/Concrete Distinction 62
Universals and the One Over Many Argument 64
Applying Quine’s Method 71

Nominalism and Other Options 77
Mathematical Objects 81
Notes 87
Chapter 3 Material Objects 89
What is a “Material” Object? 89
The Paradoxes of Material Constitution 91
The Problem of the Many 100
The Special Composition Question 103
Moderate Answers to the Special Composition
Question 105
Mereological Nihilism 110
Mereological Universalism 112
Vagueness 114
Back to the Paradoxes 115
Notes 117
Chapter 4 Critiques of Metaphysics 119
A Concern about Methodology 119
Carnap’s Two Critiques of Metaphysics 120
Responses to Carnap’s Arguments 127
Present Day Worries about Metaphysical Method 132
The Relationship between Metaphysics and Science:
A Proposal 134
Notes 137
Chapter 5 Time 138
Time’s Passage 138
The Argument against the Ordinary View from Special
Relativity 140
Ontologies of Time 142
The A-theory and the B-theory 146
The Truthmaker Objection 152
Time Travel 162
Notes 168
Chapter 6 Persistence 170
The Puzzle of Change 170
Some Views about Persistence 173
A Solution to Some Paradoxes of Material
Constitution 175
The Problem of Temporary Intrinsics 178
CONTENTS
VIII

Exdurantism 183
Defending Three Dimensionalism 185
Notes 189
Chapter 7 Modality 190
Possibility and Necessity: Modes of Truth 190
Species of Possibility and Necessity 191
The Possible Worlds Analysis of Modality 193
Ersatz Modal Realism 202
Rejecting the Possible Worlds Analysis 207
Essentialism and Anti-essentialism 211
Essentialism Today 213
The Relation between Essence and Necessity 215
Notes 216
Chapter 8 Causation 217
Causation in the History of Philosophy 217
Hume’s Empiricism 220
Three Reductive Theories of Causation 223
An Objection to Reductive Theories of Causation 231
Physical Theories of Causation 232
Two Projects in the Philosophy of Causation 235
Notes 237
Chapter 9 Free Will 239
What is Free Will? 239
The Problem of Free Will and Determinism 241
Determinism 244
Compatibilism 246
Libertarianism 252
Skepticism about Free Will 256
Notes 258
Chapter 10 The Metaphysics of Race 259
(with Allan Hazlett)
Race: A Topic in Social Ontology 259
Natural and Social Kinds 260
Three Views about Races 264
The Argument from Genetics 267
The Argument from Relativity 269
The Argument from Anti-racism 273
A Causal Argument against Eliminativism 275
CONTENTS IX

Notes 278
Glossary 280
Bibliography 292
Index 300
CONTENTS
X

Figures and Tables
FIGURES
1.1 Possibility and Actuality 33
1.2 Wyman’s View 34
1.3 Fundamental and Nonfundamental Metaphysics: A Toy
Theory 55
2.1 Benacerraf’s Dilemma 85
3.1 The Ship of Theseus 92
3.2 The Statue and the Clay 98
4.1 A Chain of Verification 122
4.2 Quine’s Web of Belief 130
5.1 Patrick and Emily 141
5.2 Minkowski Space–Time and the Lightning Strikes 145
5.3 A Space–Time Containing Objective Facts about Which
Events Are Simultaneous with Which 145
5.4 The Moving Spotlight View 151
5.5 Two-Dimensional Time 164
6.1 The Persistence of Lump (Endurantism) 173
6.2 The Persistence of Lump (Perdurantism) 174
6.3 The Ship of Theseus 176
6.4 The Stage Theory and the Worm Theory 182
7.1 Nomological and Logical Possibility 192
7.2 The Incredulous Stare 197
7.3 The Content of Beliefs as Sets of Possible Worlds 200
8.1 The Problem of Epiphenomena 224
8.2 The Problem of Preemption 225
8.3 Billy and Suzy (Detail) 227
9.1 Main Views in the Free Will Debate 244
10.1 Biological System of Classification 261
10.2 Borgesian System of Classification 261
10.3 2010 U.S. Census 270
10.4 Cladistic System of Racial Classification 272

TABLES
0.1 Examples of Valid and Invalid Arguments 6
0.2 The Logical Connectives 15
0.3 Four Rules of Predicate Logic 25
2.1 Distinguishing Features of Concrete and Abstract Entities 63
2.2 Trickier Cases 63
5.1 Ontologies of Time: Which Objects and Events Exist? 142
8.1 Distinction between Objects and Events 219
FIGURES AND TABLES
XII

Preface
The distinctive goal of the metaphysician is to understand the structure of
reality: what kinds of entities exist and what are their most fundamental and
general features and relations. Unlike the natural and social sciences that
seek to describe some special class of entities and what they are like – the
physical things or the living things, particular civilizations or cultures –
metaphysicians ask the most general questions about how things are, what
our universe is like.
We will have more to say in the chapters that come about what are the
main issues in metaphysics today and what exactly is the relationship
between metaphysics and those other ways we have of studying what the
world is like, science and theology. In this preface, our aim is to orient
the reader with a basic overview of the presentation and supply some
suggestions for further resources that will complement the use of this
textbook.
This book presents an introduction to contemporary analytical meta-
physics aiming to be accessible to students encountering the topic for the
first time and yet challenging and interesting to more advanced students
who may have already seen some of these topics in a first year philosophy
course. To say this book presents an introduction to contemporary analytical
metaphysics is to signal that the emphasis of this book will be in stating
views and arguments clearly and with logical precision. As a result, in many
places this book will make use of the tools of modern symbolic logic. Ideally
a student using this book will already have had a course introducing the
basics of first order predicate logic. For those who have not already had
such a course, a preparatory chapter is provided which should bring one
up to speed. This chapter may also be useful as a review to students who
have already seen this material, or may be skimmed to find the notation that
is used throughout the remainder of the text.
This textbook contains several features that have been included to
help the introductory student who may be encountering many of these
concepts for the first time. This includes a glossary at the end of the book
as well as a list of suggested readings accompanying each chapter. The
aim of the glossary, it should be noted, is not to provide philosophical
analyses of terms or views. These are in many cases up for debate in con-
temporary metaphysics. The aim of the glossary is merely to give a gloss
of the relevant term or view that will be helpful to orient a reader. Terms in
the text that have glossary entries are marked in b
bo
ol
ld
df
fa
ac
ce
e t
ty
yp
pe
e.

In addition to the suggested readings at the end of each chapter, there
are also several excellent general resources that are available. Students
planning to write papers on any of the topics in this book would do well to
consult the following websites and handbooks:
■ The Stanford Encyclopedia of Philosophy and the Internet Encyclopedia
of Philosophy are two free, online encyclopedias. All articles are written
by professional philosophers.
■ www.philpapers.org is a free website cataloging published and unpub-
lished articles and books in philosophy. In addition to including a
searchable database of works in philosophy, this website also provides
useful bibliographies on a variety of topics.
■ The journal Philosophy Compass publishes survey articles on many
topics in contemporary philosophy aimed at an advanced undergrad-
uate/beginning graduate student audience.
In addition to these online resources, two recent books in metaphysics
provide useful introductions to many of the topics we discuss here and
beyond:
■ The Oxford Handbook of Metaphysics, edited by Michael Loux and
Dean Zimmerman.
■ Blackwell’s Contemporary Debates in Metaphysics, edited by John
Hawthorne, Theodore Sider, and Dean Zimmerman.
The website accompanying this textbook provides links to many of the
articles discussed in these chapters as well as selections from the further
reading lists.
Although much of this introduction concerns contemporary meta-
physics, the topics and debates that are most discussed today and the
various methodologies that are most common now, it is often useful to
recognize the contribution of philosophers and scientists of the past. This
book adopts the convention of noting the years of birth and death for all
deceased philosophers discussed in the main body of the text. If no dates
are provided, one should assume that this philosopher is still living and
writing.
PREFACE
XIV
w
http://plato.
stanford.edu/
http://www.iep.
utm.edu/
http://onlinelibrary.
wiley.com/journal/
10.1111/(ISSN)
1747-9991

Acknowledgments
I wish to thank several people who have helped to make this book actual.
First, I would like to thank Tony Bruce of Routledge who first raised the idea
to me of writing this text. I thank Tony for his encouragement and seeing
the project through. I would also like to thank Alexandra McGregor of
Routledge for her patience and sage advice as these chapters were written
and reviewed. Thanks to Allan Hazelett (Reader in Philosophy, University
of Edinburgh) for contributing the material on race and social ontology,
which added so much to the book. I am extremely grateful to all of the very
generous anonymous reviewers who took the time to provide so many
useful comments on drafts of these chapters. I wish to thank as well Karen
Bennett, Sam Cowling, Daniel Nolan, and Alison Peterman for their
comments on the text. I am really fortunate to work in a field with so many
brilliant and generous colleagues. Thanks to my metaphysics students at
the University of Rochester for their feedback on earlier drafts, and to the
teachers who first got me passionate about metaphysics and released me
from the spell of logical positivism, especially Jose Benardete from whom
I took my first metaphysics course, Ted Sider, and Jaegwon Kim. I was not
the first and will certainly not be the last student to realize that so many of
the questions she had thought were questions for her physics classes were
metaphysical questions and that the philosophy department was where I
belonged! I am grateful to John Komdat for his work on the website
accompanying the text. Finally, I’d like to thank Michael Goldberg for
providing a warm place with the coffee, chocolate, and encouragement I
needed to finally finish this book.

