Platonism and the Objects of Science 9781350080218, 9781350080249, 9781350080225

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Platonism and the Objects of Science

Also available from Bloomsbury Experimental Metaphysics, edited by David Rose Problems in Epistemology and Metaphysics, edited by Steven B. Cowan Truth: A Contemporary Reader, edited by Douglas Edwards Truth, Time and History, by Sophie Botros

Platonism and the Objects of Science Scott Berman

BLOOMSBURY ACADEMIC Bloomsbury Publishing Plc 50 Bedford Square, London, WC1B 3DP, UK 1385 Broadway, New York, NY 10018, USA BLOOMSBURY, BLOOMSBURY ACADEMIC and the Diana logo are trademarks of Bloomsbury Publishing Plc First published in Great Britain 2020 Copyright © Scott Berman, 2020 Scott Berman has asserted his right under the Copyright, Designs and Patents Act, 1988, to be identified as Author of this work. For legal purposes the Acknowledgments on p. vi constitute an extension of this copyright page. Cover design: Louise Dugdale Cover image: © Xurzon / iStock All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage or retrieval system, without prior permission in writing from the publishers. Bloomsbury Publishing Plc does not have any control over, or responsibility for, any third-party websites referred to or in this book. All internet addresses given in this book were correct at the time of going to press. The author and publisher regret any inconvenience caused if addresses have changed or sites have ceased to exist, but can accept no responsibility for any such changes. A catalogue record for this book is available from the British Library. A catalog record for this book is available from the Library of Congress. ISBN: HB: 978-1-3500-8021-8 ePDF: 978-1-3500-8022-5 eBook: 978-1-3500-8023-2 Typeset by Deanta Global Publishing Services, Chennai, India To find out more about our authors and books visit www.bloomsbury.com and sign up for our newsletters.

Contents Acknowledgments 1 2 3 4 5 6

vi

The Overview 1 An Argument against Nominalism 19 An Argument against Contemporary Aristotelianism 53 An Argument against Constructivism 81 An Argument against Classical Aristotelianism 105 Platonism Concerning the Objects of Science 123

Appendix Notes References Index

165 166 175 181

Acknowledgments I have been fortunate to be in a department chaired by Ted Vitali for the majority of my career. His primary goal was to do whatever he could to help the people in the department be first-rate, thereby making the department first-rate. Therefore, when I asked him if I could focus my teaching and research on contemporary metaphysics and science instead of ancient Greek philosophy, the latter of which is what I was hired to do, and start investigating what is true about the nature of reality instead of investigating what the ancient Greek philosophers might have thought about the nature of reality, he was enthusiastically supportive about the idea and, perhaps more importantly, did whatever he could, for example, provided me with teaching assignments and research opportunities to help me accomplish my goal. I could not have written this book without his early and continued patient support and unfailing encouragement. Perhaps it was not a surprise that that change of focus occurred because I was drawn to working in ancient Greek philosophy in the first place due to my being convinced that Socrates had gotten some things right concerning the nature of ethics, as opposed to Kant and most of the contemporary moral theorists, and that Plato had gotten some things right about the nature of reality, as opposed to the vast majority of contemporary metaphysicians. But, I thought, those ancient thinkers were not properly appreciated because my contemporaries did not have the genuine theories before them, just rightly rejected misinterpretations. I thought that once my contemporaries saw the real views, they would at last engage with those better theories. Of course, the ancients got plenty of things wrong as well. But my interest in those ancient theories has to do with what they got right and how those ideas could be useful in the contemporary discussion about the nature of ethics and the nature of reality. In order to do that work, I had to engage more carefully with contemporary metaphysics, philosophy of science, and the natural as well as the social sciences. Many people have helped me over the years with that research but the ones who I want to thank the most for their patience and repeated generosity are Kent Staley, Anders Carlsson, Elliott Sober, Irwin Goldman, Marv Finkelstein, Jon Jacobs, Anna Marmodoro, John Heil, Matthew Tugby, Jonathan Lowe, and Scott Crothers. I could not have made whatever progress I have made without them.

Acknowledgments

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Probably the most difficult stumbling block for defending Platonism concerning the objects of science has to do with what Plato said about the objects around us, that is, the familiar objects of our sense perception such as tables, chairs, animals, trees, and so on. The vast majority of interpretations of Plato’s views on those things are murky at best and absolutely implausible at worst. But the thing that hampered me the most was an Aristotelianism about those objects that was, unbeknownst to me, deeply entrenched in my own thinking. Thinking that perceptible objects have to be substances of some sort or other, whether it be the theory Aristotle himself put forward or one of the many seemingly different other views we find populating our contemporary discussion, was not genuinely questioned until I read Ladyman and Ross’s Every Thing Must Go in 2008. Again, quite fortunately, due to the creative support of Ted Vitali, I was able to spend the 2011–12 academic year in the UK at the University of Bristol, where I participated in weekly discussions with James Ladyman (together with the also excellent Richard Pettigrew). Those discussions, along with the discussions all year long with others in the department, especially Alexander Bird, as well as with the scientists, mathematicians, and other philosophers of science passing through the department giving talks, were crucial in helping me understand, to the extent that I do, how scientists themselves understand the nature of physical objects and gave me an insight as to how Platonism, as opposed to Aristotelianism, could better cohere with how scientists think about those objects by way of the scientific notion of scale as opposed to the metaphysical and nonscientific notion of hierarchy. I am deeply grateful for their generosity, especially James and Richard, during that extraordinary year. I have of course benefited from all of the discussions on these issues with both my undergraduate students and my graduate students here at Saint Louis University and I want to thank them for their skepticism and pushback throughout those many years. They helped keep me honest in my explanations and arguments by forcing me to not use too much jargon, which can often hide even from oneself, a genuine lack of understanding. Forcing me to explain these complex issues in as plain a language as possible is more beneficial than one realizes until one is forced to do it, perhaps like Plato himself, as he expressed quite complex ideas in everyday Greek. I have also benefited immeasurably from audiences at universities where I have tested out these ideas. More specifically, I want to thank the audiences at the Universities of Bristol, Oxford, ArizonaTucson, Barcelona, Stirling, Geneva, Lisbon, Memphis, and Edinburgh. And my own university, Saint Louis University, has been a constant support for all these years in many ways: grants and sabbaticals for time off to do the research and

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Acknowledgments

writing as well as making it possible to travel to dozens of conferences where I could discuss all these ideas with others. My interest in these issues, though, really first began when I was in graduate school at the University of Wisconsin at Madison in the mid to late 1980s. I went there with the vague idea that I wanted to study applied ethics and maybe ancient Greek philosophy. Terry Penner’s seminars on Plato’s and Aristotle’s metaphysics showed me how relevant metaphysics could be to every issue we care about, including the most practical issues there are. He was also the person to convince me, over the five years I was in graduate school, that the ancients, Plato and Socrates in particular, might be closer to the truth on some important issues as compared with theories put forward by our contemporaries. And so, I want to thank Terry Penner for the extraordinary pleasure it has been to have him as my mentor and as my friend. My friends have also been instrumental in my being able to finish this book. Marv Finkelstein’s constant enthusiastic encouragement has been vital. As has the support from Chuck Sundermeyer, Azhar Shah, Joe Salerno, Alex Malpass, Hal Parker, Richard Newman, Rod Shaw, and Naomi Reshotko. I want to thank my parents who nurtured my curiosity about the world from an early age as well as my sister who has never stopped asking challenging questions. My children, Noah and Gili, have been a constant source of inspiration while I worked on this book. Their deeply philosophical natures were a joy with which to interact concerning these issues, even when having to respond to their spot-on objections, and I cannot thank them enough for their love and encouragement. I also want to thank Alex Malpass, again, who suggested that I contact Bloomsbury Publishing. All the people at Bloomsbury are lovely to work with but my first contact, Colleen Coalter, really made it all possible. I had expressed to her that I did not want my book to be aimed solely at academics. But I also did not want my book to be a popularized and non-rigorous work that academics would dismiss as not serious enough for their consideration. I had hoped that my book might be able to join the historical discussion about these issues such that both academics as well as the educated public could read and find beneficial. I think it is possible to have a book be rigorous and serious but still be expressed in fairly plain language. Colleen enthusiastically supported my goal and I owe her a debt of gratitude for being willing to do something unconventional. In addition to Colleen at Bloomsbury, the two anonymous referees for the manuscript were also very helpful and provided me with many suggestions that definitely made the book better than it was originally. Helen Saunders, Rennie Alphonsa, and Becky Holland were also absolutely lovely to work with during the rest of the process.

Acknowledgments

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Lastly, and most importantly, I want to acknowledge my wife, Ilene, who, more than anyone, made this book possible. Her love, her friendship, her intellect, her kindness, her creativity, and the many other things that she is, both known and unknown, make everything she comes into contact more beautiful and good. And so, it is to all of her everything that I dedicate this book.

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1

The Overview

1  What Is There? On July 4, 2012, scientists at CERN announced that the existence of the Higgs boson was confirmed after forty years of labor and tens of billions of dollars spent. They were clearly overjoyed. But what exactly did they confirm the discovery of after all that time and all those resources spent? They confirmed the existence of a particle, and its existence is evidence of a Higgs field, which, according to the Standard Model, is needed in order to explain why any particle has whatever mass it has. But what exactly are physicists talking about when they talk about a particle or a field or mass? Further, what are chemists talking about when they talk about an element or bonding; what are biologists talking about when they talk about a cell or a gene; what are economists talking about when they talk about a market or a business cycle; what are sociologists talking about when they talk about a class or a culture; and, in general, what exactly are scientists talking about when they talk about their subject matter? I shall be arguing for something rather surprising: the answer Plato gave twenty-four centuries ago to this question is better than the alternatives. Plato’s answer? How could that be? Science, as we know it, did not begin for almost two thousand years after Plato. How could his answer to this question be the best? The question had not even been formulated yet! Moreover, is it not well known that Plato was hostile to empirical science, as is seen in his Allegory of the Cave? Does he not relegate empirical science in that Allegory to the illusory perceptual world and exalt armchair reasoning as the true way to know anything? Further, even if he did not do that, he could not have been aware of particles, fields, mass, genes, cells, or almost anything else scientists talk about nowadays. So how could his answer to this question have been even remotely correct? Though it is true that he was not aware of any of these things, let alone the Higgs boson, I shall argue that his theory concerning what contemporary

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Platonism and the Objects of Science

scientists are talking about is a better explanation than the alternatives proposed by others since Plato. In brief, Plato’s theory is that the objects of science, that is, the explanatory things science aims to discover and talk about, are not the particles and cells seen in laboratories, or classes and markets seen in societies, but the kinds of things of which those empirical things are merely examples, for example, a kind of particle or a kind of field or a kind of cell or a kind of socioeconomic class. Moreover, these kinds of things are not seen in laboratories or societies or anywhere else for that matter, nor are they mental creations or dependent upon any mind or any spatiotemporal thing. Instead, these kinds of things are themselves additional mind-independent things, which, unlike the spatiotemporal mind-independent things, are not spatiotemporal. In short, science aims to discover and talk about the nonspatiotemporal things, that is, the kinds that explain the spatiotemporal things. It is that theory, a contemporary version of Platonism, which I will be explaining and defending in the rest of this book.

2  Clearing the Decks However, before we embark on that project, I need to emphasize that the Platonism under discussion will not be the usual picture of Plato’s view, which has been rightly rejected for its implausibility. That view has “Platonism” as being committed to the following three points: (1) the ultimate nature of things, which Plato called “Forms,” are perfect examples of themselves, (2) the things in spacetime are not really real, and (3) the ultimate natures of things are located “up in Platonic Heaven.” A consequence of that picture is that Aristotle, who is alleged to be “more moderate” than Plato, located the ultimate natures of things “down here on earth” and literally “in” the spatiotemporal things. That last alleged commitment and its consequence for Aristotle undergirds the familiar picture (beautifully represented by Raphael in his fresco The School of Athens) that contrasts Plato’s “Transcendent” Forms with Aristotle’s “Immanent” Universals, or otherwise put, contrasts Plato’s ante rem universals with Aristotle’s in rebus universals. However, I would argue that all three of these historically alleged commitments of Plato were not in fact held by Plato (and, hence, the alleged consequence having to do with Aristotle is incorrect as well). It would take an additional book to argue convincingly against that picture of Plato.1 But my aim is not to argue for an interpretation of Plato. Instead, I am going to defend the plausibility and superiority of what I think is Plato’s genuine

The Overview

3

theory in contemporary terms. However, I will very briefly summarize the exegetical argument against that picture of Plato’s theory. As for (1), all of Plato’s dialogues make it clear that examples, even perfect examples, are the wrong sort of things to be what Plato is after. The first answer to his “What is X?” question is usually an example or two, and Socrates always rejects that as the right sort of answer to his question. Even if what Euthyphro is doing is truly pious, that example does not explain what piety is. In general, Plato, through Socrates, says that examples, even perfect examples, do not explain why any example is truly the example it is. Theoretically, then, Plato would not have thought that spatiotemporal red things, like an apple or a playground ball, were less red than the Form of Redness, which is allegedly perfectly red. No, in order for an apple or a playground ball or anything truly to be a genuine example of the color red, the thing must truly be red. For the sake of an example, let us suppose that the wavelength theory of light is correct. So, in order for something to be red, it has to reflect the longest wavelength of visible light. Spatiotemporal things can do that. That is how they can be red, for example, by reflecting light whose wavelengths are in that range. Significantly, nonspatiotemporal things cannot do that. That is, nonspatiotemporal things cannot reflect any light of any wavelength, let alone the longest one visible to humans. The nonspatiotemporal thing called Redness is so far from being a perfect example of itself that it is actually one of the worst examples of a red thing you could possibly pick! Why? Because Redness is not any color at all, nor could it be. In order for something to reflect light at all, it has to be spatiotemporal. Therefore, since Redness is neither spatial nor temporal, it cannot reflect any light. And that difficulty generalizes to the vast majority of nonspatiotemporal things. So, if there is a nonspatiotemporal thing, which Plato called the Form of Human Beingness, it is not itself a perfect example of being human. Human Beingness is not human at all if being human requires that the thing in question at least be living and breathing, which non-temporal things cannot do, since living and breathing at least involves being temporal. The nonspatiotemporal thing Plato would have called the Form of Cancer, that is, what cancer is, is not itself a cancerous thing as the Form of Cancer does not itself grow, either uncontrollably or at all, again because growing requires the passage of time. Something that is non-temporal cannot engage in a temporal process. And further, the nonspatiotemporal thing Plato called the Form of Triangularity is not a perfect triangle because, for starters, being non-spatial, it does not have any sides within which to contain its spatial area. Something that is non-spatial cannot have two-dimensional spatial dimensions!

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Platonism and the Objects of Science

Despite those defects as examples, though, Plato thought that the Forms, that is, the nonspatiotemporal things, are indeed perfect as explanatory entities. Redness, for example, explains why this apple or that painting are both red (as opposed to some other color), by being the kind of wavelength this apple and that painting exemplify while not being itself an example of that kind of wavelength. The nature of cancer explains why this spatiotemporal tumor is cancerous (as opposed to benign) by being the kind of disease this tumor exemplifies while the nature of cancer is not itself a cancerous tumor. Human beingness explains why this spatiotemporal living thing is a human (as opposed to a dog, say) by being the kind of living thing this spatiotemporal thing exemplifies while not itself being a human being. Triangularity explains why this chalk figure or that graphite figure are triangles (as opposed to squares, say) by being the kind of shape those spatiotemporal things exemplify while not itself being a triangle. And so on and so forth. This is the first major thing to keep in mind: Platonism is not committed to the truly false idea that the nonspatiotemporal things are perfect, or ideal, examples of themselves. As for (2), despite the way it has looked to many, the Cave Allegory passage in Plato’s Republic is not representing the idea that spatiotemporal things are illusory or less real objects of reality, but instead, representing the idea that spatiotemporal things are illusory or less real objects of knowledge. The Allegory occurs within the larger context of explaining why it would be best that nonphilosophers not be rulers of a political community. The point of this larger context is to argue that nonphilosophers, those who deny the existence of nonspatiotemporal things, do not believe in the existence of things that are necessary for the purpose of being able to have knowledge, and since only knowledgeable people should be rulers, those who deny the existence of nonspatiotemporal things should not be put in charge of the community. The problem with the objects that the nonphilosophers believe in and only believe in, that is, spatiotemporal things, is that none of them is epistemologically reliable, a feature which Plato thinks is necessary for any object that is supposed to be useful for the purposes of knowledge. What is the problem with using spatiotemporal things as one’s objects of knowledge? In brief, as Plato explains it, because spatiotemporal things can appear to be their opposite, can be their opposite, and can become their opposite, they make bad objects of knowledge. For example, a healthy thing can appear to be a cancerous thing, as when one gets a false positive. A thing can be healthy and also be not healthy, but in different respects, as when one’s brain is fine but one’s lungs are not. Further, a healthy thing can become unhealthy, due to aging or external influences. On

The Overview

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the other hand, because nonspatiotemporal things cannot appear to be their opposite or be their opposite or become their opposite, they make good objects of knowledge. For example, the nature of health never appears to be the nature of illness. The nature of health is not the nature of illness. Lastly, the nature of health could never become the nature of illness.2 None of these contrasts require anything about the spatiotemporal things not being really real. His point here in the Republic, and everywhere else in his corpus, is just about what it takes to be a good object of knowledge as opposed to a bad object of knowledge. That distinction is the fulcrum upon which Plato’s argument against his opponent rests, and I shall be using it as well, but from a contemporary perspective, that is, using it to argue for a Platonism concerning what the good objects of science are in opposition to theories that have only bad objects of science. As far as (3) is concerned, the (arguable) fact that neither Plato nor Aristotle thought that the natures of spatiotemporal things were themselves spatiotemporal rules out the idea that the difference between them had to do with geography, that is, where their preferred universals exist. Neither one of them thought that the universals which they argued for existed anywhere and neither one of them thought that these universals had a beginning, an ending, or could change, because both of them thought that the universals they argued for were nontemporal.3 So, since Plato thought that the universals, which he called “Forms,” were non-spatial, these Forms could not be “up” in Platonic heaven or “in” God’s mind or anywhere else. Since Aristotle thought that the universals were nonspatial, the universals he believed in could not literally be “in” things or “here” on Earth or anywhere else. On the other hand, it is true that both Plato and Aristotle thought that there exists more to reality than just the spatiotemporal things. That is, they both think that there exists nonspatiotemporal things in addition to the spatiotemporal things. Though there is an important difference between them as regards the ontological status of these nonspatiotemporal things, which we shall discuss, the point here is that difference cannot be cashed out in terms of geography, as it is usually done. Further, the difference between Plato’s and Aristotle’s theories concerning the nature of nonspatiotemporal objects cannot be explained in terms of “dependency,” as it is sometimes done. The alleged difference would have it that the existence of Aristotle’s universals depend on particulars in a way that Plato’s universals do not. The nature of that dependency is supposed to allow for the denial of the existence of a universal if there is not some particular that exemplifies it. So, it is alleged, if Mick Jagger gets his way and paints every red object black, then not only will there no longer be any red objects, but additionally, the color

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Platonism and the Objects of Science

red will cease to be (cf. Jagger and Richards 1966). And if one of those red objects gets scratched and there is then something red, then at that same time there also comes-to-be the color red (cf. Lowe 1998: chapter 6; 2006: chapter 3). Or, alternatively, if nothing in the history of the entire universe is ever red, then the color red does not exist and if at least one thing in the history of the entire universe is red, then there also exists the color red. Plato, it is said, thinks that whether there is anything red or ever anything red, if it is possible for something to be red, then whether any thing is ever actually red, the color red exists. The difference is supposed to give us a way to avoid having to admit the existence of countless universals that are never exemplified, for example, countless kinds of diseases that no one ever (thankfully) gets. Unfortunately for this interpretation, Aristotle (in many passages in his Posterior Analytics and others) sides with Plato and agrees that science would not be possible if the existence of universals depended upon whether examples of them existed or not. But even if it is thought, as it is sometimes claimed, that universals somehow “emerge” at a “higher level” of reality, the things that emerge would have to be more complex substances (as Aristotle thinks of them) and not universals. And since Aristotle argued in his Posterior Analytics that it is the latter that are required for science, the usual way of explaining how Aristotle’s version of realism is committed to the existence of less universals than Plato’s version misfires. On the other hand, there really is a difference between Plato and Aristotle on the nature of universals, but it has nothing to do with where they are or how many there are. Instead, the difference concerns something subtle and has proved much more explanatorily powerful throughout the history of philosophy, namely, the logical mode of their existence. I will explain that idea in detail in Chapter 5. The important point here is that both Plato and Aristotle agree that kinds of things are mind-independent, nonspatiotemporal, and are the objects of science. There is no difference between them on any of these important features, which is why they are both in the same family of views correctly called metaphysical realism. It is quite unfortunate that those pictures of Plato’s and Aristotle’s views have disfigured the contemporary debate among philosophers over the nature of universals, that is, the nonspatiotemporal things, because it has also hidden from contemporary philosophers a more scientifically respectable way of understanding particulars, that is, the spatiotemporal things, and therefore, has disfigured our grasp on the relation between those two sorts of things. Specifically, contemporary philosophers continue to think, mistakenly I shall argue, of universals, qualities, and/or properties as spatiotemporal parts of particulars where particulars are supposed to somehow have or possess these

The Overview

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properties, qualities, or universals. Spatiotemporal things, then, would be the physical objects that have physical properties. For example, a particular apple is thought to be a physical thing that has the property of being red, among other properties. Some theorists think of a physical property, like being red, as being uniquely located “at” or “in” one object, for example, in this apple, and some theorists think of a physical property as being located “at” or “in” multiple objects, for example, in every red thing throughout spacetime. But either way, these theorists think, spatiotemporal things are constituted by two different ontological categories: objects and properties, where both constituents are in some way physical or spatiotemporally located. A better way of thinking, I shall argue, is that properties of spatiotemporal things are not “borne along” or “had” or “possessed” or “grounded in” spatiotemporal things at all. Physical things do not have physical properties because properties are not, I shall argue, physical. Instead, physical things are the instantiations of nonphysical properties. Otherwise put, particulars are the spatiotemporal manifestations of nonspatiotemporal universals. Universals, qualities, properties, or whatever else we call them, on the other hand, are not physical parts (or constituents) of physical objects because they are nonspatiotemporal, and so could not literally be part of a spatiotemporal particular. For example, a particular human does not have the property of being human; the particular human is an instantiation of the kind human beingness. A particular triangle does not have the property of being triangular; the particular triangle is an instantiation of the kind triangularity. A particular tumor does not have the property of being cancerous; the particular tumor is an instantiation of the kind cancer. And a particular red thing, for example, an apple, does not have the property of being red; the particular red thing is an instantiation of the kind redness. The goal of science, I shall argue, is to understand, that is, intellectually grasp, the nonspatiotemporal things so that we can correctly identify spatiotemporal examples of those kinds of things and thereby correctly differentiate spatiotemporal examples of different kinds of things from each other. I argue in this book that the existence of these mind-independent fully existing nonspatiotemporal things are required for the possibility of engaging in those sorts of activities, the most rigorous of which is the activity we call science. Before we can get to that conclusion, though, we have to see first what our options are and why the options other than Platonism are insufficient. As one might expect, there have been many theories put forward since Plato. However, my aim is to argue for what I take to be the core idea of Platonism concerning the objects of science as that contrasts with the core ideas of its main opponents.

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Platonism and the Objects of Science

So, since I take the core idea of Platonism to be that spatiotemporal things, which exist, have things in common that are neither spatiotemporal nor mind-dependent nor exist in a lesser sense of existence, I think that to argue for Platonism requires that I show that a theory whose core idea is that spatiotemporal things do not have anything in common is false, and that a theory whose core idea is that what spatiotemporal things have in common are also spatiotemporal is false, and that a theory whose core idea is that what spatiotemporal things have in common are mind-dependent is false, and finally that a theory whose core idea is that what spatiotemporal things have in common exists in a lesser sense of “existence” is also false. Those four decision points are the framework that will guide our discussion. I have laid out a flowchart of the options in the Appendix and we will be moving from right to left through the different options by means of successive destructive dilemmas. The idea behind the flowchart, then, is that we will start from the most general ontological dilemma and then move through the more specific dilemmas, “sifting and winnowing” our way toward Platonism. I do not want us to get sidetracked by controversies concerning how best to understand the specific writings of the various defenders of the options in all of their many slightly different flavors. That work is important, but we are going to be doing the equally important work of critically examining the core ideas themselves. And though there are different ways of expressing each core idea, I want to keep the argument for Platonism at the core idea level without having to get sidetracked by whether the interpretation of this person’s way of expressing the idea is correct or not (cf. Bigelow and Pargetter 1991: viii). I aim to present the core ideas in such a way that all of the many different advocates for those ideas will be able to see the core of their idea, if not the details they attach to those core ideas, being charitably and honestly discussed. In every case I hope to motivate those core ideas from as uncontroversial a starting point as possible so that anyone could see why such ideas are thought to be worthy of further consideration, as I think they all are. But, I will not present numerous passages from the works of various thinkers and then defend my interpretations of those passages. Instead, I will present the core ideas that I have inferred, hopefully well, from all of those advocates and then critically discuss those ideas. The goal is to engage in philosophy and not in exegesis: to figure out what is true and not to figure out whether some interpretation of some thinker is true of that thinker. The latter activity is interesting, but it is not what will interest us here. I hope the ideas themselves will be that for us. I will also do my best to keep footnotes to a minimum, providing citations and short discussions only when necessary, so as to not break the intellectual flow of thinking through the arguments in the text (cf. Heil 2012: xiii). What then, are the core ideas?

The Overview

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3  The Ontological Options First, if the statements and utterances of scientists are not written or spoken merely for the sake of producing marks on paper or sounds in the air, and second, if scientists do not write or speak merely for the sake of producing pleasant sights or sounds, as, for example, when Ella Fitzgerald is singing scat, then why do scientists produce linguistic sights or sounds? They are hoping, at a bare minimum, to use those sights or sounds to get their readers or hearers to have something, as opposed to nothing, in mind, whether pleasant or not. But what? What exactly do scientists hope their readers or hearers have in mind after seeing or hearing their linguistic acts? Each different possible answer to this question is what philosophers call a theory of ontology. What, then, are the different possible ontological theories? The default ontological theory when it comes to the objects of science is that the terms in scientific discourse refer to spatiotemporal things. So, the term “the Higgs boson” would refer to particles located in spacetime. With very little doubt now, it was at least one of those that was discovered at CERN. The term “DNA” would refer to particular molecules located in spacetime, for example, in every cell of every living thing. The term “recession” would refer to particular economic processes located in spacetime, that is, historical periods. And so on. The reason that this ontological theory is the default theory is that it is arguably the first plausible theory humans come up with when attempting to understand and explain themselves and the world around them. Why? For a very simple reason: perception. The natural world (including ourselves) is something we come into contact with first and foremost via our senses, for example, by seeing it, hearing it, feeling it, tasting it, and smelling it. As babies, we are awash in sense experiences, and over time, we start to figure it out, that is, we start to make connections by means of reasoning, the commonalities in those experiences. For example, once we have the requisite brain structures, we infer that the visual experience we are now having is of the same thing of which we have had experiences before, which is called “object permanence” by developmental psychologists.4 So when one reflects on the developmental process whereby humans come to understand themselves and the world they live in, by making inferences about those experiences, it is very natural to think—at first—that what one is getting an intellectual grasp on, by means of one’s reasoning, are the very things one is experiencing, that is, those spatiotemporal things. Though we are often making inferences about these things, such as here’s my mother again, we are just as often, if not more often, making inferences involving

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Platonism and the Objects of Science

kinds of things, for example, this new thing before me is the same kind of thing as that other thing of which I have already had an experience, so that we infer that this new thing is an additional thing of the same kind as that other thing of which I was already familiar. Additionally, we very often, if not all the time, make predictions about what kind of thing is going to happen in the future based upon what kind of thing is happening right now. To do this, we make connections between two different kinds of things, which are, in general, the relations between those different kinds. For example, if I eat something and then feel ill, I will be on the lookout not for the very thing I ate in the past, as it no longer exists, but some other thing of the same kind as that earlier thing. I am hypothesizing that that kind of thing is somehow connected with the kind of feeling I had from eating the earlier thing. Since I cannot experience the very same feeling I had in the past, I can only experience the very same kind of feeling. I then guess that this kind of thing is related somehow to that kind of feeling. I could be wrong about their connection, but that is what I am making a prediction about—specifically, about the relation between two different kinds of things and not about the particular relations between the different manifestations of those kinds of things. The complex question before us, then, is this: Do these kinds really exist, and if so, what are they, and how are they related to each other, if they are? The default ontological view, I submit, claims that these kinds of things and these relations between kinds are themselves spatiotemporal. Let us call this theory “spatiotemporalism.” Spatiotemporalism, then, is the view that everything that exists is spatial and temporal. Nonspatiotemporal things are nothing at all. And so, if kinds of things and the relations between kinds of things exist, then they must exist somewhere and somewhen. If they do not, then they are nothing at all. Some spatiotemporalists deny that kinds of things or relations exist at all. They explain away their existence in terms of just the spatiotemporal things there are. Other spatiotemporalists who accept that kinds (and relations) do exist, however, have to explain how kinds of things (and relations) exist spatiotemporally in addition to the spatiotemporal things that are not kinds (or relations). The first option usually, if not always, involves appealing to some sort of linguistic device for explaining away the apparent reference to kinds and relations. So, the linguistic utterances of scientists that seem to include reference to kinds of things and to relations between kinds of things are really just shorthand for all of spatiotemporal things there are. For example, the term “Higgs boson” does not refer to a kind of particle, not located in spacetime, but to every Higgs boson particle located everywhere and everywhen in spacetime (and, for some theorists, in every possible world). And with respect to relations

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between so-called kinds—“causation” being one such term for a putative relation—these terms refer not to anything other than just the pairs of things themselves said to be so related. So, the claim that smoking causes cancer is just shorthand for pairwise collections of spatiotemporal acts of smoking and cancer cells. Spatiotemporalists of this ilk often boast that it is in this way that we can explain science without having to commit it to the existence of any allegedly unscientifically respectable things such as universals, kinds, laws, or any other of the allegedly nonscientific sounding things. I am going to call this version of spatiotemporalism “nominalism.” The second way of being a spatiotemporalist is a version of the orthodox view of Aristotle outlined earlier. That is, it is committed to there being kinds of things in addition to spatiotemporal things but that these kinds of things are themselves just further spatiotemporal things, typically called “universals.” So, the term “Higgs boson” does not refer merely to spatiotemporal particles but also to that kind of particle which is not itself a particle, though like particles, it is located in spacetime everywhere there is a Higgs boson particle. It would be the spatiotemporal property of being a Higgs boson that the particle has, just as some shape might have the spatiotemporal property of being triangular. Moreover, since the spatiotemporal property is one and the same thing, even though it is located in a plurality of disjoint spatiotemporal regions, it is best thought of as a universal (property). For example, since the property of being gold is literally located both in a region of spacetime very close to the ring finger on my left hand and in a quite different region of spacetime inside the Tower of London, it is one thing “had” or “possessed” by many things, in other words, a universal (as opposed to a particular). That one and the same thing— the property of being gold—is, according to this view, literally located fully and completely in both of those spatiotemporal regions. So while my gold ring and the gold crown are two different (particular) things and located in two different regions of spacetime, the property (i.e., the universal) being gold, although only one thing, is located at both of those regions of spacetime, making the claim that both are gold true. Therefore, as it is claimed, since this view can explain what makes scientific claims true, it is more plausible than nominalism, which denies that two different regions of spacetime could have any thing in common, and so lacks any explanation of why the linguistic device or shorthand is true, as opposed to being merely said, either verbally or in writing. Science, according to this second view, identifies the kind of thing spatiotemporal things are correctly due to there being one and the same thing, that is, a spatiotemporal universal, literally located in the exact same regions of

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spacetime where the spatiotemporal particulars are, even though the particulars can only be located in one region of spacetime. It is argued, then, that science discovers and examines these universals so that it can identify the kind of thing the particulars are wherever they happen to be. I am going to call this second sort of spatiotemporalism “contemporary Aristotelianism” in order to distinguish it from the view that, I think, best captures what Aristotle had in mind, which I shall explain subsequently and what I shall call “classical Aristotelianism.” Chapter 3 explicates and examines contemporary Aristotelianism. Now, despite the near consensus on this way of thinking about science, that is, thinking that science is about spatiotemporal things and only spatiotemporal things, I will argue in Chapters 2 and 3 that this general way of thinking about the objects of science, that is, spatiotemporalism, is insufficient for explaining how science succeeds and progresses in helping us understand ourselves and the world we live in, as clearly science does. The problem for nominalism, in short, is that science cannot explain anything if, ex hypothesi, all science is doing is referring to lists of particular things, particular events, particular pairs of particular things, and so forth. Why any term refers to whatever is on its list will be, ex hypothesi, inexplicable. Figuring out which particulars do or do not go on some list and why they do or do not is what scientists do by means of understanding what all those things have in common, that is, why they are what they are. In order to do that, scientists need to have kinds of things or event types, and so on as the entities that do the explaining and grounding of science’s predictions and explanations. That is what contemporary Aristotelianism has over its spatiotemporalist bedfellow, nominalism. Contemporary Aristotelianism has kinds, or what it calls universals, in its ontology, in addition to particulars, and can at least explain how science succeeds in explaining why something is true as opposed to merely saying that something is true. However, despite that improvement, contemporary Aristotelianism also falls short in giving science what is necessary for scientific explanation as well as committing science to something that is not, well, scientific. The latter problem with spatiotemporal universals is that they are somehow supposed to be spatiotemporal parts of spatiotemporal particulars but not in the same way as, for example, organs are parts of animals. Contemporary Aristotelians claim that universals are spatiotemporal aspects of physical things. But, unlike the usual way parts seem to function in physical things, namely, by being uniquely located, one and the same universal can be wholly located in many different spatiotemporal particulars. As they put it, universals are the “non-mereological parts” of spatiotemporal things. The head-scratching part of this idea is that when one traces the technical term

