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What Is Reality?: An Introduction to Metaphysics
What Is Reality?: An Introduction to Metaphysics
What Is Reality?: An Introduction to Metaphysics
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What Is Reality?: An Introduction to Metaphysics

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What is real? How do we determine what the fundamental structures of reality are?
In this Questions in Christian Philosophy volume, philosopher Ross Inman offers an introduction to metaphysics. He introduces us to the tradition of metaphysics in Western philosophy, what it means to do metaphysics as a Christian, and considers timeless and universal inquiries into the central topics of metaphysics: identity, necessity and possibility, properties, universals, substances, and parts and wholes.
With this academic but accessible primer, readers will be introduced to the key topics explored in contemporary metaphysics.
The Questions in Christian Philosophy Series features introductory textbooks that offer students a Christian perspective on the various branches of philosophy, enabling them as they seek to understand all facets of life including existence, knowledge, ethics, art, and more.
LanguageEnglish
PublisherIVP Academic
Release dateOct 8, 2024
ISBN9781514006818
What Is Reality?: An Introduction to Metaphysics
Author

Ross Inman

Ross D. Inman (PhD Trinity College Dublin) is associate professor of philosophy at Southeastern Baptist Theological Seminary. He also teaches Great Books courses at the College at Southeastern and is the editor of the journal Philosophia Christi. He is a former research fellow at the University of Notre Dame’s Center for Philosophy of Religion and at Saint Louis University. He is the author of Christian Philosophy as a Way of Life: An Invitation to Wonder and Substance and the Fundamentality of the Familiar: A Neo-Aristotelian Mereology. He and his wife, Suzanne, have three children and live in Wake Forest, North Carolina.

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    What Is Reality? - Ross Inman

    Cover pictureRoss D. Inman, What Is Reality?, An Introduction to Metaphysics

    For Jay,

    who first modeled for me how to get metaphysical in the power of the Holy Spirit

    Contents

    List of Figures

    List of Getting Theological Callouts

    Series Introduction: Questions in Christian Philosophy

    Preface

    Acknowledgments

    1 What Is Metaphysics?

    2 Are Metaphysical Discoveries Possible?

    3 Doing Metaphysics as a Christian

    4 Creaturely Existence

    5 Classifying Creaturely Reality: Identity and Ontological Categories

    6 Creaturely Natures: Essence and Modality

    7 Creaturely Characteristics: Properties and Universals

    8 Creaturely Objects: Substances

    9 Creaturely Objects: Parts and Wholes

    Conclusion: On Metaphysics and Mapmaking

    Notes

    Next Steps

    General Index

    Scripture Index

    Praise for What Is Reality?

    About the Author

    Questions in Christian Philosophy

    Like this book?

    List of Figures

    1.1 Ross’s grocery list

    1.2 Suzanne’s grocery list

    5.1 Metaphysically deep versus shallow groupings

    6.1 Metaphysical target practice: Accidental and nonaccidental truths

    8.1 Bundle Theory of Substance

    8.2 Universal Bundle Theory

    8.3 Trope Bundle Theory

    8.4 Mereological Bundle Theory

    8.5 Nuclear Bundle Theory

    8.6 Thick versus thin particular

    8.7 Thick versus Thin Particularism

    8.8 Mixed Particularism

    9.1 Special Composition Question

    List of "Getting

    Theological" Callouts

    4.1 The Mystery of Creaturely Being

    5.1 Relative Identity and the Doctrine of the Trinity

    5.2 Is the Nature of Marriage Metaphysically Shallow or Deep?

    5.3 The Transcendentals

    6.1 Divine Foreknowledge and De Dicto/De Re Necessity

    6.2 The Modal Ontological Argument

    7.1 Powerful Properties, Human Nature, and the Valuable Edges of Human Life

    8.1 Substance, Free Will, and Moral Responsibility

    9.1 God, Creation, and Mereological Composition

    Series introduction

    Questions in Christian Philosophy

    JAMES K. DEW JR.