Visual Tour of Metaphysics:
An Introduction
LEARNING POINTS
At the beginning of each chapter, a number of Learning
Points are set out so that the student understands
clearly what is to be covered in the forthcoming chapter.
EMBOLDENED GLOSSARY TERMS
A Glossary at the back of the book helps with new
terms and their definitions. Where these terms are
used for the ﬁrst time in the book they can be found
in b
bo
ol
ld
d and in the margin.
EXERCISES
Each chapter includes Exercises that students can
undertake inside or outside the class. These give
students an opportunity to assess their understanding
of the material under consideration.
ANNOTATED READING
At the end of each chapter there are Suggestions for
Further Reading with annotations explaining their
context.
Learning
Introduces onto
Presents the Ou
commitments,
ontology
Considers the
ONTOLOGY: A CENTRAL SUBFIELD OF
METAPHYSICS
Glos
ts
.s u b f i 1 e dofmetaphysics
for determining one's o n f o g i c a l
I t h o d of paraphrase
data that get used in deciding an
Pamental metaphysics and several
cal dependence relatons.
In this chapre, we will introduce one of tha most cenlral subfields of meta-
Glo
s, e x a m p l e s include properties or
ma
A b s t r a c t S i process o1 considering an object while
ignoring s o m e WipiHBoîes; for example ignoring all other features of a
w of Time's
Kit w e might call the c o m m o n s e n s e
s G
mg and introductory logic textbooks
l introduced in this chapter further.
are Richard Feldman's R e a s o n and
Jsons, Explanations, and Decisions:
excellent introductory logic texis are
Jac
k Nelson's the Logic Book and
A First Course.
el
THER READING
Learning
Introduces onto
Presents the Ou
commitments,
ontology
Considers the
Abstract: a class
mathematical objec
Abstract: a class
ignoring some of its
table(its color, ma)
EXERCISE 5.1
The Ordina
Passage
SUGGESTION
There are many excel
available that will dev
Some excellent criti
Argument and The
ma
tion of on
alines fo

Preparatory Background
Logic for Metaphysics
ARGUMENTS
In metaphysics, as in most other branches of philosophy and the sciences,
we are interested in finding the truth about certain topics. For this reason,
it would be nice to have a reasonable, reliable method to arrive at the truth.
We aren’t going to find what is true by random guessing or stabs in the dark.
And in philosophy, we don’t think that the best method to find the truth is
to simply trust what one has always believed, those views one was raised
with (though common sense should be respected to some extent). Nor do
we think there is a group of elders who have the truth so that the correct
method of discovery is just to seek them out and find what they have said.1
Instead what we do is seek out arguments for various positions, a series of
statements rationally supporting a particular position that can allow us to
see for ourselves why a position is correct. It is because philosophers want
a trustworthy method for arriving at the truth that much of our time is spent
seeking out good arguments.
The word ‘argument’ has a specific meaning in philosophy that is
different from its ordinary usage. When we say ‘argument,’ we don’t mean
two people yelling at each other. Also, we should emphasize since this is a
common confusion, that when we say ‘argument,’ we don’t simply mean one
person’s position or view. Rather an a
ar
rg
gu
um
me
en
nt
t is typically a series of state-
ments presenting reasons in defense of some claim. Most arguments have
two components. First, they have p
pr
re
em
mi
is
se
es
s. These are the statements that
are being presented as the reasons for accepting a certain claim. Second,
Learning Points
■ Introduces the concept of an argument and tools for assessing
arguments as valid or invalid, sound or unsound
■ Gives students tools for recognizing incomplete arguments
(enthymemes) and applying the principle of charity
■ Presents basic notation and valid inference forms in propo-
sitional and first-order predicate logic.
Argument: a series of
statements in which
someone is presenting
reasons in defense of
some claim.
Premise: a statement
offered as part of an
argument as a reason for
accepting a certain claim.

they have a c
co
on
nc
cl
lu
us
si
io
on
n. This is the claim that is being argued for, the
statement for which reasons are being given. Here are examples of some
metaphysical arguments you might have seen in your ﬁrst philosophy class:
The Argument from Design (for t
th
he
ei
is
sm
m: the thesis that God exists)
The complexity and organization of the universe shows that it must
have been designed. But there cannot be something which is designed
without there being a designer. So, the universe must have a designer.
Therefore, God exists.
The Problem of Evil (for a
at
th
he
ei
is
sm
m: the thesis that God does not exist)
If there were a God, he would not allow evil to exist in this world. But
there is evil in this world. Therefore, God does not exist.
Each set of statements constitutes an argument because there is a claim
being defended, a conclusion, and reasons being offered in defense of
that claim, the premises. To better reveal the structure of an argument,
throughout this book we will often display arguments in the following form,
numbering the premises and conclusion. We will call this n
nu
um
mb
be
er
re
ed
d p
pr
re
em
mi
is
se
e
f
fo
or
rm
m. Here is how we might present the Argument from Design in numbered
premise form:
The Argument from Design
1. The complexity and organization of the universe shows that it must
have been designed.
2. But there cannot be something designed without there being a
designer.
3. So, the universe must have a designer.
Therefore,
4. God exists.
And similarly for the Problem of Evil:
The Problem of Evil
1. If there were a God, he would not allow evil to exist in this world.
2. But there is evil in this world.
Therefore,
3. God does not exist.
When we present arguments this way, it allows us to refer easily back to
the premises, and if we are interested in criticizing the argument, to single
out which ones are questionable or in need of more defense. In the two
PREPARATORY BACKGROUND: LOGIC FOR METAPHYSICS
2
Conclusion: the part of
an argument that is being
argued for, for which
reasons are being offered.
Theism: the thesis that
God exists.
Atheism: the thesis that
God does not exist.
Numbered premise
form: a way of stating
arguments so that each
premise as well as the
conclusion are given a
number and presented
each on their own line.

examples we have just now considered, it is quite easy to figure out which
are the premises and which is the conclusion. Sometimes in a text it is more
difficult to figure out which is which, or to figure out in which order one
should state the premises. The following exercises will help you work
through some more challenging cases.
One tool that will help you get these arguments into numbered premise
form is to look for the sorts of words that typically signal a premise or a
conclusion.
■ Words and phrases that tend to indicate premises: since, for, because,
due to the fact that, . . .
■ Words and phrases that tend to indicate conclusions: hence, thus, so,
therefore, it must be the case that, . . .
You will then want to organize the premises in such a way that they naturally
lead to the conclusion.
VALIDITY
What we would like in philosophy is to find good arguments that present
us with compelling reasons to believe their conclusions. This comes down
to two issues. First, we want to find arguments that have premises that are
PREPARATORY BACKGROUND: LOGIC FOR METAPHYSICS 3
EXERCISE 0.1
Recognizing Premises and Conclusions
The following paragraphs present the kinds of arguments that were presented in the United
States in 2009 for and against nationalized health care. Decide which are the premises and
which is the conclusion in each case, and state the argument in numbered premise form. Note
that the conclusion may not be presented last in the argument.
A. Americans should reject nationalized health care. This is because a system with nation-
alized health care is one in which someone’s parents or baby will have to stand in front of
the government’s death panel for bureaucrats to decide whether they are worthy of health
care. Any system like that is downright evil.
B. If we don’t nationalize health care there may be those, especially the young and healthy,
who will take the risk and go without coverage. And if we don’t nationalize health care,
there will be companies that refuse to give their workers coverage. When people go
without coverage, the rest of the country pays for them. So, if the young and the healthy
or employees go without coverage, then the rest of the country will have to pay more in
taxes. No one should have to pay more taxes. Therefore, we should nationalize health
care.

independently reasonable to believe. Second, we want to find arguments
whose premises logically imply their conclusions.
What we are going to do in the first part of this chapter is provide you
with tools that will allow you to articulate clearly in what way a certain
argument is a good argument or a bad argument other than just by simply
stating, “That argument is good,” “I like that argument,” or “That’s a bad
argument,” “I don’t like that argument.” When debating important topics at
a high level, we want to be more articulate than that and these next few
sections will give you the vocabulary to be so.2
The first important feature we look for in a good argument is that it be
a valid argument. ‘Validity’ is a technical term referring to a logical feature
of an argument. By definition, an argument is (d
de
ed
du
uc
ct
ti
iv
ve
el
ly
y3
) v
va
al
li
id
d just in
case there is no way for its premises to all be true while its conclusion is
false. In other words, in a valid argument, if the premises are all true, then
the conclusion must also be true. In valid arguments, we say the conclusion
“follows deductively” from the premises. An argument is (d
de
ed
du
uc
ct
ti
iv
ve
el
ly
y) i
in
nv
va
al
li
id
d
if it is possible for all of the premises of the argument to be true while the
conclusion is false. In an invalid argument, the truth of the premises does
not guarantee truth of the conclusion.
When we speak about validity, I will emphasize again, this is a logical
feature of an argument. It is all about whether the conclusion can be said
to logically follow from the premises. It is not about whether the premises
of an argument are as a matter of fact true. It is only about whether if the
premises were true, the conclusion would also have to be true. The question
about the truth of the premises is of course important and it is something
we will discuss in the next section. It is just not what we care about when
we are interested in validity. Let’s run through a few examples of arguments
to illustrate this definition of validity.
Argument 1
1. If the universe were to end tomorrow, we would never know if
there exist alien life forms.
2. The universe will not end tomorrow.
Therefore,
3. We will get to know if there exist alien life forms.
What should we say about this argument? Is this a valid argument? To
assess this, all we need to do is ask ourselves the following question: Is it
possible for there to be a situation in which the premises of this argument
are all true and yet its conclusion is false? This is what you should ask
yourself every time you are asked to assess the validity of an argument. This
is all that matters. If it turns out there is a possible scenario, one we can
imagine without contradiction, in which the premises are all true and yet the
conclusion is false, then we know automatically this is an invalid argument.
We are not talking about a likely situation, just one we can understand that
4
Deductively valid: an
argument is deductively
valid when there is no
possible way for the
premises of the argument
to all be true while its
conclusion is false. The
premises of the argument
logically imply its
conclusion.
Deductively invalid: an
argument is deductively
invalid when it is possible
for the premises of the
argument to all be true
while its conclusion is false.