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etymologically back to its ancient Greek root, namely, meros, which is the word for “part,” a universal turns out to be a “non-part part.” Hard to know how to make sense of what kind of part a universal is if it is a non-part kind of part. However, I shall argue that the key problem for the contemporary Aristotelian is not with their commitment to the universals being non-mereological spatiotemporal parts, strange as that may be. Rather, it is with their insistence that the universals have to be literally located somewhere in order for them to exist at all. As I shall show, that insistence will prevent scientists from being able to know what things could happen regardless of whether those things ever do, which might seem slight enough to be able to give up on, but it has ramifications for scientific inquiry that make such a restriction weighty enough to cause contemporary Aristotelianism to be unacceptable as the best way to think about the objects of science. I will argue, in the end, that the contemporary Aristotelian view would be better if they jettisoned their commitment to spatiotemporalism and instead expressed the view as Aristotle himself did. Before we can undertake examining that better way of thinking about Aristotelianism, though, we will critically examine another fallback anti-Platonic view, namely, constructivism. In Chapter 4 I articulate and examine constructivism, the view that there are indeed kinds of things in addition to particular things but that these kinds of things are somehow “mind-dependent.” Becoming clear on exactly what is being put forward by this notion of “mind-dependence” will garner most of our attention. The initial and most common way of thinking of this idea is that a mind, or a group of minds, has to exist in order for a kind to exist. So, there do indeed exist Higgs bosons and DNA molecules and economic recessions, but the kinds of things those spatiotemporal things are only exist when concept users such as ourselves create those kinds and sustain their existence by means of our thinking them, in much the same way that some have thought that an all-powerful deity created and continues to sustain the existence of the spatiotemporal world. The idea is supposed to be, then, that though an allpowerful deity is no longer required for the creation and maintenance of the spatiotemporal world, beings such as ourselves are required for the existence of abstract things, as kinds are alleged to be. These kinds are more often than not called “concepts” by proponents of this view. So, the idea of constructivism is that the spatiotemporal things exist mind-independently, but the classifications or groupings of these spatiotemporal things, that is, the concepts, are themselves in some way mind-dependent. The reason, as we will see, that constructivism is not just another version of spatiotemporalism is that even though it is arguable that an instance of someone’s

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thinking a concept is literally located, to some extent in someone’s skull and across some period of time, it is not ultimately plausible to claim that the concept someone is thinking about is literally located there and then. A reason for this is that if more than one person (with presumably more than one brain involved) can think about one and the same concept or if more than one noncontiguous spatiotemporal brain processes of the same person can think about one and the same concept, then since those thinkings are each located at nonoverlapping regions of spacetime, and hence are different thinkings, what those thinkings are about could not be spatiotemporally located if they all have one and the same thing as their content. Another reason that the concepts in constructivism are not spatiotemporal is that the constructivist typically thinks that the concepts exist even when no one is actively thinking about them. So, while it seems prima facie plausible that instances of thinking of concepts are spatiotemporal, it is less plausible, once one thinks about it, that the concepts one is thinking about are literally located anywhere at all. There are two ways to go from here though. One could think that these minddependent abstract objects are, in some attenuated sense, “objective,” because there are “intersubjective” constraints on what they are—this is a Kantian form of constructivism—or one could think that they are ultimately “subjective” in that there are no mind-independent constraints on what they are—this is a Protagorean form of constructivism and is the more extreme version of the same view. However, both of these ways of being a constructivist are, I shall argue, ultimately mistaken. Moreover, they are both mistaken because of the same thing: they both explicitly deny the existence of something that they implicitly accept has to exist. It is that “bootstrap” problem that ultimately dooms them. More specifically, they each have to presuppose that, as I shall argue, in order to get constructivism of any sort off the ground and for it to do any of the work it is designed to do, namely, explain why scientific truths are true and not just said or agreed to, there has to exist non-spatial and non-temporal entities which ultimately explain how our mental or social activities could make something true, and not just thought or done. For example, simply calling a dog’s tail a leg does not make it true that the dog’s tail is in fact a leg. Calling the tail a leg makes it true that the tail is called a leg, but it does not make it true that the tail is now actually a leg. Same with agreements. Simply agreeing that something is true does not make what was agreed to true. It just makes it true that it was agreed to. What would also need to be the case, independent of any mental activities or agreements or any other social activities, is that it is true that such mental activities or agreements or social activities in fact make what was thought or

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agreed to or the like become true. But that connection would be something that is discovered, if it is in fact true, and therefore, not created. Therefore, even if we only have access to the nonspatiotemporal things, that is, the kinds, by means of our intellect, then we must be using that mental activity, ulimately, to discover them, and not, ultimately, using that mental activity to create or construct them. Interestingly, despite the ultimate incoherence of constructivism, it does have a kernel of how best to avoid Platonism, if one wants to still resist such a thing, namely, figure out a way to mitigate one’s commitment to whatever is necessary in order to explain why scientific truths are true. As I shall discuss in Chapter 5, Aristotle’s real view, and not the contemporary presentation of that view, is that strategy. And though I shall not argue for the exegetical point about how best to interpret Aristotle, I will explain how it attempts to lessen, but not eliminate, the ontological commitment to nonspatiotemporal things so that it does not face the bootstrap problem of constructivism or the nonscientific mysteriousness of contemporary Aristotelianism or the insufficiency problem of nominalism. Classical Aristotelianism fares far better than any of those views when it comes to providing an ontology for the objects of science. Aristotle’s genuine strategy was to claim that though nonspatiotemporal things exist, they exist in a lesser, secondary, sense of existence, than the sense of existence in which spatiotemporal things exist. Nonspatiotemporal things are not additional things besides the spatiotemporal ones, but they are not nothing either. They exist in a lesser sense or degree or mode of existence. This view has been used by many throughout the history of philosophy, though mostly not acknowledged as such. For two especially notable examples, let us briefly consider functionalism in the philosophy of mind and neo-Kantianism in moral philosophy. Philosophers have been trying to figure out what the mind is, what consciousness is, since the beginning of philosophy. It just seems so different than everything else around us. Once it became clear that the organ in our skulls had something to do with our mental life, the question became this: Is the mind, that is, the conscious thing, the same thing as the brain or is the mind something other than the brain? Because our being conscious seems so different than everything else, it has been thought that the mind and the brain are two different things. That view is called substance dualism. It is called that because it is thought that there are two different kinds of things, that is, substances, namely, the material things (brains), and the immaterial things (minds). But because substance dualists have had no success in explaining how immaterial substances can causally interact with material substances, it has not been seriously maintained by philosophers for countless generations. The opposite view to

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dualism eliminates the mind as a separate, that is, additional, thing altogether and claims that all there is to the mind is just the brain. This view is called, not surprisingly, the mind/brain identity theory. Unhappy with these two options, though, the majority of philosophers opt for a compromise position whereby the mind is not just the brain, but it is not some other thing in addition to the brain either. This view is called functionalism and functionalists argue that the mind is not another thing besides the brain—as substance dualists think—nor is it nothing at all—as mind/brain identity theorists think—but is instead merely the way the brain is organized or how it functions. So, there are minds, but not in addition to brains. Minds are not nothing at all, but are instead merely ways of being a thing and not things themselves. So, we get the benefits of believing in minds (and not just brains) but at a lower ontological cost, because minds are not a whole other thing in addition to brains. Minds are merely the way brains function. The other domain in which a Classical Aristotelian theory could provide ontological savings occurs in contemporary moral theory. We would like to be able to explain how someone could be good at getting one’s own happiness but not be, because of that, a morally good person. If all there is to being good is being good at getting one’s own happiness, then, we think, there will be all sorts of people who we would like to be able to say are bad people, but because they are getting what makes them happy, we will be without the wherewithal to do so. Therefore, because a theory that eliminates moral goodness and only has prudential goodness seems not rich enough to explain all that we would like to explain in our lives, it has seemed plausible to believe in an additional kind of goodness, namely, moral goodness, which is independent of prudential goodness. But, since believing in moral goodness as a whole other kind of goodness seems ontologically extravagant, contemporary neo-Kantians claim that moral goodness is not a “substantial” kind of goodness but is instead merely a regulative principle. A regulative principle is not as weighty, ontologically speaking, as another substantial kind of goodness. It is merely formal, that is, not substantial. Again, it is in this way that we can get all the benefits of believing in moral goodness as distinct from prudential goodness but without the full ontological costs.5 Aristotle himself was the first thinker to propose this way of getting explanatory benefits for a lower ontological cost. He was, like Plato, a realist about nonspatiotemporal universals, but unlike Plato, he thought that universals did not exist in the same sense of existence as spatiotemporal particulars (cf. Aristotle Metaphysics IV.1-2, VII.1, XIII.4, 9). Their “mode” of

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being was secondary or lesser or derivative as compared to the mode of being spatiotemporal particulars have, which is primary or fundamental. Universals are not additional things alongside the spatiotemporal things, that is, the substances, but merely modifications of substances. Modifications of substances are not additional things, that is, substances, but they are not nothing either. With Classical Aristotelianism, then, you get all of the benefits of Platonism, but for less of an ontological cost. Who does not love a bargain! It is also thought by those who take Aristotle’s suggestion that if one recognizes these different ways of being a thing, then particularly knotty problems can be solved or dissolved. For example, if one would like to explain how complex things (human beings) can be just one thing and not really just a heap of things, then since the thing that unifies all the many parts into being just one thing is not itself another thing, we are not forced into then having to explain how all the parts and the thing that unifies all the parts are, as a group, themselves unified. Since the thing that unifies the parts into being one thing is not another thing, we can block the requirement that we then have to say what unifies all the parts with the thing that unifies them. Classical Aristotelianism gives you lower ontological costs and even greater explanatory benefits than Platonism! Seems too good to be true! Unfortunately, like everything that is too good to be true, Classical Aristotelianism is too good to be true. The benefits are great indeed, but the hidden cost is greater. In order to get that bargain, you have to be willing to commit yourself to a view that is, as I shall argue, ultimately self-referentially incoherent. It is self-referentially incoherent because if the view is assumed to be true, then its truth would entail, as I shall argue, that the view itself is meaningless. No amount of explanatory benefits are worth it if the price is internal incoherence. Or so I shall argue. The only position left standing after those arguments will be Platonism. In Chapter 6, I shall explain how Platonism addresses the issues left unexplained by its competitors and how it is, surprisingly, naturalistic in those explanations. A commitment to the existence of nonspatiotemporal things is not surprising for Platonism, but its being naturalistic is. A commitment to their existing in the same mode of existence as spatiotemporal things is not surprising, but with a better understanding of what they are not—that is, that they are not perfect examples of themselves—that commitment will seem far less bizarre. I shall show how they explain the identities of the spatiotemporal objects of scientific experiments. Part of what will be required in those explanations will be some understanding about those spatiotemporal things, which I will provide as well.

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The key to understanding Platonism concerning spatiotemporal things will be these two related ideas: spatiotemporal things are complex dynamic systems at specific scales and spatiotemporal essentialism is false. As we will see, this comports extraordinarily well with how contemporary scientists talk about their own subject matters, whether it be physics, chemistry, biology, psychology, sociology, or economics. And if the argument against constructivism in Chapter 4 is correct, we might at long last be able to add ethics and aesthetics to our list of scientific disciplines. That would be, as I think, all to the good.

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An Argument against Nominalism

1  The Most General Ontological Dilemma: Spatiotemporal or Not? Questions about the nature of reality have the widest scope of any questions there are because they cover everything without exception. Given that, we shall begin our discussion concerning the nature of the objects of science with as uncontroversial a vocabulary as possible in order to keep the most number of options on the table as possible.1 Much as any good inquirer, we shall sift and winnow our way, reducing the number of options as we go. With that in mind, let us begin by asking simply this: What exists? The simplest, and least controversial, answer we can give to that question is this: everything. Of course, when we get more specific as to what all those things are, we very quickly get into more controversial issues. To see why, let us get more specific by making a list of everything that exists. What could be on that list and what should not be on that list? To engage in this inquiry is to engage in what philosophers call “ontology.” Different lists constitute different ontologies. A list with nothing on it, for example, is called “nihilism.” A nihilist believes that there exists literally nothing at all. There are no existent things at all. We are not going to consider nihilism. It is being mentioned merely so that we can set it aside. An ontology which is more congenial to commonsense, on the other hand, is one in which the list of everything includes all and only the concrete particulars that there are. Anything that is a concrete particular is on the list and anything that is not a concrete particular is not on the list. Well, what is a concrete particular? At the level of commonsense, I am a concrete particular. You are a concrete particular. The chairs we are sitting on are two more examples of concrete particulars. The tables in the rooms we are in are concrete particulars. The buildings we are in are concrete particulars. The trees outside those buildings are concrete particulars. All of our living friends and

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family members are concrete particulars. Every other living human being is a concrete particular. Every animal and every plant is a concrete particular. Every rock and every grain of sand is a concrete particular. The earth and every other planet anywhere in the universe are concrete particulars. The sun and every other star are concrete particulars. And so on and so forth. It will be a long list, a very long list. In fact, even the list you write everything down on will be another thing on the list! What should not be on that list? Any “thing” that is not a concrete particular. And what are those? Answering that question is harder because if any thing, which is not a concrete particular, does not exist, then it will be hard, if not impossible, to refer to that thing since that thing does not exist! But if we had to make a list of all the “things” that do not exist, that is, that do not go on the list of things that do exist, then it would have to be by way of using a special device for indicating that to the reader of that second list. So, we could preface it with “None of these exist” or “These are nothing at all.” What might go on that list? Again, starting with the most “down to earth” or commonsensical position as possible, we would probably start with these: Zeus and the other Greek gods, Santa Claus, the Loch Ness Monster, God, ghosts, angels, Satan, the Tooth Fairy, and disembodied souls. Sure, many people believe in God. Probably a majority of people in the world believe in God. So, if we are starting at the level of commonsense, what could be more an indication of what is commonsensical than what a majority of people believe, especially since it is probably a very comfortable majority of people? And many people believe in disembodied souls. So, why do they not go on our list of existents? Moreover, many children believe in Santa Claus and the Tooth Fairy. Some people believe in Nessie, the Loch Ness Monster. However, all of those beliefs are controversial, even if widely believed. They are controversial precisely because people can plausibly deny that any of those things are concrete, that is, genuinely located in spacetime. The foundation of such a denial gets us one important measure of a thing’s being concrete: its being observable. If there is no genuine empirical evidence that a thing exists, then it does not exist. People argue about whether there is any genuine empirical evidence for the existence of God and, to a lesser extent, disembodied souls, but they do engage in those arguments and what that shows is that a belief in God (or disembodied souls) needs supplemental argumentation in a way that the commonsense beliefs in concrete particulars do not, at least not initially. Believing in concrete particulars may in the end be controversial, but not initially. Believing in God and so forth is initially controversial even if in the end they come to seem not controversial for some people. The arguments for

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Zeus and the other Greek gods were defeated once humans started having a more careful understanding of the natural world such that the regularities we see in nature do not seem best explained by capricious gods. In other words, the empirical evidence of the Greek gods came to be seen as genuine evidence not of their agency but of something else entirely. And despite what children believe about Santa Claus and what some people believe about Nessie and others with respect to ghosts, we think that the result is in: those things do not exist. But there are other so-called things that could be on our list of things that do not exist. If Santa Claus did exist, he would be a particular and concrete. Some people claim that there exist some things that are particular but are not concrete. In other words, some people believe that there are particulars that are abstract, that is, nonspatiotemporal. We typically think of ideas as examples of abstract things. That is, we think of ideas as not being located in spacetime. But thinking that way is slightly confused. Certainly the brains having those ideas are spatiotemporal. We can observe them using fMRIs. In thinking that ideas are abstract, it is plausible to think that we are thinking that these ideas are simplified ways of representing complex concrete particulars to ourselves. A playground ball, for example, is red, round, and bouncy, just to name a few of its features. We can think just about its being red and ignore the rest. In doing so, we are engaging in the cognitive activity of selective attention, that is, we are filtering our complex experience of some concrete particular and just thinking about one aspect of that experience, for example, its being red. Thinking about the ball’s being red is supposed to be an idea that is abstract. If my thinking is something one can see using an fMRI, then clearly that thought is located in spacetime, that is, it is concrete. But if we are thinking that what I am thinking about is not identical to my thinking about it, just as if I am thinking about you, what I am thinking about is you and you are not identical to my thinking about you, then what I am thinking about is not identical to my brain activity. Just as, if I am thinking about you, then my brain activity, my thinking, is one thing, and what I am thinking about, namely, you, is another thing. So, if the only things that go on the list of existent things are concrete particulars, then if what I am thinking about is not located in my cranium, but is some abstract thing not located anywhere, for example, the abstract thing I am thinking about when I think about the ball’s being red which is not identical to the concrete ball itself, then there would not exist those abstract ideas. The denial of there existing any abstract things at all is going to be the key claim to be defeated in this chapter. What about things that do not exist because they are not particulars? What is it to not be a particular? There are many ways that things can not be particular but still be concrete. A group of particulars, a basketball team, for example, is

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not a particular, but it is located in spacetime. It is spread out in spacetime. We can group them together as one thing, as a team, but it is doubtful that a commonsense ontology would put a basketball team on its list of existent things in addition to the individual players, who are already on that list. The commonsense idea would be that there is nothing more to a basketball team than just its members. There is nothing “over and above,” or additional to, a team’s existence than just its members. So, a team is spatiotemporal but its being spread out—that is, noncontinuous or noncontiguous in spacetime—makes it not a thing in its own right but merely a conventional grouping of other things that do exist in their own right. Another way for something to not be a particular is for the thing to be a universal. A universal, as opposed to being a particular, is, as alleged by some philosophers, a concrete thing that is wholly located in multiple spacetime locations. So, unlike a basketball team, which is only partially located where each of its members is, a universal is supposed to be one and the same thing in every location where one finds it. For example, suppose that the color red is a universal. If true, then the color red is wholly located where every red playground ball is and where every red apple is and where every stop sign is. A commonsense ontology of only concrete particulars would deny that there are any universals on the list of existing things. No thing can be wholly located in more than one region of spacetime. The genuine things on that list of existent things are the apples, the balls, and the stop signs. Each one of them exists wholly where it is located. There is no thing, the color red, on the list also. No universal, the color red, on the list of things that exist also; there are just red apples, red balls, red stop signs, and so on. There are two interconnected reasons for adopting this commonsense ontology. The first has to do with causation and the second has to do with observation. When someone puts forward a claim about the existence of something that another person doubts, the doubter will say: “OK, where is it? Show me.” The idea is that in order for something to really exist, it has to be somewhere and at some time and if the alleged existent really does exist, then it can be observed in some way. In other words, if something exists, then it can cause someone to have an observation of it. If the alleged existent cannot cause anyone to actually observe it, then commonsense will tell you that, without argument, it does not exist. The alleged existent thing would be just that: alleged, but not really an existent thing. No one has ever observed a large jolly generous red-suited person living at the North Pole with elves who has the ability to visit children all around the earth in one night and we are pretty sure at this point no one ever will. So, Santa Claus does not really exist. There is no monster in Loch Ness. So, Nessie does not really

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exist. And until the skeptics get some empirical evidence that there is life after death, they are not going to believe that disembodied souls really exist. In order to get that evidence, the souls have to be located somewhere such that someone can get some observations of them somehow. Since that is not possible, it just seems like commonsense to say that they do not exist. If, on the other hand, someone insists on believing in Santa Claus, or God, or ghosts, or Nessie, or disembodied souls, despite that lack of empirical evidence, we think that such a belief would just be based on faith and not on reason. To be justified in believing in something, that is, to have a good reason to believe in something, one has to, according to this commonsense ontology, have good empirical evidence to believe in it. The human activity that aims to get good empirical evidence for believing something is, arguably, the activity we call science. In the broadest possible terms, scientific activity is reasoning well about good observations. Of course, determining what counts as good empirical evidence and how that good empirical evidence is to be used in support of a belief is difficult and controversial and ongoing. But what is not controversial at this point in history and is no longer up for debate is that no human activity other than science has been as successful in describing the world, understanding and explaining the world, and making predictions about the world. Given the truth of that, it is all the more plausible to believe in a commonsense ontology. After all, it claims that the world we have been so successful in describing, explaining, and about which we make predictions is a world that causes us to have experiences of it. Things that are not able to cause experiences are nothing at all. So, since abstract objects, that is, objects that are not located in spacetime, cannot cause any effects, they are nothing at all. Universals, even though they are located in spacetime, do not cause anything either as it is the particular and not the universal itself that does the causing. Abstract objects and universals are causally inert. They do not do anything and they cannot be affected by anything. If true, then they cannot be the cause of any observations, and so, cannot be the cause of any good empirical evidence. And so, we cannot have any good scientific reason for believing in them. Therefore, in order for us to have a good reason to believe that something exists, it has to be capable of causing an observation. And in order for something to be able to cause an observation, it has to be a spatiotemporal thing, that is, a concrete particular. Can one, though, account for the possibility of science if one restricts one’s ontology, one’s list of existent things, to just concrete particulars? If two of the necessary conditions for being on the list of existent things are being locatable in spacetime and being particular, that is, being wholly located in only one region

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of spacetime, then nothing abstract or universal can be on the list. Can such an ontology, though, explain how science is possible? The conclusion of this chapter will be that it cannot. For science to be possible, there must exist either abstract things or universals. An ontology restricted to concrete particulars would make science impossible. However, one might think, at least initially, that a commonsense ontology has to be what science is about. After all, in rejecting non-concrete things, that is, things not located in spacetime, it seems to be the most scientifically respectable ontology there could be. Science is, after all, about the natural world. What is more natural than the world of spacetime? Nature is stuff like the trees around here and over there and all the rest of the stuff around here and over there. Those who believe in nonscientific things like God or ghosts or spirits or other such things would not have this commonsense ontology. What is especially problematic about these so-called things? They cannot be seen. People who believe in them, though, think that such things may not be able to be seen but they do have effects. In other words, they believe in them because they think that these things can cause something to happen or something to change. Anything that can cause some effect has to exist if it is to explain why that effect occurred. And though that general idea may be true, people who do not accept the existence of such things attempt to show that those effects can be explained as the results of other causes. For example, if one believes in Santa Claus because one believes that Santa Claus put the presents under the tree, the non-SantaClaus-believer will counter that explanation with a different explanation: it was the parents that caused the presents to appear under the tree. The appearance of the presents under the tree is not good evidence for the existence of an unseen Santa Claus but instead is good evidence for the existence of adult humans with sufficient economic means and the ability to be active while their children are asleep. But even if that is just a less sophisticated case than the cases we look at in science, is it not also an example of what we think of as the kind of prime activity of science, specifically, explaining why effects occur? So, if we engage in that activity, we need to explain why something happened. What happens and what made it happen are clearly things (effects and causes, respectively) that scientists have to believe in. When I accidentally knocked into a chair, I made the chair move and the chair’s moving happened as a result of my accidentally knocking into it. So, there needs to be me and a chair if that effect, the chair’s moving, was made to happen by some cause, my knocking into it. A thing’s being able to be a cause, that is, to initiate a causal chain, or a thing’s being able to be an effect,

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seems fundamental to a commonsense ontology. Something that is causally inert, that is, something that cannot do anything or be affected by anything, seems idle. Why believe in it? It is literally not doing any (explanatory) work. Abstract objects, that is, things that are not located in spacetime, cannot initiate any causal chains or be part of any causal chains as effects.2 In order to do either of those activities, a thing needs to be located somewhere and somewhen. An abstract thing that has no causal role to play is not needed to explain anything. Likewise with a universal. Universals do not do anything. It is the particulars that do everything. For example, the universal humanity does not cause anything to happen: particular humans do. When we say that humanity is benefited by clean air and water, what we are saying is that particular human beings are benefited. The universal humanity cannot itself be benefited. The key ontological feature here is being locatable in spacetime and the key epistemological feature here is being observable. A thing’s being observable gives us reason to believe that it is locatable, and therefore, existent. This just seems like commonsense and what science, we think, aims to explain more carefully and more rigorously with the aim of being helpful in our lives. Let us now examine this very down to earth commonsense view and how it connects or does not connect with scientific activity. Suppose we make our complete list of existent things, that is, all the concrete particulars that there are. And, in accordance with that commonsense ontology, we have left off that list any abstract objects or universals. We could then refer to each and every thing on that list by a proper name (in principle, if not in practice). We typically give proper names only to particular humans and to some other animals which we take a particular interest, namely, our pets. But we could, in principle, give a proper name to every thing on that list. Every human, every other animal, every plant, every tree, every chair, every table, every grain of sand, and so on and so forth. Given the sheer number of things to be named, properly, that is, with unique names, it might be prudent to just give every thing on the list a unique natural number. Let us then suppose, for the sake of argument, that we have successfully given every single thing that goes on our list its own natural number and labeled them with that number. So far so good. But now the question arises: Will that list be useful? If one does not want to do anything with the list, then perhaps it will be fine as is. However, on the assumption that we would not want to make such a list just for the sake of making the list, that is, for no other reason than merely to make the list, but we do in fact have a reason for making the list, namely, that we want to be able to do something with the list, for example, we might want to use

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the list for understanding the world we live in, or for predicting what will exist in the future, or for retrodicting what did exist in the past, or for manipulating the world now so that the world in the future will be different, or some other use, then our list will be completely useless. Why? Because a list with infinitely many unique symbols on it will not represent how any of the things on the list relate to each other. In terms of information theory, it will just be all noise and no signal (Shannon 1948). Without knowing how any of the things on the list relate to each other, we will not be able to glean anything from it. It will just be an utterly uninformative list of symbols. Well, what sort of relations could there be and why would they be useful to know? First, depending upon what your goals are, it could be useful to know that it would be best for the first thing on the list (i.e., you) and the ninety-fourth thing on the list (i.e., a chunk of plutonium) to be as far apart from each other as possible. Why would that be useful to know? Well, if your goal was to stay alive as long as possible and as healthily as possible, then knowing that plutonium can make you unhealthy and shorten your life would be useful. Simply having both you and that chunk on the list does not help you in any way. But knowing that one of those things is harmful to the other is useful. In other words, knowing a way that those two things relate to each other is useful. A commonsense view might call this the relation of causation, which is, in general, asking the question, what effects do various things have on each other? It is in virtue of knowing the causal relations, or the effects that some things have on other things, that we can make reliable predictions about the future (and the past) and thereby change our behaviors with the aim of having a good effect on our futures. So, if you want thing #1 on the list, namely, you, to exist in the future, then keep far away from thing #94. Useful indeed. But another sort of relation, which, if it exists, could be useful to know, is the relation of commonality. Knowing that two or more things on our list have something in common could be quite useful to know.3 So, for example, not just knowing what effects some things have on other things, but also knowing that because these two things have something in common, they will both have the same effects on other things. That is, it is no doubt useful to know the causal relations between things in addition to knowing all of the things there are. But it would also be quite useful to know what commonalities there are between things on the list. So, it could be useful to know that both thing #94 and thing #422 are to be avoided for the same reason. For example, if one figured out a causal relation between things #1 and #94, such that it would be best for thing #1 to stay away from thing #94, it could also be quite useful to know that the reason it would

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be best for you to stay away from thing #94 also applies to thing #422. If thing #94 and thing #422 have something in common, say, that they are both chunks of plutonium, then that commonality will be useful to know. Just knowing that it would be best to stay away from thing #94 is not the same thing as knowing why it would be best to stay away from thing #94. If you knew why it would be best for you to stay away from thing #94, then you could apply that understanding to any thing on our list regardless of what else was true of any of those things. So, if thing #94 is spherical and thing #422 is cubical, you may think that the reason it would be best for you to avoid #94 is because of its spherical shape and hence you would not avoid thing #422, given that is not spherical, but cubical. That would be a harmful belief for you. But if you knew that the reason it is best for you to avoid #94 is not because of its shape, but because of its radioactivity, then even though thing #422 is not spherical, it is radioactive, and hence, best avoided. The reason the relation of commonality is so very useful is that we do not have to carry around a previously made list of things to be avoided (e.g., avoid #94, #422, #859, and so on) and a previously made list of things to be sought out (e.g., seek #3, #9, #66, and so on) and a previously made list of things for every other more fine-grained purpose. We just need to figure out why the things we want to avoid are best avoided, that is, what it is they have in common that makes them best avoided, and why the things we want to seek out are best sought out, that is, what it is they have in common that makes them best sought out, and then apply that to things as we happen upon them as we go. In fact, figuring out these commonalities will save a tremendous amount of time (cf. West 2017: 280). We do not have to consider each thing in toto and determine if it is best avoided or not. Rather, we can limit our consideration of each thing to just those bad-making commonalities or good-making commonalities. In general, it is by focusing on these two sorts of relations, or patterns, that is what initially gets scientific activity off the ground.

2  Spatiotemporalism: Nominalism Someone who is a nominalist will claim that all there is to these so-called commonalities and causal relations are really just the things on our commonsense list. Patterns are not additional things that have to go on our list. Talk of these patterns is just that: talk. What we, and scientists, are really talking about are just these commonsense things on our list. Though I shall argue that the nominalist cannot explain how science is possible if all talk of commonalities is just talk and

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there are not really things that commonsense particulars have in common, let us first motivate and explain their view. First, how does the nominalist attempt to reconcile their commonsense ontology with scientific activity. The idea to be defended, then, is that science is possible even if all that there exists are concrete particulars. Success in science, or progress in science, does not require that there exist any abstract objects or universals. Every thing that exists is both a spatiotemporal thing, that is, located somewhere and somewhen, and a particular thing, that is, located wholly in only one contiguous region of spacetime. With respect to the nature of science, let us start off with what is, but should not be, a controversial claim: science aims to explain why something happens (or does not happen)—for example, why someone gets cancer or why planets have the orbital path they do—and to explain why something is what it is (and not something else)—for example, why this organism is a mammal as opposed to a fish or why this growth is malignant as opposed to benign. We do not engage in scientific activity merely to list every thing there is, that is, just for the sake of doing it, and we do not engage in scientific activity merely to make a list of every thing there is and in the (temporal) order in which they exist. Such a list would be as useful as an infinitely long string of completely random symbols. In order for such a list to be even minimally informative, let alone explanatory— and thereby useful—it needs to be able, as we said before, to symbolize patterns. Knowing patterns is useful. Why? Well, suppose you want to symbolize the temporal sequence of things in the world. If every thing on the list is completely unique, that is, has no relation at all to any other thing on the list, then you would not be able to even think about any of the things on your list. You could experience them but you would never have any thoughts about what you are experiencing (cf. Price 1953: 8). In other words, if you are going to be able to recognize (cognize, think or know, again) what you are experiencing, then what you are experiencing cannot be entirely new. Something about your experience must be the same as some previous experience. Experiences must in some way be capable of repetition, if you are ever going to be able to think about your experiences. Let us see why. Experiences are spatiotemporal things. If you are having an experience here and now, you cannot have that experience again. That experience can only be had where and when you experienced it. As time passes and locations change, your experiences have different spacetime locations. For example, your experience of drinking coffee at breakfast is a different experience than your experience of drinking coffee after lunch. Those are two different experiences. You are not having

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the drinking-coffee-at-breakfast experience you had at breakfast after lunch. You are having a different experience: the drinking-coffee-after-lunch one. These are two different experiences. So, particular experiences cannot repeat. Every particular experience is a one-off. But that creates the problem. If every experience is unique and non-repeatable, then how is it that you can think about what you are experiencing? Suppose, for the sake of argument, it is true that you can have experiences without any thought about what sort or type of experience you are having. But if your experiences are radically novel at every moment, will you be able to say to yourself what experience you are having? Could you be cognitively aware of what that experience is, be it a red experience or a green experience or a tree experience or whatever?4 You would not be able to do so because any cognitive awareness you might be able to have will have to classify or group this one with others that are at least similar in some way. If there are no similarities at all between any two things, and every thing is completely unique, then you could only have successive experiences that are completely random “noise.” However, could you even have that quite disorienting experience? We have assumed thus far that you could. But could you? If every thing that exists is completely unique, then, as we shall now see, you would not even be able to have any experience of any thing at all. Why? The basic reason is that unless the thing which has the experiences, for example, you, is receptive in the right way, that is, has receptors which are sensitive to that kind of stimulus, the organism, that is, you, will not have any experience at all. Let me explain. In order for an organism to have an experience of something, the organism has to have receptors that are sensitive to that thing. If every thing that exists is unique and has nothing in common with any thing else, then in order to be sensitive to some particular thing, the organism will have to have a receptor that is sensitive to that particular thing. Such a set up would require that organisms have as many different receptors as there are things that exist if that organism is going to be able to experience every thing there is. Remember, we are not talking about having one receptor for sand, and one receptor for trees, and a different receptor for humans, but a different receptor for every grain of sand and every tree and every human and so on and so forth for every single thing that exists. Fortunately, such is not required. From what we have learned thus far about the brain and its sensory systems, humans have different sensory receptors, that is, neurons, for different kinds of stimuli, and do not have a different sensory receptor for each and every particular stimulus. What makes it possible, then, for you to experience a red light, is that you have neurons that are sensitive to a kind of stimulus: electromagnetic

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radiation within a certain range of wavelengths. So, you can experience red light because you have neurons of a particular kind that are sensitive to a kind of electromagnetic radiation between 500 and 700 nm wavelengths. That specific kind of neuron, called “L cones,” is able to detect red light, and hence, you are able to experience red light (assuming the rest of the visual system is intact, of course). The same is true with respect to somatic experiences (e.g., experiencing a smooth surface), auditory experiences (e.g., experiencing a loud sound), olfactory experiences (e.g., experiencing a flowery scent), and gustatory experiences (e.g., experiencing a sweet taste). Corresponding to each sensory system there are different kinds of neurons that differ relative to the kinds of stimuli to which they are sensitive. It seems, then, that even being able to have an experience is partly grounded in an organism’s being able to be receptive to a kind of stimulus. Otherwise, we would have to have a sensory receptor for every single individual thing there is that exists. So, it is not just that the possibility of having a thought about our experiences is diminished by the utter uniqueness of every single thing that exists, so is the realistic5 possibility of even having an experience. Therefore, if there are kinds of stimuli, that is, stimuli that have something in common with each other such that the same receptor neurons can be excited again, then it seems possible for you to be able to think to yourself: I am having another example of that same kind of experience. In other words, you can re-cognize something about your experience as being the same. But since the experience you are now having is a different experience from the one you had before, that is, since it is occurring at a noncontiguous region of spacetime, for example, at lunch as opposed to at breakfast, then the experience may or may not be an experience of the same spatiotemporal thing. That is where your reasoning comes into play. And that is where things get controversial. How might reasoning help us? A very straightforward case is one we learn, once the relevant brain structures have developed properly, at around twenty-four months of age: object permanence. We learn that an object that we saw at one time is the same object we see at a later time even though we did not see the object in between those two times. So, we learn to not infer from these two different experiences that there are two different objects, but we infer, based on a multitude of factors, that the two different experiences are of one and the same object. A less straightforward case is also one we learn, but how best to explain it is the crux of our issue in this chapter and the next. Consider the following example. At 9:00 a.m., you see a 12” red rubber playground ball bouncing past you. At 1:00 p.m., you see a 16” red rubber playground ball bouncing past you. Suppose that both of these balls were made at the same factory and on the same day