    AND

    W. PAUL FRANKS

    C. S. Lewis once remarked, Good philosophy must exist, if for no other reason, because bad philosophy must be answered. ¹ About that he is surely right. Unfortunately, many today are in the same position as those Americans Alexis de Tocqueville described in 1835: They possess, without ever having taken the trouble to define its rules, a certain philosophic method which is common to all of them. ² That is, many people today have embraced, often without even realizing it, an approach to knowing reality that undermines their ever coming to truly understand it. They draw inferences about everyday life, theorize about major events and developments in the world, and do all of this while blindly utilizing philosophical categories and tools. In other words, they’ve embraced a philosophic method that generates bad philosophy. The cure is not to reject philosophical discourse altogether but to embrace good philosophy.

    Thankfully there is more to good philosophy than simply answering bad philosophy. It also enables one to entertain questions that are central to one’s worldview—questions related to the nature of truth, the nature of goodness, and the nature of beauty. However, finding examples of those doing philosophy well can be difficult. Yet, given the importance of questions we are interested in, doing philosophy well is critical.

    For this reason, a contemporary introductory series to the major questions in philosophy is incredibly valuable. IVP Academic’s Questions in Christian Philosophy series seeks to meet that need. It provides introductory volumes on the various branches of philosophy for students with little or no background in the discipline. Our authors have written their volumes with their students in mind. They don’t presume prior philosophical training but instead provide careful definitions of terms and illustrate key concepts in ways that make philosophy tangible and useful for those who need it most. After all, it is not just professional philosophers who seek answers to philosophical questions—anyone attempting to love God with their mind will find themselves asking questions about the world God has created and seeking answers to them.

    The authors have also approached their volumes in a way that takes seriously the claim that all truth, goodness, and beauty is found in God. That is, in undertaking Questions in Christian Philosophy, the authors are not merely engaging in these philosophical pursuits and then adding Jesus to the mix when they’re done. Instead, they are pursuing these questions out of a love and devotion to Jesus that not only guides the questions asked but also motivates attempts to answer them.

    It is our hope that each volume in this series will not only help readers become acquainted with various approaches to important topics but will also encourage people in their devotion to our Lord.

    Preface

    There are many outstanding books out there designed to introduce you to contemporary analytic metaphysics, why yet another? A good question! Here’s one thing that sets this book apart from the others: It aims to introduce you to key concepts in contemporary analytic metaphysics from the standpoint of Christian theism. Let me unpack this statement, piece by piece.

    First, the book is an introduction to contemporary analytic metaphysics in particular, which is the dominant mode of metaphysical inquiry in most English-speaking colleges and universities today. So, the book doesn’t attempt to directly interact with historical figures or how certain topics developed in the history of metaphysics in the Western philosophical tradition (although we will certainly meet some historical figures along the way!). Of course, this is not to say that the history of metaphysics is unimportant, or that the analytic mode of doing metaphysics is the only respectable mode worth pursuing; far from it! Rather, the limitation in scope is, alas, a feature of my own intellectual limitations; my competence to write an introductory book like this is limited to contemporary analytic metaphysics.

    Second, the book is geared toward those with little philosophical background and toward those who strive to learn more about analytic metaphysics in a distinctively Christian key. It is written and designed for motivated and engaged students who are distinctively Christian. I have tried very hard to offer some concrete steps on how to go deeper in your study of metaphysics. Toward this aim, I have included Going Deeper sections at the end of each chapter and a Next Steps? at the end of the book. At the end of each chapter in the Going Deeper section, I have included a list of central concepts and terms (Key Concepts) that are keyed to the helpful and accessible resource titled Metaphysics: The Key Concepts, edited by Helen Beebee, Nikk Effingham, and Philip Goff. ¹ I have also included a list of noteworthy subject-specific readings in metaphysics for further exploration, from both a historical and contemporary perspective.