doesn’t commit us to something of the form P and not-P (this is all we
mean by a c
co
on
nt
tr
ra
ad
di
ic
ct
ti
io
on
n). If the premises could all be true while the con-
clusion is false, then the conclusion doesn’t follow logically from the
premises. And so, by deﬁnition, the argument is invalid.
So what we should do to assess Argument 1’s validity is try to see if
we can understand how the following situation could obtain without a con-
tradiction:
T
TR
RU
UE
E If the universe were to end tomorrow, we would never know
if there exist alien life forms.
T
TR
RU
UE
E The universe will not end tomorrow.
F
FA
AL
LS
SE
E We will get to know if there exist alien life forms.
Can we tell a story in which this is the case? Could it be that the ﬁrst two
statements are both true and yet the third is false? Yes, this is easy to see.
We start by supposing that (1) is true. We haven’t yet discovered alien life
forms, and so if the universe were to end tomorrow, we would never know
if there are any. Then we imagine it is also true that the universe does not
end tomorrow. This doesn’t rule out the conclusion being false: that even
though the universe doesn’t end tomorrow, we still never get to learn
whether there are alien life forms. Perhaps we never learn this because the
universe ends next week rather than tomorrow. Since there is a coherent
situation in which both premises are true and yet the conclusion is false,
the argument is invalid.
In general, when you provide an example to show that the premises of
an argument are true, while the conclusion is false, what you are doing is
providing a c
co
ou
un
nt
te
er
re
ex
xa
am
mp
pl
le
e to the argument.
Let’s try this with another case:
Argument 2
1. All events have a cause.
2. The Big Bang is an event.
Therefore,
3. The Big Bang has a cause.
What should we say about the validity of this argument? Remember: validity
is a logical property of an argument. It is not about whether the premises
of an argument are in fact true, but whether they as a matter of logic
deductively entail their conclusion. So to assess this argument’s validity,
we should set aside any skepticism we might have about the actual truth
of the premises themselves. We just want to know in the possible (though
perhaps not actual) scenario where the premises are true, could the
conclusion be false.
So, is this a valid argument? To settle this again all we need to do is
see whether there is a possible situation in which the premises are all true
Contradiction: any
sentence or statement of
the form P and not-P.
Counterexample: an
example that shows an
argument is invalid, by
providing a way in which
the premises of the
argument could be true
while a conclusion is false;
or an example that shows
a statement is false, by
providing a way in which it
could be false.

and the conclusion is false. And again, by ‘possible,’ we mean logically
possible. We are asking is this a situation we can imagine, one that involves
no contradiction, in which the premises are all true and the conclusion false.
Here, it turns out: no. There is no possible situation in which the
premises of this argument are both true and yet this conclusion is false.
T
TR
RU
UE
E All events have a cause.
T
TR
RU
UE
E The Big Bang is an event.
F
FA
AL
LS
SE
E The Big Bang has a cause.
Once we ﬁx the premises and make them true, the conclusion has to
be true too. If all events have a cause and the Big Bang is an event, then
the Big Bang must have a cause too. To assume the conclusion is false is
to assume the Big Bang does not have cause. So, a situation in which the
premises are true and the conclusion is false is one in which the Big Bang
both is and is not an event – a contradiction. Since there is no possible
situation in which the premises are true and the conclusion is false, the
above argument is valid. This doesn’t mean the above argument is good in
every way. There may be some other negative things to say about it. For
example, one might be skeptical of the actual truth of one or more of its
premises. But at least in terms of its logic, this is a good argument; it is valid.
Table 0.1 illustrates one key point that you should draw from this
section: the question of an argument’s validity is independent of the actual
truth or falsity of its premises and conclusion. There can be invalid argu-
ments with all actually true premises and an actually true conclusion. There
can be valid arguments with all actually false premises and an actually false
conclusion. All that matters for validity is the logical connection between
the premises and the conclusion, and we assess that by considering what
follows in possible situations.
This table shows the four possible cases for combinations of premises
and conclusion. As you can see, there is only one combination that can
6
Table 0.1 Examples of Valid and Invalid Arguments
P
Pr
re
em
mi
is
se
es
s:
: A
Al
ll
l t
tr
ru
ue
e P
Pr
re
em
mi
is
se
es
s:
: A
Al
ll
l t
tr
ru
ue
e
C
Co
on
nc
cl
lu
us
si
io
on
n:
: T
Tr
ru
ue
e C
Co
on
nc
cl
lu
us
si
io
on
n:
: F
Fa
al
ls
se
e
V
Va
al
li
id
d A
Ar
rg
gu
um
me
en
nt
t V
Va
al
li
id
d A
Ar
rg
gu
um
me
en
nt
t
1. If Paris is in France, then it is in Europe. It is not possible to have a valid argument with true
2. Paris is in France. premises and a false conclusion
Therefore,
3. Paris is in Europe.
I
In
nv
va
al
li
id
d A
Ar
rg
gu
um
me
en
nt
t I
In
nv
va
al
li
id
d A
Ar
rg
gu
um
me
en
nt
t
1. If Paris is in France, then it is in Europe. 1. If Paris is in Spain, then it is in Europe.
2. Paris is in Europe. 2. Paris is in Europe.
Therefore, Therefore,
3. Paris is in France. 3. Paris is in Spain.

never occur. You will never find a valid argument in which the premises are
actually true and the conclusion is actually false. This follows from the
definition of validity: a valid argument is one in which there is no possible
way for the premises to all be true while the conclusion is false.
SOUNDNESS
If there were just one thing philosophers were looking for when they seek
out good arguments, most would probably say what they are looking for is
soundness. An argument is s
so
ou
un
nd
d just in case it has two features. First, it
must be a valid argument, in the sense just defined. Second, all of its
premises must actually be true. When an argument is sound, it presents
P
Pr
re
em
mi
is
se
es
s:
: A
At
t l
le
ea
as
st
t o
on
ne
e f
fa
al
ls
se
e P
Pr
re
em
mi
is
se
es
s:
: A
At
t l
le
ea
as
st
t o
on
ne
e f
fa
al
ls
se
e
C
Co
on
nc
cl
lu
us
si
io
on
n:
: T
Tr
ru
ue
e C
Co
on
nc
cl
lu
us
si
io
on
n:
: F
Fa
al
ls
se
e
V
Va
al
li
id
d A
Ar
rg
gu
um
me
en
nt
t V
Va
al
li
id
d A
Ar
rg
gu
um
me
en
nt
t
1. If Paris is in China, then it is in Europe. 1. If Paris is in Spain, then it is in Asia.
2. Paris is in China. 2. Paris is in Spain.
3. Paris is in Europe. 3. Paris is in Asia.
I
In
nv
va
al
li
id
d A
Ar
rg
gu
um
me
en
nt
t I
In
nv
va
al
li
id
d A
Ar
rg
gu
um
me
en
nt
t
1. If Paris is in France, then it is in Asia. 1. If Paris is in Spain, then it is in Asia.
2. Paris is in Asia. 2. Paris is in Asia.
3. Paris is in France. 3. Paris is in Spain.
EXERCISE 0.2
Testing Arguments for Validity
Are the following arguments valid or invalid?
A. All lawyers like basketball. Barack Obama is a lawyer. Therefore,
Barack Obama likes basketball.
B. Some snakes eat mice. Mice are mammals. Therefore, some
snakes eat some mammals.
C. If the Pope is a bachelor, then the Pope lives in an apartment.
The Dalai Lama is a bachelor. So, the Dalai Lama lives in an
apartment.
D. All birds can fly. Penguins are birds. But penguins cannot fly.
Therefore some birds can’t fly.
Sound: an argument is
sound just in case it has all
true premises and is
deductively valid.

good reason to believe its conclusion. This is because by knowing it is
sound, we know (i) that if its premises are true, its conclusion must be true
as well, and (ii) that its premises are, as a matter of fact, true.
In the last section on validity, we considered two arguments. We can
now evaluate whether these are sound arguments. The first we considered,
about the universe ending tomorrow and the aliens, fails to be sound
because it is invalid. The second, about the Big Bang, one might think also
fails to be sound, but not because it is invalid. Rather one might think the
second argument is unsound because it has at least one false premise.
Here is an example of a sound argument:
Argument 3
1. Greece is a member of the European Union.
2. All members of the European Union lie north of the Equator.
Therefore,
3. Greece lies north of the Equator.
This is a sound argument because it satisfies both conditions: (i) it is valid,
and (ii) it has all true premises. We can check to see that it is valid by using
the method in the previous section. We see if we can coherently imagine
a situation in which all of its premises are true while its conclusion is false:
We can’t do that though. To imagine that would involve imagining a
contradiction obtaining, Greece being both north of the Equator and not
north of the Equator. So, the argument is valid. Since its premises are both
actually true, it is also sound.
We are most of the time interested in whether arguments for or against
a position are sound. So, in general when you are asked to assess an
argument in this course, you should first look for the following:
■ Are all of the premises of this argument true? If not, which do you think
are false and why?
■ Does the conclusion follow from the premises? That is, is the argument
valid?
If the answers to these questions are ‘yes,’ then the argument is sound. The
premises are true and the conclusion logically follows from them. So, one
has reason to believe the conclusion is true as well.
8
T
TR
RU
UE
E Greece is a member of the European Union.
T
TR
RU
UE
E All members of the European Union lie north of the
Equator.
F
FA
AL
LS
SE
E Greece lies north of the Equator.

CRITICIZING ARGUMENTS
Once one understands what we are looking for in metaphysics (sound
arguments for the positions that are of interest to us), one can also see how
to rationally evaluate these arguments. One always has two options for
criticizing an opponent’s argument. One can either (i) challenge one of the
argument’s premises, or, one can (ii) challenge the validity of the argument.
Let’s brieﬂy discuss each of these in turn.
First, let’s again consider the Argument from Design presented in the
ﬁrst section:
The Argument from Design
1. The complexity and organization of the universe shows that it must
have been designed.
2. But there cannot be something which is designed without there
being a designer.
3. So, the universe must have a designer.
Therefore,
4. God exists.
We now have the tools to criticize this argument, if this is something we are
interested in doing. We can either criticize premise (1) and argue that the
complexity and organization of the universe have either (a) no bearing on
whether it was designed, or (b) perhaps shows instead that the universe
lacked a designer (perhaps a designer would prefer a simple universe over
one with so much complexity). Alternatively, one might instead criticize
premise (2) and argue that the fact that something is designed doesn’t
imply the existence of a designer. This would be to get into a debate about
what it means to say that something is designed. Either way, if one wants
to deny this argument is sound because premise (1) or (2) is false, one
would need to present a compelling reason to think the premise in question
is indeed false. Since (3) is just supposed to follow from (1) and (2) on the
way to the conclusion (4), we call it a m
mi
in
no
or
r c
co
on
nc
cl
lu
us
si
io
on
n, as opposed to (4)
EXERCISE 0.3
Assessing Arguments for
Soundness
Go back to Exercise 0.2 at the end of the previous section and assess
these arguments for soundness.
Minor conclusion:
a statement that is argued
for on the way to arguing
for an argument’s major
conclusion.