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and cut from the same sheet of red-pigmented rubber. In both experiences, you had an experience of a red ball bouncing past you. But, you did not infer that the two experiences were of the same spatiotemporal thing given that the balls were of different sizes. Instead, you inferred that these two experiences were of two different things. Let us say that that inference was correct. Those were in fact two different things. On the other hand, you did also infer from those two experiences that there was something similar in those two experiences, namely, their being red. One way to explain that experience of similarity or sameness or commonality or repetition between both experiences is to say that the two red balls literally were, at one time in the past, the same because both red balls were part of that one sheet of red-pigmented rubber, which is now separated between the two balls. So, in one very real way, you are actually having two red experiences of what used to be just one red thing, which is somewhat similar to having two different experiences of two different parts of one sheet of red-pigmented rubber. But we can change our example slightly and then that simple way of explaining the sameness of the two experiences will not be open to us. Instead of saying that the two balls were literally cut from the same one sheet of red-pigmented rubber, let us suppose that the two red playground balls were cut from two different sheets of red-pigmented rubber that were made from natural and synthetic rubber and pigments that have no overlap in their histories other than having been cured and cut in the same factory. How can we explain why these two red experiences seem the same to you? On the assumption that there is literally nothing in common to those two red playground balls—because they are not two parts of what was once one thing— how can we explain how these two different experiences seem the same to you, that is, how can we explain why both experiences had the same specific receptor neurons, namely, the L cones as opposed to the M and S cones within your retina, as part of why you had those experiences? It could seem simple enough to explain. How about this: it is because both of the red playground balls reflect the longest wavelength of visible light, to which the L cones are sensitive, that those two different things caused the same neural pathway in your perceptual system to be activated. Seems plausible enough. But why did those two different things cause the same neural pathway in your perceptual system to be activated? The answer, again, seems simple enough: the reason that two different things activated the same neural pathway is because the two different things both reflect the same wavelength of visible light. That sounds right, but how are we to explain that curious fact? In other words, if the two playground balls have literally

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nothing in common, then how could they both reflect one and the same wavelength of light? Would not that be something they have in common, specifically, being reflective of the longest wavelength of visible light? Would they not have to have that feature or characteristic or quality or property in common, thus violating our assumption that the two playground balls have literally nothing in common? But if they have that feature or characteristic or quality or property in common, then they do have something in common, namely, that feature or characteristic or quality or property! If they do not have at least that in common, then it is completely inexplicable why those two different things cause us to have two experiences that seem in some way to be the same kind of experience again. So, what are we to make of these features, characteristics, qualities, properties, or whatever we want to call them? What are they? One possibility is to count those properties as additional things on our list of things that exist. So, in addition to the concrete particulars, as in our two playground balls, there also exists another thing, namely, the property of being red, and this property is one and the same thing in both cases, that is, both playground balls have one and the same property, namely, being red, in common. Another possibility is to count properties as additional things but treat the properties that each ball has as being a different thing. So, there would be two properties of being red: the one the 12” ball has and the other one that the 16” ball has. That possibility is also a nominalistic answer and it typically labels these properties “tropes” or “modes.” We will not be discussing that option. I only mention it here.6 A third possibility is to reduce the talk of properties to concrete particulars. In other words, and this is the focus of our chapter, properties do not exist in addition to the concrete particulars. All there is, that is, all that goes on our list of things that exist, are the concrete particulars, for example, the red playground balls and every other concrete particular. Properties are not additional things and so do not go on our list. The property of being red just is all the many red concrete particulars that there are. That is the view of the nominalist. And so, nominalism is committed to the view that perception, cognition, and science are possible without having to put non-concrete, non-particular, things on our list of existent things. Spatiotemporal things are all that exists, that is, the concrete particulars. How, then, do nominalists explain the useful patterns and commonalities that seem needed for the possibility of perception, cognition, and science? Since all nominalists accept the idea that reality is the sum of particulars and particulars cannot have any thing in common with each other, there cannot be any thing which is a pattern or a commonality because a particular is not something that can happen again. But, nominalists are reductionists about patterns and typically

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not eliminativists about patterns. There are patterns, they claim, but all there is to a pattern is the particulars. That is a subtle move. Let us be sure we understand it. All sides of the debate agree that there is something that needs to be explained. What is it? All sides agree that we have the ability to perceive, reason, and know (scientifically speaking) the spatiotemporal world. And everyone party to this debate agrees that perception, reason, and science are only possible if there exist patterns. If the spatiotemporal world is patternless, that is, if every experience is radically novel, then perception, reason, and science are not possible. The question is, what is the best way to explain those patterns? Eliminativists deny the existence of patterns. There are no patterns. Reductionists, on the other hand, agree that there are patterns, which make perception, reason, and science possible, but deny that anything but spatiotemporal particulars are needed in order to explain those patterns. Platonists, who are anti-reductionists, do not think that patterns can be reduced to spatiotemporal particulars but instead think that patterns have to be additional, albeit nonspatiotemporal, things. A reductionistic nominalist believes in redness, say, but explains redness in terms of red things. And the nature of that explanation is that it is reductive. There is not any thing more to redness than just red things. That is not the idea that there is not any such thing as redness. There is such a thing as redness. But despite its surface grammar, that is, “redness” being a singular term, the word really refers to many things: all the red things there are. An eliminativist would claim that “redness” does not really refer to any thing, or things, at all. The reductionist, at least, does accept the challenge of trying to give an explanation of redness. Eliminativists just deny that there is anything to explain, but that also prevents them from being able to explain how perception, reason, or science is possible. So then, can the reductionistic nominalist pull off the explanation of patterns such as redness by having only spatiotemporal particulars in their ontology? The Platonist thinks not. What is the measure of success here? As in the beginning of this chapter, the measure of success is usefulness. Why is this the measure? The pursuit of knowledge, that is, science, came from the fact that it was more useful than other methods for achieving our goals, the most general of which is to survive. Praying to the gods did not work as well as engineering when it came to bridge building. We had and continue to have very practical needs and over time whatever works best is pursued and what does not work as well is not. As we get better and better at a method that works, the separation between the more effective methods and the less effective methods grow. Such is science. It is the best method we have hit upon for achieving our goals. And there is good evidence that the same is true for why our perceptual and cognitive systems

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were selected for over time: their being useful for survival. So, for example, it is because our perceptual system typically produces veridical experiences as opposed to non-veridical experiences that we survive. If it typically produced hallucinatory experiences, we would not survive long enough to pass along our genetic information. For example, if we always saw cliffs where paths are or if we always saw paths where cliffs are, we would have difficulties. The function of our perceptual system is to give us experiences of our environment that are accurate enough for purposes of survival. A perceptual system that just produced experiences regardless of whether or not they were accurate enough for our survival would not have been selected for in organisms that live in environments where negotiating complex environments by using visual clues is needed for survival. The same seems to be true for our cognitive systems. They were selected for, also, because they provide us with some advantages in our pursuit of survival. It is plausible that being able to perceive one’s environment correctly is useful. Mobile organisms will not survive long in their environments if they typically have hallucinatory experiences. So, it is plausible to infer that mechanisms for producing perceptual experiences in organisms were selected for over a long stretch of time due to their usefulness in helping the organism to survive given the environment in which that kind of organism spends its life. As we have seen, since a patternless list of random symbols is useless, if we are going to have a list of symbols for representing the world in a way that is useful, we need to have recurring terms. So, for example, suppose that we use the term “dangerous” as something to indicate that we should avoid the thing so labeled. If thing1 is dangerous and thing2 is dangerous, then it will be helpful to avoid thing1 and thing2. Knowing how to identify a dangerous thing will be helpful if one wants to survive. Of course, if one had the complete list of dangerous things, for example, (thing1, thing2, thing14, thing542, and so on), then one could achieve one’s goal just by avoiding everything on that list. But the problem is perception, reason, and science do not work that way. Organisms with perceptual and cognitive systems, for one, do not have such a list. Such a list would, in fact, be exceedingly long because it would not be a list of kinds of dangerous things, but would be a list of each and every single dangerous thing. So, instead of listing hemlock, the brown recluse spider, the rattlesnake, and so on, it would have to list this hemlock plant, that hemlock plant, this other hemlock plant, for every hemlock plant, and this brown recluse and that brown recluse, this other brown recluse, for every brown recluse spider, and this rattlesnake, that rattlesnake, this other rattlesnake, for every rattlesnake, and so on and so forth for every dangerous thing there is in the entirety of spacetime. Moreover, if such a list is to be useful then the organism

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would have to able to match the name on the list with the named item in the world. But making those matches in a timely manner given the exigencies of action would require the organism to be able to run through that list containing an exceedingly large number of things each and every moment looking for matches. Having that list would require something approaching omniscience and processing it would require an exceedingly fast processor. Since we are not remotely close to being omniscient and do not have processors that approach that processor speed, the latter being physically unrealizable, a different method must be used in order for an organism to avoid dangerous things. So, in order for those perceptual and cognitive systems to provide an advantage to their hosts for survival, a different method is required. A one-to-one mapping of inputs to outputs is not feasible for less-than-omniscient organisms, like ourselves, with less than hyper-fast processing mechanisms, again, like ourselves. A mechanism is needed which can output kinds of behaviors from nonunique inputs, that is, from kinds of inputs. How we explain the nature of nonunique inputs, that is, kinds, gives us our different views. The two most plausible versions of a reductionistic nominalism are class nominalism and resemblance nominalism. Class nominalism, best articulated in many articles and books by David Lewis, explains kinds in terms of classes. Resemblance nominalism, best articulated by Gonzalo Rodriguez-Pereyra in his 2002, explains kinds in terms of resemblances. Let us take each of them in turn.

3  Class Nominalism: What It Is and Why It Does Not Work The fundamental starting point of class nominalism is the idea that all there is to reality is the many spatiotemporal particulars that are there. Further, each of these particulars is fundamentally independent of every other particular. Every spatiotemporal particular is only related to every other spatiotemporal particular accidentally and not at all necessarily. Think of each and every thing as an atom unconnected to every other atom. However, the class nominalist does not want to leave it there. In addition to all of those particulars, there also exist collections or groupings of those particulars.7 So, in addition to the large number of different particulars, there is an even larger number of different collections of them. As one can easily see from the equation for figuring out how many different collections there are from some number of things, namely, 2n − 1, there are exponentially more collections of things than there are things. So, if there are two different

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things, then there are 22 − 1, that is, three, different collections: the collection of one of them, the collection of the other of them, and the collection of both of them. If there are three different things, then there are 23 − 1, that is, seven, different collections of them. If there are four different things, then there are 24 − 1, that is, fifteen, different collections of them. And if there are just 100 different things, then (2100 − 1) there are 2100 − 1, that is, 1,267​,650,​600,2​28,22​9,401​,496,​ 703,2​05,37​5, different collections of them. Clearly, there are more than just 100 different things in the universe. For example, if one were to grab just a handful of sand on the beach, there are about 400,000 grains of sand in your hand, which would amount to 2400,000 − 1 different collections of those grains of sand. So, given there is an exceedingly large, but finite, number of things in the universe, there is an exponentially larger finite number of collections of those things. Here is the result: every single one of those collections constitutes a class. For example, the collection of the sun and Muddy Waters constitute a class. It will not be a useful class to know, but it will be a class nonetheless. Class nominalists typically place no restrictions at all on what things can constitute a class. Any thing and every thing in any combination whatsoever can and does constitute a class. The vast majority of these collections will be completely random and hence not useful to know about. But, the class nominalist claims, a few of them will be useful to know about. For example, the collection of all of the red things there are forms a class. And it is those useful classes that are the ones that science aims to discover. So, the class nominalist will identify scientific kinds with those useful classes. But, how are we to differentiate between the useful classes and the non-useful classes? Remember, the non-useful classes are no less real than the useful ones. Every class is equally real. It is just that a very small number of those classes are useful to us. The reason that class nominalists believe in classes at all, as opposed to being an eliminativist about them, that is, not believing in them at all, is that classes do some explanatory work. If we were not interested in being able to explain how science is possible, how reasoning is possible, how perception is possible, then we could just let our ontology consist merely in all of the many utterly unique particulars that there are. It is precisely because we humans do seem able to perceive things, and reason about them, thereby producing a scientific knowledge, that nominalists are pushed to explain how those activities are even possible. They are possible given the real existence of classes. As Price admirably puts the problem (in general): When we consider the world around us, we cannot help noticing that there is a great deal of recurrence or repetition in it. The same colour recurs over and over again in ever so many things. Shapes repeat themselves likewise. Over and

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over again we notice oblong-shaped things, hollow things, bulgy things. Hoots, thuds, bangs, rustlings occur again and again. . . . There is another and very important sort of recurrence which we also notice. The same pattern or mode of arrangement is found over and over again in many sets of things, in many different pairs of things, or triads, or quartets, as the case may be. When A is above B, and C is above D, and E is above F, the above-and-below pattern or mode of arrangement recurs in three pairs of things, and in so many other pairs of things as well. Likewise we repeatedly notice one thing inside another, one preceding another, one thing between two others. . . . These recurrent features sometimes recur singly or separately. The same colour recurs in this tomato, that sunset sky, and this blushing face; there are other features, if any, which repeat themselves in all three. But it is a noteworthy fact about the world that there are conjoint recurrences as well as separate ones. A whole group of features recurs again and again as a whole in many objects. Examine twenty dandelions, and you will find that they have many features in common; likewise fifty cats have very many features in common, or two hundred lumps of lead. In such cases as these there is conjoint recurrence of many different features. Again and again they recur together in a clump or block. This is how comes about that many of the objects in the world group themselves together into Natural Kinds. A Natural Kind is a group of objects which have many (perhaps indefinitely many) features in common. From observing that an object has some of these features, we can infer with a good deal of probability that it has the rest. . . . These constant recurrences or repetitions, whether separate or conjoint ones, are what make the world a dull or stale or boring place. The same old features keep turning up again and again. The best they can do is present themselves occasionally in new combinations, as in the black swan or the duck-billed platypus. There is a certain monotony about the world. The extreme case of it is found where the same old features repeats itself in all parts of a single object, as when something is red all over, or sticky all through, or a noise is uniformly shrill throughout its entire duration. . . . Nevertheless, this perpetual repetition, this dullness or staleness, is also immensely important, because it is what makes conceptual cognition possible. In a world of incessant novelty, where there was no recurrence at all and no tedious repetitions, no concepts could ever be acquired; and thinking, even of the crudest and most primitive kind, could never begin. For example, in such a world nothing would ever be recognizable. Or again, in so far as there is novelty in the world, non-recurrence, absence of repetition, so far the world cannot be thought about, but only experienced. (1953: 7–8)

As I have previously argued, if every experience was in fact unique or novel, we could not even have experiences because we could not have even developed a set of sensory mechanisms whereby such utterly unique experiences could be

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detected! But what Price is calling features of things, the class nominalist calls classes. So, the feature of being oblong is the collection of every oblong thing. The feature of being a cat is the collection of every cat. Class nominalists call the useful classes natural and the non-useful classes nonnatural. So, science is aiming to explain the natural classes and opposed to the nonnatural classes. For example, scientists study the class of red things or cancerous things but not the class of Muddy Waters and the sun and my left foot. Here, therefore, we have our answer from the class nominalist: inputs can be nonunique by virtue of being parts of a larger whole, which together form a class. So, all the red things there are is a class of red things. However, we should not be misled by this reference to classes. The class of red things just is all the red things there are.8 In other words, there is nothing more to the class of red things than those red things. A class is not some further thing. What exists does not fundamentally include classes. What fundamentally exists are just the spatiotemporal particulars. The myriad collections of those particulars are not some further things that exist also. That is why class nominalism is reductionistic: it explains away kinds in terms of particulars. At the bottom, the world is just the many absolutely unique things that have no things in common. There are two, related, problems for the class nominalist. First, how can the class nominalist explain the apparent usefulness of our perceptual systems? And second, how can the class nominalist explain the apparent usefulness of science? Both problems are sorting problems: how to find the signal within the noise. Let us take up perception first. We raised the issue earlier concerning how our perceptual systems can detect and thereby make us aware of what is in our environment. We do not have, nor does it seem feasible to have, a unique detector for every unique thing that is relevant to our survival. We would have to have as many red-thing detectors as there are red things, and likewise for every unique thing that is relevant to our survival which exists in our environment. Instead, we seem to have detectors for kinds of things that are relevant to our survival. We can detect any red thing given that we have something in our visual system that responds to a specific range of wavelengths of light, specifically, the L cones. But, and here is the first problem, how could such a detector have been selected for if all of the red things have literally nothing in common? The class nominalist will answer that all of the red things are all part of a collection, namely, a collection of red things. That collection of red things constitutes the class of red things. But, the class nominalist will say, they are not part of that collection because all of the red

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things share any thing in common. They are just part of that collection. That is all the class nominalist will affirm. It is just a brute fact. There is no thing in addition to those red things to which we can appeal to as the thing that explains why those red things constitute the class they do. They just do. However, each and every red thing is also part of infinitely many other collections. For example, this red apple is part of the class of red things, but it is also part of the class of apples and it is also part of the class of sweet things and it is also a part of the infinitely many other completely random classes, one of which could be the collection of Muddy Waters, the sun, my left foot, and this red apple. The question for the class nominalist is this: How could a detector that is responsive to a specific collection of things as opposed to any other specific collection of things have been selected for over time if the things in the specific collection have nothing in common? Detecting something requires making a differentiation, that is, noticing that this is different from that. In information theory, the process whereby useful information is differentiated from non-useful information is talked about in terms of differentiating the signal from the noise. So, for example, if being able to detect red things in one’s environment provides some advantage for survival, say because the organism can differentiate ripe (red) fruits from the (green) leaves surrounding them (Dulai et al. 1999), then being able to differentiate red things (the signal) from non-red things (the noise) will be a required ability for the organism’s perceptual detector. How can the class nominalist explain how such a sorting is even possible? Suppose it is true that red things are red. That is, suppose that their surface structures are such that their surfaces can absorb every wavelength of visible light except those in the range of 620 to 750 nm, which can reflect off their surfaces. The class nominalist’s idea is that each of these red things is truly red but that they, as a collection, have nothing in common. That is, each of these red things have a surface such that it can reflect light with wavelengths only between 620 and 750 nm and that all those many surfaces have nothing in common. How, then, would a mechanism for detecting surfaces that can reflect just that range of wavelengths of light get selected for? The required chemical reactions in the cones in the retina occur only when stimulated by electromagnetic radiation with wavelengths above 620 and below 750 nm. Electromagnetic radiation with wavelengths below 620 nm or above 750 nm does not initiate the chemical reaction that then leads to electrochemical reactions in the neurons that connect up with the visual system in the brain. The detector has to be able to initiate a specific chemical reaction with only light between those wavelengths. Therefore, being able to be sensitive to wavelengths only within that range is required.

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Consider the following analogy: a keyed lock. The most common keyed lock is called a pin tumbler lock. Inside of a pin tumbler lock are two cylinders, one inside the other. The inner cylinder is prevented from turning because there are metal pins, called “driver pins,” that go between the two cylinders in virtue of the springs in the outer cylinder that drive them down across what is called the “shear line,” that is, the line between the two cylinders. It is because the driver pins are partly in both cylinders that the inner cylinder cannot spin freely inside the outer cylinder, thereby making the lock locked. The inner cylinder also has metal pins in it, which are called “key pins.” But the key pins are of different lengths. Their different lengths correspond inversely to the different-sized cuts on the key. So, when the key is inserted in the lock, the taller teeth on the key push up the shorter key pins and the shorter teeth on the key push up the taller key pins such that the top of every key pin pushes up every driver pin so that the top of every key pin and the bottom of every driver pin are at the shear line, that is, the line between the two cylinders. Now that there are not any pins in between the cylinders, the inner cylinder can turn freely, thereby making the lock unlocked. As one can see, in order for this to work, the sizes of the teeth have to be the right size: not too tall and not too short. And that right size has to be within a certain range: within about 25 microns (for standard locks). In other words, keys whose teeth are 50 microns too high or 50 microns too low will not work (as many have frustratingly found out only after leaving the locksmith!). The height of each of the teeth have to be within a very small range (±25 microns) if they are going to get the top of the key pins to be at the shear line between the inner and outer cylinders so that the inner cylinder can turn. Now most keyed locks can be opened by only one key. But even with those, one can make copies of that key such that one can have many different keys that open one and the same lock. How is this possible? That is, how can we explain the fact that all of these many different keys can unlock one and the same lock? Presumably, we can say that such is possible because all of those many different keys have some thing in common, namely, their shape. It is precisely because they all have the same shape, that is, the heights of their teeth are the same length (within a certain tolerance) and in the same order, such that all of the many keys push up the key pins in that one lock the same amount (within a certain tolerance) so that there are no pins laying across the shear line, making it possible for the inner cylinder to turn inside the outer cylinder, thereby making the lock unlocked. The class nominalist, on the other hand, will deny that all of those working keys have any one thing, for example, their shape, in common. Each key has its

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own shape that unlocks the lock. The working keys form a class but not because they have any thing in common. In other words, the class nominalist will have an explanation for why each particular key unlocks the lock. Each key has the right shape to unlock the lock. But they also claim that there is no additional explanation, no additional thing needed, as to why all these keys successfully unlock the lock but all those other keys do not. That is, there is no explanation that is not ultimately reducible to each of the many particular explanations for each key. And here is the worry: How can a keysmith set up the key cutting machine with the goal of making multiple keys that all successfully unlock one lock? Can she not adjust the settings on the machine once and then cut multiple blank keys using that same setting? She can. But what explanation for that can the class nominalist give? None. If all of those keys have some one thing in common, namely, their shape, then the activities of our keysmith are explicable. So, even if a class nominalist can explain why one key works on the lock, say, because its shape allows for the two cylinders to turn freely. A class nominalist cannot explain why the keysmith can pick one particular setting (within a specific range of tolerances) that will successfully produce multiple keys that work on one lock. But surely we can explain why she can do so, namely, every key that works has something in common: its shape. With respect to our earlier example involving perception, how does a mechanism for differentiating red wavelengths of light from other wavelengths of light get selected for over time if there is not some one thing, that is, some one range of wavelengths (within a tolerance), that is different from some other thing, that is, some other range of wavelengths (again, within a tolerance), such that the mechanism can successfully differentiate red things from other colored things? A mechanism for accomplishing such a feat would be utterly mysterious if all of those red things had nothing in common at all. Just as there needs to be one particular setting (within a tolerance) on the key cutting machine (as opposed to other settings) in order to produce multiple working keys, there needs to be one particular range of wavelengths (as opposed to other ranges of wavelengths) in order for a perceptual system to be selected such that it will be able to differentiate one specific range of wavelengths from the many other specific ranges that there are. That is why humans need only one detector and not infinitely many in order to differentiate all the many red things from all the many other colored things: all the red things have some thing in common, namely, they all reflect the same specific range of wavelengths of light (within a tolerance) that is different than all of the other wavelengths of light. It is in virtue of that one thing that all of

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those many things have in common that a mechanism for detecting a useful feature can come to be. Just as a keysmith selects one specific setting (as opposed to any of the other possible settings) on the key cutting machine, a mechanism for detecting one specific range of wavelengths of light (as opposed to any of the other possible ranges of wavelengths of light) gets selected for over millions of years by the normal evolutionary processes. But the class nominalist has no explanation as to how either outcome could ever happen. It is just a brute fact that the class of red things is made up of these things and not those things (Lewis 1986: 352). Likewise with the working keys. But given that there is no explanation for it, class nominalism requires that the explanation science seems to offer as to why it is these and not those is nothing at all. That makes the fact that science does seem to be able to provide explanations completely mysterious. Lewis claims that each individual particular is whatever it is, with whatever shape it has, or mass, or whatever, and that all of those infinitely many individual things can be the parts of a mosaic, as the points of paint are in Seurat’s pointillist painting A Sunday Afternoon on the Island of La Grande, which gives us a large picture, a picture that scientists can describe. But if there are no kinds, no commonalities, then how could any particular have a shape or mass or any other identifiable common feature for science to propose as the regularities of any sort? There has to be the kind of thing a shape is, or the kind of thing mass is, or whatever, if Humean “constant conjunction” can be explanatory. Regularities, or constant conjunctions, can only exist between types of events and not tokens of events (cf. Davidson 1967: 691–92). In other words, since particular events cannot happen again, an event cannot be constantly conjoined with some other one-off event. Only kinds of events can figure in regularities.9

4  Resemblance Nominalism: What It Is and Why It Does Not Work At this point, a nominalist will likely admit that just appealing to classes is not going to provide what we need for the possibility of explanations that we clearly can and do have: explanations of why, for example, multiple keys can work on one lock and why a mechanism for differentiating red things from green things could have evolved. The explanation in both cases, as well as every other case of explanation, seems to require that the multiple things can in fact have some thing in common, either a shape in the case of keys or a range of wavelengths in the

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case of red things. But the nominalist will not give up their nominalism yet. They will at this point fall back on what has seemed to many to be their best gambit. Nominalists can say that what provides what we need for these and many other explanations is not that multiple things have some one thing in common, but that the multiple things resemble each other. They are similar. That is what does the explaining: the resemblance or similarity each of the many different things have to each other. The idea is that things can resemble each other or be similar to each other without having any thing in common. Family members can resemble each other, more or less, without being the same person. They are each different. And the resemblance might be so close, as in the case of maternal twins, that they look exactly like each other but, given that they are now two different people, that is, two different things, they do not share one thing in common. (Of course, they both came from the same zygote, but at that point in time, there was just one thing and not two things. Once that zygote splits into two zygotes, those two zygotes are two different spatiotemporal things with no spatiotemporal thing in common.) Therefore, it would not be the case that the working keys literally have some one thing in common. Rather, each working key simply resembles all of the other working keys in the shape of their teeth. The shape of each key may be a few microns off here and there from each other and as long as those differences are within the tolerance for being able to open the lock, they will work. Likewise with red things. They will not each reflect the exact same wavelength of light. The exact wavelength of light each of them reflect can be many nanometers different from each other and still cause the L cones to fire. They do not have to have any one thing in common at all. As long as they are all similar enough, we can explain how a receptor for that range of wavelengths could have been selected for and why all the working keys work. At first glance, the response just given on behalf of the nominalist looks plausible. But when pushed just a little, it completely falls apart. Yes, it is possible that none of the working keys are exact duplicates of each other and that they are all just a little bit different. And even if we were to use a laser-cutter key cutting machine, which has a smaller tolerance, the keys will still all be a little bit different from each other. But the nominalist needs more than that. They need it to be the case that even if the keys were exact duplicates, they still would not have any thing in common! In other words, given that each of the keys are spatiotemporally distinct, that is, different, and that the nominalist is committed to there being only spatiotemporal things, the keys will not have any spatiotemporal thing in common even if they are all exact duplicates, that is, cut

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with perfect precision. So, arguing that they are all slightly different in shape does nothing to bolster their case. The nominalist has to claim that even if every key’s shape were perfectly cut, the keys would still have no thing in common. And part of that does seem right. It seems right that completely distinct spatiotemporal things have no spatiotemporal thing in common.10 But, on the other hand, how can such a view explain how each of the keys can be duplicates (whether exact or not)? What makes it true that they are in fact duplicates? To answer that question, we need to know more about the nature of resemblance, upon which the resemblance nominalist relies. When we say, for example, that two things resemble each other or are similar to each other, to whatever extent, we are making a claim that can be evaluated as true or false as regards the appearance of those two things. Family members resemble each other for a reason: they have similarly shaped faces or bodies. People disagree about whether and to what extent people resemble, or look like, each other. But when they do, they are not arguing about whether the people are identical to each other, but whether the people have traits or features that seem similar. So, many members of a family might have facial features that are closer in appearance to each other than those family members do to people not in their family. Their eyes, nose, mouth, and ears might be similar in their shapes and/ or the placements of those features might be similar. And with maternal twins, whom we call “identical twins,” their visual appearances are often quite close indeed. But when we make these claims and argue about these claims, we are making them in order to claim, truly, that these multiple things have something in common: the way they look. And the way they look can be truly more or less similar, that is, within some range of precision, but whether that is the case or not will depend on those things having certain features that are the same within some degree of precision. So, the claim that two different things resemble each other amounts to a claim that though the two things are two different things and therefore not one and the same in every respect, as they have at least some one thing that differentiates them, there is at least some one respect in which they are the same and as such, is the reason for their similarity. So, though the working keys may be made of different clumps of brass, or may be made of different metals, or maybe be of different colors, or may be of different weights, or may be of different levels of reflectivity, they resemble each other nonetheless because their shapes are not different. That is, they both have the same shape. They can be made of different metals or reflect different wavelengths of light, and due to those differences, be dissimilar in their appearance or density. But the reason that those different keys can in fact be similar is due to what they have in common.

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It is in virtue of that commonality that they can in fact be duplicates. But since they cannot have each other’s spatiotemporally located shape, it must be the case that they both have the same type or kind or sort of shape. They have that kind of shape in common. They are each an example of the same kind of shape. Likewise, the apple does not have the ball’s surface, but both the apple and the ball have the same kind of surface structure in common such that they both reflect the same kind of wavelengths of electromagnetic radiation such that either one will cause a particular kind of receptor neuron to initiate a chemical reaction. But if that is true, then when people talk about spatiotemporal things resembling each other, they must resemble each other in virtue of those things having some aspect in common as opposed to the other aspects that they do not have in common. That is what it is for things to resemble each other. And if they are “exactly similar,” (cf. Martin and Heil 1999: 43–48) then those two things are, again, two different things but with some aspect in common that is as precise as can be, as when two different people can be exactly similar to each other in both having two legs. There is no lack of precision in having two legs. They are both bipeds. They share that aspect. They both have exactly a pair of legs. They each have their own pair of legs, and their legs may be longer or shorter, and of different colors, and so on, but the reason they truly do resemble each other is both have some one thing in common: being bipedal. The point is that when we are correct that things resemble each other, there exists something that explains that resemblance. We cannot correctly think that things resemble each other if they have nothing in common. What makes our claims correct that things resemble each other is that they share something in common, whatever that is, and it is in virtue of that commonality, at whatever degree of precision, that our claims are true or false. Saying that two distinct things are “exactly similar” implies that though they are different in some way, they are the same in some other way. That is what being similar but not identical requires: that the two things are at least not numerically just one thing. Otherwise we would just say that those two things are not just similar to each other, but identical to each other. On the other hand, if two things are really two different things but are “exactly similar” to each other, then we need to be able to specify the way in which those two different things are exactly similar. That will require that that feature they both exactly are be the same in both. But if what grounds multiple different things’ exact similarity is a feature that is the same in both, then unless the multiple things can in fact have a feature in common, that is, one and the same feature, we will not be able to say truly that those multiple things can resemble each other. And so, the resemblance nominalist is going

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to have to assent to the claim that multiple things can have some one thing in common if they want to rely on multiple things being able to resemble each other, whether perfectly or not. What that one thing is exactly we have not said. But the nominalist who denies that there is any one thing in common between multiple things cannot provide an explanation of our ultimate explanandum: How can we have perceptions of the world which could be reasoned about and thereby produce knowledge about it? If every single thing in the universe is unique and has absolutely no thing in common with anything else, then we would never be able to have a working perceptual mechanism and would thereby never be able to make any inferences about what we are experiencing, which is what we are doing, albeit more sophisticatedly, when we are doing science. The ubiquitous last gambit of the nominalist is to claim that the resemblance is just brute (e.g., Devitt 1980; Simons 1994: 556, 559; Rodriguez-Pereyra 2002; Heil 2015)11. Things resemble each other and that is that. There is no explanation for it nor is there any need for any explanation for it. They just do. That might seem like a foot-stomping response (because it is) but nominalists attempt to soften the move by pointing fingers at everyone else: every metaphysical framework, they say, has to stop the explanations somewhere. Nominalists stop at the brute resemblances between things. There is no deeper or further explanation. Ultimately, they assert, every explanatory system has to be grounded in something that is itself not explainable. That is just where the nominalists stop and it allows them to avoid being committed to there being anything in common to the many things that resemble each other other than just those many resembling things. All there is to the resemblance of the many red things is just those red things and their brute, that is, unexplainable, resemblance. Aristotelians stop their explanations at Aristotelian universals; Platonists at Platonic Forms. So, since everyone claims that something, that is, the ultimate foundation, is brute, just because nominalists stop at the resemblance of spatiotemporal particulars it is no reason to reject nominalism unless one is going to reject every metaphysical view because all of them ultimately claim that something is brute or ultimate in their explanatory system. I have two replies. First, even if we grant that every explanatory system has something in its system that is brute or in principle without explanation, it still could be the case that the nominalists stop too soon and that in order to get the explanatory benefits we need, we do have to go further and admit that abstract or universal things exist also. Second, I do not think that an explanatory system has to commit itself to a foundationalist framework such that its foundation is ultimate, that is, brute. Let me take these in reverse order.