    I have also written the book in a distinctively Christian key when it comes to both content and method. Regarding content, there are topics and questions treated that are uniquely important for Christian metaphysicians (a fancy name for a philosopher who reflects deeply on the nature and structure of reality). Along the way, you will find various Getting Theological callouts that aim to apply the specific concepts in metaphysics to an area of theology or philosophical theology. My aim here is to put on display the long-standing and enduring relevance of metaphysical reflection for Christian theology. I simply can’t put it better than Gisbertus Voetius, the metaphysically astute Dutch Reformed theologian (1589–1676), when he said, A theologian can miss metaphysics and logic no less than a carpenter a hammer and a soldier weapons. ² I hope to show you why.

    As for method, I seek to model for you, the reader, a posture in how to approach the study of contemporary analytic metaphysics as a Christian—in particular, how one’s distinctively Christian theological beliefs can and should shape one’s metaphysical inquiry. My hope for you (as it is for my students) is that you would not only learn something about the contemporary lay of the metaphysical landscape, but that you would also catch a posture concerning what it means to be a Christian metaphysician and how to take seriously one’s theological convictions when doing metaphysics. For the Christian, metaphysics is about wading into the wonder and depths of created being, ultimately for the sake of being enthralled by the depths of God’s own uncreated being, the wonder of it all.

    Acknowledgments

    Measuring the influence of one’s teachers and friends on one’s own moral and intellectual formation is not always exact. Nevertheless, there are a few individuals that come to mind who embody an approach to metaphysics that has shaped my own in clear and unmistakable ways. More than anyone else, J. P. Moreland has modeled for me in his Spirit-led life, teaching, and his academic work what an exemplary Christian metaphysician looks like. J. P. was the first to model for me how to take metaphysics seriously as a Christian and to strive for philosophical excellence as an act of piety unto the Lord. Over the course of nearly twenty years, I’ve learned from J. P. far more than I can convey in words about philosophy and the Spirit-led Christian life. Indeed, it’s often difficult to know where I end and where he begins.

    My personal and professional relationships with Jonathan E. J. Lowe (1950–2014), Anna Marmodoro, and Peter Simons (my doctoral supervisor) have further clarified and fortified my conviction that serious ontology should continue to play a fundamental role in contemporary analytic metaphysics. Moreover, Jonathan Lowe’s gentle, sincere, and nonconfrontational philosophical posture modeled a different way for those seeking refuge from the often cutthroat one-upmanship that sadly marks many professional philosophical circles.

    I owe a debt of personal and professional gratitude to Christian metaphysicians Fred Blackburn, Jeffrey Brower, William Lane Craig, Robert Garcia, Paul Gould, Robert Koons, Timothy Pickavance, Alex Pruss, Michael Rea, and Eleonore Stump. Each is a superb metaphysician from whom I have learned and continue to learn a great deal; more importantly, each is an outstanding human being and exemplary follower of the Way. I want to thank each of them for their friendship, support, encouragement, and philosophical influence over the years.

    I want to note my appreciation for my college and seminary students, past and present, with whom I’ve had the joy and privilege of exploring the contours of metaphysics for nearly a decade. Your simple and not-so-simple questions and comments have helped make me a better teacher and a better metaphysician.

    I also want to thank both Southeastern Seminary and the Eidos Christian Center for providing generous research grants in support of this work.

    Last, I am grateful to the friends and colleagues who read portions of the book and offered helpful feedback, including Paul Gould, J. P. Moreland, Timothy Pickavance, and J. T. Turner. I’d also like to thank Chris Lee, my graduate teaching assistant at Southeastern Seminary, for reading the entire draft and for his invaluable help with some of the figures and charts. Any remaining metaphysical blunders in the book are my own.

    1

    What Is Metaphysics?

    In this first chapter I want to introduce you to several prominent characterizations of metaphysics, both past and present. What exactly is metaphysics? What are the distinctive aims of metaphysical inquiry that set it apart from other areas of inquiry like the natural sciences and theology?