which we call the m
ma
aj
jo
or
r c
co
on
nc
cl
lu
us
si
io
on
n of the argument. If (3) is the premise
that seems the most problematic, then what one should really take issue
with is either (1), (2), or the validity of the inference that is supposed to take
one from (1) and (2) to (3).
There are two inferences that are made in this argument. First, there
is the move from (1) and (2) to (3). Then there is the move from (3) to the
final, major conclusion (4). Both are places one may try to criticize the
argument. Here, what one should do is check both steps for validity. First,
is it possible for (1) and (2) to be true, while (3) is false? Probably not. (1)
and (2) do seem to logically imply (3). So, it is not the validity of that step
that is mistaken here. On the other hand, it is open for one to challenge the
validity of the inference from (3) to (4). One might think there is no
contradiction that results from assuming that (3) is true, the universe has
a designer, and yet (4) is false, God doesn’t exist. Perhaps the universe was
designed by someone other than God. This situation would constitute a
counterexample to the argument.
Either way, if the argument fails to make all valid inferences, or the
argument has premises that are false, the argument will fail to be sound.
In this case, it fails to provide a compelling reason to believe its conclusion.
Note that one may criticize an argument in this way even if one as a matter
of fact believes its conclusion. Not every argument for a true conclusion has
to be a good argument.
10
EXERCISE 0.4
Criticizing Arguments
Consider the following argument for the conclusion that God exists.
The Cosmological Argument
1. Everything that happens in the universe must have a cause.
2. Nothing can be a cause of itself.
3. So, there must exist a first cause.
4. If there is a first cause, then this first cause is God.
5. Therefore, God exists.
Identify which premises are supposed to follow from earlier premises
in the argument (as minor or major conclusions). Label the indepen-
dent premises (i.e., those that are neither major nor minor conclusions).
If there are reasons to be skeptical about the truth of any of the
independent premises, then state these reasons. Then, evaluate
whether the inferences that are made to minor and major conclusions
all appear valid. Is the argument sound? Why or why not?
Major conclusion:
the final conclusion of
an argument.

THE PRINCIPLE OF CHARITY AND ENTHYMEMES
One thing to keep in the back of your mind as you go about evaluating
arguments in metaphysics is that all of us are trying to work together as
part of a common enterprise to discover the truth. And so, it is a convention
of philosophical debate that one applies what is called the p
pr
ri
in
nc
ci
ip
pl
le
e o
of
f
c
ch
ha
ar
ri
it
ty
y. What this means is that when it is reasonable, one should try to
interpret one’s opponent’s claims as true and her arguments as valid. For
example, if you are reading a text or having a philosophical discussion and
someone makes a claim that could easily be interpreted in several ways,
some of which are true and some of which are obviously false, the principle
of charity recommends that you choose the true way to interpret the author.
Another thing you will find is that some of the time when an author
presents an argument in a text they will present their argument only
incompletely. That is, they will present what is called an e
en
nt
th
hy
ym
me
em
me
e. An
enthymeme is an argument that is incomplete and invalid as stated, yet
although the premises as stated do not logically entail the conclusion, one
still has reason to believe the argument the author intended is valid. In the
case of an enthymeme, an author leaves out some premises because they
are simply too obvious to state. Stating them would perhaps bore the reader,
or insult his or her intelligence. So, she leaves them out. The principle of
charity compels us in such cases, where it is obvious the author intended
these missing premises, and the argument needs them in order to be valid,
to fill them in for her.
Here is one example of an enthymeme. Suppose you read in a text an
author saying the following:
Argument against Abortion
Anytime one ends the life of a person, it is murder. Abortion ends the
life of a fetus. So, abortion is murder. Therefore, abortion is wrong.
One might at first try to state the argument this way in numbered premise
form:
1. Anytime one ends the life of a person, it is murder.
2. Abortion ends the life of a fetus.
3. So, abortion is murder.
Therefore,
4. Abortion is wrong.
One might then criticize the argument for being invalid. For there are two
inferences made in this argument: the first is the move from (1) and (2) to
the minor conclusion (3):
Principle of charity:
a convention of
philosophical debate to,
when reasonable, try to
interpret one’s opponent’s
claims as true and her
arguments as valid.
Enthymeme: an argument
that is incomplete as stated
and invalid, although it is
easy to supply the missing
premises that the argument
would need to be valid. In
the case of an enthymeme,
the author left out the
missing premises for fear
of boring the reader or
insulting his or her
intelligence.

Inference 1
3. So, abortion is murder. (Minor conclusion)
The second is the inference from (3) to (4):
Inference 2
3. Abortion is murder.
Therefore,
4. Abortion is wrong. (Major conclusion)
Neither of these inferences is deductively valid. In the first case, (1) and (2)
could be true, but (3) false because although ending the life of a person is
murder and abortion ends the life of a fetus, abortion doesn’t count as
murder because a fetus is not a person. The second inference is not valid
because it could be the case that abortion is murder and yet abortion is not
wrong, because murder is not wrong. (Imagine a world very different from
ours where the presence of human life is such a plague that murder is
altogether a good thing. Such a world might be very different from ours, but
there is no contradiction in the possibility.)
At this point, one may just conclude that this argument against abortion
is invalid, and so unsound, and so does not present a compelling reason to
think abortion is wrong. However, this response would miss something.
Here’s why. There is a very simple way to fill in both inferences in this
argument using supplementary premises that it is reasonable to think the
author assumed. And so a better thing to do would be to grant the author
the obvious intermediate steps she intends that would make the argument
valid. Then we can make sure we have given the argument the best shot
we can.
What are the missing links that will give us a valid argument from the
premises to the conclusion? How about this:
*2.5 A fetus is a person. (fixes the validity of Inference 1)
3. So, abortion is murder.
*3.5 Murder is wrong. (fixes the validity of Inference 2)
Therefore,
4. Abortion is wrong.
12

We are allowed, indeed compelled by the principle of charity, to supply the
author with premises (2.5) and (3.5) only because it is obvious that these
are claims the author intended. This is why we say her original argument is
an enthymeme. It is invalid as stated, but it can easily be made into a valid
argument by supplying premises that are obvious she intended, and may
only have left out because they were so obvious to her.
Note that just because it is often reasonable to reconstruct an author’s
argument in such a way as to make it valid, this does not mean that we have
to accept any argument we ever come across in a text. We still have tools
with which to disagree. For although now we can see the above argument
is valid, there are several premises whose truth one may take issue with.
And this includes the originally unstated premises (2.5 and 3.5) that we
added to make the argument valid. All are fair game and open for rational
disagreement.
Applying the principle of charity and recognizing enthymemes is a skill
that one develops over time as one grapples with more and more philo-
sophical arguments. The following exercises will help you develop this skill.
PROPOSITIONAL LOGIC
We’ve seen that deciding validity is an important tool in assessing the
strength of an argument. But sometimes, when an argument has many
premises or its inferences are complicated, it is difficult to assess whether
or not an argument is valid using the method we introduced in the section
on validity. For this reason, philosophers have developed systems of formal
logic, rigorous methods for deciding which forms of argument are or are
not valid.4
Here we will just cover a few basics that will give you tools to tell
EXERCISE 0.5
Supplying Missing Premises
Some call the ancient Greek philosopher Thales (624 BC–c. 546
BC) the first philosopher. Thales is famous for arguing that everything
is water. Consider the following texts containing arguments against
Thales’s thesis. Provide the missing premises that will make the
arguments valid.
A. There is no water on Saturn. Therefore, not everything is water.
B. There were things that existed in the first seconds immediately
after the Big Bang. Water did not come into being until hundreds
of thousands of years after the Big Bang. So, not everything is
water.

which argument forms can be trusted to yield valid arguments. These are
argument forms that recur throughout the discussions in this book.
First, let’s clarify what is meant by an argument form. When we talk
about the form of an argument, we are talking about the kind of shape or
structure an argument has, independent of its speciﬁc subject matter. For
example, consider the following two arguments:
Argument 4
1. If Sally is human, then she is mortal.
2. Sally is human.
Therefore,
3. She is mortal.
Argument 5
1. If determinism is true, then no one has free will.
2. Determinism is true.
Therefore,
3. No one has free will.
These arguments concern very different topics; their subject matter is dis-
tinct. And yet, they have something in common: their form. To see this most
clearly, logicians will replace the premises and conclusion of an argument
with symbols. In the system of logic we are considering now, propositional
logic, one chooses upper or lower case letters to represent individual
statements or propositions. For example, let’s introduce the following
symbols to represent the basic propositions that make up the premises
and conclusions of Arguments 4 and 5.
H: Sally is human.
M: Sally is mortal.
D: Determinism is true.
N: No one has free will.
In propositional logic, the premises and conclusion of an argument will be
represented by either single letters (for the basic or ‘atomic’ propositions)
or complex symbols formed out of single letters and some linking symbols,
the l
lo
og
gi
ic
ca
al
l c
co
on
nn
ne
ec
ct
ti
iv
ve
es
s. The logical connectives are what are used to build
complex propositions out of simpler ones.
The logical connectives typically recognized in propositional logic are:
‘and,’ ‘if . . . then,’ ‘or,’ ‘not,’ and ‘if and only if’; they are often replaced by
symbols. The chart in Table 0.2 lists some symbols that are often used to
represent these words in logical notation.
14
Logical connectives:
symbols used to build
complex propositions out
of simpler ones.