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First, though it has seemed to many throughout history that deductive systems of knowledge are both ideal and plausible, I do not think that they are (cf. Plato’s Theaetetus 201–10 as well as McKenzie 2017). The idea of a deductive system of knowledge is that to know something is to prove it deductively, that is, where the form of the inferences is such that the truth of the premises guarantees the truth of the conclusions. In a foundational system, the theorems are things one knows, that is, are proved using the truth-guaranteeing rules of inference, and are based ultimately in the system’s axioms, that is, the ultimate foundation of the system. But, if the axioms are the ultimate foundation, then the axioms are not provable because they are, by design, the foundation. It is from the foundation, that is, the axioms, that one proves the theorems by means of the formal rules of inference. And since the axioms are not provable, then they are not knowable, since knowability just is provability. Hence, a deductive system of knowledge is ultimately grounded in things that are, by design, not knowable because they are not even in principle provable. However, the idea that everything we know is based upon that which is in principle not knowable is embarrassing. How can we say with a straight face that genuine knowledge is based on that which cannot be known? Unless we are trying to be mysterious on purpose, we cannot. Some people might have that goal, but nominalists do not. People who aim to be mysterious do not spend their time trying to give clear and truth-evaluable theories which aim to explain the subject matter. Since nominalists are not aiming to be mysterious, what can they say to this problem? Nominalists, as well as others who accept that sort of foundationalist framework for explanations, respond to the embarrassment by asserting that the axioms of the system are “self-evident” or that they “wear their justification on their sleeves” or some other such stipulation. If correct, then since things that are self-evident or are self-justifying are in no need of proof, the foundation of all of our knowledge is not grounded on things that are not knowable but are, by fiat, known. We know them, we stipulate, without proof. Embarrassment eliminated. Of course, as Bertrand Russell (1919: 71) colorfully pointed out: stipulation has all of the advantages of “theft over honest toil.” If, however, we would rather put forward an explanation with some intellectual integrity, then a better way to think about our systematic framework for knowledge, I suggest, is to not commit ourselves to a deductive system of knowledge but to commit ourselves, instead, to a nondeductive system of knowledge. I think that the way scientists think about how they are contributing to the accumulation of knowledge is exactly by that sort of intellectual endeavor. Science is ultimately a nondeductive system

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of knowledge because, though scientists use some deductive inferences in their work, most of their intellectual work and their most important intellectual work are via nondeductive inferences, that is, inferences whose form do not guarantees the truth of their conclusions but are instead either stronger or weaker inferences. For example, scientists often predict from any number of observations, with higher or lower probability, that similar observations will be made in similar situations in the future, or retrodict that similar observations would have been made in similar situations in the past, or just infer in general that similar observations would be made in similar situations regardless of when or where. The better the sample, in both size and representativeness, the stronger the inference, that is, the higher the probability. The only way to have a guarantee is to have every observation. Therefore, since scientists do not and will not have every observation when they make an inductive inference, they will not have any absolute certainty but only better and worse guesses, that is, hypotheses. However, the most important kind of inference scientists make, and upon which all of the explanatory knowledge they acquire is based, ultimately uses what are called abductive inferences. An abductive inference is an argument that starts from observations but instead of inferring a generalized observation from those particular observations, infers from those observations an explanation of those observations. For example, Mendel first inductively inferred from his observations that he was going to keep seeing the same proportion of tall to short pea plants and so would anyone else who did the same experiments. But second, he went deeper and inferred from those observations an explanation as to why that pattern occurs, namely, that there exist what we now call genes and they combine in a particular complex way, which if they do exist, would explain why we get the observations we do as far as the proportion of tall to short pea plants. And though that abductive inference does not guarantee the truth of its conclusion, it is how we actually make progress in science. And it is in general abductive inferences that are how we ultimately, without certainty, ground what we, to some extent, know. The upshot here is that given that the foundation of our knowledge can be known to some degree (as opposed to not at all, that is, brute, or stipulated to be known with certainty, that is, self-evident), every explanatory framework does not have to claim that some part of that framework is brute. A scientific framework does not do so and it seems to be making all sorts of progress. For example, physicists currently accept the Standard Model as the basis of their discipline, but as an inference to the best explanation. The enormity of observations, that is, data, collected thus far gives them extraordinarily good reason to accept

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the model, with its panoply of particles and their relations to each other, as an excellent framework within which to make further discoveries. Chemists currently accept the Periodic Table of Elements as the basis of their discipline and again as an inference to the best explanation. And again, the enormity of observations collected thus far gives them an extraordinarily good reason to accept the table, with its various elements and their relations to each other, as an excellent framework within which to make further discoveries. Biologists currently accept evolution by natural selection as the basis of their discipline because it is the best explanation of the enormity of observations collected thus far, and it also provides an excellent framework within which to make further discoveries. None of these disciplines assumes their foundational explanatory model or framework as brutely true or self-evidently true. On the contrary, every scientific discipline assents to the truth of their foundational explanatory model based upon vast amounts of observations and careful mathematical calculations and both deductive and nondeductive reasoning. We will be considering a theoretical objection to the confidence we have in science providing us with genuine knowledge of the world in Chapter 4, but since nominalists do not share that stance, they would not object to my characterization of science as an activity that does in fact provide us with genuine knowledge. And given that they agree that science can and does provide us with such and plausibly without having to claim that its foundational claims are brute (or self-evident), their defense of nominalism’s commitment to resemblance being brute, that is, incapable of further explanation, by virtue of the claim that every explanatory framework has to at some point say that its foundational claims are brute, is not a persuasive move and is not a good enough reason to not demand more from them about why it is true that multiple things can and do resemble each other, whether exactly or not. And second, even if we grant the nominalists that every explanatory theory has to stop its explanations somewhere and say that where they stop is not capable of explanation, the nominalists stop where they do just so that they can avoid being committed to the existence of abstract things or universals, in addition to the spatiotemporal ones observable either to the naked eye or with the use of scientific instruments. That would be a good reason to stop where they do if one’s goal was to be dogmatic and defend one’s theory no matter what. But if one’s goal is to pursue truth wherever the intellectual process leads, then given that we can explain why this multitude of red things resemble each other even though in many ways they do not resemble each other given that some are round and some are square and some are hard and some are soft and some are sweet

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and some are bitter and some are small and some are large and so on and so forth for many other differences, despite that myriad of differences, they all share some one thing in common: they all reflect the longest wavelength (at the scientifically appropriate level of precision) of visible light. It is because they all share that one thing in common that a mechanism for differentiating red things from green things can be selected by natural processes in order to give organisms that can differentiate red things from green things an advantage in their quest to survive given the environments they find themselves. We saw this same point (without the mechanism of natural selection, which does not affect the point being made) when we inquired why successful keys are successful versus the keys that are not: they all share some one thing in common, specifically, the shape of their teeth is the same (within the appropriate level of tolerance for cutting keys). It is because they all share that one shape in common (again, within a certain tolerance level) as opposed to the shapes every other key has that is different than the ones that work, that they all work. We could say the keys’ resemblance to each other is just brute and that they have nothing in common. But given that we can explain what the resemblance that they have is and why that explains why they all work: the pattern and shape of their teeth is (within a certain tolerance level) the one necessary for pushing up the pins at the right amount so that the inner cylinder can freely slide within the outer cylinder thereby allowing the lock to be unlocked. Given that we can explain what the resemblance is between things that do in fact resemble each other in some ways and not in other ways and, more importantly, why that resemblance explains something else, it seems poorly motivated to deny that things that resemble each other do in fact have something in common. I conclude this chapter, then, simply with the claim that it is more plausible to assent to the view that unique spatiotemporal things do have something in common than to the view that they do not. In other words, some version of not being a nominalist is more plausible than being a nominalist. We do seem to have a mechanism for producing experiences of one and the same kind. And we do seem to have a mechanism for reasoning about those experiences. And as that reasoning has become more and more rigorous, we do seem to be able to have knowledge about those experiences, the most rigorous of which we call science.12 But we are not yet entitled to say exactly what those multiple spatiotemporal things could have in common. Since we want to move through our options as conservatively as we can, the next view we shall consider, assuming that we have rejected nominalism (cf. the Appendix), is a view that is also committed to the

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idea that only spatiotemporal things go on our list of existent things. As I said at the outset, spatiotemporalism is the default ontological view. And so, since there is a theory which is also committed to spatiotemporalism but denies that nominalism is true, I want to start with that view. The vast majority of scholars and philosophers since the medieval period have thought that that view was Aristotle’s. As I mentioned in the previous chapter, I do not think that Aristotle actually held the view attributed to him. And so, I want to turn to that view, as it is defended nowadays, which I am calling “contemporary Aristotelianism” (as opposed to classical Aristotelianism, which we will consider in Chapter 5). The contemporary Aristotelian accepts our anti-nominalist conclusion, namely, that there exists more to reality than just the many unique spatiotemporal things; there also exist universals, which those many unique spatiotemporal things literally have in common. So, in addition to all of the red things, there also exists the universal Redness, which all of those red things have in common and which is spatiotemporal. Let us examine that view now.

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1  Spatiotemporal Universals As we saw in the previous chapter, in order to explain how a mechanism for perception could have been selected by natural selection in virtue of its usefulness for survival and therefore how science could use those observations and experiences to gain knowledge of the spatiotemporal world, it is more plausible to believe that the many spatiotemporal things have something in common than that they do not. But what they have in common is still unclear. In the next three chapters, we will consider three different attempts at giving a theory about what it is that the many spatiotemporal things have in common. One of the motivations that these three theories have in common is the desire to avoid having to accept Platonism as the best explanation for it. All three of these theories view Platonism as going “too far” in one or more features and attempt to get the same explanatory benefits of Platonism without having to accept what they view as Platonism’s high costs. In this chapter, we will consider a theory that has its roots in Aristotle, namely, that what the many spatiotemporal things have in common is a universal. But unlike Aristotle, whose view we will consider in Chapter 5, the contemporary version, which is ultimately due to the medieval thinkers, I would argue, misinterpreting Aristotle, claims that universals are spatiotemporal. A universal, the contemporary Aristotelian asserts, is another thing on our ontological list of things that exist but it, unlike the more familiar spatiotemporal things, can be multiply located. For example, in addition to all the red things there are wherever they are, there also exists another thing in those red things, the universal redness, which is located literally everywhere each of those red things are located. That idea gives us an easy solution to our explanatory problem. All of the red things literally have some one thing in common: the universal redness which is in each

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and every one of them. So, just as Mendel inferred the existence of genes from the observations as the best explanation of those observations, contemporary Aristotelians infer the existence of universals as the best explanation for the fact that we can have advantageous perceptions and can come to understand why things are the way they are, that is, we can have science. And at that level, it seems like an easy and plausible solution. However, whether this inference is the best explanation for those facts depends upon the details and it is to those that we must now turn.

2  Contemporary Aristotelianism Contemporary Aristotelians reject the nominalist’s claim that spatiotemporal particulars have nothing in common (Armstrong 1980, 1989, 1997; Lowe 2006; Jacobs 2010). They assent to there being more to reality than just spatiotemporal particulars. There also exists, they admit, these additional things, which they call “universals.” And it is these universals that are the things the many spatiotemporal particulars have in common. An important assumption made by contemporary Aristotelians is that these universals are literally located in spacetime. The idea is that the many spatiotemporal particulars have some one thing in common and that that one thing is literally one and the same thing everywhere it is. For example, the redness of this playground ball is one and the same thing as the redness of that playground ball and the redness of that apple and the redness of that flower. There are not many different rednesses. Rather, there is just one redness that is literally located in many different places. To really bring this view into better relief, though, consider as a contrast the view that assents to the redness of this playground ball which exists in addition to the playground ball, as against nominalism, but also claims that the redness of that playground ball is a different redness from the rednesses of other playground balls, apple, and flowers. These different rednesses are sometimes called “tropes,” sometimes “abstract particulars,” and sometimes “modes” (Williams 1953; Campbell 1981; Heil 2003, respectively). The idea is that these additional things are also particulars and therefore, not universals, that is, all the red playground balls and red apples and so on do not have one particular redness in common but that they each have their own unique redness to themselves. A contemporary Aristotelian, then, thinks that even if there are tropes (or modes and abstract particulars),1 there also exist universals, which are what the many spatiotemporal particulars have in common and are needed for the reasons we gave in the previous

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chapter. Theorists who admit to there being tropes (or abstract particulars or modes) but deny that there are universals face the same problems we examined in the previous chapter, namely, that of explaining how the tropes resemble each other without having anything at all in common. Just saying, as they do, that their resemblances are brute faces the same insurmountable problems as when the nominalists say that the spatiotemporal particulars brutely resemble each other. Therefore, I will not discuss their view any more than I just have. I only bring it up so that we can see to what contemporary Aristotelians are committing themselves, namely, that a multiplicity of different spatiotemporal particulars can share literally one and the same thing with each other even though these many different spatiotemporal particulars are potentially located in a vast number of different disjoint regions of spacetime. It is one and the same universal, for example, redness, that is located in each and every region of spacetime where there is the relevant particular, for example, a red apple or red playground ball. When explained like that though, one may begin to worry. How can one and the same spatiotemporal thing be located in many different disjoint regions of spacetime? That just seems wildly implausible. A scattered thing is not a thing, one might say. A scattered thing is really just a lot of different things. A heap of sand is really just a lot of different things, that is, a lot of different grains of sand. Besides, thinking that a universal is one and the same thing located in many different disjoint regions of spacetime is not even a scattered thing like a heap of sand. It would be more like a heap of sand that is literally made up of only one grain of sand located in many different places at the same time. But how can one and the same thing be wholly present in multiple places at the same time? Parts of a thing could be, but not the whole thing. For example, US Interstate Highway 70 runs from Utah to Maryland, connecting those two states with Colorado, Kansas, Missouri, Illinois, Ohio, West Virginia, and Pennsylvania. Interstate-70 is thereby located in many different places at the same time. But it is not wholly located in all those different states at once. Only parts of I-70 are located in those different places. And if spatiotemporal particulars are spread out in time just as they are in space, then just as I am spread out in space, for example, as my left hand is over here and my right hand is over there, I am also spread out in time, for example, my teenage years are back in the 1970s and my adult years are in the 1990s through now. So, just as I might have spatial parts that do not make up all of my spatial displacement, I also might have temporal parts that do not make up all of my temporal duration. The point here is that being multiply located does seem plausible if we are talking about my parts, whether spatial parts or temporal parts. But what contemporary Aristotelians claim is quite different. They claim

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that a spatiotemporal universal can be wholly, and not just partly, located in multiple regions of spacetime. How can that be motivated? How can one and the same spatiotemporal thing be wholly located in many different regions of spacetime? One and the same playground ball cannot be wholly located in more than one place. Their view seems quite implausible, in the extreme. Unfortunately, contemporary Aristotelians have rarely tried to motivate that claim. They usually just assert it and say that it is necessary to believe in if we are going to have a chance of explaining how a plurality of spatiotemporal things can literally have something in common such that the possibility of advantageous perception is possible and more importantly that science is possible. David Lewis, who is himself a nominalist, charitably says on behalf of the contemporary Aristotelian: “By recurring repeatedly, universals defy intuitive principles. But that is no damaging objection, since plainly the intuitions were made for particulars” (1983: 345). In other words, it is no wonder that it seems wildly implausible to us that any spatiotemporal thing could be wholly located in many different regions of spacetime at once because what seems plausible or intuitive to us has been constructed and shaped by our experiences with particulars that can only be wholly located in one place at a time or at one particular contiguous region of spacetime. Since Lewis’s helping hand in 1983, contemporary Aristotelians have (gratefully) adopted that way of waving their hands at the issue in order to move on with their theory. And given how helpful it would be to believe in such things as universals that can be wholly located in more than one place or more than one contiguous region of spacetime, it does not seem unreasonable to accept their existence in spite of that intuitive discomfort. In other words, the explanatory benefits of believing in such things do seem to outweigh the costs to our intuitions. That calculation seems plausible to me, however, only if these, namely, nominalism and contemporary Aristotelianism, are our only options. We should indeed make that deal unless, and until, something better, that is, a better benefit-to-cost ratio, comes along. In other words, if a necessary feature for believing in the existence of a thing is that it be located in spacetime, then given that nominalism and contemporary Aristotelianism are our two best options, I myself think that we are much better off going for the latter and not the former. But we can sweeten the deal a little bit. There is one contemporary thinker who at least attempts to lessen our intuitive costs. Cody Gilmore describes contemporary Aristotelianism this way: To say that universals are immanent is to say that they exist in their instances, where this is taken to mean that each universal is wholly present at each location at which it is instantiated. Consider, for example, charge –1, which is a property

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of electrons. Construed as an immanent universal, this property is a multiply located entity, one that can be found, in its entirety, wherever an electron can be found. (2003: 420)

He then motivates the idea that such is imaginable or intuitive by means of the following thought experiment: Suppose that material objects persist through time not by having different temporal parts existing at different times (not by “perduring”), but rather by being wholly present at each moment of their careers (by “enduring”). Now let a be a persisting point-particle located at the North Pole and let b be a numerically distinct persisting point-particle located at the South Pole. Suppose also that backward time travel is possible. In particular, suppose that in the year 2011 a and b are sent back to the year 2003 (i.e., now), at which time they both coexist with “younger versions” of themselves. Thus it so happens that right now there are “two versions” of a in existence and “two versions” of b in existence. Further, suppose that two collisions are occurring right now: at the North Pole, the older version of b (the version that has returned from the future) collides with the younger version of a; and at the South Pole, the older version of a collides with the younger version of b. This puts us in the following situation. Since a is an enduring rather than a perduring object, we cannot say that the younger version of a (which is located at the North Pole) and the older version of a (which is located at the South Pole) are numerically distinct temporal parts of a; rather, we must say that the younger version is numerically one and the same thing as the older version. And mutatis mutandis for b. So, right now, at the moment of the collisions, a and b coincide with each other at the North Pole, and these very same particles coincide with each other at the South Pole. (2003: 424)

The thought is that since we can imagine the idea of someone traveling back through time and meeting an earlier self, or later in time and meeting a later self (cf. the movie Back to the Future, Part II) thereby having the same exact person wholly existing in two different places at the same time, then the idea of universals wholly existing in more than one place at the same time is at least imaginable. Whether it is plausible, though, is what we now must examine. The main advantage that contemporary Aristotelianism has over nominalism is that it can explain how a perceptual mechanism could have been selected for by natural selection and it can explain how scientific explanations are possible (as opposed to just have a lot of so-called brute explanations, which are not really explanations at all) given its commitment to there being universals in common to the many different spatiotemporal things. But contemporary Aristotelians

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more often than not think that they also need to distance themselves from Platonism, as both views are committed to the existence of universals and both views describe those universals as being discovered, and not created, by some sort of objective intellectual inquiry, for example, science. So what advantages do contemporary Aristotelians think accrue to their view as against what they think of as Platonism? As we saw above in Gilmore, contemporary Aristotelians describe the universals they believe in as being “immanent,” as opposed to Platonists who allegedly think that the universals are “transcendent.” What is supposed to be the difference, according to the contemporary Aristotelians? “Immanent” universals are (1) literally “in” things but (2) not capable of “separate” or “independent” existence, which are usually explained by what they call “the principle of instantiation,” and are therefore only capable of “dependent” existence. Having universals literally in spatiotemporal particulars gives the contemporary Aristotelian the advantage over the Platonist by having to believe only in spatiotemporal things, thereby giving their view the appearance of being more naturalistic, that is, scientific, due to its lack of commitment to anything nonspatiotemporal, which seems prima facie non-naturalistic, that is, nonscientific. And having universals being incapable of separate or independent existence gives the contemporary Aristotelian the advantage over the Platonist of cutting down on, they claim, the number of things in which they will have to believe. Let’s take the second benefit first. Contemporary Aristotelians sometimes talk about universals as “ways things are” (Levinson 1978). If universals are “ways things are,” then there can only be “ways things are” if there are things that are that way. There cannot exist a way a thing is if there are no things that are in fact that way. So-called transcendent Platonic universals, by contrast, are not “in” things but are, it is claimed, “outside of ” things and are capable of “separate” or “independent” existence and therefore, are thought to be able to exist even if they are not instantiated. An example that illustrates the difference might help. Suppose you live in a housing development where there are many houses that have the same shape. What is the shape of your house? If there are tropes or abstract particulars or modes, then the shape of your house is a different thing, a different trope or abstract particular or mode, than the shapes of the other houses; each house’s shape being its own unique thing, trope, abstract particular, or mode. So, besides the bricks, boards, and mortar of your house, there also exists your house’s shape. And just as your neighbor’s bricks, boards, and mortar are different from your house’s bricks, boards, and mortar, the shape of your

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neighbor’s house is a different thing from the shape of your house even if they were built using the same blueprint. And if that is what we are talking about, then it is very easy to see how the shape depends on the bricks, boards, and mortar. If those materials are in three distinct piles on the land where your house used to be, it does seem that the shape of your house has ceased to be even though all of the bricks, boards, and mortar still exist. But the issue, which divides the contemporary Aristotelian from the Platonist, does not concern shapes thought of as tropes, abstract particulars, or modes. The issue we are talking about concerns the one and the same shape that is common to all of the houses in your housing development and not the unique, or particular, shape specific to each house. The shape of your house is one and the same thing as the shape of every other house in that development. Since the contemporary Aristotelian thinks that universals are wholly present everywhere they are, this has to be what they are talking about: a spatiotemporal thing that is wholly located in every house in that neighborhood. That thing, which all of those houses have in common, would be what the universal is. (If artifacts do not share a universal, then just switch the example to redness, or being negatively charged, or having an up spin, or whatever scientifically acceptable commonalities there are. The point is the same: there exist universals that are wholly present in multiple numerically distinct particulars.) The constructivist, as we will see in Chapter 4, claims that there do exist these common things, these kinds or types of shapes, but that they are created or constructed by the mental activities of conscious beings, for example, ourselves. And as we will see in Chapter 5, the classical Aristotelian claims that these common things exist, but that they exist in a “lesser” type of existence. The Platonist does in fact agree with the contemporary Aristotelian, though, that these common things are genuinely additional things, as against the classical Aristotelian, and that these common things are discovered by conscious beings and not created by them, as against the constructivist. But the Platonist disagrees with the contemporary Aristotelian when the latter claims that those common things are spatiotemporal things and are thereby literally located in any region of spacetime. The Platonist claims, instead, that these common things are nonspatiotemporal and are therefore not literally present, wholly or partially, in any region of spacetime. They do not “depend” for their existence on being located anywhere and so, as the contemporary Aristotelian claims, these common things are independent of whether they are exemplified anywhere or anywhen. The alleged advantages of contemporary Aristotelianism over Platonism, again, are two: first, given that everything that exists, both the particulars and

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the universals, are spatiotemporal, contemporary Aristotelianism is allegedly more amenable to what people prima facie think of as being naturalistic, that is, scientific, since believing in nonspatiotemporal things seems, again, prima facie, non-naturalistic, that is, nonscientific, and second, one’s ontology can be smaller with contemporary Aristotelianism because one does not have to believe in the existence of common things that are not common to anything, for example, a kind of living thing that, due to historical accidents, never came to be, or a kind of disease that no one ever got. Contemporary Aristotelianism allows us, it is claimed, to remain scientific, that is, naturalistic, and to be ontologically lean and to believe only in what is needed in order to explain what has happened or what is happening or what will happen and no more than that. What I will argue in the rest of this chapter is that the contemporary Aristotelian is mistaken on both counts: their view is not more scientifically respectable or naturalistic, but rather less so, and it badly constrains what science needs if it only allows for science to be committed to the existence of universals that have been or are or will be exemplified.

3  The Argument against Contemporary Aristotelianism: Preliminaries I shall take up these issues in reverse order due to the fact that resolving the issue concerning whether uninstantiated universals exist or not will greatly help us in determining whether believing in the existence of things that are not spatiotemporal is naturalistic and scientifically respectable or as the contemporary Aristotelians think, a belief in something that is non-naturalistic and scientifically suspect. Re-consider our example concerning houses: suppose that my house and your house have the same shape, the same universal, wholly present in both. Destroying my house does not seem to destroy the shape that your house still has present in it even though there is no longer that same shape where my house used to be. But does that shape, that universal, exist only if it is wholly present somewhere and somewhen? Certainly, that is the case with respect to the spatiotemporal particulars, such as you, me, trees, planets, and so forth. If a spatiotemporal particular is not located in any region of spacetime, then it does not exist at all. Do the existence of universals, likewise, depend upon their being located in some region of spacetime? The contemporary Aristotelian answers that question affirmatively and calls this commitment “the principle of

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instantiation.” And it makes good sense given that if universals are spatiotemporal things, then if they are not located somewhere and somewhen, then they do not exist! Universals are different than particulars in that the former can be wholly present in multiple places whereas the latter cannot. But, given that they are both spatiotemporal, universals do share with particulars the requirement that if they are not located somewhere and somewhen, then they do not exist. The Platonist’s answer to that question, on the other hand, is that universals do not depend on being located in some region of spacetime in order to exist because the Platonist thinks that universals are not spatiotemporal things, but instead, nonspatiotemporal things. So, the Platonist rejects the principle of instantiation. The Platonist, that is, is committed to the idea that universals are independent of whether they are instantiated or not. Let us now get clearer on this principle. Suppose one believes in a weak version of this principle:2 in order for a universal to exist at time t, there has to exist an instantiation of that universal at t. For example, take all of the white objects in the universe at t1. Let Mick Jagger have his way at t2 and paint all of those white objects black (Jagger and Richards 1966). At t3, there would exist no white objects. Therefore, according to the weak version of the principle of instantiation, not only would there be no white objects, but also the universal whiteness would itself cease to exist at t3. If one of those recently painted objects got scratched at t4, then in addition to that white object coming into existence, so also would whiteness. Such is a consequence of the weak version of the principle of instantiation. Contemporary Aristotelians are typically not sanguine about such a view concerning universals given that the universals, as we just saw, could be coming into and going out of existence from time to time. That view makes science, which has those universals as its objects of knowledge, problematic at best and impossible at worst. The objects of scientific knowledge, whatever they are, cannot be coming into and going out of existence potentially from moment to moment if our knowledge of those scientific truths is to be of any use. Scientists would be able to know what whiteness is only when there are white objects. So, if Mick Jagger does get his way, then unbeknownst to themselves, the scientists who at least thought they knew what whiteness is do not in fact know what whiteness is because whiteness does not exist and so there is no thing in existence for them to know. But clearly, scientists can know what whiteness is even if Mick Jagger get his way. They would still be able to explain what whiteness is and would still know how we could go about trying to make some white objects, if we so desired. It is largely due to that consequence of the weak version of the principle of instantiation that contemporary Aristotelians (e.g., Armstrong and Lowe)

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have more commonly committed themselves to a strengthened version of the principle of instantiation such that if a universal is instantiated at any time, then that universal exists at all times. It is in that way that universals will not come to be and pass away, that is, will not be subject to change, and could therefore be suitable objects for scientific knowledge.3 Well then, let us say that one accepts the stronger version of the principle.4 If so, then one will be committed to the idea that as long as a universal is instantiated at some time in the whole history of a spacetime continuum, then that universal exists for the whole history of that spacetime continuum. This view has the advantage that universals will not be coming into and going out of existence depending on their current instantiation status. For example, if a house shape is instantiated at least one time, then that house shape exists even for those times when it is not instantiated. (The architect would have discovered that house shape, then, and not invented it.) Or, if anything reflects 680 nm wavelengths of light at least one time, then that kind of light (in this case: red) exists for every time even if nothing at that time is reflecting that wavelength of light. Just as with spatial locations, if I exist in one spatial location, for example, the region of space I am now displacing with my body, it is also true (enough) that I exist in the city of St. Louis, and on earth, even though my body is not displacing the entire spatial region of St. Louis or the earth with my body. Likewise, even though the universal is not existing at all of the times of the spacetime continuum in which it is instantiated, it is true (enough) that the universal exists for all of those times. One way of thinking about the stronger version of the instantiation principle is in terms of a container: if we think of a spacetime continuum as a container, then a spacetime continuum, as a whole, truly contains a universal as long as the universal in question is somewhere in it even if it is not everywhere within that continuum. The stronger version of the principle, then, can avoid the danger to scientific knowledge that afflicts the weaker version: the objects of scientific knowledge will be stable and will not be popping into and out of existence over time thereby allowing scientists to have knowledge regardless of whether or not the thing they know is instantiated at that moment or not. As long as it is instantiated at some time, then scientists can know it. If it is not instantiated at any time, then there is nothing for scientists to know. Seems plausible enough. As a side note, scientific research does seem best explained by that idea. A scientist proposes that there exists some kind of particle or element or mechanism or structure and then empirical research is undertaken to find an example of that kind of particle or element or mechanism or structure. For example, Peter Higgs, a physicist at the University of Edinburgh, proposed that the mass of particles

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might be best explained by a mechanism that requires the existence of another kind of particle, the Higgs boson, which no one at that point had ever had any evidence. It was the empirical discovery of those particles, those Higgs bosons, at CERN in 2012 that confirmed that there does exist that kind of particle, the kind of thing a Higgs boson is. If examples of that kind of particle were never found, scientists would have been skeptical that such a kind of particle really does exist. So, if Higgs is to be right that there is such a kind of particle, then there had better be some spatiotemporal examples of it if we should believe in it. Without those empirically confirmed spatiotemporal examples, we do not seem to have a good reason to believe in the existence of that kind of particle. So far so good.

4  The Argument against Contemporary Aristotelianism: Objections However, despite there being so many good benefits of the contemporary Aristotelian theory conjoined with the stronger version of the instantiation principle, it does have, I shall argue, two heavy costs that are not worth paying. The first is that it suffers from a related problem that brought down the weaker version of the instantiation principle, and the second is that its quintessentially metaphysical solution puts it at odds with its naturalistic, that is, physicalistic, pretensions. Again, one of the benefits of using the stronger version of the principle of instantiation is that it gives us a way to keep down the number of (even scientifically respectable) universals to which we have to be committed, given that we do not have to believe in the existence of universals that are never instantiated, such as universals for species that are never exemplified or all of the many diseases that (hopefully) are never instantiated. Why believe in a universal for a species or a disease that can be instantiated in spacetime but never is? If we have to believe in the existence of a universal for each and every kind of thing that can be instantiated in spacetime but never is, we end up having to believe in far too many (explanatorily idle) universals. The other alleged benefit of the theory is that universals are located in spacetime, which seems beneficial if one is trying to give a theory concerning the objects of science. Avoiding having to believe in things that are not located in spacetime seems to be a very scientificfriendly thing to do. I shall now argue that neither of these alleged benefits is worth the cost in an explanation of the scientific enterprise.