    After we get an initial handle on metaphysics in this chapter, we’ll turn in chapter two to explore whether genuine metaphysical discoveries are indeed possible. I’ll guide you through several well-worn historical and contemporary criticisms of metaphysics and argue that no matter how hard you might try, metaphysical inquiry is unavoidable and conceptually necessary. Wherever you run, metaphysics will find you. If so, we’d better learn how to do metaphysics well as distinctively Christian philosophers (chap. 3). So, let’s get to it already!

    WHAT IS METAPHYSICS, EXACTLY?

    As my first metaphysics professor and friend J. P. Moreland likes to say, metaphysics currently has a bad public relations problem. Before we attempt to unpack what metaphysics is and how it has been understood by several influential historical and contemporary practitioners, let’s briefly reflect on a common misconception of metaphysics as a systematic area of philosophical study.

    Every budding philosopher studying metaphysics has the firsthand experience of that look of sheer puzzlement or terror when they mention to their immediate family (or better, their in-laws) at the Thanksgiving table that they are enrolled in a metaphysics course. "You’re studying what?! How can a Christian institution offer a class on the paranormal?" Alternatively, one might try taking a leisurely stroll through the metaphysics section at a brick-and-mortar bookstore (if you can find one!) and see what I mean when I say that metaphysics has a bad public relations problem. In fact, it’s a custom of mine to head straight to the metaphysics section whenever I visit a new or used bookstore; I just can’t contain my curiosity as to what awaits me. Without fail, my eye quickly lands on book titles (real titles, I might add!) such as Metaphysics of Astrology: Why Astrology Works; The Top Ten Things Dead People Want to Tell You; Crystal Skull Consciousness; and so on (I could go on, really). I recall an instance several years ago when I was delightfully hunkered down, surrounded by stacks of old dusty tomes at of one of my all-time favorite used bookstores in my hometown of San Diego, California. As I was browsing the titles in the philosophy section, back turned toward the door, I heard a woman enter the store and ask the clerk for the metaphysics section. As a philosopher, of course, my ears perked up and I immediately thought: Absolutely splendid! Another aspiring metaphysician looking to go deeper in the quest to understand the fundamental nature of reality. I wonder if she’s majoring in philosophy at San Diego State University. Perhaps I’ll go over and start up a conversation about metaphysics . . . But my elation soon came to a screeching halt. As the clerk ushered the woman to the metaphysics section, he asked, What exactly are you looking for? Spell books, the woman replied, I’m looking to learn how to cast spells, she said. As you can imagine, my elation quickly dissipated.

    What, then, is metaphysics if not the study of the paranormal and the art of casting spells? Before we get to some of the more formal characterizations of the subject given by ancient and contemporary practitioners of the discipline, let’s remind ourselves of the fact that wonder has traditionally been the lifeblood of philosophy from beginning to end. ¹ And metaphysics, one of the main branches of philosophy in the Western tradition, is no different. In fact, I’d go so far as to say that wonder, astonishment, and awe are perhaps most intense and pointed when it concerns matters of existence and ultimate reality. Wonder suffuses the study of metaphysics from beginning to end. In the opening lines of his Metaphysics, Aristotle famously remarks, All men by nature desire to know. At our core, we have a deep hunger to understand reality—for knowledge of what kinds of entities exist, how these entities exist, and why these entities exist.

    It is largely historical happenstance that we use the word metaphysics today to pick out the types of inquiry and questions that you’ll typically find in introductory metaphysics courses and textbooks like this one. The word originally derives from the title of one of Aristotle’s works Ta meta ta physika, which literally means after the physical ones. As the story goes, about a decade after Aristotle’s death, his lecture notes were compiled and edited into treatises, one being what we now call Aristotle’s Physics. The editor decided to call the lecture notes immediately after Physics in Aristotle’s corpus Metaphysics (meta- being the Greek prefix meaning after). And there you have it.