In this book, we will always use ‘∧’ to symbolize ‘and,’ ‘⵪’ for ‘or,’ ‘傻’ for
‘if . . . then,’ ‘¬’ for ‘not,’ and ‘⬅’ for ‘if and only if.’
Using this notation, we can now symbolize Arguments 4 and 5:
Argument 4
1. H 傻 M
2. H
Therefore,
3. M
Argument 5
1. D 傻 N
2. D
Therefore,
3. N
Once we symbolize the arguments, their logical structure is more clearly
revealed and we can see they share the same logical form.
Table 0.2 The Logical Connectives
English Logical symbolism
A
An
nd
d ∧,, &
&
Sally is human and Sally is mortal. H ∧ M
H & M
O
Or
r (inclusive or, meaning: either a, b, or both a and b) ⵪
Either Sally is human or Sally is mortal. H ⵪ M
I
If
f .. .. .. t
th
he
en
n →
→,, 傻
傻
If Sally is human, then she is mortal. H →
→ M
H 傻
傻 M
N
No
ot
t ~
~,, ¬
Sally is not human. ~ H
¬ H
I
If
f a
an
nd
d o
on
nl
ly
y i
if
f ↔,, ⬅
Sally is human if and only if she is mortal. H ↔ M
H ⬅ M

As we saw, using the representational tools of propositional logic, we can
see more easily that Arguments 4 and 5 have the same logical form. The
form of both of the above arguments is called m
mo
od
du
us
s p
po
on
ne
en
ns
s.
Modus Ponens
1. If A, then B
2. A
Therefore,
3. B
or, using the notation of propositional logic:
1. A 傻 B
2. A
Therefore,
3. B
16
EXERCISE 0.6
Translations in Propositional
Logic
Using the key below, symbolize the following sentences in logical
notation.
Key:
I: The universe is infinite.
U: The future is unknown.
O: The future is open.
F: Humans have free will.
A. Either the universe is infinite or the universe is not infinite.
B. If humans have free will and the future is open, then the future
is unknown.
C. Humans have free will if and only if the future is open.
D. It is not the case that either the universe is infinite or the future
is open.
Modus ponens:
the logical form:
If A, then B
A
Therefore,
B,
where A and B are
any propositions.

It doesn’t matter which order the premises are written in. Modus ponens is
one form of argument that logicians nearly always regard as valid.
Three more commonly seen valid argument forms are the following.
Note in each case, A and B may stand for any proposition whatsoever, no
matter how complex.
Simplification
1. A ∧ B 1. A ∧ B
Therefore, or Therefore,
2. A 2. B
Modus Tollens
1. A 傻 B
2. ¬B
Therefore,
3. ¬A
Disjunctive Syllogism
1. A ⵪ B 1. A ⵪ B
2. ¬A 2. ¬B
Therefore, or Therefore,
3. B 3. A
All of these are valid forms of inference. If you find an argument that uses
one of these argument forms, you can be sure it is valid.
EXERCISE 0.7
Recognizing Valid Argument
Forms in Propositional Logic
First symbolize the arguments below using the notation of propo-
sitional logic and the key from the previous exercise. Then decide
whether the argument’s logical form is (a) modus ponens, (b)
simplification, (c) modus tollens, (d) disjunctive syllogism, or (e) none
of the above.

FIRST-ORDER PREDICATE LOGIC
In the previous section we considered some valid forms of inference in
propositional logic. Building upon the foundation of propositional logic,
logicians have built more powerful logics, logics that recognize more valid
argument forms than propositional logic alone. These logics delve deeper
into the structure of our statements, and will be indispensable to represent-
ing the views and arguments one encounters in contemporary metaphysics.
For the remainder of this chapter, we will consider first-order predicate
logic, initially developed by Gottlob Frege (1848–1925). This will afford us
some tools that will be helpful for our discussion of ontology in the next
three chapters. In later chapters, we will build on this foundation, adding
modal and tense operators. But let’s start simple. Consider the following
argument:
Argument 6
1. Alex respects everyone who loves the Beatles.
2. Betty loves the Beatles.
Therefore,
3. Alex respects Betty.
If we just used the tools of propositional logic from the previous section,
we would not be able to prove that this is a valid argument. We could not
see it as having anything but the following form:
1. A
2. B
Therefore,
3. C
18
A. Either the future is open or the universe is not infinite. The future
is not open. Therefore, the universe is not infinite.
B. If humans have free will, then the future is open. The future is
not open. Therefore, humans don’t have free will.
C. If humans have free will, then the future is open. The future is
open. Therefore, humans have free will.
D. If humans have free will, then the future is open. Humans have
free will. Therefore, the future is open.
E. The future is open and it is unknown. So, the future is unknown.

And this is not a valid argument form. We would be forced to symbolize it
this way because each proposition (1), (2), and (3) is distinct and none
contain the sort of parts that would allow us to use the connectives intro-
duced in the previous section.
But the above argument is intuitively valid, and so, to show this using
symbolic logic, we need more tools with which to symbolize the argument.5
First-order predicate logic gives us the relevant tools. The key insight is to
recognize that in general we can separate propositions into subjects (or
noun phrases) and predicates.
To take a simple case, consider the sentence:
Shaq is tall.
In predicate logic, the symbol for a predicate (‘is tall’) is always a capital
letter. In this case, we will use ‘T.’ The symbol for the predicate is placed
before the symbol for the subject (‘Shaq’). We will use ‘s’ to stand for ‘Shaq.’
The entire sentence or proposition will then be symbolized in predicate
logic in the following way:
Ts.
Similarly, ‘Ludwig is a philosopher’ could be symbolized as:
Pl.
We might also want to symbolize the sentence:
Shaq admires Ludwig.
This would be:
Asl.
Notice again that the symbol for the predicate (in this case, ‘admires’)
always goes in the front. Here our predicate, ‘admires,’ is a two-placed
predicate because it takes two noun phrases as inputs. But of course there
exist predicates that take more than two inputs. For example, if you’ve
played the game Clue, you’ve probably stated sentences using predicates
like:
‘__ murdered __ in the __ using the __.’
For example you might say:
Professor Plum murdered Mr. Body in the kitchen using the candle-
stick.
This can be represented as:

Mpbkc.
One thing that will be especially important in the next chapters is that we
are able to represent sentences that make reference to some person(s) or
object(s), but without using a name. These are general sentences such as:
■ Somebody is tall.
■ Somebody murdered Mr. Body in the kitchen using the candlestick.
or:
■ Nobody is tall.
■ There is nothing Professor Plum murdered Mr. Body with in the kitchen.
To represent sentences like this, first-order predicate logic uses v
va
ar
ri
ia
ab
bl
le
es
s
(symbols like x, y, z, etc.) and what is called the e
ex
xi
is
st
te
en
nt
ti
ia
al
l q
qu
ua
an
nt
ti
ifi
fie
er
r. The
existential quantifier is represented using: ∃. So, for example, consider the
sentence:
Somebody is tall.
This will be symbolized as:
∃xTx.
This may be read aloud in any of the following ways:
■ There exists an x such that x is tall.
■ There is at least one x such that x is tall.
■ Some x is tall.
■ Something is tall.
Or if we know that our domain of quantification includes only persons (more
on domain of quantification momentarily), we may read this as:
■ Somebody is tall.
We can also use a variable and an existential quantifier to translate the
sentence:
Somebody murdered Mr. Body in the kitchen using the candlestick,
as:
∃xMxbkc.
We may read this as: “There exists an x such that x murdered Mr. Body in
the kitchen with the candlestick.”
20
Variables: symbols like x,
y, z, etc. used to stand in for
other things in a sentence,
called the values of the
variable.
Existential quantifier:
∃, a symbol of first-order
predicate logic. When
combined with a variable,
it can be used to represent
a statement to the effect
that something exists that
is a certain way.

Or, we can represent the sentence:
There is something that Professor Plum murdered Mr. Body with in
the kitchen,
as:
∃xMpbkx.
Note that the variable ‘x’ replaces the name of the object we are quantifying
over, the referent of the quantifier phrase ‘something’ or ‘somebody.’ In the
first case, the ‘somebody’ refers to the x that is the murderer, so the variable
goes in the first place. In the second sentence, the ‘something’ refers to the
x that is the murder weapon, so the variable goes in the last place.
We can also represent more complex sentences using the existential
quantifier. For example, we can symbolize ‘Nothing is tall’ as:
¬∃xTx.
To say that there is something that is tall and friendly, we can use the
following translation:
∃x (Tx ∧ Fx),
where ‘Tx’ means x is tall, and ‘Fx’ means x is friendly.
Or,
There is at least one baby eagle on that mountain,
Can be symbolized as:
∃x ((Bx ∧ Ex) ∧ Mx).
Finally, in some cases, one will find sentences that need more than one
variable of quantification. For example, one might want to express in predi-
cate logic the sentence:
Some cats love some dogs.
This sentence has two quantifier phrases. It says both that there exists
some x such that x is a cat, but also that there exists some y such that y is
a dog, and that the cat (the x) loves the dog (the y). So that we do not
confuse which variable is referring to the cat and which the dog, we will use
distinct variables x and y in the symbolization of this sentence:
∃x∃y ((Cx ∧ Dy) ∧ Lxy),
which we may read back into English as, “There exists an x and there exists
a y such that x is a cat and y is a dog, and the x loves the y.”

Note that in all cases where one uses a variable (x, y, z, and so on) as
part of a complete sentence, the variable should always be contained within
the s
sc
co
op
pe
e of a quantifier. Either it is right next to the quantifier in the sen-
tence, or there should be parentheses reaching from a quantifier and
surrounding the occurrence of that variable. Consider the variables in the
following two sentences.
Fx
∃xFx ∧ Gx
In the first sentence, x is not contained within the scope of any quantifier,
and so this sentence does not express a complete thought. It says ‘x is F,’
where ‘x’ does not have any clear meaning. In the second case, the x in the
phrase ‘Gx’ is not contained within the scope of any quantifier, and so again,
the reference of this ‘x’ is unclear. Is this x that is G supposed to be the same
as the x that is F? This isn’t clear. To fix this, we may introduce parentheses:
∃x (Fx ∧ Gx).
Now all variables in the sentence lie within the scope of the quantifier
‘∃’ and we can understand this sentence to be saying: “There is something
that is both F and G.” To say that a variable lies within the scope of a quantifier
is to say that it is a b
bo
ou
un
nd
d v
va
ar
ri
ia
ab
bl
le
e. When symbolizing complete sentences
in predicate logic, it is important that all variables be bound by quantifiers.
In general, when one makes an existentially quantified claim, one is
saying there exists some thing that is a certain way. What kind of thing we
have in mind generally depends on the context. The way logicians put it, this
depends on the d
do
om
ma
ai
in
n o
of
f q
qu
ua
an
nt
ti
ifi
fic
ca
at
ti
io
on
n, the set of entities over which the
quantifiers range. For example, suppose we used ‘Bx’ to symbolize ‘x is
blessed,’ and then see the sentence:
∃xBx.
What this sentence is supposed to represent depends on the relevant
domain of quantification. The domain of quantification may be:
■ the set of all entities that exist whatsoever, so that the sentence may
be read as: “Something is blessed,”
■ the set of persons there are, so that the sentence may be read as:
“Someone is blessed,”
■ the set of persons in a particular community under discussion, for
example, those in this house. Then ‘∃xBx’ would mean: “Someone in
this house is blessed.”
The relevant domain of quantification is fixed by the context. In later chap-
ters we will see philosophers sometimes making reference to this fact.
They will explicitly exploit the fact that our quantifiers may sometimes be
restricted, so that they range over a limited set of objects. Or at other times,
22
Scope (of a quantifier):
the part of the sentence
containing the variables the
quantifier is binding. In
symbolic logic, the scope of
a quantifier is either the
part of the sentence
immediately after the
quantifier phrase (in a
simple sentence like
‘∃xFx’), or the part of the
sentence contained in
the parentheses that
immediately follow the
quantifier phrase. (For
example, in ‘∃x(Fx ∧ Gx) ∧
Hx,’ the xs in ‘Fx’ and
‘Gx’ are contained in the
scope of the quantifier.
The x in ‘Hx’ is not.)
Bound variable:
a variable that is within
the scope of some
quantifier phrase.
Domain of
quantification: the set
of objects over which
the quantifiers range in a
given context, the set of
possible values the
variables can take.