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First, staying within the confines of scientific concerns, where one believes in the existence of universals because of considerations relevant to the scientific enterprise, it makes sense to believe only in the existence of universals that are required for the truth of scientific theories. Universals that are not needed for scientific theories to come out true are thereby “too many.” Both contemporary Aristotelians and Platonists, then, grant at least this much: universals that are instantiated serve that purpose. So, the divide between them would be over whether or not the universals that are not instantiated do so as well. Contemporary Aristotelians answer in the negative while the Platonists answer in the positive. And to the contemporary Aristotelian’s credit, it is hard to see how universals that are not instantiated in any region of spacetime are needed for any scientific theory to come out true. The question is: Are uninstantiated universals needed for science? The first reason for thinking that science needs uninstantiated universals is that scientists seem to be able to draw a distinction between three different kinds of discoveries: (i) discovering what kinds of things have happened, what kinds of things are happening, and what kinds of things will be happening; (ii) discovering what kinds of things could never happen because they are not scientifically possible; and (iii) discovering what kinds of things could happen, but may not ever happen because they are scientifically possible. First, for example, scientists have discovered that there was, is, and will be a kind of physical particle hypothesized by Peter Higgs, which physicists call “the Higgs boson,” that explains why elementary particles have the mass they do. As for an example of the second kind of discovery, scientists have discovered that a perpetual motion machine could never happen because it is not scientifically possible due to the fact that it would violate the first and second laws of thermodynamics. Those are the first and second kind of discoveries scientists can make and both are important. The third kind of discovery, though, is where we will see the scientific need for uninstantiated universals. An important aspect of scientific theorizing and activity concerns not just the piecemeal explanations for observations that they have had or are having or will have. Scientists are also interested in figuring out explanations for observations that they (or we) could have, whether they (or we) ever do or not, in order to get a more holistic understanding of how and why our world is the way it is but also why it is not some other way. Scientists can and do predict, through some explanation, that the same kind of things we have observed in the past will be observed in the future, for example, that if we put sugar in water, it will dissolve, just as it has in the past. But they also aim to predict, again, due to some explanation, that we could observe some new kind of thing in the future

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which we have not observed in the past. This is a key part of how we advance our understanding of the world: predicting novel experiences. But in order to predict novel experiences that have a chance of coming out true, they have to be able to think about how the world is structured such that the gaps in our observations might be explained by gaps in our explanatory structure so that were there this kind of thing, we just might observe examples of it. Being able to reason their way to those unseen yet possible experiences requires that there is a truth about what that kind of thing is. And if there is a discoverable truth about what that kind of thing is, whether anyone ever sees an instance of that kind of thing or not, requires that there be a universal for it, that is, that there exist that kind of thing. As an example, let us consider a small part of the history of chemistry (cf. Scerri 2007). Based on the best research of the day, some eighteenth-century chemists, who aimed to find the most basic material elements that there are— the material elements that could not be further broken down into more basic matter by means of chemical reactions—had discovered many different kinds of elements, namely, phosphorus, cobalt, platinum, nickel, bismuth, magnesium, hydrogen, oxygen, nitrogen, barium, chlorine, manganese, molybdenum, tungsten, tellurium, and strontium. Examples of all of those had been found and therefore, according to both Aristotelians and Platonists, there exist universals for each of those kinds of elements. But what was truly remarkable was when Dmitri Mendeleev, in 1869, proposed that these elements as a whole exhibited a pattern, which he called “a law of periodicity,” and which he laid out in his “Periodic System,” which we call the “Periodic Table of Elements.” The idea is that not only is there a discoverable relationship between the atomic weight of an element and how that element behaves in various contexts, that is, its causal profile, but there is also a discoverable relationship between various intervals of atomic weights and causal profiles such that different elements at specific intervals will share the same casual profile. For example, sodium and potassium explode if they come into contact with water, whereas copper and silver will not. On the other hand, copper and silver are good conductors of electricity while sodium and potassium are not. Mendeleev then used those patterns to predict the existence of other kinds of elements that no one had ever found an example of before. More specifically, given the atomic weights and causal profiles of the already discovered elements, Mendeleev was able to guess (correctly) that there are kinds of elements in the gaps between the ones scientists had already discovered. Because there was a gap in the table he laid out, he inferred that there could be a kind of element that

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fills that gap. He correctly predicted, for example, that there is a kind of element with an atomic weight of roughly sixty-eight and with a causal profile similar to that of aluminum. That element is gallium and it was discovered in 1875. Not insignificantly, moreover, Mendeleev’s “law of periodicity” also helps chemists to rule out the possibility of the existence of other kinds of elements. For example, chemists can predict (correctly) that we will never find any kind of element that is a kind of noble gas but with a causal profile similar to that of phosphorus. Both of these sorts of predictions are quite useful because it narrows down where one’s research should look and where one’s research should not look. Anyone who had tried to figure anything out realizes very quickly that the more kinds of things one can rule out, the easier it is to find what one is looking for! The upshot of this history (and similar ones in physics having to do with symmetry principles and the discovery of antiparticles) is that chemists can make true predictions about what sort of causal profile an element with a particular atomic weight could have whether chemists ever see examples of that kind of element or not. Chemists did discover examples of the predicted elements, but all that did was confirm Mendeleev’s prediction. And that certainly helps with our confidence that his prediction was correct. But confirming the truth of a prediction is not the same thing as the prediction being correct. He was correct in his prediction even if we never found out. For example, suppose I retrodict that Napoleon had ten thousand hairs on his head when he died. We will never find out if my retrodiction is correct or not. Nevertheless, I could actually be correct. So, there is a truth, an objective nature, a fact of the matter as to what a kind of element is and what its causal profile is before we ever confirm our guess or hypothesis as to what that nature in fact truly is and whether we ever do confirm it. The thing that we are confirming the existence of by finding examples, if we ever do, is the universal. The Aristotelian will likely respond by saying, quite correctly, that there currently are instances of gallium and there were instances of gallium before Mendeleev ever made his prediction that there existed just such a kind. The challenge for the Platonist is to prove that we need uninstantiated universals and not that we need instantiated ones. And if there are examples of gallium, then the kind of element gallium is is not an uninstantiated universal. But while that response is correct, it does not really touch the point being made. To see why, let us consider kinds of elements that have instantiations due only to being made by humans, in other words, elements that are produced only artificially. The first kind of element that was thought to exist due only to human production was, aptly named, technetium. It was predicted to exist by Mendeleev

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and examples of it were produced in the early twentieth century. However, naturally produced examples of technetium were found in the earth’s crust later in the twentieth century. The second such kind of element was plutonium, but naturally occurring examples of it were also found. At this time, the only kinds of elements that are now thought to have only artificially produced examples are the ones whose atomic numbers range from 95 to 118. But here is the idea: though all of those specific kinds of elements have been artificially produced by humans, they need not have been. Even if humans had never made any examples of these kinds of elements, they could have. The fact that they were in fact successful confirms that it is in fact possible to make the examples. But even if they had not successfully made any of those examples and confirmed that such kinds of elements exist and therefore could be instantiated, the natures of those kinds of elements exist. In other words, scientists can discover what kinds of elements can be instantiated whether those kinds of elements are ever instantiated or not. Finding, or producing, examples of those kinds of elements confirms that they were right. But they were right, regardless of whether they get confirmation of it or not. Therefore, they could only be right that that kind of element is scientifically possible, that is, possibly instantiated, if such a kind of element exists. And the reason that scientists in the seventeenth century were wrong to think that there is a kind of element as phlogiston was not that no examples of it were ever found or produced. The reason they were wrong to believe in phlogiston is that that kind of element does not exist. It does not exist because it is not scientifically possible. No such kind of element with the causal profile it was alleged to have had is scientifically possible. Just as if it is not in fact truly possible to produce, artificially or naturally, a kind of element that is a noble gas and has the same causal profile of phosphorus, then there exists no universal for it.5 Therefore, we may conclude, whether any universal is instantiated or not is irrelevant to whether it exists or not. It may be relevant to confirming that such kinds exist, but it is not relevant to whether the kinds exist or not. Another way to put the idea is that spatiotemporal examples or instantiations or manifestations confirm that a universal is possibly exemplified or instantiated or manifested, but examples or instantiations are in fact possible only if that kind of thing, that is, that universal, does exist. Whether or not any examples of technetium or plutonium or carbon or aluminum or gallium or copper or whatever are produced, naturally or artificially or both, the kinds of elements, that is, universals, which explain why it is possible for those examples to come to be already exist and will always exist. If that is correct, then we have a good reason for thinking that universals are not dependent on being instantiated. Moreover, if

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that is true, then we clearly have a good reason for thinking of universals as being independent of being instantiated. And if that is true, then, I think, we have lost our grip on how kinds or universals could be spatiotemporal, which opens the door to thinking of them as nonspatiotemporal, as Platonism would have it. My objection to the strong version of the principle of instantiation, then, is similar to the objection to the weak version. The objection to the weak version was that if universals come to be and pass away from moment to moment depending upon whether they are instantiated at that moment or not makes scientific knowledge of those universals impossible to have during moments when there are no examples because the object of knowledge, the universal, will not exist. But clearly scientists can know what the color white is even if Mick Jagger gets his way and all white objects are painted black, or even if all examples of bubonic plague are destroyed. Scientists can still know, or correctly hypothesize, during those times what that kind of disease is. With respect to the strong version of the principle, then, even if chemists never did and never will produce any examples or instantiations of the elements that only come into being artificially, chemists can still make correct predictions concerning what would happen if such examples were to be produced. So, they might correctly hypothesize that an earthly version of kryptonite is possible and because of that make sure that no examples of it are ever produced given how dangerous it would be. Therefore, just as the temporal instantiation status better not matter to whether a universal exists or not, the whole-history-of-spacetime instantiation status better not matter to whether a universal exists or not. A scientist can have knowledge or a correct hypothesis regardless of whether that universal is currently instantiated or not, or is ever instantiated or not. Being able to have that knowledge or at least be correct in one’s hypothesizing is an important part of scientific research. Some of that research results in the discovery of examples, which confirms the hypotheses, but confirming a hypothesis does not make the hypothesis true. It is the existence of the universal, whether confirmed or not, that makes the hypothesis true. Confirmation just confirms that we were right. It does not make us right. The contemporary Aristotelian’s insistence, therefore, that only instantiated universals are necessary for science is misguided. Though it is true that confirmation or confidence that a universal exists requires finding examples of it, the empirical discovery just confirms what was already the case: that the universal existed before we ever found examples of it or produced examples of it. Even if there are no examples anywhere in the entire history of a spacetime continuum, scientists are in fact able to discover that there could have been some.

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And in so doing, what scientists have discovered is the existence of a universal, which is not dependent on being instantiated, but is, instead, a completely independently existing thing. Contemporary Aristotelians, however, will not be convinced. They will say that my objection falls flat because the universals for unproduced elements are really just a difference of degree and not a difference in kind, for example, just a different range of quantities within a larger range of quantities and not a different kind of quantity (Armstrong 1986: 581). As such, the natures of any instantiations of any point, or any range of points, within a larger range of quantities can be figured out just by triangulation from the natures of the points or ranges on that continuum that are instantiated. In fact, that is very close to what Mendeleev did. Once he figured out that atomic weights and causal profiles varied periodically, he was able to triangulate from that pattern to guess correctly that there are kinds of elements in the gaps between the already discovered ones and in virtue of that periodic pattern of causal profiles what their causal profiles would likely be. However, the contemporary Aristotelian’s objection to my argument has to claim that the newly discovered or potentially newly discovered things are not really different kinds of things but really only different amounts of the same kind of thing. Specifically, they have to claim that the uninstantiated kinds of elements are really just more or less of the same kind of thing—a difference of degree— and not really a different kind of thing from what was elsewhere exemplified— which is what a difference in kind requires. In other words, the uninstantiated kinds of elements would have to be just different quantities of the same kind of thing and therefore not requiring any commitment to there existing a universal for that kind of thing were it a different kind of thing. That claim seems plausible only if chemistry, for example, is reducible to and fully explained by quantum mechanics, as some (Bensaude and Stengers 1996: chapter 5; Knight 1992: chapter 12) have argued. The idea is that elements can be explained as the total energy of a system, that is, the kinetic and potential energies, which can be calculated, in principle if not in practice, using Schrödinger’s equation, and therefore there is no real difference in kind between the “different” elements, just as there is no real difference in kind between the “different” colors as they are really just different amounts of electromagnetic radiation, and hence there is really just a difference in degree and not a difference in kind between the “different” colors. Therefore, there is no need for a plurality of universals for the different colors or the different elements when just one, for example, total energy, is sufficiently explanatory. That initially sounds plausible, but is it ultimately so?

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The issues here are complex. They have to do with the relation between the different sciences and whether some of them can be reduced to others or not. For example, can chemistry or biology be reduced to, that is, completely explained by, physics, or can psychology or sociology be reduced to biology? Though I do not find the arguments in favor of reductionism convincing, we can make progress in our argument with the contemporary Aristotelian just by showing that they themselves do not want to embrace the kind of reductionism required by their objection. The idea behind reductionism is that the so-called “higher levels” of reality are reducible to, or completely explained by, the “lower levels” of reality. For example, heaps of sand are really just a plurality of individual grains of sand. There is nothing more to being a heap of sand than just being a plurality of individual grains of sand. In general, then, reductionists claim that there is nothing more to a collection or aggregate of things than just those many particular things. Sociologists, for example, may appear to study social structures as if they were genuine things, but really, social structures are just aggregates of human beings. And psychologists may appear to study human beings, but really, human beings are just aggregates of organs and cells. And biologists may appear to study organs and cells, but really, organs and cells are just aggregates of organic molecules. And biochemists may appear to study organic molecules, but really, organic molecules are just aggregates of atoms. And nuclear physicists may appear to study atoms, but really, atoms are just aggregates of subatomic particles, for example, fermions and bosons. And potentially so on. If the contemporary Aristotelian wants to reduce the need for different universals wherever differences between apparent kinds is really just a difference in some quantity, then if chemical elements are really just quantum systems with more or less total energy, that is, the system’s kinetic and potential energies as measured by using Schrödinger’s equation, then the only universal one would need, according to this objection by the contemporary Aristotelian, is one: a universal for energy. And if colors are really just different quantities of electromagnetic radiation, then there is no justification for scientists to make any real distinctions between gamma rays, x-rays, the color red, microwaves, and radio waves. They are all just different amounts of electromagnetic radiation. Moreover, since electromagnetic radiation is really just varying amounts of energy, again, we would not need a universal for electromagnetic radiation either, but only this one: energy. Every spatiotemporal thing is really just different amounts of (potential and kinetic) energy.

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But if varying amounts of energy is the only thing that any spatiotemporal things can have in common, and every other apparent commonality is reducible to just differing quantities of energy, then the richness and usefulness of science goes out the window. That sort of extreme reductionistic framework will wipe away the explanatory power, that is, usefulness, of a great number of commonalities. In other words, just having Schrödinger’s equation does not help us understand why higher energy photons (e.g., x-rays) can cause cancer but lower energy photons (e.g., red light) cannot. Likewise, Schrödinger’s equation does not help us to understand why apparently different elements have the different causal profiles that they do and why some other apparently different elements have the same causal profiles that they do. The periodic pattern that those different elements seem to have would be completely mysterious as those “higher level” discoveries are not deducible from an application of Schrödinger’s equation (Scerri 2007: 243–45). Therefore, because different ranges or points on a continuum sometimes have different causal profiles, the differences are qualitative, that is, differences in kind, and not just quantitative, that is, differences in degree. Here is another way to put the point: sometimes a large enough difference in degree is a difference in kind (Anderson 1972). Take, for example, any of the familiar “slippery slope” fallacious arguments concerning being a heap, being bald, being wealthy, or being a person. One grain of sand is not a heap. Adding one grain of sand to that one grain of sand does not make those two grains a heap. Since adding one grain of sand to a non-heap cannot make a non-heap into a heap—and here is the slippery part of the argument—no matter how many grains of sand one adds, one will never get a heap of sand because adding just one grain of sand cannot make a difference in kind, going from the kind of thing a non-heap is to the kind of thing a heap is. We can also go the other way, that is, from a heap of sand with, say, one million grains of sand, if we take one grain of sand away, the heap of sand is still a heap. And so, if taking away one grain of sand cannot make a difference as regards whether a heap of sand is a heap or not, then no matter how many grains of sand one takes away, you will always have a heap of sand. Of course, both of those conclusions are wrong. If one has a million grains of sand, clearly one has a heap. And if one has just one grain of sand, then clearly one does not have a heap. Adding enough grains of sand or taking away enough grains of sand does make a difference, that is, a difference in kind. There are indeed differences in the quantities of sand, but sometimes those differences in quantities do make for a difference in quality, that is, kind: heap or non-heap.

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Suppose one has a full head of hair. Does pulling out one hair make one bald? Clearly not. So, no matter how many hairs one takes out of one’s head, one will never be bald. But that is not true. Take out every hair and one will be bald! Suppose one has a penny. Does adding one penny to that collection make one wealthy? No. One penny does not make a difference in kind from being poor to being wealthy. So, no matter how many pennies one adds, one will never be wealthy. Clearly that is not true either. And lastly, if a newborn baby human being is a person, then surely the day before being born it was a person. A day cannot make a difference between being a person and not being a person. After all, if it had been born the day before, it would have been a person. So, going back another day cannot make a difference. Therefore, since a day cannot make a difference between being a person or not, then, it is fallaciously claimed, the thing was a person from the moment it was conceived. But like the rest of the examples, something has gone wrong here as well. What is going wrong with all those slippery slope arguments? Clearly there is a mismatch between the scales of measurement. The scale of measurement one uses in determining a grain of sand is different than the scale of measurement one uses in determining a heap. Grains of sand are—pun intended—at a finer or smaller grain of measurement than heaps are, which are a coarser or larger grain of measurement. There is a mismatch. That is why a large enough difference in degree can be a difference in kind. More of the same kind of thing at a finer grain of measurement, then, can sometimes produce a different kind of thing at a coarser grain of measurement such that those different kinds of things, those different universals, cannot be deduced just by the addition or subtraction of those things at the finer grain. It is the atomic weight of the atoms integrated (not just added to) with the law of periodicity that helps get the different kinds of elements. We will be discussing these issues again in Chapter 6 when we get to the positive account of Platonism concerning both what nonspatiotemporal and spatiotemporal things are. For now, all that is important is that the discoveries by scientists of universals that may or may not be instantiated cannot be explained away as just a matter of a difference in the quantity of some already instantiated universal unless one is willing to limit oneself to the idea that there is only one universal. Contemporary Aristotelians are loathe to do so because they themselves see that it will do genuine damage to science, even if they are willing to reduce all “higher level” sciences to fundamental physics, which itself requires more than one universal, that is, more than one kind. Moreover, the contemporary Aristotelian in particular needs to agree with that conclusion because typically part of their motivation for putting forward

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an Aristotelian theory is the desire to provide for a middle ground between extreme reductionism and extreme inflationism. They do not want there to be just one universal, which would be too few, and they also do not want there to be universals for things that are not instantiated, which would be too many. They want there to be a moderate amount of universals. So while they are happy to reduce the need for universals for uninstantiated things, as well as universals for artificial things like chairs and tables, the vast majority of contemporary Aristotelians want there to be universals for all the different biological things (e.g., humans, dogs, cats, trees), as well as atomic things (e.g., hydrogen and carbon), as well as subatomic things (e.g., electrons and protons). Tables and chairs and other artificial things are usually thought of as being reducible to the “fundamental” non-artificial things. So while they are typically happy to talk about tables and chairs as existing in a loose way, when push comes to shove, what fundamentally exists are just the many things of physics and biology. That is how they get a world full of what they would call “substances” which are, fundamentally, particulars that have universals as non-particular parts, for example, particular human beings all have one and the same universal, humanbeing-ness, as a part. Every particular hydrogen atom has one and the same universal, hydrogen-ness, as a part. Every particular electron has one and the same universal, being negatively charged, as a part. We cannot reduce human beings to atomic things or subatomic things or, more to the point, just different amounts of energy. Therefore, as long as contemporary Aristotelians themselves do not want to be forced to embrace the kind of extreme reductionism that lies behind the objection we have been considering, they will be better off if they accept that uninstantiated universals can and do exist. Where the contemporary Aristotelian and the Platonist find common ground, though, is that both deny that there exist universals for things that cannot be instantiated. In other words, if both restrict the number of universals to things needed by science, then they both still avoid an extreme inflationary option. More specifically, if they both grant that there exist universals for what is physically possible, what is chemically possible, what is biologically possible, what is psychologically possible, what is sociologically possible, and what is politically possible, for example, that still allows them to deny that there are universals for what is logically possible but not scientifically possible. Again, we shall discuss that issue in much greater detail in Chapter 6 when we discuss the positive theory of Platonism. For now, all that it is important to see is that both contemporary Aristotelians and Platonists need to admit that universals in fact exist for any kind of particular thing that is scientifically possible whether there

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exist any instances or examples of those kinds of things or not. In order for scientists to be able to discover that it is true that things of that kind could exist, a universal for that kind of thing must exist and it is the existence of that universal that makes the scientists’ claims that such things are possible true (cf. Berman 2008: 227–29). And when scientists claim that other kinds of things are not scientifically possible, that is, cannot be instantiated or exemplified, what makes that claim true is that there exist no universal for that kind of thing.6 Therefore, since scientific activity needs the universals to exist regardless of whether they are instantiated, it is best to not claim that they are dependent on spatiotemporal particulars but are instead independently existing things. But what about the other issue which divides the contemporary Aristotelian from the Platonist, namely, whether universals are literally located in spacetime or not? Clearly universals that never are instantiated, but could be, are not located in spacetime. But what about ones that are instantiated? Are they located in spacetime? As we will now see, we will have a more naturalistic and scientifically respectable theory if we assume, surprisingly, that they are not literally located in spacetime, that is, that universals are best thought of as nonspatiotemporal things. First, as we saw before, it is not clear how coherent it is to believe that a spatiotemporal thing can be wholly located in more than one location. While it is perfectly compatible with science, or even essential to science, to believe that the parts of spatiotemporal things can be located in multiple spatiotemporal locations, it is hard to see how a scientist could take the notion of a spatiotemporal thing being wholly located in different regions of spacetime seriously. Second, it is not clear how compatible science is with the idea that a universal is literally a part of a spatiotemporal thing. The problem is that if the contemporary Aristotelian wants to maintain their scientific credibility, then they are going to have to explain how a spatiotemporal universal is a naturalistic, that is, scientifically respectable, part of a particular. It is going to be hard to see how spatiotemporal universals, thought of as parts of spatiotemporal particulars, are going to end up being something that any scientific inquiry is going to recognize as being naturalistic as opposed to “metaphysical” in a pejorative sense. With respect to the first problem, we saw earlier how Cody Gilmore tried to show us how we can think of a thing being wholly located in more than one region of spacetime using his thought experiment involving time travel. Suppose we figure out how to go back in time. And so, if time travel is for real, then I could go back to my high school years and explain to myself, better than my teachers did, why I should work harder on my assignments than I did. My twenty-firstcentury me could sit down in the twentieth century with my twentieth-century

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me and explain it in a way that makes sense! But in that case, both of me would be wholly located in two different regions of space even though both of me would be in the same region of time, for example, my high school years. Seems perfectly imaginable! But is it really? If we are genuinely to imagine this situation, we have to imagine that both of these people are wholly me. But if each person is wholly me, then given that I am a conscious thing, both of me would have to have my conscious awareness. I would have to be consciously aware both of me explaining why it is in my own self-interest to care more about learning the material and of me trying to understand that explanation. Remember, Gilmore is trying to motivate not that there are two of me, but that “both” of these people are really just one and the same thing. It is not clear that that is genuinely imaginable. I can imagine having those two experiences consecutively, but can I really imagine myself having both of those experiences simultaneously? Perhaps I just do not have a very good imagination, but such a situation does not seem quite as clearly imaginable as Gilmore needs to make it the case that his thought experiment accomplishes even the imaginability of something being wholly multiply located. Gilmore might reply that since universals are not consciously aware of anything, the problem I raise is irrelevant. But even if he were correct on that point, the more general problem remains: all he has minimally shown is that we can imagine that there could be two of the same object. But what he was supposed to motivate was not the idea that there can exist duplicates, but that a plurality of nonoverlapping objects could all be just one thing and not two instances of the same kind of thing. The quantum particles belonging to one kind of quantum particle might all have the same kind of intrinsic features—as do, implied by Gilmore, my twenty-first-century me and my twentieth-century me—but the particles are each different things from each other (cf. Ladyman, Linnebo, and Pettigrew 2012). Gilmore needs something stronger, namely, that there are not two of me, but that there is just one of me in the time travel scenario. So far as I can see, Gilmore has not motivated that claim with his thought experiment at all. But the second, and more serious, problem with thinking that universals are spatiotemporal has to do with the claim by contemporary Aristotelians that universals are literally spatiotemporal parts of spatiotemporal particulars. They are not, it is claimed, physical parts, for example, as organs are parts of whole animals, or subatomic particles are parts of atoms, or atoms are parts of molecules, or planets are parts of solar systems, and so on. So what kind of parts are universals? Given that universals are supposed to be different in kind from what contemporary Aristotelians think of as particulars, universals

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will be parts of particulars in a different way than particulars could be parts of other particulars. So, one could think of atoms as particulars and one could also think of molecules as particulars and the way in which atoms can be parts of molecules is going to be different than how universals are parts of particulars. For example, hydrogen atoms and oxygen atoms are particular things and so are water molecules. And a water molecule has hydrogen and oxygen atoms as its parts. But universals are not parts of particulars in that way. Contemporary Aristotelians use the study of mereology, which is the study of parts and wholes and how they relate to each other, to answer that question. Universals are, it is asserted, parts in a different way than physical particulars could be parts of other physical particulars. They are, it is said, “non-mereological parts.” However, since meros is the ancient Greek word for “part,” to say that universals are nonmereological parts of particulars is to say that universals are non-part parts. Non-part parts? Let us suppose, for the sake of argument, that that makes sense. What sort of part could they be? Well, if these universals, thought of as spatiotemporal things, that is, as spatiotemporal parts of spatiotemporal particulars, are more naturalistic, that is, scientifically respectable, than the Platonist’s idea that universals are nonspatiotemporal, then how would scientists think of parts? Presumably, physicists would think of parts, if they did, as physical parts (e.g., the particles or waves or both of a physical system), chemists would think of parts, if they did, as chemical parts (e.g., the protons, neutrons, and electrons of an element), biologists as biological parts (e.g., the cells and organs of an animal), and so on. Clearly, spatiotemporal universals thought of as parts of any of these things would not be physical, chemical, or biological parts. When one decomposes or analyzes or breaks apart some spatiotemporal thing using any scientific process, will one be able to isolate the spatiotemporal universal allegedly literally located in the thing one is breaking apart? No. There is no scientific process that could do that. The contemporary Aristotelian might respond that that is to be expected given that the universal is an “abstract” spatiotemporal part of the spatiotemporal particulars and not a physical spatiotemporal part. Fair enough, let us grant that also. Let us suppose, then, that universals are abstract, and not physical, spatiotemporal parts of spatiotemporal particulars. In other words, these abstract universals are literally located where and when the particulars are located. But no scientific process can separate these abstract parts from the other parts of the particular. That would make universals very unusual spatiotemporal parts, especially if one is trying to constrain one’s commitments to only scientifically

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respectable ones. Abstract spatiotemporal universals are, according to the contemporary Aristotelian, literally all around us in everything we see and touch, but no scientific process could isolate them from the other physical parts of all of those things. (cf. Simons 1994: 563) Universals are starting to seem rather spooky. But it gets even worse. Most contemporary Aristotelians think that for any thing to be naturalistic and thereby have any kind of scientific respectability, the thing in question has to be able to initiate a causal chain. This is called the “Eleatic Principle.” And if that principle is correct, then one of the benefits of thinking of universals as being spatiotemporal is that it allows them to have causal power and therefore, scientific respectability. Nonspatiotemporal universals are causally inert. Since they are not located anywhere in spacetime, they cannot cause something in spacetime to happen. (As we will see in Chapter 6, the Platonist argues that nonspatiotemporal universals do explain what is happening in spacetime but not by causing it or casually interacting with it.) Contemporary Aristotelians, then, would have to believe that there are causally efficacious (abstract) things literally all around us, but that we cannot isolate them by any scientific process. Is that supposed to give us a naturalistic, that is, scientifically respectable, theory? On the contrary, contemporary Aristotelianism seems rather to be some sort of supernaturalistic view. For example, it is fairly typical for people who believe in something supernatural to believe that their favored supernatural being is not discoverable using scientific methods but that it, nonetheless, can be wholly located anywhere and everywhere and can cause things to happen. It is hard, then, to see how contemporary Aristotelianism is anything other than a non-naturalistic, that is, nonscientific, theory. If, on the other hand, the contemporary Aristotelian denies that their spatiotemporal universals have causal power themselves, that is, they cannot be part of any causal chain either as a cause or as an effect, but instead, claim that it is the particulars that are the parts of a causal chain and that the universals just explain why the particulars have the causal power that the particulars do, then it will be mysterious how their being spatiotemporal in particular plays any explanatory role. The Platonists also think that universals non-causally explain why certain spatiotemporal things cause other spatiotemporal things, but they do not think that those universals are, or need to be, spatiotemporal themselves, as we will see in Chapter 6. Therefore, given the failure of both of these strategies, it is hard to see what good reason there is for us to believe that universals, the things that spatiotemporal things have in common, are spatiotemporal. Their being spatiotemporal makes them either non-naturalistic or unmotivated. It seems best, then, to think of universals as nonspatiotemporal (cf. the Appendix).

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5  What the Contemporary Aristotelian Should Do Due to the problems that the principle of instantiation, the requirement that universals be wholly multiply located, and their not being physical parts, has on contemporary Aristotelianism’s alleged naturalism, that is, scientific respectability, I conclude that it is not ultimately plausible to think of universals as being spatiotemporal things. We are still in need, then, of having some way of explaining how a plurality of spatiotemporal things can have some one thing in common such that perception, reason, and therefore science can be possible, as they clearly are. In the next chapter, we will consider another way people have tried to resist Platonism’s answer, namely, by denying that universals are ultimately discovered by us and are instead created or constructed by us. So yes, spatiotemporal things can have some one thing in common, but that one thing, that abstract thing, or concept, is created by our mental activity, by our abstracting it, and is not discovered by it. But before embarking on that examination, it is worth considering one more pushback from the contemporary Aristotelian. When pushed by these objections, the contemporary Aristotelian almost always responds as follows: Of course universals are not physical parts of spatiotemporal particulars. They are metaphysical parts of spatiotemporal particulars. Aristotelianism is a theory within metaphysics and not science. But you, the platonist, are thinking of universals as if they were things in the same sense of “thing” as the particulars. But that is a category error. Universals and particulars are in different ontological categories. Just as no one thinks of the shape of a house as if it is in the same category as the bricks, boards and mortar, which are the physical parts of a house. The shape of the house is literally located where the house is but it is not isolatable by any scientific process. The shape is merely the way the bricks, boards and mortar are organized, but the way those physical things are organized is not another thing in the same sense of “thing” as those physical parts are things. The universal is merely the principle which explains why those bricks, boards, and mortar are a house as opposed to just a heap of bricks, boards, and mortar. That is the real strength of aristotelianism. It can explain why those many things are, at a higher-level of organization, one thing, namely, a house. But the principle of organization is not another thing besides the bricks, boards, and mortar. It is not nothing at all, but it is not something either. Universals, or ways things are, are merely principles of organization.

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The import of their response, I think, is to mitigate their ontological commitment: universals are merely “ways things are” and not additional things. Mitigating one’s ontological commitments does seem to be a good way to go: one can get the same explanatory benefits but with a lower ontological cost (cf., for example, Armstrong 1997: 28–30 and Lowe 2006: 15, 18, 20, 90–91). In fact, the historical Aristotle thought that that was what he was doing when he tried to differentiate his own view from that of his teacher, Plato. And almost every contemporary Aristotelian, either implicitly or explicitly, accepts that move at some point in order to extricate their view from the problems we have raised above.7 We will examine that move and its theoretical commitments in Chapter 5. Let me briefly anticipate that view here. Aristotle did not think that Plato’s mistake was in believing in nonspatiotemporal universals or in believing in uninstantiated universals. Aristotle thought that Plato’s mistake was in believing that universals existed in the same sense of “existence” as particulars (Penner 1987: passim; Kung 1981). Plato thought that both spatiotemporal things and nonspatiotemporal things are both things in one and the same sense of “thing.” A thing either exists or does not, which explains why Plato constantly asked about anything whether it was “something or nothing.” Aristotle, on the other hand, thought that particulars and universals existed in different senses of “existence,” stated as “being is said in many ways” or what other people refer to as “the equivocity of being.”8 So, Aristotle thought of particulars as existing in “primary” or “fundamental” sense of existence whereas he thought of universals as existing in “secondary” or “derivative” sense of existence. This allowed Aristotle to grant that universals were real, and hence his realism about universals, but avoid what he thought were Plato’s metaphysical extravagances, specifically, in thinking that universals were additional things, as opposed to being merely universals. When contemporary Aristotelians make this same move, that is, by denying that universals are things in the same sense of “thing” as particulars, but that they are not nothing at all either, they are at that point adopting the classical Aristotelian view, which is, as we will see, a different ontological theory as it is not committed to the idea that universals are spatiotemporal. In Chapter 5, we shall take up the theory behind what I think is the best way to understand the theory behind the historical Aristotle. A minority of self-described Aristotelians think that they are putting forward classical Aristotelianism and many other thinkers implicitly rely on the classical Aristotelian view even while denying that they are. Regardless, we shall take up

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the theoretical commitments of classical Aristotelianism and see why, alas, it too fares worse than Platonism. To conclude, what spatiotemporal things have in common, and are the objects of scientific knowledge, are best thought of as being things that are not spatiotemporal. If we have scientific knowledge, then what we know are nonspatiotemporal things. But are those nonspatiotemporal things discovered by us or created by us? Let us now turn to that question.

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An Argument against Constructivism

1  Mind-Dependence as a Strategy As we saw in the last couple of chapters, perception, reason, and science based upon perception and reason about our spatiotemporal world seem to require that the spatiotemporal things have something in common, as against nominalism, and that those common things are not themselves spatiotemporal, as against contemporary Aristotelianism. But believing in the existence of nonspatiotemporal things is a hard sell. After all, they are not perceivable even in principle. It is one thing to believe in things that are not perceivable directly but only indirectly, as we see the evidence of electrons indirectly in a cloud chamber or Higgs bosons in the particle detectors of the Large Hadron Collider (LHC) at CERN, but if arguments of the previous chapters are correct, then the commonalities between spatiotemporal things will not be located anywhere making them not even indirectly perceivable. Historically and intellectually, the usual way to mitigate having to believe in unperceivable commonalities of spatiotemporal things is to focus on the fact that these commonalities can at least be objects of our thinking even if they cannot be objects of our perception. And if we grant that there do exist things that we cannot perceive but can only think about, then perhaps we reason our way to discovering these nonspatiotemporal things?1 Perhaps. But, it has not seemed and still does not seem plausible to many to think that we discover nonspatiotemporal things, as if they were “there” and existed before we ever thought of them. What has seemed to be more plausible to many is to claim, instead, that we should think about these nonspatiotemporal things, these abstract things, as created by our conceptualizing, that is, our abstracting, and not discovered by our reasoning. That, after all, seems more likely when it comes to abstract things such as concepts: they are simply the products of our conceptual activity and as such are somehow dependent on our minds. Before there were any minds, there could not

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be any concepts because there were no minds to think them up, that is, create them! Things that we discover, on the other hand, were there or existed before we ever thought about them. But abstract things could not have existed before anyone thought them up, created them, or made them. It seems more plausible to think that these abstract things come to exist by means of our conceptual activity after we perceive the spatiotemporal things. We create the abstractions in order to explain those spatiotemporal things to ourselves. Or so it seems. The first part of this chapter motivates and explains constructivism in a way that we can see why it has seemed plausible as another way of avoiding Platonism. After seeing what constructivism ultimately depends on for its plausibility, an argument will be presented in the second part of this chapter against that constructivistic foundation so that we can see why constructivism about anything—science, ethics, aesthetics, and even linguistics—is ultimately incoherent.

2  Constructivism: Mind-Dependence The root idea of constructivism is that our explanations of the spatiotemporal world are ultimately dependent on some person’s or some group’s mental activities such that the commonalities between spatiotemporal things turn out to be ultimately dependent on that mental activity. Constructivism is not just the view that some person’s or group’s mental activities are involved in coming up with or discovering the commonalities between things. If the commonalities between spatiotemporal things are at least non-spatial, as it seems best to think of them given the arguments in the previous two chapters, then of course those non-spatial commonalities will only be discovered by us if we use our reason. Non-spatial things cannot be perceived. So, if we are going to be able to think about those non-spatial commonalities, then our minds will have to be involved somehow. The key difference between constructivism and Platonism (and either sort of Aristotelianism) has to do with how mental activity is involved. The Platonists and the Aristotelians are realists and think that the human mind can discover and come to know those commonalities by reasoning about our perceptions. That is how our mental activity is involved. Therefore, the commonalities are independent of our minds. They exist independently of any mental activity in which we may or may not engage and existed before we ever do discover them using our minds as tools to do so. The constructivist, on the other hand, is not a realist about those commonalities and thinks that we do not discover those commonalities, but that we, instead, create them.

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The most natural way of expressing how something is mind-dependent is by simply stating that if there were no minds, then there would be no things that depend on them. Minds somehow ground or underwrite or sustain the existence of those things that depend on them. That is no different, at least at first, to any theory about any kind of “dependent” entity, which requires some kind of “independent” entity upon which the dependent entity depends. It is just that in the case of the commonalities between spatiotemporal things, the entities upon which they depend are our minds, either individually or collectively. The idea that a thing could be ontologically dependent on another thing is difficult to pin down because the term is used by many different authors to refer to different kinds of relationships. The most general way of putting any dependence is this, where something, x, would depend on some other thing, y, in some way: (D) x only if y. And consider the following examples: (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14)

Universals exist only if minds exist. Molecules exist only if atoms exist. Relations exist only if relata exist. Wholes exist only if parts exist. Descendants exist only if ancestors exist. Theorems exist only if axioms and rules of inference exist. Effects exist only if causes exist. Markets exist only if individuals exist. Biological organisms exist only if chemical compounds exist. Chemical compounds exist only if physical particles exist. Properties exist only if substances exist. Substances exist only if properties exist Spatiotemporal things exist only if spacetime exists. Spacetime exists only if spatiotemporal things exist.