    More seriously, the careful reader will notice that the very question "What is metaphysics?" itself appears to be a metaphysical question on its face, a question about the nature, boundaries, and proper modes of inquiry of a particular subject matter. Historically, metaphysics has been one of the main branches of philosophy in the Western tradition, and there have been a few prominent characterizations of the discipline down through the ages.

    Yet I think it is important to clarify at the outset, lest I set you up for disappointment, what we are not seeking when we ask the question "What is metaphysics?" in this context. Many philosophers, myself included, are less than optimistic about the prospects of finding a complete, airtight definition of metaphysics. While we can provide a loose but helpful characterization of metaphysics—its distinctive aims, goals, and methods—identifying a clear-cut, universally satisfying definition of the discipline of metaphysics turns out to be extremely challenging.

    What exactly do I mean by a precise, airtight definition in this context? When I speak of a definition your mind may immediately think of a dictionary or verbal definition, the kind you’d find in a trusted dictionary (as in the definition of the word abdicate as to fail to fulfill one’s duty or responsibility). While dictionary definitions are important, they are historically not the sorts of definitions philosophers are after. Rather, philosophers aim primarily at defining things, what things are at their core—in other words, their essential natures. Socrates’s unrelenting quest to discover the nature of piety, temperance, justice, courage, virtue, and beauty was a quest to grasp what each of these things is at its essential, defining core.

    Aristotle himself, along with many metaphysicians who followed suit, referred to this sort of definition as a real definition. ² In fact, the great medieval Christian theologian Thomas Aquinas (1225–1274) said that it is clear that the essence of a thing is what its definition signifies. ³ So, to illustrate, a common real definition of a human being, one that is predominant in the Western philosophical tradition, is that human beings are rational animals; both rationality and animality are definitive of human beings and distinguish them from every other kind of being.

    Let me make an honest admission to you: It’s actually quite challenging to come up with a complete, clear-cut real definition for most matters of substance—whether beauty, goodness, or justice (just read Plato’s dialogues and you’ll see what I mean!)—let alone entire conceptual disciplines like theology, philosophy, science, and in this case, metaphysics.

    One reason metaphysics is so hard to define in this complete, clear-cut sense is that any proposed real definition will likely (a) favor one particular, heavyweight metaphysical view over another (and thus be highly controversial), (b) leave out an important aspect of traditional metaphysical inquiry or unconsciously cross over into foreign disciplinary territory (and thus not be complete or clear-cut, respectively), or (c) be so large and unruly that it will be profoundly unhelpful as a useful working definition (what philosophers call a conjunctive definition: metaphysics is a and b and c and d and e and f and . . . ).

    So, what we are after in this chapter is better described as a loose characterization of the aims and methods of metaphysical inquiry that help set it apart from other forms of conceptual inquiry, nothing more. With this important qualification in mind, let’s look at some of the most influential characterizations of metaphysics, past and present.

    METAPHYSICS AS THE SCIENCE OF BEING QUA BEING

    One traditional way of characterizing metaphysical inquiry, going all the way back to Aristotle himself, is the idea that metaphysics is the study of being qua being (i.e., being as such), as Aristotle put it. In fact, let’s hear from Aristotle himself on the nature of metaphysics as the science of being qua being:

    It is the work of one science to examine being qua being, and the attributes which belong to it qua being, and the same science will examine not only substances but also their attributes, both those above named and what is prior and posterior, genus and species, whole and part, and the others of this sort.

    Try not to be thrown off by Aristotle’s use of science here. By science Aristotle roughly means an organized and articulable body of knowledge. ⁶ But what exactly does Aristotle mean when he says that there is a single body of knowledge that examines being qua being or being as such? Aristotle and many subsequent philosophers in the Aristotelian tradition, were of the opinion that being (and similar terms like existence) had different senses or meanings relative to the kind of thing in question. Another way of saying this is that, for Aristotle, being is not univocal (i.e., of the same sense or meaning). While we can predicate being or existence of both a kite and a dog, for instance, the kite and the dog are not said to exist in precisely the same sense for Aristotle. For Aristotle, since a dog and a kite belong to very different categories of being, they cannot be said to exist in precisely the same way. For those squarely in this Aristotelian camp, a key task of metaphysics is discovering what it is to be in each sense of the word.