a philosopher will exploit the fact that in some cases our quantifiers may
be “wide open,” meaning they range over the largest domain of quantifi-
cation possible, including any entities whatsoever.
We can now distinguish three types of letter symbols that are used in
first-order predicate logic.6
■ Predicates, which are symbolized by upper case letters: F, G, H , . . .
■ Names, which are symbolized using lower case letters from the
beginning of the alphabet: a, b, c, . . .
■ Variables, which are symbolized using lower case letters from the end
of the alphabet: x, y, z, w, u, v, . . .
In addition to the existential quantifier, there is also another quantifier, the
u
un
ni
iv
ve
er
rs
sa
al
l q
qu
ua
an
nt
ti
ifi
fie
er
r, which is used to symbolize claims involving ‘all’ or ‘every.’
For example,
Everyone is happy,
may be symbolized as:
xHx.
We may read this as:
■ For all x, x is happy.
■ Every x is happy.
■ Everyone is happy.
(Note that if the only kinds of entities we ordinarily take to have emotional
states like happiness are persons, the relevant domain of quantification is
the set of all persons.)
To take another example, ‘Everyone is a happy philosopher,’ may be
translated as:
x (Hx ∧ Px)
or, every x is such that it is happy and a philosopher.
How would we symbolize ‘All philosophers are happy’? This says
something different than saying that everyone whatsoever is both happy
and a philosopher (x(Hx ∧ Px)). ‘All philosophers are happy,’ is symbolized
using the symbol ‘傻’ for ‘if . . . then’:
x (Px 傻 Hx).
We can read this back into English as ‘For all x, if x is a philosopher, then
x is happy.’ This says the same thing as our original ‘All philosophers are
happy,’ which of course is different than saying ‘Some philosophers
are happy,’ which is expressed in first-order logic as:
Universal quantifier:
, a symbol of first-order
predicate logic. When
combined with a variable,
it can be used to represent
a statement to the effect
that everything is a certain
way.

∃x (Px ∧ Hx),
or ‘There exists an x such that x is a philosopher and x is happy.’
In the next chapter and throughout the book, we will find that the
formulation of theses and arguments in the language of first-order pred-
icate logic is often essential. Particularly when we are considering issues
of existence, we will be required to formulate statements in predicate logic.
Only then can we be clear about what follows from them. To do so, we will
need to have under our belts some basic rules of inference involving exis-
tentially and universally quantified statements.
There are four basic rules which are summarized in Table 0.3. Some
of these rules are a bit complicated, but for our purposes in this book, the
rules that will be used most often are Existential Quantifier Introduction
(EI) and Universal Quantifier Generalization (UG). So let’s just briefly con-
sider some examples using these rules of inference.
24
EXERCISE 0.8
Translating Sentences into
First-Order Predicate Logic
Using the key below, translate the following sentences into the
language of first-order predicate logic.
Key:
a: Alex
b: Barney
Cx: x is clever
Sx: x is a student
Tx: x is a teacher
Rxy: x respects y
1. Alex is a student.
2. Alex is a clever student.
3. Someone is a student.
4. Someone is a clever student.
5. Alex respects Barney.
6. Alex respects someone.
7. Someone respects Alex.
8. Some teachers respect some students.
9. Everyone is a teacher.
10. All students are clever.

Here is an example of the kind of inference that will be employed in
Chapter 2. Suppose one believes the following:
Humility is a virtue.
This will be symbolized in first-order predicate logic as:
Vh.
Using the rule EI then, we can conclude:
∃xVx.
This may be read back as: There exists some x such that x is a virtue.
And, to consider another example, if we have reason to believe the
following:
Plato is a philosopher who taught Aristotle.
We may symbolize this as:
Pp ∧ Tpa (Plato is a philosopher and Plato taught Aristotle.)
And then using EI, we can infer:
∃x(Px ∧ Txa).
In both cases of the application of EI, what we are doing is introducing a
variable x to stand in for a particular subject.
Note then that when you have established an existentially quantified
sentence, however complicated, that is one where the existential quantifier
∃ is on the outside of any parentheses in the sentence, you now know that
Table 0.3 Four Rules of Predicate Logic
E
Ex
xi
is
st
te
en
nt
ti
ia
al
l Q
Qu
ua
an
nt
ti
ifi
fie
er
r I
In
nt
tr
ro
od
du
uc
ct
ti
io
on
n (
(E
EI
I)
) U
Un
ni
iv
ve
er
rs
sa
al
l Q
Qu
ua
an
nt
ti
ifi
fie
er
r I
In
nt
tr
ro
od
du
uc
ct
ti
io
on
n (
(U
UI
I)
)
From anything of the form: Fa If one has introduced a new term ‘a’ as an arbitrary
name, and shown for it that: Fa
One can infer: ∃xFx Then one can infer: xFx
E
Ex
xi
is
st
te
en
nt
ti
ia
al
l Q
Qu
ua
an
nt
ti
ifi
fie
er
r G
Ge
en
ne
er
ra
al
li
iz
za
at
ti
io
on
n (
(E
EG
G)
) U
Un
ni
iv
ve
er
rs
sa
al
l Q
Qu
ua
an
nt
ti
ifi
fie
er
r G
Ge
en
ne
er
ra
al
li
iz
za
at
ti
io
on
n (
(U
UG
G)
)
If it has been established that: ∃xFx From anything of the form: xFx
Then one can introduce a new term ‘a’ into the One can infer using any name ‘a’ that refers to
language to refer to whatever is the object in something in the relevant domain of quantification
the domain of quantification that satisfies the that: Fa
description ‘is F’ and conclude: Fa

there is something in the relevant domain of quantification that has the
relevant features. Thus from existentially quantified sentences we can infer
that something exists in the domain of quantification that has the relevant
features. There is some x that can stand in as the value of this variable that
makes the sentence true. For the sentence,
∃x (Px ∧ Txa),
the object that can stand in as the value of the variable to make the sen-
tence true is (as we just saw) Plato.
Before leaving this point, it is worth noting that not all sentences
containing existential quantifiers will allow us to infer that there is something
that exists that has certain features. In general, even if a sentence contains
an existential quantifier, if the quantifier is not outside of all of the paren-
theses in the sentence, then one is not licensed to conclude that there
exists anything with the relevant characteristics. For example, consider
these sentences in first-order logic:
Fa 傻 ∃xPx (read as: If a is an F, then something is a P.)
∃xPx ⵪ ∃xQx (read as: Either something is a P or something is a Q.)
¬∃xPx (read as: It is not the case that something is a P.)
None of these sentences imply the existence of anything that is a P. You
can tell that immediately because the existential quantifier is not on the
outside of the entire sentence.
Finally, we should emphasize a difference between universally quan-
tified and existentially quantified sentences. In general, the way to think
about the difference is that existentially quantified sentences tell you that
something exists whereas universally quantified sentences (those with a
‘’ on the outside of the parentheses) say that everything is a certain way.
Universally quantified sentences on their own don’t entail the existence of
anything. So, for example, if you see a claim like ‘All electrons are negatively
charged,’ we can write this in first-order logic as:
x(Ex 傻 Nx).
This sentence on its own doesn’t entail that there are any electrons. It just
says, if there are electrons, then they are positively charged. The following
sentence entails the existence of electrons:
∃xEx.
So does:
∃x (Ex ∧ Nx),
26

which symbolizes the statement that there exists at least one electron and
it is negatively charged. So, if we are looking for claims that imply the
existence of something in metaphysics, our attention should turn to those
that are existentially quantified as opposed to those that are universally
quantified.
Universally quantified sentences have other uses. They are especially
useful when one wants to state universal principles. Examples of universal
principles one finds in metaphysical debates are:
Nominalism: Everything is concrete. xCx
Idealism: Everything is an idea in a mind. xIx
Presentism: Only present objects exist. x(¬Px 傻 ¬∃y(x=y))
Actualism: Everything is actual. xAx.
Once one establishes a universal claim like this, one can then use universal
generalization (UG) to conclude about particular objects in the domain of
quantification that they have the relevant features. For example, idealists
usually intend their thesis to be comprehensive, in other words, a claim
about the nature of everything whatsoever that exists. This implies that the
domain of quantification that is relevant to the idealist is the set of all entities
that exist. So if one is an idealist and thus believes that everything that
exists (whatsoever) is an idea in a mind, then using universal generalization,
one can conclude from:
xIx,
and the fact that (say) Barack Obama exists:
∃x x=o (There exists some x such that x is identical to Obama),
that:
Io.
This may be read back as: Obama is an idea in a mind.
Note that in formulating some of the claims in the last pages, we have
made use of the symbol ‘=’ to represent the relation of identity. Identity is
another two-placed relation like the admiring relation (symbolized above
using ‘Axy’). It is a relation that is of special interest to metaphysicians and
is particularly useful in formulating metaphysical theses. We will have much
more to say about identity beginning in the very next chapter.