The problem with this list is that all of these dependences cannot be explained in the same way and the differences between them make a difference. Let us try to unearth the ultimate motivations for believing (1). Suppose that it is true. What could the thought behind it be? If the constructivist is persuaded both that nominalism is false, specifically, that it is false that spatiotemporal things have nothing in common, and that universals, or concepts, or abstractions, or whatever the commonalities are called, are not perceivable, then it would

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make sense that it is we who create those ways of grouping the perceptible spatiotemporal things together and then impose those ways of grouping on the spatiotemporal things for the sake of having the spatiotemporal world make sense to us. We would not, then, be discovering those commonalities by perceiving them as we can only perceive the spatiotemporal things and not the things those spatiotemporal things have in common. That has to be true if the commonalities among the spatiotemporal things are not themselves located anywhere in spacetime (and we can only perceive things that are spatiotemporal). In other words, you cannot see what is (literally) not there. But we can create ways of grouping the perceptions we have of the spatiotemporal things. Therefore, if one thinks of a universal or a concept or an abstraction as giving the spatiotemporal particulars their identity, that is, as being the explanation for what all of these many different spatiotemporal things have in common, then without such mental constructions, particulars would just be indefinite, that is, no definite way. If one claims that universals are mind-dependent and are the things that give the spatiotemporal things their identity, then what one thinks is that the mind is itself somehow an identity-imposing device. How could that work? Well, if the mind has some physical structure to it, much like a cookie cutter has a physical structure, then when the mind comes into contact (via sensory input) with the external world, it structures that input into being a certain way, much like the cookie cutter structures the dough into being a certain shape. That could be explained purely physically, namely, that the brain, a physical thing, literally gives structure to the unstructured sensory inputs. As a contrast, the realist, that is, the theorist who thinks that the mind does not impose structure on the external world, would say, instead, that the mind came to have the structure-detecting neurons it did as a result of natural selection and thereby helps the organism survive in its environment given that it can detect the real structures, that is, the commonalities, of the external objects themselves. So let us be clear: constructivism commits its adherents to the idea that the sensory inputs do not have a structure or identity in themselves, or at least not one to which we can have any access. On the other hand, again just for contrast, if the identities of spatiotemporal things are mind-independent, as the nominalist, the contemporary Aristotelian, the classical Aristotelian, and the Platonist all believe, then our minds, that is, brains, would be structured as they are, as explained by evolution by natural selection, in order that they can detect the mind-independent identities already true of the spatiotemporal things. And instead of being identity-imposing devices, minds would be identity-detecting devices. If minds were just identity-detecting devices, then the external things

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would have to already have those identities. But as we shall see, there is a very compelling reason to believe, according to the constructivist, that such discoveries are beyond our mental reach. Before we see why constructivism might be forced upon us, we have to first examine the nature of the identities being imposed. Are these mental structures intrapersonally stable across time or not? If they are stable, why are they stable? If they are not stable, why are they not stable? Further, are these mental structures interpersonally stable or not? If they are stable, why are they stable? If they are not stable, why are they not stable? If these structures are stable, that is, stay the same across time, then why would that be? If one accepts that we, including our minds, are products of evolution by natural selection, then there is good reason to think that, if we have such stable structures, they were selected to provide some advantage for survival. But that cannot be presumed here because if we did, we would be making these structures identity-detecting devices and not identity-imposing devices. If there are mind-independent identities true of the external world, it would make sense for stable identity-detecting devices to have been selected for over time. Evolution only explains what it explains with a feedback loop given stable external environmental structures. For example, horizontal-edgedetecting neurons in the brain detect horizontal edges in our environments. If falling off a cliff causes death only randomly, then being sensitive to edges would not have been selected for. Detecting those kinds of things in one’s environment would be advantageous for survival if one’s environment has reliably that kind of thing. But if one thinks that the mind’s identity-imposing device is stable, then one is not allowed to think that it developed as a result of evolution by natural selection. If there are no mind-independent structures among the spatiotemporal world, then evolution is a nonstarter. Therefore, if the mind has diachronically stable identity-imposing devices, then it is not because having such things provides any advantage to the organism in having them. It would have to have them independent of the mind’s relation to the external world or any objective usefulness of having such a relation. Let us suppose that that is the case. It would then be nothing short of a miracle that any two people had structurally identical identity-imposing devices. If true, then there will not be any interpersonal sameness with respect to these devices. If so, then each person would be the measure of what is for them and it would be exceedingly unlikely that any two people could have the same measures, and hence, share a world. Clearly such a result would prevent anything like science from being possible, let alone apparently achievable. So we can safely put it aside

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given that we are examining different theories that aim to explain the objects of science. A theory that results in no shared understanding of the spatiotemporal world at all, as existentialism arguably does, but just billions and billions of worlds, each isolated from each other, is not a plausible theory if one is trying to explain the nature of science and how it, at least apparently, seems to be able to make progress on explaining how the world works, even if that explanation is only what we all agree on and not really true of the world independent of that agreement. As a second possibility, then, suppose each mind does not have its own unique diachronically stable identity-imposing device. Suppose each mind has only unstable identity-imposing devices. Even more so would that prevent the sharing of a world and therefore even more so would anything like science be possible. A third possibility would be that groups of people can share a world in virtue of their sharing their identity-imposing devices. If such is the case, then either these devices can change or they cannot. If they cannot, then we need some explanation of this fact within the constraint that the external world does not have mind-independent identities. The classic statement of such a view was given by Immanuel Kant in the eighteenth century. He argued, in effect, that all rational beings have the same kind of identity-imposing device and because his argument for that was, as he thought, purely nonempirical, devices such as the ones all rational beings have cannot change, that is, are diachronically stable. Hence, the way in which the universals are mind-dependent is that they are features of our rationality and not of the world as it is in itself. We shall discuss the Kantian view together with the next possibility as they both, at least, provide some way of comporting their theory with the possibility of scientific knowledge. The fourth and last possibility, then, is that groups of people can share a world in virtue of their sharing the same kind of identity-imposing device but that the kind of identity-imposing device they share can change over time. Such a view has a plurality of theories associated with it but we are going to group them all together as being some version of constructivism. Neo-Kantianism, pragmatism, constructive empiricism, cultural relativism, and others all aim to explain how the identity-imposing devices are constructed, maintained, altered, or discarded in one way or another by a group of agents that can form, that is, create, concepts and conceptual structures. The key common assumption of all of these different theories is that the kind of identity-imposing device we share is ultimately created by the agreements of those who make the agreements and are not ultimately due to some agreement-independent way nature in fact is.

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And it is ultimate because the constraints on the construction of the identityimposing device a group shares come from the group, via agreements they make, and not ultimately from nature itself. The way in which universals are mind-dependent on this view, then, is that they are non-spatial things ultimately created by our agreements, thinking of an agreement as a collective thought. So, though constructivism is committed to the existence of universals, the nature of those universals is such that universals are mind-dependent, that is, universals are created by the collective mental activity of some group of conceptualizers2. Let us take up the Kantian view first. This view achieves a degree of objectivity by making all the identity-imposing tokens all instances of the same identityimposing device type. So, even though all of the identities of spatiotemporal things, that is, the concepts, are imposed by each rational person’s mind, the kinds of identities imposed, that is, the concepts, are the same ones for all rational beings. And though these identities or concepts are all discovered, as Kant argued, discovering these concepts is a synthetic a priori discovery and not an empirical one, that is, the concepts are discovered based on a transcendental argument and not by making any observations. It is not possible to know if these universals or conceptual structures are really true of the world. What we discover is that these concepts are necessary presuppositions of our experience of the world. Given that stability and universality, a Kantian framework does give us a way to explain the apparent “objectivity” of science. So, on Kant’s view, science would not be an inquiry into the real nature of the world as it is in itself, as that is impossible, but would be, instead, an inquiry into the world-as-structured-by-our-rationality. The other kind of constructivism claims that the concepts through which we can experience the world as coherent and ordered “scientifically” are not the unchanging presuppositions of the nature of rationality, but instead, are ultimately the products of our agreements with each other about what we find acceptable at the time (cf. Wittgenstein 1953, 1958; Bloor 1976; Rorty 1979; van Fraassen 1980; Barnes and Bloor 1982; Sidelle 2002). These agreements about the structures we find acceptable at those times are what explains the spatiotemporal world at those times for as long as we find them acceptable. The theories differ as regards what counts as what we find acceptable, ranging from what is completely arbitrary to what gets called “empirical adequacy.” Underlying all of them is the idea that it is ultimately up to us, that is, depends on us, to stipulate (and not discover) what is going to count as acceptable as the best way to categorize or group or identify what the spatiotemporal things have in common. Crucially, those decisions are not ultimately constrained by anything that is independent of what we decide or to what we agree.

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3  Constructivism: The Nature of Mental States What motivates such restrictions on scientific inquiry? That is, what specifically limits, as it is claimed, our ability to inquire into the world as it is in itself? Why think that our intellectual inquiry about the world is restricted to the more limited world-as-structured-by-our-rationality or the equally limited worldas-structured-by-our-agreements? What, according to those constructivists, constrains our inquiry into the world around us? The limitation comes, ultimately, from a very plausible theory concerning how the mind interfaces with the world. It is a view whereby our minds can never be in a direct unmediated relation with the external world itself. Instead, all of our mental relations with the world are mediated. So we are, at best, only indirectly related to the external world. Getting the world as it is in itself in our minds is beyond our mental ability. We can only directly experience the spatiotemporal world or think about the spatiotemporal world as it appears or seems to us and not as it is directly in itself. But why think that we can never directly experience or think about the world as it is in itself and that we can only experience the world as limited by what our rationality allows or by what our more or less arbitrary agreements allow? The view is motivated by an alleged reductio ad absurdum: supposing that our mental relations with the external world are direct and unmediated entails two absurdities. First, if our mental relations with the world were direct and unmediated, then we could never think about nonexistent things, but that is absurd: clearly we can think about non-existent things. And second, if our mental relations with the world were direct and unmediated, then we could fail to know our own mental states, but that is also absurd: clearly we cannot fail to know our own mental states. As to the first, if our mental relations with the spatiotemporal world were direct, that is, unmediated, then given that we cannot have a nonexistent object in our minds if it does not exist, then we could never think about things that do not exist. But clearly we can think about things that do not exist! An atheist claims that that is exactly what theists are doing: theists are genuinely, truly, thinking that God exists, but, according to the atheist, thinking about something that does not exist. But if thinking is a direct, that is, unmediated, relation, then when there is nothing in the world for someone to be thinking about, that is, be related to, then that person is not able to think about it. Just as in physical relations with the spatiotemporal world: when one is eating nothing, one is not eating. One may be moving one’s mouth, but one is not in fact eating. Therefore, if the alleged thing one is experiencing

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or thinking about does not exist, then one could not be thinking about that thing. But, it is plausibly objected, we can truly have non-veridical beliefs, that is, we can truly have thoughts about things that—unbeknownst to us—do not exist. As to the second, suppose it is true that (1) I am eating some nacho-cheeseflavored tortilla chips and also suppose it is true that (2) those nacho-cheeseflavored tortilla chips = poison. It then follows from (1) and (2) that (3) I am eating poison. However, even if it is true that (1*) my daughter thinks that the Tooth Fairy is magical, and it is also true that (2*) I am identical to the Tooth Fairy, it does not follow that (3*) my daughter thinks that I am magical. She does not think that I am magical, though she does think that the Tooth Fairy is. And it seems quite reasonable to most people, and not just constructivists, for her to deny that she thinks that I am magical. After all, she does not know that I am the Tooth Fairy! And unlike in the eating case, where my knowledge of the nachocheese-flavored tortilla chips being poisoned does not affect the truth of (3), my daughter’s ignorance of (2*), namely, that I am identical to the Tooth Fairy, does affect the truth of (3*), specifically, whether she thinks that I am magical or not. It would be absurd to think that things that she does not even know about, for example, that I am identical to the Tooth Fairy, could have an effect on what she is thinking. Sure, things that she does not know about can have an effect on her life. But can things that she is not even aware of have an effect on what she is thinking? That seems absurd. We can only have things in mind, that is, in our thinking, about which we are aware! Is that not the essence of what thinking is, namely, what one is aware of? That which one is not aware cannot be in someone’s awareness or thoughts. So, if one claims that when we think about the world, we are thinking about the world directly, that is, unmediatedly, one is claiming exactly that absurd idea. Therefore, because we can truly think about things that—unbeknownst to us—do not exist and because we do not have things that we are unaware of in our minds, our mental relation with the world must be indirect at best such that when we think about the world, we must think about it and experience it mediated by our “ways of presenting” it to ourselves. And those “ways of presenting” the world to us are constrained either by the concepts our rationality provides or by whatever concepts we agree to use in thinking about “the world.” Kant thought of these “ways of presenting,” or mediary concepts, as fixed for all rational beings. The concepts of space, time, and causality are what make identifiable experiences of spatiotemporal things possible for us. Whether things in themselves (outside of our awareness of them) are really extended in space, exist through time, and relate to each other causally, we can never know. All

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we can know or experience of the external world, all we are able to know or experience, is that we can experience or know the world given those concepts, specifically, as extended in space and as existing through time and as related to each other in terms of cause and effect. Neo-Kantians, pragmatists, constructive empiricists, cultural relativists, on the other hand, think of these mediary concepts as capable of being changed by various processes. The differences in how the concepts can change does not matter as all share the same idea that the concepts—the things through which we experience the world—are not absolutely unchanging and that what they are is ultimately up to us and can be changed by us depending on whether we agree to change them or not. Common to both sorts of reality-as-mind-dependent theories is the idea that direct unmediated mental relations with the world are not possible. We humans can only experience or think about the world via or through or mediated by a conceptual structure, that is, a set of concepts. Given that assumption, there is no way for us to investigate the world directly, in itself, in order to see if those concepts are really true of the world as we are necessarily investigating the world as filtered or conditioned by those concepts. There is no way to bypass those concepts and investigate the world directly, that is, unmediated. As we saw above, the root idea driving constructivists (and others) is that ultimately we know what our own mental states are, whether those mental states are perceptual experiences like seeing red or those mental states are cognitive states like believing that it is raining outside (cf. Sidelle 2001). We are infallibly right about what our experiences and beliefs are such that if we say that we are experiencing red, then we are right, we are having an experience of red. And if we say that we are not experiencing red, then we are right, we are not experiencing red. And if we say that we believe that it is raining outside, then we are right, we do believe that it is raining outside and if we say that we do not believe that it is raining outside, then we are right, we do not. That is why it seems absurd to deny that someone can truly believe in something that does not exist. If someone claims that they do believe in some thing, then they are right, they do truly believe in that thing that—unbeknownst to them—does not exist. And if my daughter denies that she believes that I am magical, then she is right, she does not believe that I am magical even though I am the Tooth Fairy and she thinks that the Tooth Fairy is magical. Because she does not know that I am the Tooth Fairy, she can truly believe that the Tooth Fairy is magical and deny that I am magical. If someone honestly reports to themselves or to others that they are having a particular experience or that they believe something to be

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true, then we should accept that they are right about what they are experiencing or what they believe; it is true that they are experiencing or believing what they think they are. Thinking that I am thinking something makes it true that I am thinking that thing. Or, agreeing that we are agreeing to something makes it true that we are agreeing to that thing. And if, on the other hand, someone sincerely reports that they are not experiencing something or that they do not believe something, then they are right, it is true that they are not experiencing or believing what they do not think they are. In other words, people infallibly know what their experiences are or not, and what they believe or not, because their thinking it so makes it so. Likewise with groups—their agreeing that it is so makes it so. While we may not be able to know what is in fact true about the world in itself, according to constructivists, we can at least know what our experiences of the world are and what we believe about the world. Let us call that idea the TT-principle: (TT) If I think that I believe that p, then it is true that I believe that p and if I think that I do not believe that p, then it is true that I do not believe that p. For example, if the Archbishop of Canterbury reports or claims to us or to himself that he believes that God exists, then it follows that it is true that he believes that God exists. What makes him correct about what he believes? That he thinks that that is what he believes. Whether there exists a God in the world or not is irrelevant to the truth about whether he believes it. All that matters as regards whether he truly does believe that God exists is this: does he sincerely, that is, honestly, think that that is what he believes? As long as he is not trying to deceive himself or others, then his thinking that he believes that God exists makes it true that he does believe that God exists. Note well that the underlying assumption about our mental states is not just that we experience what we experience or we think what we think. The underlying assumption is that we are right about what we are experiencing or what we believe. It is only if we are right about what we believe that we can then justifiably affirm or deny the truth about what we do, or do not, believe. For example, when we affirm that we believe in something that—unbeknownst to us—does not exist, the claim is that we at least know what we are thinking even if we do not know whether what we are thinking is true or false about the world. To claim just that we experience what we are experiencing or that we believe

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what we believe is not to claim anything about being right about what we are experiencing or believing. And affirming truly that we are having a particular experience or not, or affirming truly that we are thinking something or not, requires that we be right about what we are experiencing or thinking. One thing that does not make us right about what we are thinking, according to the constructivist, is the world itself. If it was the world itself that made us right when we were right, then our mental states would have to somehow be directly, that is, unmediately, related to the world. For example, if what made it true that the archbishop believes that God exists is that God truly does exist in the world, then the archbishop could not truly believe that God exists unless God did in fact exist. But that is supposed to be absurd. Of course we can believe in things that do not exist. So, according to constructivists, what makes the archbishop right that he believes in God is not that God in fact exists, but simply that that is what he thinks he believes. What makes it true that one is thinking whatever one is thinking is that one thinks that that is what one is thinking. So, we may not know that what we are thinking about does not exist (e.g., as an atheist would describe the archbishop’s state of mind), but we can at least know what we are thinking (e.g., as when the archbishop affirms his belief in God; that is truly what he believes regardless of whether or not there is a God). His conception of the way the world is has God as a part of that conception. And the archbishop can know what his conception of the world is regardless of whether there is in fact a God outside of that conception or not. Therefore, what makes it the case that he is right about what he thinks is his thinking that that is what he thinks. His thinking that he believes that conception of the world makes it true that he does truly have that conception in mind. Likewise, if my daughter sincerely reports that she does not think that I am magical, then she is right that she does not think that I am magical. She knows what she thinks and what she does not think. What she thinks may or may not be true. But either way, she is authoritative when it comes to the contents of her own mind, both what is and what is not part of her conception of the world. Even people who accept Freud’s hypothesis that parts of our minds are conscious and parts are subconscious accept, by definition, that the TT-principle is true about our conscious thoughts, namely, that we know what we are consciously thinking (cf. Freud 2005). We may not know what we are subconsciously thinking—in fact, by definition!—but we do know what we are consciously thinking—again, by definition—as that is how the two are differentiated from each other by Freud and his followers.

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4  Why Are We Always Right about Our Own Mental States? For the sake of argument, then, let us suppose that the constructivists are correct and that the TT-principle is true. But why is it true, that is, what makes it true? Specifically, why is it true that our (conscious) mental states are truly whatever we sincerely report that they are? Why can we not be wrong about our own mental states? What ultimately makes that true? Here are our options: (R) the TT-principle is true because that is the way the world in fact is, that is, we have discovered that the TT-principle is true by nature and mind-independently, or, (C) the TT-principle is true not because of the way the world in fact is but instead because some mental activity made it true, that is, we made the TT-principle true by our thinking it so or agreeing that it is so and therefore, the TT-principle is true mind-dependently. If the former, then we discovered something true about the world in itself, namely, that given the way the world is, specifically, that given the way mental states in fact are in themselves, we have an infallible access to them. If the latter, then we did not discover anything about the world in itself, that is, we did not discover anything true about mental states in themselves. Rather, the TT-principle is true about our mental states because we agreed that it is. Obviously, constructivists cannot assent to (R). They cannot say that the TT-principle is true because that is in fact the way the world is for the simple reason that constructivists cannot admit that anything is true ultimately because that is the way the world in fact is. Why not? Constructivists think that the way the world in fact is is beyond our mental reach. We could never know that the TT-principle is true given the way the world is. We could never be right that it is true because we cannot, they claim, have direct access to it, only indirect access to it, that is, mediated by the concepts our rationality provides us independently of the way the world in fact is or by the concepts we accept as true whether they are the way the world is or not. The fundamental idea of constructivism is that it is impossible for humans to think about the world directly but only indirectly as mediated by the conceptual structure, that is, the concepts, produced by the mental activities of human beings. Therefore, the reason we are right about our own mental states cannot be because that is the truth about what mental states

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in fact are. So, it must be the case that if the TT-principle is true, then it is true because of (C), namely, that we agreed that the principle is true. Our agreeing that the principle is true makes it true. As an aside, one might think that if one were a Kantian that the TT-principle would be true not because anyone agreed to it or because that is the way the world in fact is. Instead, Kantians should claim that the TT-principle is true because that is what is true about the nature of rationality as discovered not by examining the world in itself, as that is not possible, nor just by our agreeing to it. They claim that there is a middle ground between those two options. We can, just by using reason itself, discover the conditions for the possibility of experience, which are the concepts through which we can have any experience at all. Therefore, the concepts, or universals, are mind-dependent but discovered by means of reasoning about rationality itself and not by means of reasoning about perceptions of the spatiotemporal world. However, and without getting into a detailed examination of a Kantian framework, the plausibility of there being this third way presupposes that there are in fact truths about the nature of rationality for us to discover just by reason alone. Why think that there are such empirically independent truths about the nature of anything? The Kantian idea is that reason itself requires that various empirically independent truths be true. On the other hand, that claim can only be true, if we presuppose, that is, stipulate, a particular theory about the nature of rationality. Neo-Kantians were, in fact, the first to question the Kantian claim when they argued that the kind of rationality Kant took for granted, one that any rational person could discover autonomously, that is, just by themselves, was false and that in fact, the nature of rationality was itself something that was produced, that is, the result of dialogue between people, and depended on what people in dialogue with each other accepted together. Regardless of whether the neo-Kantians are right or not, though, the same two options are in the offing: Is the nature of rationality the way it is in itself independent of any mental activity or is the nature of rationality the way it is dependent on the mental activity of one or more persons? If the nature of rationality is in fact the way Kantians think it is independent of what any mental activities making rationality that way, then they are committing themselves to (R). So, despite the claim of Kantians that they are putting forward a third way between these options, they are not in fact doing so, and their claim about what is in fact true about the nature of rationality is scientifically evaluable, that is, based partly on our empirical engagement with the spatiotemporal world.

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Here, then, is our question: Can (C) be the ultimate reason the TT-principle is true? Constructivists need it to be the case that the ultimate thing that makes one be right about one’s own mental states is not the way the world actually is but some mental activity of humans. The fundamental idea in every constructivistic theory is that what ultimately makes any mind-dependent judgment true is someone’s or some group’s mental activity, for example, my thinking-it-true or our agreeingit-true. That is what mind-dependence is. Remember, constructivism is not just that minds, and their mental activities, are involved. Realists, that is, anticonstructivists, think that minds are involved in figuring out what is objectively true about the world, but they do not think that that mental activity ultimately makes those truths true. The way the world in fact is ultimately makes whatever truths there are true. The constructivistic notion, on the other hand, is that some kind of individual or collective mental activity ultimately makes whatever truths there are true. For example, when someone says that “beauty is in the eye of the beholder,” the idea behind that thought is that each person, or each community, ultimately creates the standard or criterion for what counts as beautiful to that person or to that community. There exist no person-independent or communityindependent standards for what beauty is such that anyone or any community could ever be wrong when they judge something to be beautiful. The constructivist about the nature of reality as a whole as inquired into by science would say, then, that the concepts or standards for what an experience is or what kinds of things there are are ultimately up to whatever we agree that there are. The concepts through which we experience the world are not, according to the constructivist, discovered by the mental activity of reasoning carefully about our experiences, as a realist would suppose. No, the concepts that constitute our conceptual structure for understanding the world are created or constructed ultimately by means of our experience-independent mental activities. Even to those who think that “empirical adequacy” is what governs those agreements, it is still the case that what counts as being empirically adequate is up to what we agree that it is. Constructivism, then, requires that it be ultimately up to us to decide or stipulate how we will experience the world and thereby how we will categorize or conceptualize or organize those experiences. But is that true? I shall now argue that it is not even possibly true.

5  Constructivism’s Bootstrap Problem Constructivism suffers from a bootstrap problem. Less metaphorically, constructivists explicitly deny the truth of the very same thing that they implicitly

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have to accept as true. Specifically, constructivists explicitly deny that anything is mind-independently true but at the same time have to accept that something is mind-independently true. Let us now see why. Let us see why constructivism has a fatal internal problem by examining an example that is almost universally thought to be ultimately constructed and not discovered: traffic laws. Surely what we ought to do when we drive is ultimately up to us to decide. There are no objective traffic laws, for example, there is not an objective truth about which side of the street we ought to drive our cars on! So, what ought I do when I drive down a street? It does seem ultimately up to whatever we all agree we should do when we drive down the street. For example, suppose it is true in the United States that (1) I ought to drive on the right-hand side of the road. What makes (1) true? Why ought I drive down the right-hand side of the road when I am in the States? If (1) is not true in virtue of a natural law concerning the nature of roads and driving, which we discover by examining the spatiotemporal world, for example, then it is not the case that I ought to drive down the road on the right-hand side because (N1) if anyone is driving, then they ought to drive on the right-hand side of the road. We might think, plausibly enough, that certainly part of what makes (1) true, brutally over-simplifying, is that (C1) President Obama3 commands that people of the United States drive on the right-hand side of the road. Think of (C1) as the mental activity constructivists claim ultimately makes something true. Of course, the command is communicated by means of something that is said aloud or written down, which is a physical activity. But that is just a physical manifestation of the mental activity of commanding, which President Obama does by thinking it. However, (C1) is not sufficient for making (1) true, just commanded. What is wanted is an explanation of why President Obama’s commanding that we drive on the right-hand side of the road makes it true that we ought to drive on the right-hand side of the road. In other words, the fact that President Obama truly commanded something just makes it true that he commanded it. Our question is, what makes what President Obama commanded truly what we ought to do as opposed to merely truly commanded?

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I think that both constructivists and realists, that is, anti-constructivists, would likely agree that part of what makes what President Obama commanded truly what we ought to do is, again brutally over-simplifying, that (R1) President Obama has the right to make commands for the people of the United States of America. So, if (R1) President Obama has the right to make laws for the people of the United States of America and (C1) President Obama commands that people of the United States drive on the right-hand side of the road are both true, then it follows from the combination of (R1) and (C1) that (1) I ought to drive on the right-hand side of the road is true. So far, so good. But what about (R1)? What makes that true? How do people get the right to make laws? That discussion is the subject matter of political philosophy: What legitimizes (or justifies or grounds) political authority? We cannot delve into that discussion in any detail, but we do not need to do so. Our purpose is not to figure out what truly legitimizes political authority. We just need to see why mental activity cannot be what ultimately does so. That is, all we need to do is see why a constructivistic answer to that question is no good, despite the fact that it might seem, at first, to be the most plausible. Assuming that we are having our discussion in the context where political authorities are democratically elected, we probably think that it is false that military might justifies political authority. For example, if a military force invaded the country in which we live and demanded our allegiance, we would likely think that we ought to not give it and that we would be justified in resisting those commands, even if we ended up being killed in the process. So, we would reject the idea that brute force legitimizes political authority. Likewise, if George W. Bush declared that he is a descendant of King George III and that we all now have to do whatever he commands, we would reject that claim for many reasons but fundamentally because we do not think that bloodline legitimizes political authority. (We reject monarchy as a legitimate political system.) Likewise, if Jeff Bezos declared that since he is the wealthiest American, we have to do

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whatever he commands, we would reject that claim fundamentally because we do not think that wealth legitimizes political authority. (We reject plutocracy as a legitimate political system.) Instead, we think that only the consent of the governed legitimizes political authority. (We accept, then, democracy as the only legitimate political system.) If so, then it seems as if (R1) is made true by the fact, again brutally over-simplifying, that (A1) the majority of the people of the United States agree that Barack Obama has the right to make laws for the people of the United States. But, as (A1) is an agreement, or collective will, can it be the thing that makes (R1) true? The constructivist will claim that it is. But a realist will think that as such it cannot all by itself make (R1) true. Why? (A1), if true, is what makes (R1) a truly agreed upon thing, the realist will point out, but, it does not make what they agreed to true. In other words, though (A1) makes it true that (R1) is agreed to, we need to know more than that according to the realist. We need to know what makes what was agreed to true, and not just that it is truly an agreement. As a parallel, you could say that our handshake makes it true that we agreed that I am 5’9” tall. But what makes what we agreed to true? (Clearly not just our handshake, but something else, namely, my being 5’9” tall. If I am not 5’9” tall, as I am not, then despite it being true that we agreed that I am 5’9” tall, what we agreed to, namely, that I am 5’9” tall, was not true.) In exactly the same way, we need something else in addition to (A1) to also be true. The realist thinks that it needs to be the case that the democratic theory of political authority is true as well, for example, (DTA) if any group G agrees that person S has the right to make laws for G, then for so long as G agrees that S has that right, S has the right to make laws for G. So, if (DTA) is true and (A1) the majority of the people of the United States agree that Barack Obama has the right to make laws for the people of the United States of America is true, then (R1) President Obama has the right to make laws for the people of the United States of America

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is true. (Both (DTA) and (A1) need to be true if (R1) is going to be true.) Therefore, it is not the case that an agreement, or act of collective will, namely, (A1), is sufficient to make it true that anyone has the right to make laws, as in (R1). In addition to that collective mental activity, that vote, it also has to be the case that that kind of collective mental activity, the kind of agreement, that is, a vote, makes what is voted true. And for that, we need a principle that is a conditional. If people do this sort of thing, then what they do truly makes this other sort of thing. That is even true when it comes to making agreements. It is not the case that just shaking hands is sufficient for making what was done truly an agreement. It also has to be the case that if people shake hands, then they are making an agreement. What legitimately counts as an agreement is determined by what the nature of an agreement is, not simply some mental or physical activity. So, yes, people do need to shake hands, or vote, or whatever, but doing those things alone is not sufficient. In other words, even if mental activity is necessary for there to be any thoughts or agreements, what makes what is thought true or what was agreed to true is not just that there were those mental activities. There also has to be a principle, a conditional principle, that is mind-independent and is the thing that makes that mental activity be true. It has to be mind-independent because any mental activity will be insufficient for making the thinking true. We need a mind-independent principle to make any mental activity true. To see that, let us push on with our example concerning traffic laws. So, we can ask: What makes (DTA) true? There are two possibilities. (DTA) can be true either due to the way the world in fact is, which we have discovered, or due to some mental activity making it so. If the former, then it is true that I ought to drive on the right-hand side of the road, ultimately, because of something that is true given the way the world is, namely, (DTA). But if (DTA) is itself true by virtue of someone’s mental activity, then someone’s say-so is needed to make (DTA) true. How about the following: (FF) We, Founding Framers, agree to (DTA). But how does (FF) make (DTA) true? Certainly the fact that the Founding Framers agree on (DTA) makes (DTA) truly agreed upon. But we need to know what makes what they agreed upon true? It would have to be something like this: (FFA) If any Founding Framers agree to some principle of authority, then that principle is true. But now we can ask, what makes (FFA) true? Is it true by nature or by some mental activity?4 Either way, the point is now clear: thinking something to be true

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cannot make that thing true all by itself. In order for a mental act or activity to make something true, there also has to exist some mind-independent principle,5 some “if-then” principle, that is the thing that is making the thought true, if it is true.6 Constructivism about anything, then, suffers from a “bootstrap” problem. It has to presuppose some sort of mind-independent principle that gets the mental activity in question off the ground, as it were. Constructivism’s claim that some sort of mental activity ultimately makes anything true, therefore, falters. A mental activity all on its own cannot make anything true. The problem for constructivism about any domain is that it has to presuppose a mind-independent truth about its explanation of some truth while denying that anything is mind-independently true. That problem applies to constructivism’s core idea and so whether it be applied to science or to ethics or to aesthetics or even to linguistics: the truths within those or any domain, cannot be ultimately created by anyone or any group’s mental activity. With respect to the idea that anyone’s thinking something is true can make it true, or that any group’s agreeing that something is true can make it true, if the view is to be able to get off the ground and explain the truth of anything in any domain, it has to be mindindependently true that someone’s thinking something is true makes what they think to be true or it has to be agreement-independently true that when a group agrees that something is true, that agreement makes what they have agreed to be true. Just as the nature of agreement has to be true of what we are doing in order for what we are doing to be truly an agreement, what the nature of thinking is has to be true of what we are doing in order for it to be true that we are thinking. But since constructivists deny that there are any mind-independent truths or agreement-independent truths, then they will not be able to get their view off the ground, that is, offer it up as an explanation of what makes something true. They, as with everyone else, cannot pull themselves up off the ground just by tugging on their bootstraps (or shoelaces)! Applying that insight to constructivism about our relation to the external world, even if we do construct or create the concepts for our experiences and beliefs, such as the concepts of space, time, causality, redness, God, or whatever, our creating those concepts do not create what is true about our experiences or beliefs. What makes those concepts true about our experiences or beliefs can not be just that we created them, for that just makes them created. What makes whatever concept we create true of any experience or belief is that the concept we (let us grant) create does in fact truly explain our experience or belief. A concept in fact truly explains our experience or belief, then, is due to the way the world in fact is, for example, that we are in fact having an experience of something

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extended in space, or of something existing through time, or something being related to another thing causally, or something being red, and that requires that those things really be those ways. Therefore, to the extent that the concepts we create are right about the experience or belief we are having, then to that extent we are right about our own mental states. But to the extent that the concepts we create are wrong about the experience or belief we are having, then to that extent we are wrong about our own mental states. For example, to the extent that I am right about what brown in fact is, to that extent I can be right that I am having a brown experience, but to the extent that I am wrong about what brown is, as when I mistakenly identify the color of these dark taupe kitchen cabinets with the color brown, to that extent I am wrong that I am having a brown experience. Or, to the extent that I am right about what love in fact is, to that extent I can be right that I am having a loving experience, but to the extent that I am wrong about what love is, as when I identify the feeling of lust I am now having with the feeling of love, then to that extent I am wrong that I am having a loving experience. The idea is that the mind-independent truth about what the color brown is, what color dark taupe is, what lust is, what love is, what the color red is, what space is, what time is, what causality is, what God is, what gold is, what knowledge is, and so on and so forth are the measures, the criteria, even of my own experience. Whether I know what my own experience is or not, then, depends on my being right about what knowledge is. To the extent that I am wrong about what knowledge is, then to that extent I will be wrong that I know what my own experiences or beliefs are. To say that I at least know what I think my experiences are just pushes the same issue back one step. What makes it true that I know what I think my own experiences and beliefs are? It cannot be simply that I think that I know what my own experiences and beliefs are. What is required, as we have seen, is that what knowledge in fact mindindependently is is true of my mental state about my mental state. And whether it is true of my second-order mental state, or my meta-mental state, depends not on another mental state, my thinking it so, but on the mind-independent nature of knowledge being true of my mental state. Therefore, when we reason, when we abstract, when we conceptualize, what we are doing is getting the mind-independent universals in mind by virtue of which we are right or wrong about our own experiences. Our reason allows us to get into a mental relation with those nonspatiotemporal things, that is, those universals. It is not, as some have argued, some special mysterious mental faculty (cf. Gödel 1944). It is just plain boring old reason. When we use nondeductive reasoning, for example, induction and abduction, we are

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discovering those nonspatiotemporal things. We infer from many perceptual experiences, our evidence, to either generalizations or explanations. When we infer from seeing thousands of pea plants reproduce in a particular way that we are going to keep seeing that in the future, we are coming into mental contact with a generalization which itself is not perceived. The instances or examples of pea plant reproduction are observed but the generalization that we are going to see the same kind of thing in the future is not observed. Nevertheless, we have that unobserved thing in mind due to our inductive reasoning. And when we infer from seeing thousands of pea plants reproduce in a particular way that genes are the explanation for that happening, we are coming into mental contact with a thing that is not perceived, namely, the nature of genes. The manifestations are perceptible and confirm our explanations, but what they are manifesting is not perceptible but only intelligible, that is, only accessible by virtue of our reasoning when we reason abductively. In general then, claiming that it is true that the ground of some truth is the mental activity of someone or some group presupposes that that truth is not true because of the mental activity of anyone or any group. The constructivist has to accept the idea that even truths involving mental activity cannot ultimately be true due to any mental activity. Therefore, the claim that the concepts we organize our experience by cannot be ultimately mind-dependent. The concepts, or universals, have to be ultimately what they are, independent of any minds. So, we can discover those concepts, or universals, with the help of our mental activity, as when we have perceptions and then reason about them, but those concepts, or universals, cannot be what they are ultimately due to our, or any, mental activity. They have to be what they are, instead, independent ultimately of any mental activity. The activity of abstraction is really, then, just our reasoning about what those concepts in fact are. So when we limit our thinking about our perceptual experiences to an aspect of that experience, we are not creating those aspects. We are, instead, discovering them. And to the extent that we discover what universals, which are those aspects, in fact are, to that extent we can even know what our own experiences in fact are. In sum, even though mental activity is required for us to be able to know and think about the nonspatiotemporal universals, mental activity is not the ultimate ground of those universals (cf. the Appendix). We have access to them by using our minds, but our thinking about them is not constrained by what we are aware of. We can have more in our minds than what we are aware of, just as when we eat things that are, unbeknownst to us, poisoned, we are eating poison. So, if we can

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be wrong about what we are thinking, then we can think about the world in itself, that is, we can have the world as it is in itself in mind. How else could genuine scientific progress be possible anyway? It could not. We have to be able to think about things that we do not fully know. We need to be able to have the world as it is in itself in mind. So, when we reason about our perceptual experiences of the world, we discover the commonalities among those spatiotemporal things. That is, we discover the nonspatiotemporal universals that explain those experiences. Before we examine Platonism concerning those nonspatiotemporal universals, we have to eliminate one last way that philosophers have tried to avoid the Platonic explanation. It was proposed by Plato’s most famous student: Aristotle. Aristotle’s theory, though, has been largely ignored due to the medieval misinterpretation of it. What is that last stopgap measure? Aristotle argued that universals are nonspatiotemporal and discovered by our thinking but he also claimed that these mind-independent nonspatiotemporal universals exist in a different sense of “existence” than spatiotemporal things. To think that universals and particulars exists in the same sense of “existence,” a classical Aristotelian will say, is to commit what is called a “category error.” Since spatiotemporal things and nonspatiotemporal things exist in different senses or modes of existence, we cannot group them together. The reasons for adopting such a view are very powerful and we need to examine that classical Aristotelian theory before we can at last fully explore Platonism as the best explanation of the objects of science.