    At the heart of Aristotle’s conception of metaphysics as the science of being qua being is the notion of an ontological category. You might roughly think of ontological categories as reality’s objective classifications or groupings; the deepest joints that carve up reality (we will explore the ontological categories in much more depth in chap. 5). ⁷ For Aristotle, there were ten categories of being—Substance, Habit, Position, Time, Place, Passion, Action, Relation, Quality, Quantity—with Substance being the most primary and fundamental category insofar as substances exist in their own right; for Aristotle, if substances did not exist, nothing else could exist. ⁸ You can think of the category of Substance as the root or foundation of all the other ontological categories, for Aristotle.

    According to this rich and long-standing Aristotelian view, metaphysics aims to discover not only the different kinds of beings (tigers, poodles, numbers, people, etc.) that exist but also different kinds of being. Did you catch that very subtle distinction? So, we might predicate the quality of being healthy to a thing, say a lion, when we say, The lion is healthy. But, for Aristotle, the quality of being healthy and the lion itself do not exist in the same way since they belong to the distinct ontological categories of Quality and Substance, respectively. Since qualities (like being healthy) characterize substances (like a lion) and not the other way around, qualities do not exist in themselves and are thus not primary. They ultimately depend on substances (which are the modified things that don’t themselves modify anything).

    Since metaphysics is the science of being qua being, in particular, it differs from other areas of inquiry, like biology, physics, or even theology. Biology, for example, specifically aims to study a limited category of existing things, namely living beings, primarily by way of empirical observation; biology is the natural science of being qua living, we might say. Moreover, theology, as the science of God and all things in relation to God, can be thought of as an organized and articulable body of knowledge that works from principles supplied not from empirical observation (as in biology) or the natural light of reason (as in arithmetic), but from the more radiant and enduring light of divine testimony in Holy Scripture, first and foremost.

    Metaphysics as the science of being qua being, on the other hand, aims to investigate the many senses of being along with the most general categories of being as a whole, including how these different senses of being relate to one another. As such, metaphysics is uniquely different from other sciences (e.g., physics and biology) by virtue of its generality/universality: Metaphysics stands under and is arguably conceptually necessary for every other science that is limited to a particular domain of reality (what is physical and exists in space and time, what is living, what has a chemical structure, etc.). And as we will see in the next chapter, metaphysical inquiry is both indispensable and unavoidable at some level.

    METAPHYSICS AND WHAT THERE IS: A QUINEAN APPROACH

    While the above Aristotelian conception of the nature and aim of metaphysics is very old and is perhaps the most common way that metaphysics has been understood throughout the history of Western philosophy, a very different conception of metaphysics now dominates the contemporary metaphysical landscape.

    One contemporary way of characterizing the discipline of metaphysics, a way that has been very influential among analytic philosophers of the latter half of the twentieth century, stems from the work of Willard Van Orman Quine (1908–2000), whose influence on the contemporary metaphysical landscape is hard to overstate. Quine was a professor at Harvard University from 1936 to 1978 and worked primarily in philosophy of logic. He is one of the most influential analytic philosophers of the second half of the twentieth century. Without question, David Lewis (1941–2001), Quine’s most famous student, has had the most significant influence on how metaphysics is conceived of and practiced today.

    Quine is often credited with reclaiming the discipline of metaphysics from its demise at the hands of the logical positivists, an influential group of European philosophers who thought metaphysical claims were strictly nonsensical (you’ll meet the positivists up close in the next chapter). Be that as it may, Quine was a sharp critic of traditional metaphysics as it had been practiced throughout much of the history of Western philosophy. The irony here is sharp; the very person who is largely credited with restoring metaphysics to its rightful place in contemporary philosophy was himself a sharp critic of a traditional, Aristotelian approach to metaphysics.