SUGGESTIONS FOR FURTHER READING
There are many excellent critical thinking and introductory logic textbooks
available that will develop the material introduced in this chapter further.
Some excellent critical thinking texts are Richard Feldman’s Reason and
Argument and Thomas McKay’s Reasons, Explanations, and Decisions:
Guidelines for Critical Thinking. Some excellent introductory logic texts are
Merrie Bergmann, James Moor, and Jack Nelson’s The Logic Book and
Gary Hardegree’s Symbolic Logic: A First Course.
NOTES
1 See C.S. Peirce “The Fixation of Belief.” We will discuss the role of common
sense in metaphysics further in Chapter 1.
2 Most college philosophy departments offer courses in Critical Reasoning and
Logic that develop this material further.
3 Deductive validity is the default notion of validity with which philosophers operate.
It is controversial whether there is any genuine sense of validity other than
deductive validity; however, I put in the qualiﬁer ‘deductive’ to explicitly contrast
this notion with what is sometimes called ‘inductive validity.’ An inductively valid
argument is one in which the premises do not logically imply the conclusion, but
the premises make it reasonable to believe the conclusion in some weaker sense
of giving evidence for it. For example, from the premise that the sun has risen every
day up until now, we may infer the conclusion that the sun will rise tomorrow. This
argument is (one might argue) inductively valid but not deductively valid.
4 The method for assessing the validity of arguments introduced in the section
on validity is what is referred to as a semantic method because it is based on
28
EXERCISE 0.9
Recognizing Valid Argument
Forms in Predicate Logic
In the following examples, state which of the four valid argument
forms the arguments instantiate (EI, EG, UI, or UG), or whether the
answer is ‘None of the above.’
A. Everyone is mortal. Therefore, Barack Obama is mortal.
B. Some humans have free will. Therefore, Barack Obama has free
will.
C. Socrates lived in the past. Therefore, there exists something that
lived in the past.

the meanings of the premises and conclusion. In these final sections we will be
introducing methods for assessing validity syntactically, that is, based on the
forms of the premises and conclusion, independent of their specific meanings.
5 Of course, we could alternatively use the method introduced in the validity section
to show that this is a valid argument.
6 We can now also explain why this logic is called first-order logic. In the kind of
predicate logic we are discussing here, variables are used to range over entities
(people, cats, dogs, cell phones, and so on). They may be used to replace names,
as when we move from Ts (Shaq is tall) to ∃x Tx (Someone is tall). In second-
order logic, variables are also introduced to stand for properties or attributes,
ways entities are. They may then replace predicates, for example if we wanted
to move from Ts (Shaq is tall) to ∃F Fs (Shaq is some way). The status of second-
order logic is controversial. And this controversy is directly related to the meta-
physical issue over the status of abstract entities like properties or attributes.
We will discuss this debate further in Chapter 2. For now, we will just continue
to use first-order logic.

CHAPTER 1
An Introduction to Ontology
ONTOLOGY: A CENTRAL SUBFIELD OF
METAPHYSICS
In this chapter, we will introduce one of the most central subfields of meta-
physics in the past century: ontology. O
On
nt
to
ol
lo
og
gy
y is the study of what there
is. In metaphysics, just as in science, one of the main things we want to find
out is what kinds of things there are in the world.1
Although in the various
sciences, discussion is usually confined to a particular domain of reality –
biology may be concerned with what kinds of living things there are, physics
with the subatomic constituents of matter – in metaphysics, we want to
know what kinds of things there are in a sense that is even more general.
Suppose physics tells us that the basic constituents of matter are lep-
tons and quarks. The metaphysician will then ask: Are there only these
physical objects, or are there also other types of entities? For example, are
there, in addition to these electrons and quarks, also some nonphysical
entities, like minds? Are there also abstract entities like numbers or qual-
ities? And in addition to objects (abstract and concrete), are there other
categories of entities – events, processes, spatiotemporal manifolds? All
of these are ontological questions, questions about what types of entities
exist.
In the mid-twentieth century, philosophers like W.V.O. Quine (1908–
2000), inspired by developments in formal logic, initiated a new method for
addressing ontological questions. This method has since become standard
Learning Points
■ Introduces ontology, a central subfield of metaphysics
■ Presents the Quinean method for determining one’s ontological
commitments, including the method of paraphrase
■ Considers the various types of data that get used in deciding an
ontology
■ Introduces the notion of a fundamental metaphysics and several
ways to understand ontological dependence relations.
Ontology: 1. the study of
what there is; 2. a particular
theory about the types of
entities there are.

in metaphysics and it is the main topic of this chapter.2
In the following two
chapters, we apply this method to two speciﬁc debates in metaphysics.
Quine’s view is presented in his extremely inﬂuential paper from 1948,
“On What There Is.” In this paper, Quine undertakes two projects. First,
he argues that many philosophers before him have been misled in matters
of ontology. Metaphysicians of the past have been too quick to believe
in all manner of controversial things from abstract entities like numbers
and qualities (Virtue, Beauty, the Good) to even nonexistent objects (like
Pegasus or the Land of Oz).3
According to Quine, many of these philosoph-
ical errors can be traced to an ignorance of matters of logic. An examination
of the logical structure of sentences thus plays a large role in Quine’s
critique. This negative part of “On What There Is” is followed by a positive
part in which Quine develops what he takes to be the correct method to
decide which entities one ought to believe in; in other words how to decide
one’s o
on
nt
to
ol
lo
og
gi
ic
ca
al
l c
co
om
mm
mi
it
tm
me
en
nt
ts
s.
THE PUZZLE OF NONEXISTENT OBJECTS
Quine begins his paper by criticizing what he takes to be a clearly mistaken
ontological view – a view according to which there are nonexistent objects.
This is a good place for us to begin as well, for seeing the errors with this
view will lead us to have a better handle on what is a good method for
settling what types of things one should believe in.
First, let’s see why anyone would believe there are nonexistent objects.
To see the motivation for this surprising view, consider the following two
sentences:
Pegasus does not exist.
Santa Claus does not exist.
Both of these sentences are true. But if a sentence is true, it must at least
be meaningful. And if a sentence is meaningful, then each part of the sen-
tence must itself have a meaning. But then from this it follows that the word
‘Pegasus’ means something and the phrase ‘Santa Claus’ means something.
But what are their meanings? ‘Pegasus’ and ‘Santa Claus’ are names (they
aren’t adjectives or predicates), and so their meaning must involve what they
name. So, ‘Pegasus’ names something: Pegasus. And ‘Santa Claus’ names
something: Santa Claus. Therefore, there is something that is Pegasus. And
there is something that is Santa Claus. So, from the plain fact that the
sentences we started with are true (these sentence saying these things do
not exist), we are forced into believing that these things are, and so we look
to be ontologically committed to them. In other words, these are entities in
which we should believe given the sentences we take to be true.
This point is traced by Quine all of the way back to Plato (c.428
BC–c.348 BC).4
It seems that just accepting the claim that something does
not exist commits us to its being. As Quine puts it in “On What There Is,”
AN INTRODUCTION TO ONTOLOGY 31
Ontological
commitments: the types
of entities one ought to
believe in, given the
sentences he or she
accepts.

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Fig. 63.
Fig. 64.
What is the present state of the coast of Greenland in this respect? Have
the changes of level of the same place always been in the same direction?
Give the evidence of elevation and depression in South America. In Italy.
Fig. 65.

What general conclusion may we draw in respect to the stability of the
earth’s surface?
To what extent can we ascertain the geography of past epochs?
What former relations of land and water are suggested as not
improbable?
SECTION IV.
How can we estimate the denudation which the igneous rocks have
suffered?
How do faults indicate the denudation of the stratified rocks?
How do valleys indicate denudations?
Describe the instance in Scotland.
What is the evidence of denudation in the Connecticut valley? How are
valleys produced?
Fig. 66.

What is the condition of the surface rock in the colder portions of the
temperate zones?
Fig. 67.
Fig. 68.
With what is the surface rock generally covered?
How are soils formed?
How may soils be improved?
What is necessary to render soils fertile?
SECTION V.
What means have we of judging of the climate of former periods?

What was the climate of the coal period?
What animal fossils indicate a former warm climate?
What evidence that Siberia once enjoyed a milder climate?
Do similar indications appear in the southern hemisphere?
When has the climate of the earth been most uniform?
Has the climate been growing gradually colder to the present time?
What is the evidence of a somewhat recent period of intense cold?
What recent local changes of climate are mentioned as having occurred?
SECTION VI.
State the general advantages of geological changes.
By what changes have the coal-beds and other stratified rocks become
accessible?
What advantage from these elevating forces in reference to the granitic
rocks?
Fig. 69.
How do these changes affect our means of knowing the structure of the
earth?
Explain the origin of springs, wells, and artesian wells?
By what changes have the metallic ores become accessible?

In what light, then, are we to regard disturbances of geological
structure?

CHAPTER IV.
What is the object of the preceding chapters?
How can we arrive at a knowledge of the causes which have produced
geological phenomena?
Have geological causes always operated with the same intensity?
How are the means of forming correct geological theories increasing?
SECTION I.
How does oxygen become an agent in the disintegration of rocks?
How does carbonic acid operate in the disintegration of rocks?
What is the effect of moisture and rain?
What is the effect of variations of temperature?
What other atmospheric causes are mentioned?
How do these causes become important?
What are some of their effects?
SECTION II.
What are the changes which are to be referred to chemical agency?
Mention some of the disturbances which give rise to chemical changes.
What are the principal effects of chemical action?
How is the cleavage structure accounted for?
Mention instances which show that a cleavage may be established in a
body in a solid state.

Fig. 70.
Fig. 71.
In it a crystalline arrangement of the particles of
the mass?
What other divisional planes exist in rocks?
Mention instances of concretionary formations.
Why may not these concretions have been
deposited as nodules?
How have these concretions been formed?
Mention instances of segregation without the
concretionary structure.
How was the segregation in these instances effected?
How is the columnar structure produced?
What is the origin of the mineral veins which are first
mentioned?
How is it shown that other veins are not injected?
How were these veins formed?
What is the force by which these molecular changes have been
effected?
SECTION III.
In what ways are geological changes produced by human agency?
Of what are the organic remains, in rocks, the record?
What rocks contain organic materials in large quantity?
What is the most abundant organic product?
Explain the mode of growth of corals.
Give instances of extensive coral reefs.
What is the total amount of surface covered by the coral reefs?