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An Argument against Classical Aristotelianism

1  How Aristotle Differed from Plato The last way that philosophers have tried to avoid committing themselves to Platonism was originally put forward by Plato’s most famous student: Aristotle. The view most often associated with him, which we considered in Chapter 3, was not, I could argue if interpretation were the goal of this book, put forward by him. What Aristotle actually thought, I submit, was this: (i) he agreed with Plato that nominalism was false; (ii) he agreed with Plato that the commonalities between spatiotemporal things were neither located in spacetime nor dependent on being instantiated; and (iii) he agreed with Plato that those commonalities were not dependent on any minds to create them. But (iv) he disagreed with Plato on the “ontological status” of universals as well as on the nature of spatiotemporal particulars, which he called “substances.” Specifically, Aristotle thought that universals exist—and so he is a realist—but in a “lesser” or “diminished” sense of “existence” and that spatiotemporal particulars have essences, which explain their being unified, as well as accidents, which explain how a substance can remain the same thing even while changing. We shall not discuss Aristotle’s essentialism about spatiotemporal particulars in this chapter, but only his alternative way of being a realist about universals. The view, which we shall call “classical Aristotelianism,” is attractive because it provides us with a way to get all of the same explanatory benefits of realism but for a lower ontological cost. As I have said before, who does not love a bargain! The question for this chapter, then, will be this: Do all existent things, both spatiotemporal and nonspatiotemporal, have some one thing in common or not? A Platonist thinks that they do, that is, all existent things, whether spatiotemporal or nonspatiotemporal, have something in common, namely, the universal being. All existent things exist in one and the same sense of “existence” because for a Platonist, there is only one sense of “existence,” that is,

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“being” is univocal. Aristotle, on the other hand, thought that spatiotemporal and nonspatiotemporal things do not have something in common. There is “no genus of being” (cf. Aristotle’s Metaphysics III.3-4, IV.1-2, VII.1, XIII.4, 9). Spatiotemporal things and nonspatiotemporal things are categorically different as things. As our goal is just to examine the theoretical positions as explanations in order to see which of them is the best explanation for the objects of scientific knowledge, namely, those nonspatiotemporal commonalities or universals, we will not engage in textual exegesis of Plato’s and Aristotle’s works. Doing so would be a different project. A worthwhile project, but not the one in which we are engaged. In the end, though, despite the attractiveness of the classical Aristotelian view due to its vast explanatory power, it has an internal problem that will render it not ultimately acceptable as an alternative to Platonism. As we shall see, classical Aristotelianism is self-referentially incoherent, that is, it turns out to be meaningless if true. But before getting to that point, let us first motivate and explain the view in order to see just how powerful it actually is.

2  Classical Aristotelianism Platonism is committed to the idea that nonspatiotemporal things are things in the same sense of “thing” as spatiotemporal things. For the Platonist, there is only one sense of “being” or “being a thing.” All beings or things are beings or things in the same sense. There is not a fundamental sense of existence as opposed to a derivative sense of existence. All things, which exist, exist at the same level of reality. There is only one level of reality. The Platonist is what gets called an “ontological monist.” Spatiotemporal things and nonspatiotemporal things are different kinds of things in the same way that dogs and cats are different kinds of animals but are both animals in the same sense of “animal.” The classical Aristotelian, on the other hand, thinks that spatiotemporal things and nonspatiotemporal things are not just different kinds of things, as if they had anything in common as things, but are things in different senses of “thing” such that they belong to different categories. If things belong to different categories, then comparing them is meaningless as they have no thing in common in virtue of which to compare them. Believing in different categories of existence, where the things in those different categories cannot be compared with each other, that is, cross-categorically, in addition to believing in different kinds of things, where things in those different kinds can be compared with each other, is the essential feature of a classical Aristotelian view. The classical

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Aristotelian is what gets called, nowadays, an “ontological pluralist” (cf. Turner 2010, 2012; McDaniel 2009, 2010, 2013, 2017). Those different categories of existence are labeled in different ways: sometimes as different types of existence and sometimes as different levels of reality. Perhaps the most perspicuous way of keeping them separate is by calling the categorical differences different logical types and the non-categorical differences, which can be compared meaningfully, different natural kinds. But why opt for pluralism over monism when it comes to the nature of existence? In other words, why think that there are different logical types in addition to there being different natural kinds? It definitely seems, at first sight, quite opaque and bizarre. As we will see, the reasons for doing so are numerous and quite attractive indeed.

3  The Explanatory Benefits There are at least six related reasons why someone might adopt the classical Aristotelian view and therefore be an ontological pluralist.1 First, it is a way to mitigate one’s commitment to the existence of universals in addition to particulars. That was in fact Aristotle’s own reason for first putting the view forward. Second, again as Aristotle thought, it is a way to explain why particulars are unified things. Third, it is a way resolve the mind-body problem. Fourth, it is a way to block infinite regresses. Fifth, it is a way to mitigate one’s ontological commitment to the existence of intensional objects in addition to extensional objects. And sixth, it is a way to mitigate one’s ontological commitment to normativity in addition to descriptivity. Let us examine these six reasons in turn. First and foremost, if one accepts that nominalism is false, that is, that there is more to reality than just the spatiotemporal things, specifically, that in order to explain the commonalities between spatiotemporal things, that is, the spatiotemporal particulars, one must expand the kinds of things one believes in to include some additional things, namely, the nonspatiotemporal things, that is, the universals, then believing in universals as well as particulars seems extravagant. It just seems to be having to go too far. It is too extreme. It is largesse. It gives us a bloated ontology. It would be better, it is thought, to have a more lean ontology. That is, it seems to be better to have to believe in fewer things on one’s list of existent things. But since nominalism does not have the things on its list of existent things that make perception, reason, and therefore scientific explanation possible, as we saw in Chapter 2, we do need to commit ourselves to universals in addition to particulars. Spatiotemporal particulars,

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all on their own, cannot do the job. On the other hand, if we can somehow lessen that commitment to universals by claiming that universals exist only in a lesser or diminished sense of existence, merely as universals and not as fullfledged other things, then perhaps it will not be so bad. After all, if we understand universals merely as the ways particulars are—in other words, adjectively or as mere modifications of things—then universals will not be another thing. They will just be the ways things are. In other words, suppose one is convinced that universals are needed for our being able to explain perception, reason, and scientific knowledge. Then universals cannot be nothing at all, otherwise one will not have something that explains the commonalities of spatiotemporal particulars, which are needed for that explanation. But, it also seems odd to think of universals as being things, like you and me are things. We, and other spatiotemporal particulars, are fully real and fundamentally exist. The nominalist gets at least that much right. But being human, for example, seems to be merely the way we are and not another thing besides us, at least not on the same “level of reality” as us. If they need to exist, as it seems that they must, then let us just admit that they exist in a lesser sense of existence. A universal is not a thing, but it is not no-thing either. It is merely a universal. That “merely” is a way of indicating that we are mitigating, but not eliminating, our commitment to its existence. (cf. also Simons 1994: 565) The benefit of doing so is plain: we will get the same explanatory power, that is, we can still explain how perception, reason, and science are possible, but for a lower ontological cost. Universals, that is, nonspatiotemporal things, will exist, but in a lesser sense of existence, thereby not having to count as additional things in the same full sense of existence in which spatiotemporal particulars exist. That elegantly solves the worry about having a bloated ontology. It gives a nod to the nominalist while still being a realist about nonspatiotemporal explanatory entities. And since nonspatiotemporal things exist in a lesser sense of existence, you do not have to add them to your list of existent things, as if nonspatiotemporal things were comparable as things to spatiotemporal things. Nonspatiotemporal things are categorically different as things than spatiotemporal things. The latter exist in the full-blooded fundamental sense of existence and the former only exist in lesser or diminished sense of existence. As far as the second problem which classical Aristotelianism also elegantly solves, the same reason for thinking that existence is not univocal also helps us explain how spatiotemporal things can be unified things and not heaps of things. The problem to be solved is this: if, as a Platonist thinks, for example, a sculpture is both a sculpture and a piece of marble, then that one thing will be

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at least two things: a sculpture and a piece of marble. But that thing there seems, intuitively, to be just one thing: a marble sculpture. How can that common sense intuition be explained? The ontological pluralist can do so elegantly. If the material aspect of the thing, its being made of marble, and the formal aspect of the thing, its being a sculpture, are not both things in the same sense, then they can fit together to be one thing. The idea is that, initially, the piece of marble is a thing. But then, a universal—for example, being a sculpture, which is not another thing added to the marble—is merely a way of transforming the piece of marble into a different thing, much like a mathematical function, for example, x2, takes you from one thing, the number 2, say, to a different thing, the number 4. So, it is not the case that the number 2 is part of the number 4. The number 2 and the number 4 are each just one number. Just as the word “cat” is not part of the word “cattle,” as they are both simple words and not compound words, the piece of marble is not another thing that is part of the sculpture (Cf. Quine 1943: 114; 1961: 140). According to the classical Aristotelian then, universals are ways of going from one thing to another thing. So, when Michelangelo sculpts the piece of marble, a thing itself, into the David, there is a different thing there and not an additional thing. Michelangelo does not increase the number of things that exist by engaging in sculpting. He changes the one thing into another thing by means of his understanding of what a sculpture in fact is. Therefore, the elegant idea is that universals are not additional things that get added to the material things. They are merely ways that material things are formed or transformed. Another way to see the power and elegance of that explanation is by looking at how a plurality of things at a “lower level” of organization can be one thing at a “higher level” of organization. Consider a human being. A human being is one thing, but it has a plurality of material parts, for example, organs and a skeletal system. Why is that collection of organs and a skeletal system one thing? It seems to be a heap of things. According to the classical Aristotelian, the universal, being a human, is not another thing added to that collection of things. It cannot be another thing added to that collection because then we would need to know what unifies that new collection, that is, what unifies the organs, the skeletal system, and the universal being human? Instead of thinking of the universal, being human, as another thing, added to the organs and the skeletal system, the universal is thought of, instead, as an organizing principle. An organizing principle is not another thing besides the organs and such. It is merely that which organizes, that is, unifies, all those things into being just one thing, namely, the human being. The same explanation can be applied to molecules, which have atoms as their parts, or any complex unified thing. The parts of a complex thing

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are not themselves other things. The universal is that which unifies all those parts into being just one thing: the human being or the molecule or whatever. If the parts of a thing were other things, then a human being or molecule, which seems to be just one thing, would be a heap of things and not just one thing. The classical Aristotelian is able to explain why human beings, molecules, and other complex things are really just one thing and not a heap of things. But of course, this only works if the universal is not another thing that is added to the parts as if it were just another thing. That would just enlarge the heap of things by one thing. Therefore, the universal has to be merely a unifying principle where unifying principles are not thought of as things. They are not nothing at all, but they are not something either. They are merely unifying principles. Perhaps another way to understand what that transformation or unification amounts to is by thinking about organization or unification not just at a time, or synchronically, as we have just done, but across time, or diachronically. Humans have often wondered what their own minds are. Are minds some other thing in addition to their bodies? Could a mind be a spirit or some other kind of nonmaterial thing in addition to a material body? The historical Plato and Descartes were two of the more famous philosophers to argue that the mind or soul is in fact another thing besides the body. They were mind-body dualists, that is, bodies are things and minds are things and they are two different kinds of things as one might think that dogs and cats are two different kinds of animals. Others, such as Hobbes, in the seventeenth century, and U. T. Place, in the twentieth century, have pushed back against such a view and argued that the mind is really just some part of the body itself, be it the brain or the some other organ in the body (cf. Hill 1991). They did not see the need to believe in minds in addition to bodies, contrary to the dualists, who did. The standard problem for dualists has been the explication of how a mind can cause a body to move. That is, how can an immaterial thing push on or force a material thing to change direction as when I think to myself to raise my right hand and then my right hand moves up. How did my thought, an immaterial thing, cause my arm, a material thing, to move? That problem has been intractable for dualists and is why dualism is not a popular view among people who study the mind, namely, cognitive scientists together with philosophers of mind, neuroscientists, linguists, and some computer scientists, despite how popular the view is with people who are not experts. On the other hand, the standard problem for monists, namely, those who identify the mind with some body part such as the brain, is the difficulty in explaining why the mind seems to be different between when humans are alive and when they are dead. The body part, for example, the

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brain, is still there but the mind no longer seems to be. The moment after death, the brain has not changed its material in any way whatsoever, but the mind is gone. What to do? The classical Aristotelian can provide, again, an elegant solution (cf. Ryle 1949: chapter I). The mind is not another thing besides the brain, say. Nor is the mind just the brain. Rather, the mind is merely the functioning of the brain. The way the brain functions across time is the brain’s being mindful. If the mind is not another thing in addition to the brain, then we do not have to explain how those two different things interact. If the mind is not just the brain, then we can explain why the dead person’s brain is not mindful: it is not functioning. So, the brain matters to someone’s mind but their mind is not the same thing as their brain. The mind is not another thing but it is also not nothing at all. It is merely the way the brain functions. It exists, but in a lesser sense of existence. Mindbody problem? Solved. A more abstract problem, which again, the classical Aristotelian can elegantly solve, concerns infinite regresses. Suppose it is the case that every red thing is red because of its relation to the universal redness. In other words, the nature of redness explains why each thing is the color that it is. (Not: how it came to be red, but why it is true that the thing is a red thing.) But what explains why the universal redness explains why those red things are red? It must be some other universal, namely, the universal for what an explanation is, which is true of every true instance of explanation, including when we explain red things by means of the universal redness. But then, what explains why that universal for what an explanation is explains why the universal redness explains why those red things are red? It must be because there is yet another universal, namely, the universal for what explains what an explanation is, which is true of . . . But, that explanatory regress will never stop. And so, it is worried, we can never really or ultimately or fundamentally get any explanations since there is no ultimate foundation upon which any intermediate explanation rests. That seems bad. The classical Aristotelian can resolve that mess by, again, using the idea that since the universal redness exists in a different sense of existence than the particular red things exist, that is, redness and red things exist in categorically different senses of existence, we cannot meaningfully ask for an explanation of their explanatory relation. Asking for explanation of the explanatory relation between redness and red things is treating them as if they both exist in the same sense of existence, as if they are on the same level of reality. But, it is claimed by the classical Aristotelian, they are not. Therefore, since we cannot treat red things and the universal redness as if they all exist at the same level of existence,

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we cannot meaningfully ask why they are related to each other. If two things are not comparable, then one cannot ask how they compare, or relate, to each other. In other words, we can explain why we can group all of the red things together: the universal redness explains why all of those red things can be grouped together. All of those red things have redness in common. But, the classical Aristotelian will tell us, we can group all of the red things together only because the red things all exist in the same sense, that is, only because all of the red things are at the same level of reality. If, though, redness and red things exist in different senses, as the classical Aristotelian claims, then we cannot group or collect redness and red things together and ask what they all have in common. Red things and redness cannot have some thing in common since, according to the classical Aristotelian, they are not comparable with each other at all. They are incomparable. Therefore, we can block the above infinite regress due to the meaninglessness of even asking about what a group of incomparable things have in common. It is meaningless even to ask the question! Therefore, the regress is blocked and we get to reach an ultimate explanation for red things after all. The next problem that a classical Aristotelian can nicely solve has to do with an idea we looked at in the previous chapter: the nature of our mental relation with the world. The orthodox, though not Platonic, view about the nature of mental states is that we can think about something that does not exist. Children can think about Santa Claus, the Tooth Fairy, and so on. Adults can think about potentially nonexistent things as well, for example, phlogiston, (possibly) God, perpetual motion machines, and so forth. The orthodox explanation for how that is possible is that we are thinking about the world via some conception of the world we have. Conceptions of the world are the things through which we think about the things of the actual world. The former are called intensional objects and the latter are called extensional objects. The intensional objects are those things through which we think about the extensional objects. And the key idea of this view is that intentional objects are the same things regardless of whether or not they refer to anything in the world or not. Therefore, we can think about nonexistent things, for example, the Tooth Fairy, because the intensional object, which gives our thinking its intensionality—its directedness—is false of the world, that is, there is no Tooth Fairy in the external world, no extensional object for the intensional object to “connect with,” as it were. So, we can truly think about nonexistent things. It is the intensional object that explains how such is possible. The Platonist, however, will reject that claim because the explanation for how it is possible for someone to think about a nonexistent thing is by changing the object of that person’s thoughts from an extensional object, which does not exist,

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to an intensional object, which does exist. So, the Platonist will object, we are not thinking about a nonexistent thing. We are thinking about an existent thing, namely, the Tooth Fairy thought, that is, the intensional object. The intentional object, at least, exists! On the other hand, the classical Aristotelian will again explain that embarrassment away by claiming that intensional objects do not exist in the same sense of existence as extensional objects. After all, the idea that Tooth Fairy thoughts exist in the same sense as a real live Tooth Fairy, were it to exist, is preposterous. Tooth Fairy thoughts are not nothing at all, but they are not something either. They are merely intensional objects. Intensional objects exist, yes, but in a lesser sense of existence than extensional objects. Once again, ontological problem averted. And sixth, neo-Kantians in contemporary discussions of morality want to be able to claim that there is an important distinction between ethics, with its different substantial theories of the good—that is, different theories about how best to live—and morality, which has to be neutral as regards every theory of the good and places binding obligations on everyone regardless of their own personal conception of the good. The idea is that substantial theories of the good, theories about how best to live, are empirical and discovered by seeing what actions lead to what consequences. They are descriptive of the way the world in fact is. But morality, it is claimed, is not empirical and does not depend on consequences. Morality has to do with what one ought to do regardless of the consequences. Morality, then, does not aim to describe the way the world is, but prescribe how it ought to be. It is prescriptive or normative. According to neoKantians, moral obligations or rules are binding on people only if people would reasonably accept the obligation or rule in an ideal discourse with each other. These nonempirical rational ideal agreements are not substantial theories about what is in fact good or best to do. They are impartial, that is, neutral as regards any substantial theory of the good. That is why everyone is obligated to obey them. The moral rules ideally reasonably agreed upon are, neo-Kantians say, merely formal regulative principles and not part of any substantial theory of the good. The distinction, then, is between substantial ethical theories of the good, which are descriptive, and merely formal regulative moral principles, which are prescriptive or normative and hence apply to every rational being telling them what they ought to do. Neo-Kantians claim that that distinction allows us to sidestep intractable differences between people about what is in fact good and helps us to accept formal principles that everyone ought to follow regardless of their own substantial theory of the good. That is, if they can pull it off, a nice way of getting universality into morality.

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Of course, the ontologically honest way to justify the distinction between there being substantial theories of the good as opposed to merely formal, that is, not substantial, regulative principles, is to commit oneself to the classical Aristotelian idea that the reason mere regulative principles are not substantial theories of the good is that mere regulative principles are not nothing at all but they are not substantial things either: they are merely formal things. NeoKantians cannot say that regulative principles are not nothing at all because their theory does whatever explanatory work it does by appealing to, or referring to, those formal regulative principles. It is these merely formal principles that do the explanatory work in their moral theory. It is these regulative principles that explain why everyone has the moral obligations that they do. So, these principles have to exist in some sense. If they do not exist in any sense, then they cannot do the explanatory work neo-Kantians claim that they do. On the other hand, neo-Kantians do not want these principles to be anything substantial, such as theories of the good are supposed to be. Neo-Kantians need some way to lessen their commitment to the regulative principles so that the principles are not just other substantial theories of the good, which are not binding on everyone. That is why they say that the regulative principles are merely formal. It is that lessening, that mitigating, that allows them to get the explanatory benefits but with a lower ontological cost. Or so they think. We see, now, the pattern. Something is in need of explanation: How can we explain that many spatiotemporal particulars seem to have something in common? How can we explain that spatiotemporal particulars seem to be unified? How can we explain the mind? How can we prevent infinite explanatory regresses? How can we explain being able to think about things that do not exist? And how can we explain normativity? The pattern of explanation offered always involves two things: (1) the explanatory thing that solves the problem exists in a categorically different sense than the thing(s) it explains and (2) the explanatory thing which solves the problem exists in a lesser sense than the thing(s) it explains. Universals, minds, intensional objects, and regulative principles exist in a categorically different and lesser sense of existence than particulars, brains, extensional objects, and substantial theories of the good. The latter things exist in a fundamental or “fullblooded” sense of existence whereas the former exist in a lesser or diminished sense of existence. Universals, minds, intensional objects and regulative principles exist, sure, otherwise there would be nothing that does the explaining, but we need to avoid treating those explanatory things as if they were additional things. The explanatory things are not other things, but they are also not nothing

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at all. The explanatory things are things in a categorically different sense of existence. And what mitigates our commitment to their existence is that their existence is a lessened sense or mode or way of existing. David Armstrong’s work provides us with good examples of both contemporary Aristotelianism and classical Aristotelianism. He explains the idea of classical Aristotelianism in this way: David Seargent (1985: chapter 4) has argued that the correct way to conceive of universals is not as things, or even, he says, as entities, but rather as ways. Properties are ways things are, relations are ways that things stand to each other. He even suggests that it is a category mistake to treat them in any other manner. . . . I demur at his suggestion that properties and relations are not entities. Seargent would not deny that universals exist, and it seems convenient to say that whatever exists is an entity. But I do accept that it is wrong to substantialize universals. To think of them as ways that things are or stand to each other is to de-substantialize them. What is more, it seems plausible to say that to substantialize them, as, for instance, does the theory that particulars are bundles of universals (and mutatis mutandis the theory that particulars are bundles of tropes) is to make a category-mistake. . . . Ayer spoke of sense-data as “junior substances,” and this excellent phrase might also be applied to universals conceived of in the substantializing manner. How is such a conception to be shown to be a category-mistake? Seargent suggests that this is done by Bradley’s regress. Once properties and relations are conceived of in a thing-like way, then they will need real relations to attach them to their particulars (in a substance/attribute theory) or to attach them to each other (in bundle theory). These relations will in consistency have to be conceived of as substantial also, and the regress is off to infinity. By contrast, ways things are or ways things stand to each other seem to inform so much closer a unity with the things involved, that perhaps further relations are not required. (1997: 30; italics in the original)

That is, since universals (or properties) and particulars do not exist in the same sense, but in categorically different types of existence, many problems, including Bradley’s Regress, can be elegantly solved. The idea behind classical Aristotelianism, then, is that one should commit oneself to not just different natural kinds of things, like cats and dogs, which are different natural kinds of animals, but also to different categories of existence itself, which can then provide important explanatory benefits with a lesser ontological cost. Armstrong, Seargent, Lowe, functionalists, neo-Kantians, Turner, McDaniel, and others2 are all attempting to mitigate their ontological

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commitments by adopting this classical Aristotelian theory. I have obviously not argued the scholarly (exegetical) point concerning Aristotle. I have, again, only aimed to present the view, which I do think is the classical Aristotelian view, is quite widespread, and, if correct, quite powerful as it can solve a significant number of important issues.

4  Objections to Classical Aristotelianism I will now argue that the situation for the classical Aristotelian is not ultimately as good as it looks. Despite how attractive the classical Aristotelian position might seem, it has two serious drawbacks: self-referential incoherence and nonnaturalism. As far as the first drawback, it has been known for well over sixty years now that a view that has categorical or logical segregations of reality in addition to there being the natural kinds of things that there are, for example, animals and plants, is self-referentially incoherent (cf. Weiss 1928; Black 1944; Gödel 1944: 149; Fitch 1952: v; Kneale and Kneale 1962: 670; Copi 1971: 71–75). And it is this well-known criticism, in addition to the initial murkiness of the idea that being is equivocal, that makes people say, explicitly, that they do not think that the classical Aristotelian view is true, even though, as I have shown, many ways of solving important problems do implicitly presuppose it. What is the theoretical worry, then, about classical Aristotelianism? What is self-referential incoherence and why does classical Aristotelianism suffer from it? A theory is self-referentially incoherent when supposing the theory to be true makes the theory itself meaningless. Logical Positivism, for example, was a theory put forward in the early twentieth century, which was notoriously rejected by one of its own founders in the mid-twentieth century once he realized that it was self-referentially incoherent (cf. Hempel 1950). The theory’s central claim is that statements about the world are meaningful only if they can be verified by observation. If a statement cannot be empirically verified, then it is meaningless. Scientific statements were the quintessential kind of statements that are meaningful because they can be evaluated as true or false depending upon whether the observational evidence confirmed the content of the statement or not. But unscientific statements, that is, ones that could not be confirmed or disconfirmed by observation, such as metaphysical or ethical or religious statements, are meaningless. Since there is no way we could verify what is being said in those statements, they are not true or false but meaningless. A meaningless statement is not capable of being true or false. However, as

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Hempel pointed out, the core statement of logical positivism is itself not capable of being verified by empirical evidence. What observation could anyone make, even in principle, that would show that only empirically verifiable statements are meaningful? There can be none. And since there can be none, the statement of logical positivism it itself meaningless if true. Its truth would entail that it is itself meaningless. Logical positivism’s being self-referentially incoherent has notoriously made it the most well refuted theory in the history of philosophy. How, though, does this apply to classical Aristotelianism? The classical Aristotelian solves all of the problems described here (and some logical and semantic paradoxes not described) by claiming that, in each problematic case, the explanatory thing—the universal, the unifying principle, the mind, or the regulative principle—exists in a secondary or lesser or diminished sense of “existence” that is not comparable with some other thing—a substance or a particular or a brain or a substantial theory of the good—that exists in a primary or fundamental or full sense of “existence.” (Remember: the different senses of existence are not just different natural kinds of things that exist all of which exist in the same sense of existence. Animals and plants both exist in the same sense of “existence.” We can compare them as things even when we point out their differences as living things, that is, their being different natural kinds of living things but both are living things in the same sense of living thing! Categorical or logical differences between types of things are not just different natural kinds of things. No, they have nothing in common and cannot be compared.) The reason the problems we considered above are problematic, the classical Aristotelian offers as their diagnosis, is due to thinking that existence is univocal such that the explanatory things and the other things all exist in some one sense of existence. Once we realize that all those things are not really comparable with each other by a univocal sense of existence or thinghood, the problems are solved, and solved elegantly due to the fact the sense of existence that applies to explanatory things is less ontologically weighty than the sense of existence that applies to the other things. As we can see from the above, the key part of the classical Aristotelian explanation stems from its claim that there are different incomparable senses of existence that are systemically related in such a way that some types of existence are more fundamental than others. But as will also be clear, if the classical Aristotelian claim is true, then one can not say meaningfully, let alone truly, that one type of existence is different than another or that one type of existence is more or less fundamental than another. In order to be able to say that X is different than Y, we have to be able to compare them in virtue of a difference in something they

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have in common. For example, we can say meaningfully, and truly, that animals and plants are different because they differ as living things: animals are living things that can move around in their environment whereas plants are living things that cannot. Animals and plants, then, would be different kinds of living things. But if being is equivocal, that is, if there are senses or types or categories that are not just different kinds of beings but beings in different incomparable senses of “being,” then it would not be possible to point to a difference between them in something they have in common because the different types of being, by stipulation, do not and cannot have anything in common. We can say how apples and oranges differ in so far as they are both different kinds of fruit. We can say how fruits and cheeses differ in so far as they are both different kinds of food. And we can say how food and oxygen differ as they are both different kinds of things that living things need to stay alive. But the classical Aristotelian’s core claim is that the different types of existence are not different kinds of anything. They have nothing in common at all. There is “no genus of being” such that the different categories or types of beings could be its species. But if that is true—that is, if it is true that they have nothing in common—then there is nothing in virtue of which we could meaningfully say that they are different. And even worse, there is nothing in virtue of which we could meaningfully say that one type or category of existence is more fundamental or less fundamental than another type or category of existence. Alas, the key idea in classical Aristotelianism makes its elegant solutions neither true nor false, but meaningless. And a meaningless or incoherent solution is no solution at all. That negative result, moreover, cannot be outweighed by the other positive results the theory “procures.” If one’s view is self-referentially incoherent, then it is best to lay it to the side and look for an alternative. The classical Aristotelian could reply to that objection that the theory can be saved as long as the theory is not asserted as a unified theory. Instead of asserting that “being” or “existence” has many different incomparable categories, types, senses, or levels, the classical Aristotelian just needs to assert a weaker sort of ontological pluralism such that (OP) fundamental or primary things exist1 and derivative or secondary things exist2 where the different subscripted “existences” are just asserted as a heap and not as a unified or systematic group. However, we need to ask two questions about (OP): (Q1) What explanation can be given for existence1 ≠ existence2?

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and (Q2) What explanation can be given for existence1’s primaryness, that is, fundamentality, as compared to, say, existence2’s secondaryness, that is, derivativeness? Someone who might assert (OP) will, likely, say that (Q1) and (Q2) are both meaningless questions. Or if they are meaningful, then they are only questions about language and not about how our language relates to the world. Here is why, though that response is utterable, it is not convincing on (OP)’s own terms: Without being able—in principle—to give an answer to both (Q1) and (Q2), (OP) cannot solve the problems it is put forward to explain.