    Quine’s influential critique of metaphysics as traditionally practiced, along with his alternative logical-formal approach, is clearly unpacked in his seminal 1948 paper On What There Is. ¹⁰ For Quine, the primary aim of metaphysics (or ontology, as he puts it) is to say what exists or ask, What is there? Thus, existence questions such as, Do numbers exist? Do holes exist? Does time exist? and Do fictional characters like Pegasus exist? are the target of metaphysical inquiry. The metaphysician is to provide a list, an ontological assay as some philosophers put it, of beings that exist. This compiled ontological list need not specify any particular ordered or structured relationship between the items on the list.

    To help illustrate the Quinean approach to metaphysics, it may help to compare two very different types of grocery lists. When I go to the store, my grocery list includes a simple itemized list of grocery items in no specific order: eggs, spinach, apples, flour, almond butter, ice cream, and (when I was in college) Top Ramen. My wife’s grocery list, on the other hand, is highly structured and organized; each item is neatly sorted into a particular category, and each category is properly arranged with respect to one another. Wait, oh yes, there’s more! My wife even has each category correlated with the various regions of the grocery store to make the trip smoother and more efficient (which helps with three young children along for the ride!). For Quine and those contemporary philosophers who follow in his wake, the metaphysical task is to simply itemize what is, in no particular order—just like my grocery list.

    Quine’s particular approach to metaphysics is very closely wedded to a particular method for doing metaphysics, namely, the use of a formal-logical framework to clarify and simplify what it is we are committed to as existing in reality (what we are ontologically committed to, as philosophers put it) when we claim that our best scientific theories of the world are true. At the risk of being overly technical here, I need to say a bit more here about the Quinean task of answering existence questions, if for no other reason than the monumental influence such a method has had on the practice of contemporary metaphysics.

    Let’s ease in here as slowly as possible. Consider the mathematical truth: 2+3=5. The statement is a simple statement of arithmetic and is clearly true. Now ask: What must the world be like in order for this statement to be true; what must we be ontologically committed to in order to affirm this simple mathematical truth? On the surface, the fact that the statement is true would also seem to require reality to be a certain way, in particular, to include things like numbers. If the numbers 2, 3, and 5 must exist in order for the above arithmetic statement to be true, then you are, according to Quine, ontologically committed to the existence of numbers. Let’s put this a bit more precisely in terms of a three-step Quinean approach to answering existence questions (which, again, is the primary task of metaphysics):

    1. Determine which statements are true in our best, scientific theories of the world.

    2. Organize, clarify, and simplify these statements by symbolizing them in a particular formal-logical framework (first-order predicate logic, for Quine).

    3.Voila! You are ontologically committed to all and only those entities needed to stand in as the values of the bound variables in order to make the statements true. ¹¹

    Here’s a quick example of this process at work; the details are a bit challenging, so let me encourage you to hang with me! It is typical for our best, contemporary biological understanding of the world to refer to biological species as the most basic unit of biological classification. As such, contemporary biologists often affirm the truth of species statements like, "There are humans that are Homo sapiens. To find out what must exist in order for this statement about humans and biological species to be true, we first need to formally clarify and simplify this statement (a process Quine calls regimentation) by translating it into a particular formal-logical framework. Philosophers call this framework first-order, predicate, or quantificational logic, a form of logic that employs predicates, variables, and quantifiers. As a quick guide, the symbol ∃ is called the existential quantifier and should be read as There exists at least one, x" is a variable, "Hx stands for x is human, and Sx stands for x is Homo Sapiens":

    (∃x)(Hx & Sx)

    This logical formula can be translated as "There exists at least one x, such that x is human and x is Homo Sapiens or, more simply, There exists a human that is Homo Sapiens. In predicate logic, what is called the domain of quantification" is the relevant group of things the quantifier aims to single out

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