SECTION IV.
What degree of importance is attached to water as a geological agent?
What are the sources of the sediment which water deposits?
Why is not the formation of the sedimentary rocks capable of being
observed?
What is the first mode in which solid matter is taken up by water?
Why are the waters of the ocean saline?
What effect has the temperature of water in the solution of silex?
What effect has an alkaline condition of water?
Fig. 72.
What rock is soluble in water charged with carbonic acid?
Give an instance of limestone formation from such solutions.
How do rivers furnish sediment for the stratified rocks?
What determines the position of rapids in rivers?
What is the effect of waterfalls on the abrading action of rivers?
What is the peculiarity of rock at Niagara which has prevented the fall
from becoming a succession of rapids?
What other circumstance increases the abrading action of rivers?

What is the principal source of the sediment which is transported by
rivers?
What is the annual amount of sediment furnished by the Kennebec? The
Merrimac? The Mississippi? The Ganges?
What is the general tendency of these abrading forces?
What is the effect of waves upon the coast, when it consists of
unsolidified materials?
Describe their effect upon rocky coasts.
How is the encroachment upon such coasts shown?
Fig. 73.
What is the effect of waves of less power?
How are marine currents produced?
How are they increased by the evaporation of the torrid zone?
What are the most important marine currents?
Which class of currents have the greater depth?
Upon what does the power of deep currents depend?
How would the effect of these currents be increased by earthquakes?
Where will the effects of these currents be greatest?

Mention instances of these effects.
Fig. 74.
What must be the effect of such currents as the Gulf-stream and
Mozambique channel?
Mention, generally, the effects of these currents.
Why does detrital matter remain suspended in the water of rivers?
How is the coarse and fine sediment separated?
Why do river currents extend some distance into the sea?
What effect does this have in distributing the sediment which the rivers
furnish?
Upon what does the transporting power of marine currents depend?
When a river enters a lake, why is its sediment deposited?
Describe the effect.
When is sediment deposited in the beds of rivers?

Fig. 75.
Describe the effects of this deposition.
Where is most of the sediment deposited?
Give the area of some delta deposits.
How do the deep-sea deposits now forming compare in extent with the
earlier formations?
State the several circumstances by which a succession of deposits would
be arranged in strata.
How are those differences produced upon which the separation into
independent formations depends?
Why are marine deposits nearly horizontal?
How are the irregular stratifications produced?
What peculiarity in the fossils will distinguish the
lacustrine and marine deposits?
What peculiarity in reference to fossils will
characterize the deep-sea deposits?
How is coal shown to be of vegetable origin?
Why will the drift wood of the sea accumulate in particular localities, and
why will it sink?
Why will it become buried beneath earthy matter?
How is it known that wood thus buried will, at length, become lignite?
How is lignite converted into mineral coal?
What is the proof of it?
Have beds of coal been formed at other periods, besides the
carboniferous?
Is it probable that coal-beds are now forming?
How did the flora of the carboniferous period differ from the existing
flora?

Fig. 76.
Are the alternations of the earthy and coal strata satisfactorily
explained?
In what portions of the geological series are the deposits of salt found?
Where is saline matter principally stored?
Explain the conjectural formation of salt in the Mediterranean Sea.
What form do rocks take when deposited from a chemical solution?
How is sand or gravel solidified by the infiltration of mineral waters?
What is the effect of drying upon the solidification of rocks?
What is the effect of pressure?
What of heat?
SECTION V.
What is a glacier?
What is the extent of the glaciers of the Alps?
What change does the mass of snow in the higher valleys of the glacier
mountains undergo?
What is the source of supply to the glacier?

What is the cause of the motion of the glacier?
What is the usual annual motion?
Why will the glacier melt but little at its under side?
Where will the waste at the surface just equal the addition?
What circumstances vary the position of the terminus of the glacier?
Fig. 77.
What, besides snow and ice, enters into the composition of a glacier?
How are these materials supplied?
How is a lateral moraine formed?
What effect has the motion of the glacier on the rocky surface over
which it passes?

What is the material by which this effect is produced?
How is the terminal moraine produced?
How may the moraines on the Jura Mountains be explained?
How has it been proposed to explain the striated surfaces of rocks found
in the north of Europe and America?
What is the objection to this extension of the glacier theory?
How does the ice accumulate along the coast in high latitudes to form
icebergs?
Why does it ultimately separate from the shore?
How does it become freighted with earthy matter?
In what direction do the icebergs float, and why?
What are the dimensions of an iceberg, estimated from the part that is
visible?
Fig. 78.
Where does the mass of ice increase, and where diminish?
What will be the effect of its melting?
How is it supposed that icebergs may have striated the rocky surface?
What is probably the condition of the bed of the seas over which
icebergs now float?
Has the north of Europe and America been so depressed, during a
period comparatively recent, as to admit of this explanation of the drift

phenomena?
SECTION VI.
What is the condition of the interior of the earth with respect to heat?
How do the observations made in deep mines and wells prove this?
How far is the temperature influenced from the surface?
What is the general law of increment of temperature?
At what depth would most mineral substances be melted?
How is this conclusion confirmed?
What was probably the original state of the mass of the earth?
What other explanation may be given of this interior heat?
What is the elastic force upon which volcanic phenomena depend?
Upon what does the fluidity of lava depend?
Upon what does its porous structure, when cooled, depend?
Why are volcanoes situated near the sea?
Describe the principal lines of volcanic activity.
What are the forces tending to repress the elasticity of the mass below?
What will be the effect when the elastic is greater than the repressing
force?
What produces the phenomena of the earthquake?
What is a volcano?
Why are volcanoes generally arranged a linear direction?
Under what circumstances will a new volcano be formed?
What instances are cited?
How is a volcanic cone formed?

Why are lateral cones produced?
How are volcanic cinders formed? Scoriæ? Volcanic glass?
Fig. 79.
Give instances of fractures as results of volcanic action. How are dikes
formed?
Fig. 80.
By what agency have the changes in the metamorphic rocks been
effected?
Give the instance of metamorphic action from intrusive granite in
Norway.
What instance is given as occurring in New Hampshire?
Give the experiment by which it is shown that these changes will result
from a high temperature.
Fig. 81.

What must be the condition of the lowest stratified rocks in regard to
temperature?
Why is not the stratification destroyed?
What changes are produced by this high temperature?
Explain the connection of denudation and earthquake action.
What is the evidence that the surface of the earth is thrown into
undulations during earthquakes?
What is the velocity of these undulations?
Give the instance which occurred in Chili.
To what parts of the earth are these undulations limited?
What condition of the surface may be regarded as resulting from this
cause?
What is the class of rocks most obviously referable to volcanic agency?
How do the trap rocks differ from ordinary lavas?
Why are they not vesicular?
Why more crystalline?
Why were cones never formed?
What is the proof that the granitic rocks have once been in a melted
state?
Why does not the mass of melted rock below the surface retain
permanently its liquid form?

Why does it, on cooling, become more crystalline than lava?
State the process by which mountains are formed.
By what law does the elevating force accumulate?
Why, then, is the process of elevation spasmodic, and not constant?
How is the inclined position of strata produced?
How are strata brought into a vertical position over large areas?
Why do subsidences occasionally follow these movements of elevation?
Mention instances.
Fig. 82.
What explanation is suggested of deep and extensive chasms?
What conditions must exist together, in the force by which continents
are produced?

What cause fulfils these conditions?
What is the proof that the temperature under given localities is variable?
What will be the result of these variations?
What is the law of expansion of rocks, as obtained by experiment?
What amount of change of level may be thus accounted for?
What circumstances would probably increase this amount?
What amount of vertical movement must be accounted for?
Why must these changes of level be very slow?
Under what conditions would there be no change of level?
Is it probable that these conditions exist to any great extent?
Why, then, are not the changes of level observed?
Why is the bed of the sea most likely to experience the change of
elevation?
Why are the continents most favorably situated to undergo depression?
What are the sources of heat upon which climate depends?
Does the interior temperature sensibly affect the present climates?
What cause may be assigned for the changes of climate which are
known to have taken place?
What are the relations of land by which the highest temperature would
be produced?
How would this distribution of land affect the temperature of the waters
of the ocean?
What would result if the opposite relations of land and water existed?
What confirmation of these conclusions is drawn from the existing
climates of different parts of the earth?
Is there any reason to suppose that the relations of land and water
which would have produced a warmer climate in former times did not exist?

Transcriber’s Notes
The following is a transcript of the Silurian System table on page 34 for
those who are using screen readers.
Key to Divisions
----------------
C - Cambrian Rocks.
S - Silurian System.
D - Devonian.
Ch - Champlain Division.
On - Ontario Division.
He - Helderberg Division.
Er - Erie Division.
Divisions as recognized Divisions as recognized Pennsylvania
Ohio.
by English Authors. by the New York and Virginia.
Geologists.
/--------^---------- /-----------^----------- /-----^---- /---
^----
{ Upper Cambrian { { Potsdam Sandstone. } No. 1.
{ { {
C { Rocks, of Sedgwick{ { Calciferous Sandrock. }
{ { { Birdseye Limestone. } No. 2. }
{ (probably). {Ch{ Trenton Limestone. } } Blue
{ { }
Limestone
{ Llandeilo Flags. { { Utica Slate. } } and
Marl.
{ { { } No. 3. }
{ { Hudson River Group. }
{ {
{ { { Gray Sandstone. } No. 4.
{ { { Oneida Conglomerate. }
{ {On{
{ Caradoc Sandstone.{ { Medina Sandstone. } No. 5.
{ { { Clinton Group. }
{ { Niagara Group.
{ { } }
{ { { Oneida Salt Group. } :
{ { { Water-lime Group. } :
{ { { Pentamerus Limestone. } No. 6. :
{ { { Delthyris Shaly } :
{ { { Limestone. } :
S { { { Encrinal Limestone. } :
Cliff
{ Wenlock Rocks. {He{ Upper Pentamerus } :
{ { { Limestone. :

Limestone.
{ { { Oriskany Sandstone. } :
{ { { } No. 7. :
{ { { Cauda-Galli Grit. } :
{ { { Schoharie Grit. } :
{ { { Onondaga Limestone. Wanting. :
{ { { Corniferous Limestone. Wanting. }
{ }
{ { { Marcellus Shales. } }
Black
{ { { Hamilton Group. } }
Slate.
{ Upper and Lower { { } No. 8.
{ { { Tully Limestone. }
{ Ludlow Rocks and {Er{ }
: { { Genesee Slate.
D : the Devonian { { }
: { { Portage Group. } No. 9. } Waver
: System. { { } }
{ { {Chemung Group. } }
Sandstone.

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