Why? Take the first problem classical Aristotelianism can solve, for example. The solution to the worry about being ontologically committed to universals is that such a commitment is too big. We do not want to have to treat universals as if they exist in the same sense of existence as particulars. So, we need to be able to say, and say truly, that the different senses or types or categories of existence are in fact different. If we cannot say, and say truly, that they are different senses or types or categories, then we cannot say truly that we are not committing ourselves to yet another thing in the same sense of thing that particulars are things. (That is what an answer to (Q1) would give us were we able to get one.) And since we do not want universals to be nothing at all, but to exist in some sense or type or category of existence which is more than not to exist at all, that is, to be nothing at all, we need the universals to exist in some sense, but in a lesser sense of “existence” than the sense of “existence” which particulars have. (That is what an answer to (Q2) would give us were we able to get one.) In brief, people who assert (OP), or any form of classical Aristotelianism, have to be able to make comparisons between the different senses or types or categories or levels of “existence” in order to say meaningfully and, further, to say truly (and not just utter sounds that would be neither meaningful nor capable of being true) that the different senses, or types, or categories are in fact different, and to say meaningfully and, further, to say truly (and not just utter sounds) that a specific comparative claim, namely that some senses, or types, or categories, or levels of reality are less fundamental than others, if their theory is going to be able to get those explanatory benefits for a lower ontological cost. And if they have to be able to make comparisons between the alleged senses, or types, or categories, then (OP) or any classical Aristotelianism is meaningless if true. If it is true that

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there truly are different senses, or types, or categories of existence that are not comparable with each other, then it is meaningless to say that there are different senses, or types, or categories of existence. The classical Aristotelian has one more reply it can make, though in the end, this too will not get the job done. When Bertrand Russell read Max Black’s devastating criticism of the former’s “Theory of Logical Types,” which was a classical Aristotelian solution to an important logical paradox, he responded by claiming that his theory is merely about our language and not about the world (cf. Black’s article and Russell’s reply are both in Schilpp 1971 [originally 1944]: 227–55 with 690–95). There are two reasons why this response will not extricate the classical Aristotelian from their mess. First, the assumption being made here is that since the theory is just about language, and therefore independent of any truths about the world, we are absolutely free to create or stipulate whatever language we want. And the second assumption being made here is that classical Aristotelianism is just about language. Both of these strategies fall flat. Let us take them up in reverse order. Irving Copi, responding to Russell, says the following: One cannot characterize a language by giving an account, however detailed, of its syntax alone. A language has a semantical dimension at least as important as its syntactical one. And when the meaning relations involved in its semantical rules are formulated, it will be found that what is said formally about the linguistic structure must be stated materially about the interpretation. If the language is one that syntactically embodies the Simple Theory of Types, then its semantical rules must presuppose or state explicitly corresponding type distinctions among elements or aspects of the model in terms of which the language is interpreted. The point can be put another way. Suppose the language in question is governed by a syntactical rule that prevents admission of a formula like “xm Ɛ yn” except where m + 1 = n. Then the classes a and b of any model which can constitute an interpretation of the language must be subject to exactly analogous restrictions. Otherwise there will be facts involving classes a and b of the model that the language in question will not be adequate to formulate. This phase of the objection has been put very clearly by Fitch (1952: 225): One way of attempting to meet the objection . . . is to assert that a formulation of the theory of types is simply the formulation of certain more or less arbitrary or conventional stipulations about the permitted ways of combining symbols. This answer seems to be all right so long as one is restricting oneself to the realm of uninterpreted symbols, but as soon as one enters the realm of

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semantical concepts it becomes necessary to apply distinctions of “type” to meanings of symbols as well as to symbols themselves. . . . In short, the objection that the Simple Theory of Types cannot be stated without violating its own provisions, is not really answered by the claim that the theory pertains only to symbols, not to things. For when a language embodying a type theory is interpreted, types must be imposed on those things in terms of which the language is being interpreted. (1971: 73–74)

Another way of making this point is that there is a difference between sounds (or symbols) and a language. Since a collection of the former make no truth claims, there are no constraints on their collation. But when the classical Aristotelian puts their view forward, they put it forward as true and not just as a collection of symbols or sounds. And only if classical Aristotelianism is true can the view actually explain anything at all. If it were just a collection of symbols, it would not explain anything, though I guess it could be aesthetically pleasing or painful! Therefore, attempting to neutralize the objection to classical Aristotelianism by claiming that the view is just about language undercuts the point in putting it forward, namely, to explain the world and not simply to make sounds or symbols. But second, a language is more than just a collection of sounds (or symbols). A language is a collection of sounds (or symbols) agreed upon for a reason, namely, for communicating. If so, then in order to communicate successfully, one has to direct another person’s mind toward one-thing-as-opposed-to-anotherthing. And being able to do that successfully puts constraints on their collation. One has to get the real differences between things in the world. That is why, for example, Mrs. McCave fails to name her twenty-three sons correctly when she names them all “Dave” (Geisel 1961: “when she calls for one, all twenty-three come on the run.”) Therefore, a language is more or less true not based simply on the fact that people agree to it as their language, but based on the extent to which the language correctly differentiates things that are in fact different from each other and groups other things together that do in fact have something in common (cf. Plato’s Cratylus 383–91). So, what Russell (and Turner3) are suggesting we do in order to avoid the self-referential incoherence of classical Aristotelianism gets the nature of language wrong. A language is a collection of sounds and symbols that people agree to for the sake of communicating with each other about the commonalities and differences in the world and not just to utter sounds and show symbols to each other for no reason. Therefore, in order to make a successful language, one’s agreements about how to use those sounds and symbols has to be constrained by the real commonalities and differences in the world. If people agree to use a collection of sounds and symbols independent

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of that constraint, then that collection will not be a true language but instead a collection that seems like a language but is not a language in much the same way that a saw made out of cotton balls could seem to be a saw but in fact is not truly a saw, no matter how much it may appear to be one. In other words, I do not doubt that someone could utter a bunch of sounds (or write down a bunch of symbols) without contradicting themselves. Even p ≠ p is not a contradiction if it just a symbol. (Perhaps it is a piece of artwork!) It is only a contradiction if one asserts it as true. With that last gambit defeated, I conclude our discussion of the first problem for classical Aristotelianism, namely, its being self-referentially incoherent. The second problem for classical Aristotelianism is this: to commit oneself to different senses or types or categories or levels of existence, thereby segregating reality into different logical categories in addition to the natural segregations of reality, is, as it sounds, not naturalistic. In other words, since science is itself committed to the existence of spatiotemporal entities and needs nonspatiotemporal entities, namely, universals, for its explanations to come out true, then naturalism is committed to the existence of two fundamental natural kinds of things: spatiotemporal and nonspatiotemporal things. To claim that nonspatiotemporal things are logically distinct, as opposed to naturally distinct, from spatiotemporal things is not naturalism at all, but nonnaturalism, the very thing classical Aristotelians had wanted to avoid. Therefore, if we want to solve the problems described above, or any others that we may come across, we will have to do it with the explanatory things that exist in the same one and only sense of existence as anything else that exists. In other words, you get what you pay for: if you want the explanatory benefits of believing in universals, then you have to pay the full price. You cannot get the explanatory benefits for a lower ontological cost (cf. the Appendix). At this point in our discussion, we can see that all the principal ways that theorists have tried to avoid committing themselves to Platonism about the objects of science have failed. In the next and last chapter, I shall lay out the positive view concerning how Platonism explains the objects of scientific knowledge as well as the objects of scientific experiments. What can be seen up to this point, though, is that the objects of scientific knowledge are going to have to be mind-independent and not spatiotemporal and exist in the same sense of existence as anything else that exists, for example, the mind-independent spatiotemporal things, which are the objects of scientific experiments. Let us turn, finally, to that positive account of the objects of science.

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Platonism Concerning the Objects of Science

1 Introduction In the previous chapters, I have laid out arguments against anti-Platonist theories concerning the objects of scientific knowledge, specifically, theories about the things that spatiotemporal things have in common. The arguments are aimed at showing that the anti-Platonist theory under consideration either is incoherent—constructivism and classical Aristotelianism—or does not explain what it purports to explain—nominalism and contemporary Aristotelianism. It is now time to show that Platonism concerning the objects of scientific knowledge delivers the goods. In order to do so, I will also have to describe how Platonism understands the spatiotemporal things, that is, the objects of scientific experiments, as they cannot be understood in the usual “common sense” way of describing them, namely, as substances. Thus far, then, we have discovered that the spatiotemporal things we see, hear, or otherwise experience through our perceptions are not good objects of scientific knowledge, and that spatiotemporal universals are not good objects of scientific knowledge, and that mind-dependent universals, that is, concepts, are not good objects of scientific knowledge, and lastly that universals thought of as existing in a lesser sense of “existence” are not good objects of knowledge. If the objects of scientific knowledge are best thought of as not being spatiotemporal, not being mind-dependent, and not existing in a different and lesser sense of “existence,” then the objects of scientific knowledge are best thought of as being nonspatiotemporal, being mind-independent, and existing in the same sense of “existence” as anything else that exists. That way of thinking of the objects of scientific knowledge is what Plato argued for 2,400 years ago, I submit, and that view will now be laid out so that we can see just how plausible the view actually is.

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2  The Objects of Scientific Experiments Let us start with something simple. Suppose it is true that (1) Scott is sitting. What is (1)?1 The most prevalent view among current theorists working on issues having to do with truth and the things that make truths true, namely, the truthmakers, is the assumption that propositions, that is, sentences capable of being true or false, are the things which bear truth or falsity. Propositions are what are made true or false either by having or by lacking truthmakers. According to that view then, (1) is a proposition. The truth of (1) is not part of its identity, except accidentally. (1) is the same thing regardless of whether it is true or false. And if (1) is true, then again according to this view, actual facts, that is, actual states-of-affairs, make (1) true. On that theory, the truths are propositions and the truthmakers are the states-of-the-world which happen to make those propositions true. Since I have been convinced that there are no such things as propositions, that is, things which maintain their identity regardless of whether they are true or false, I cannot accept propositions as what the truths are. In their place, I will take the truth (1) to be not something different than the spatiotemporal thing that is Scott’s sitting but identical to it. And that spatiotemporal thing, that truth, is not to be analyzed or decomposed or broken down into or explained away in terms of a thing, namely, Scott, and some property, namely, sitting. Instead, (1) is best thought of, as is every spatiotemporal thing, as a spatiotemporally extended complex dynamical system. Let me explain. We nowadays intuitively think about spatiotemporal things, for example, the people, tables, chairs, other animals, and so on, as things that are completely independent of each other. The spatiotemporal world is constituted by all of the many individual self-subsistent things there are. We can, for example, count how many of those things there are in the room with us. Each thing we count is one thing. And we also, nowadays, intuitively think of each of those things having various properties or qualities, for example, being 5’8” tall, being some color or other, being hairy or not, and so forth. But our intuitions about spatiotemporal things has been largely shaped by what we have needed to notice, or be aware of, given what was important for our being able to survive in the environments in which we lived. And that rough and ready idea, that spatiotemporal things are completely independent three-dimensional things that have properties, was good enough for the situations in which we found ourselves, for example,

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there is a tiger coming at me and that tiger is dangerous and so, I should run. And when we started thinking more carefully and more rigorously about those things and their properties, we largely restricted ourselves to those sorts of situations and needs. Aristotle’s systematic physical theory represents that more rigorous beginning for people in our Western culture (cf. Aristotle’s Physics and Metaphysics). But starting in the sixteenth century and continuing to the present, we started probing into the more fine-grained and more coarse-grained details of our spatiotemporal world. Scientists discovered some spatiotemporal things that were not relevant for our day-to-day survival. Those discoveries caused scientists to discard, or at least not rely on, that commonsensical and intuitive idea concerning the spatiotemporal things. That is true even about those spatiotemporal things of which we thought we had a pretty good grasp (cf. Wolpert 1992; Torretti 1999: 398; Ladyman and Ross 2007: 2, 10–12; and Tegmark 2014: 5). Scientists now think that the best way to describe spatiotemporal things is not as completely independent, that is, isolated, individual things. Spatiotemporal things are best thought of not as three-dimensional things, that is, wholly present at every moment, and not as “having” properties, whatever that is supposed to be, but, more positively, as interdependent four-dimensional complex dynamical systems (cf. Price 1970, 1972, 1995; Sober 1980: 370; Winfree 1980; Krieger 1992; Crutchfield 1994; Chaikin and Lubensky 1995; Gell-Mann 1995; Ball 1999; Camazine et al. 2001; Greene 2004; Shalizi et al. 2006; Ladyman and Ross 2007; Byrne and Callaghan 2013; Ladyman et al. 2013; West 2017; Thurner et al. 2018; Austin 2018; Petkova et al. 2019). It is easiest to see why when we think about contexts where the spatiotemporal things are quite small (e.g., quantum things) or quite large (e.g., astronomical things). Thinking of solar systems as systems does not strike anyone as being particularly counterintuitive. But even quantum “particles” are best thought of not as little independent things isolated from every other thing in existence but as waves in a relativistic quantum field, that is, extended both in space and in time, which involve different quantities, that is, the amplitudes and energies of those waves. (And that is not even bringing in “quantum entanglement” whereby two particles that could be on opposite sides of the universe can nevertheless be interdependent with each other!) A system is, in general, a plurality of functionally interdependent fine-grained things (i.e., its subsystems) that are one coarse-grained thing (i.e., the system). Again, it is easiest to see in large-scale things, such as a solar system where the planets and the star are the functionally interdependent things that relate to each other in a complex dynamic way such

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that the solar system is itself one, albeit larger, additional thing. A sports team would be another example: the players, by working well together, make a good team. If the individual players played the game independent of everyone else on their team, they would not be successful as a team, which is the goal of team sports. Each team member’s play has to be functionally integrated into every other’s play and not just be added to every other player’s activities.2 The idea, then, is that a system is complex, that is, functionally interdependent, and not just a heap of things coincidentally located near each other. In other words, the system’s complexity can only be explained if the parts of the system relate to each other in some nonadditive way. When people say that “the whole is greater than the sum of its parts,” they are thinking about a complex whole and that a complex whole is not just its parts. A solar system is not just its planets and star. A team is not just its players. When the parts relate to each other in some non-additive way, the thing that exists at a larger scale is best understood as another thing, and not just a collection, or heap, of those smaller things. The interdependency of the parts is due to their nonadditive functional relations between those different parts of the system (cf. Lewes 1875: 412–14).3 These relations are described mathematically as “nonlinear,” which is any mathematical relation involving the product (and not the sum) of two distinct variables (cf. Torretti 1999: 6–7). So, it is because the different players on a team play different functional roles that they can act together as a team, that is, there can be such a thing as a team’s activity in addition to each individual person’s activity. Another important feature of systems is that though they are not isolated independent things, they are isolatable from their surrounding environments. That is, we can isolate them. That is not to say that we create systems. It is just that we can more or less ignore the environments within which systems function. The systems of interest are in fact interconnected to their environments as those environments are just systems themselves at a larger scale. For example, suppose, for the purpose of illustration, the spacetime continuum in which we find ourselves began at the Big Bang about 13.8 billion years ago and ends some many years in the future in the Big Freeze, that is, when the average kinetic energy of the universe is very close to zero kelvin.4 That whole spacetime continuum is a spatiotemporally extended complex dynamical system. It exists at the largest spacetime scale of measurement we have (at present) and its dynamics is best explained by a differential equation, or some system of differential equations. At a smaller spacetime scale, that is, a more detailed or more fine-grained scale of measurement, other spatiotemporally extended complex dynamical systems are isolatable from the larger environment, that is, the whole spacetime continuum,

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and these systems are the galaxies, such as our Milky Way galaxy or the Andromeda galaxy. The complex dynamics of those systems are also best explained by differential equations but which are specific to the scale at which those systems function as systems. Again, at a more detailed or more fine-grained scale of measurement, other spatiotemporally extended complex dynamical systems are isolatable from their larger environment, that is, their galaxy, and these systems are the solar systems. And again, those systems are best explained by differential equations but which are specific to the scale at which those systems function as systems. Again, at a more detailed or more fine-grained scale of measurement, other spatiotemporally extended complex dynamical systems are isolatable from their larger environment, that is, their solar system, and these systems are the planets and stars. And again, those systems are best explained by differential equations but which are specific to the scale at which those systems function as systems. Again, at a more detailed or more fine-grained scale of measurement, other spatiotemporally extended complex dynamical systems are isolatable from their larger environment, that is, their planets, and these systems are the geological systems, for example, the plates, the magma, the atmosphere, and so forth. And again, those systems are best explained by differential equations but which are specific to the scale at which those systems function as systems. Again, at a more detailed or more fine-grained scale of measurement, other spatiotemporally extended complex dynamical systems are isolatable from their larger environment, that is, their geological systems, and these systems are the ecological systems. And again, those systems are best explained by differential equations but which are specific to the scale at which those systems function as systems. Again, at a more detailed or more fine-grained scale of measurement, other spatiotemporally extended complex dynamical systems are isolatable from their larger environment, that is, their ecosystems, and these systems are the sociological and political systems. And again, those systems are best explained by differential equations but which are specific to the scale at which those systems function as systems. Again, at a more detailed or more fine-grained scale of measurement, other spatiotemporally extended complex dynamical systems are isolatable from their larger environment, that is, their sociological and political systems, and these systems are the more familiar systems, for example, the humans and other animals, trees, and such. And again, those systems are best explained by differential equations but which are specific to the scale at which those systems function as systems. Again, at a more detailed or more fine-grained scale of measurement, other spatiotemporally extended complex dynamical systems are isolatable from their larger environment, that is, those

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living thing systems, and these systems are, for example, the bodily systems such as the cardiovascular, nervous, respiratory, and digestive systems. And again, those systems are best explained by differential equations but which are specific to the scale at which those systems function as systems. Again, at a more detailed or more fine-grained scale of measurement, other spatiotemporally extended complex dynamical systems are isolatable from their larger environment, that is, those biological systems, and these systems are the cellular systems. And again, those systems are best explained by differential equations but which are specific to the scale at which those systems function as systems. Again, at a more detailed or more fine-grained scale of measurement, other spatiotemporally extended complex dynamical systems are isolatable from their larger environment, that is, those cellular systems, and these systems are the molecular systems. And again, those systems are best explained by differential equations but which are specific to the scale at which those systems function as systems. Again, at a more detailed or more fine-grained scale of measurement, other spatiotemporally extended complex dynamical systems are isolatable from their larger environment, that is, those molecular systems, and these systems are the atomic systems. And again, those systems are best explained by differential equations but which are specific to the scale at which those systems function as systems. And lastly, we get to the smallest or most detailed or most fine-grained scale of measurement, which we have discovered thus far, where quantum systems are isolatable from their larger environment, those atomic systems, and for which we do have differential equations that explain how these systems function as complex dynamical systems.5 All of these systems are interdependent with each other. But we can objectively isolate them from each other using different scales of measurement. A scale of measurement concerns the detail in one’s measuring tool. The finer the grain in one’s measuring tool, the smaller the system one will be able to discover. And the coarser the grain in one’s measuring tool, the larger the system one will be able to discover. A clear illustration of that idea can be seen in a sieve. Depending upon the size of the spaces between the mesh in one’s strainer, one will catch some things but not other things, both of which were in one’s original collection of things. For example, suppose you lost your watch on the beach. If you use a sieve that has spaces in the mesh that are large enough to allow the sand to fall through but small enough to not let a watch through, then one will eventually find, that is, discover, one’s watch if one is able to put all of the sand on the beach through your sieve. The smaller you make the spaces in the mesh, the smaller the things one will be able to find in one’s sieve. The larger you make the spaces, the

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harder it will be to catch those smaller things. On the other hand, you will catch everything that does not fall through the mesh and that might give you things the size of your watch, but also many other things that are larger than your watch is, for example, beach balls, bottles, crabs, umbrellas, and other assorted things that will still make it hard for you to find your watch. Therefore, in order to isolate your watch from all of those other things, it might be best to use a series of sieves, starting with one that has rather large holes so that you can catch the umbrellas but lets everything else through. Putting those umbrellas aside, then, you can use a sieve with smaller holes on everything again, but this time you will catch the beach balls. And then so on, with each sieve having smaller and smaller openings in their mesh until you are just left with watch-sized items in your sieve. One important point is that all of those things of different sizes are there, to be caught, that is, discovered, in your original collection of things before you ever start sifting. But the main point here is that the different-sized spaces in the mesh give the sieves their different scales of measurement, which are what allows the sieves to find the different-sized things within a collection of things.6 Changing the scale with which we measure regions of our spacetime continuum, then, allows us to discover systems that function at different scales. All of those systems are already there to be discovered as subsystems of the whole spacetime continuum, which is the largest system (we have discovered, thus far). But, unlike the collection of sand, umbrellas, beach balls, bottles, and your watch, which are all discrete, all of those systems are more or less interdependent with each other. Just as with gravity in Newtonian physics where every single thing in the universe exerts some, more or less, gravitational force on every other thing, so all of those systems functionally depend, more or less, on each other. The idea is that all of the differently sized spatiotemporally extended systems are subsystems of a continuous spacetime continuum. We discover the different systems depending upon which scale of measurement we use. They are there to be discovered. But those systems are not metaphysically isolated from each other. They all “bleed” into each other as there are multiple systems in the same region of spacetime, just at different scales. For example, there is a temporal part of human system here in this region of spacetime where I am as well as (roughly) seven billion billion billion atomic systems as well as a cardiovascular system and a respiratory system as well as a temporal part of half of a married human system and so on and so forth. Those systems (and many many more) are all at this region of spacetime. That is why the spatiotemporal world is not constituted by a plurality of independently

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existing things, which Aristotle called “substances.” There are no Aristotelian substances in Platonism. That is, there are no spatiotemporal things that are essentially what they are. Every region of spacetime, according to Platonism, is contingently, or accidentally, what it is. It is true that there is a human here, but it is no less true that there is a 5’8” thing here and a white thing here and half of a married thing here and roughly 7 billion billion atomic things here and so forth. All of those systems are equally real and located at the same region of spacetime, contra Aristotle who would only countenance one thing per region of spacetime, which he thought were the substances, that is, what is essentially the thing, as opposed to all those other things, which he thought were merely the thing’s accidents. Every spatiotemporal thing is accidentally what it is in Platonism. A Platonist, then, would say that the spatiotemporal part of reality is a spatiotemporally extended complex dynamical system that has more or less identifiable spatiotemporally extended complex dynamical subsystems. We can isolate some of the finer-grained systems more or less as if they were independent of some of the coarser-grained systems because those finer-grained systems “asymptotically approach zero” (cf. Batterman 2001) in their effect on the coarser-grained system or those more coarse-grained systems make no significant difference to the more fine-grained systems because the fine-grained systems are “come-and-go” before any change happens in the coarse-grained systems. An example of the former would be the irrelevance of the details of my atoms to my seeking food. Sure, there are atoms wherever I am but their dynamic changes can be safely ignored when explaining the larger human system’s food-seeking behavior. Therefore, my food-seeking behavior is related, that is, connected,7 to my atoms, but they play no significant role in explaining the more coarse-grained food-seeking complex dynamical system. And as an example of the latter, take my food-seeking behavior again. It is insensitive to the motion of the Milky Way galaxy. My food-seeking behavior is related, that is, connected, to that larger system, but the scale of changes happening in the Milky Way are occurring at a far more coarse-grained scale to make a significant difference to the kinds of changes that are happening in the more fine-grained dynamical food-seeking behavior of mine. Ignoring those connections is not the same as those connections not being real. We can isolate systems from the systems within which they function, that is, we can safely ignore the more coarsegrained systems and just focus on the more fine-grained systems, but the more fine-grained systems are nevertheless still connected, that is, interdependent, to the more coarse-grained systems.

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Platonism, then, about the spatiotemporal things at our more familiar scale where we find humans and other animals and things with which we interact, as well as every spatiotemporal thing at every scale, is best thought of as being committed to the idea that spatiotemporal things are spatiotemporally extended complex dynamical systems. The Platonist, then, will claim that (1) Scott is sitting is a spatiotemporal extended complex dynamical system. It is the spatiotemporally extended complex dynamical system whereby there is some human sitting going on. (1) is not, therefore, a thing, namely, Scott, that has some property, namely, sitting. (1) is a thing that is extended in space and time and is complex (as opposed to simple) and is dynamic (as opposed to static): the complex dynamical spatiotemporal system correctly described as a sitting human thing. At a larger scale, there is a human thing, which is a complex spatiotemporally extended dynamical system. At a slightly smaller scale, there is a sitting thing, which is also a spatiotemporally extended dynamical system. The latter is a subsystem of the former. Both of those systems are in the same region of spacetime we are considering. And they are functionally interdependent with each other. So much for the spatiotemporal things, that is, the objects of scientific experiments. They are all spatiotemporally extended complex dynamical systems. What, then, would a Platonist say the nonspatiotemporal mind-independent fully existing commonalities of spatiotemporal things are, that is, what are the objects of scientific knowledge?

3  The Objects of Scientific Knowledge Consider the following question: (Q) Why is (1) true, that is, what makes (1) true? (Q) is ambiguous between two different why-questions. (Q) could be asking: (Q1) Why did Scott come-to-be sitting? or (Q) could be asking: (Q2) Why identify Scott’s behavior as sitting? This is parallel to the following: suppose it is true that (1*) a region of this lung is cancerous.

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If we ask: (Q*) Why is (1*) true, that is, what makes (1*) true? we could be asking, (Q1*) Why did a region of this lung come-to-be cancerous? or we could be asking, (Q2*) Why identify a region of this lung as cancerous? (Q1) and (Q1*) are asking for the causal-mechanical explanation of a particular truth. What made these truths come-to-be, for example, what made it true that Scott came-to-be sitting or what made it true that a region of this lung cameto-be cancerous? (Q2) and (Q2*), on the other hand, are asking something different, namely, they are asking about the identities of those particular truths, specifically, they are asking for an explanation of why these regions of spacetime are truly examples of sitting or cancer, as opposed to not? So, instead of asking for an explanation of how these truths came-to-be, the second kind of whyquestion is asking for an explanation of what these truths are. The answers to these two different kinds of why-questions, then, get us two different kinds of explanations: causal-mechanical explanations and identity explanations. The causal-mechanical explanations for any truths that came-to-be are spatiotemporal entities. For example, a partial answer to (Q1*) could be that (A1*) the person smoked cigarettes for forty years. This explanation refers to a spatiotemporal entity, namely, the forty-year spatiotemporally extended complex dynamical smoking-person system. That entity, that is, that spatiotemporal system, could be part of why the truth (1*) came-to-be. But, of course, (1*) could have come-to-be without (A1*) being part of the causal-mechanical explanation. Instead, (1*) could have come-to-be partially because (A1**) the person was exposed to high-levels of ionizing radiation. That explanation also refers to a spatiotemporal entity, namely, the spatiotemporally extended exposure-to-ionizing-radiation system. Either entity could be part of the complete causal-mechanical explanation for (1*), which includes every entity required to explain why (1*) came-to-be.8 The first important point to notice here is that though (1*) had many spatiotemporal antecedents, only some of them explain why (1*) came-to-be. In

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fact, most of the spatiotemporal antecedents of (1*) are irrelevant to explaining why it came-to-be. For example, (A1**) may not be part of that explanation even if it was antecedent to (1*). Not every high-level dose of ionizing radiation causes cancer. Likewise with (A1*). Smoking, even for a period of forty years, does not cause cancer every time. And a fortiori for all of the temporal antecedents that cannot cause cancer. The second point, and the more important point, is that in order to identify those things that provide the causal-mechanical explanation correctly, there have to be other kinds of things that provide explanation of a different sort, namely, the things that explain the identity of those casual-mechanical explanatory things. The reason is that in order to be able to identify correctly which parts of a historical period are the correct parts of the complete causal-mechanical explanation and which parts of that historical period are not part of the complete causal-mechanical explanation, those parts must be different from each other, that is, their identities must be different. How, then, do we successfully differentiate these different things, that is, these different spatiotemporally extended complex dynamical systems, from each other? Alternatively, what is the best way to identify a spatiotemporal thing, that is, a spatiotemporally extended complex dynamical system? Given that we are not considering Aristotelian essentialism or any of its neoscholastic descendants in contemporary analytic metaphysics as comporting well with the best science of our day (cf. Batterman 2001; Ladyman and Ross 2007), we need to give a different explanation. More specifically, if spatiotemporal things are not essentially what they are but only contingently or accidentally what they are, that is, regions of spacetime are not essentially what they are but only happen to be what they are, then any region of spacetime could have been something other than what it happens to be. It is just that whatever any region of spacetime truly is, it is only truly what it is contingently and not essentially. Therefore, the regions of spacetime described by (A1*) and (A1**) will not be essentially one thing as opposed to any of the other things that are truly located at those same regions of spacetime, though at different spacetime scales. The closest one could come to finding one thing that every region of spacetime is might be energy. In other words, the closest scientists can come to identifying any region of spacetime essentially, at least at present, is that it is energy. (Though if energy is fundamentally information, as some, following John Wheeler, have suggested, then information would be what every spatiotemporal thing is essentially.) However, even if that is true, and every spatiotemporal thing is essentially energy, or information, or whatever, if there are to be any differences at all between regions of spacetime or even within the same region of spacetime,

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then what makes any region of spacetime different from any other region of spacetime is how the energies in those regions of spacetime are structured. As a physicist might put it, matter is a form of energy (cf. Mazur 2014: 5). Now since the spacetime regions (A1*) and (A1**) could overlap partially or completely, if (A1*) and (A1**) are to be truly different from each other, the things that differentiate (A1*) and (A1**) from each other, that is, the things that explain their identities, will have to be, as we have seen above, scale relative (cf. Ladyman and Ross 2007; West 2017). It is worth thinking through another example. Take, for example, the region of spacetime that is my here-now temporal part. In other words, if I am a spatiotemporally extended complex dynamical system, then I will be spread out over time, parallel to how I am spread out in space. And just as my hand is just one spatial part of me and not all of my spatial parts, the two-hour long time period in which I am sitting is just one temporal part of me and is not all of my temporal parts, which are spread out over many years. But in that one two-hour temporal part of me, that is, that one region of spacetime where I am, there are at least, very roughly, 7 billion billion billion (7 x 1027) and one things, namely, very roughly 7 billion billion billion atoms and one human being. As we saw above, an explanation for how there could really be both roughly 7 billion billion billion atoms and one human being at this same region of spacetime can be explained if spatiotemporal things are explained using the scientific notion of scale relativity: every spatiotemporal thing there is is relative to parameters at different scales. So, there are roughly 7 billion billion billion atoms at this region of spacetime relative to some parameters at the angstrom length scale and there is one human being at this same region of spacetime relative to some parameters at the meter length scale. The kind of thing human beings are is such that humans do not function at the angstrom length scale. And the kind of thing atoms are is such that atoms do not function at the meter length scale. All 7 billion billion billion and one things are located at that same region of spacetime but relative to different length scales. The different scale-relative parameters, then, are what make it possible to identify the different things, that is, the different spatiotemporally extended complex dynamical systems, that are located at the same region of spacetime. And it is these scale-relative parameters, therefore, that are the things that make it true that there are (identifiably) different spatiotemporal things even in one and the same region of spacetime. Notice well that the relation here, that is, the relation between the scalerelative parameters and the spatiotemporally extended complex dynamical systems, is not a causal-mechanical relation but an identifying relation. In other words, the scale-relative parameters do not cause anything to come-to-be truly

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located in any region of spacetime. The scale-relative parameters just explain why the spatiotemporal things are correctly identified as examples of the kind of things that they truly are. Now given that the spatiotemporal region where (1*) is is complex, that is, there are a plurality of identifiable things at different scales in the same region of spacetime, the best way to differentiate the spatiotemporal things from each other, that is, in the way that is scientifically respectable, is via those scale-relative parameters. And if those scale-relative parameters are what are necessary for scientists to be able to differentiate the different spatiotemporally extended complex dynamical systems from each other correctly, then we have found what we have been looking for since the beginning of our intellectual journey when we asked what spatiotemporal things have in common. The commonalities are best thought of as those scale-relative parameters. And given that those parameters can be neither just the spatiotemporal things themselves nor spatiotemporal universals nor mind-dependent nor exist in a different sense of existence, they must be mind-independent nonspatiotemporal things that exist in the same sense of existence as the spatiotemporal things, just a different kind of thing that exists in the same sense of existence. We have, then, at long last found what spatiotemporal things have in common and therefore are the objects of scientific knowledge: scale-relative parameters. Given, then, that spatiotemporally extended complex dynamical systems, that is, the spatiotemporal things, are best explained by scientists in terms of differential equations, which are themselves mathematical relations between different kinds of quantities, scale-relative parameters turn out to be best thought of as kinds of quantities. These scale-relative kinds of quantities, that is, parameters, are the identities, that is, the natures, of the spatiotemporal things, and it is in virtue of these nonspatiotemporal things that we can successfully, that is, truly, identify spatiotemporal things, that is, identify the spatiotemporally extended complex dynamical systems as what they are and as what they are not. In other words, scientists are able to say truly what this spatiotemporal system is and what this spatiotemporal system is not to the extent that they intellectually grasp the nonspatiotemporal parameters that are the identities of those spatiotemporal systems. As we saw before, the spatiotemporally extended complex dynamical systems are the objects of scientific experiments, according to Platonism. It is by the careful observation, that is, measurements, of a large number of differently located spatiotemporally extended complex dynamical systems that scientists figure out what these differently located spatiotemporal systems have in common, that is, what their identities are, and what they do not have in common, that is, what

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their differences are. When they discover what those spatiotemporal systems have in common, they are discovering that that large number of differently located spatiotemporal systems have some one scale-relative parameter, which is itself nonspatiotemporal, true of all of those spatiotemporal systems. Our original questions about (1) and (1*) can now be answered. If we are asking the identity-why question, (Q2), that is, why is sitting the thing Scott is doing?, we are wanting to know what makes it true that sitting is what Scott is doing and not what caused it. The Platonist answer to (Q2), then, is that it is true that Scott is sitting because (A2) the nature of sitting, that is, having one’s weight supported on a surface with one’s torso upright, correctly characterizes, or is true of, this region of spacetime. The Platonist answer to (Q2*) is that (1*) is true because (A2*) the nature of cancer, that is, uncontrollable cell-growth, correctly characterizes, or is true of, this region of spacetime. The natures of sitting and cancer, unlike my sitting and this cancerous tumor, are nonspatiotemporal entities. More exact descriptions of them would be in mathematical terms, that is, as differential equations, which are mathematical expressions of those scale-relative parameters. At present, scientists do not know these differential equations. However, scientists are working on discovering them. Likewise with the scale-relative parameters for determining when a spatiotemporally extended complex dynamical human-smoking system exists or when a spatiotemporally extended complex dynamical ionizing-radiation system exists. These too are being sought by scientists. But on this much we already have a pretty good grasp: since the scale of measurement of the former is larger than the scale of measurement of the latter, that is, the scale of measurement of the tar in the smoke is larger than the scale of measurement of the particles involved in the radiation, (A1*) and (A1**) will be different things, that is, different spatiotemporally extended complex dynamical systems, given that their scalerelative parameters are different even if they are the same spacetime regions.

4  The Relation between Spatiotemporal and Nonspatiotemporal Things Even if one grants that there are nonspatiotemporal scale-relative parameters, and even if one grants that these could be used to identify spatiotemporally

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extended complex dynamical systems, the relation between these two different kinds of things seems completely mysterious at best, and nonscientific at worst. How do the nonspatiotemporal things relate to the spatiotemporal things? That just seems impossible to explain. How could they relate to each other? They are just so different! The relation between casual-mechanical antecedents and their effects, on the other hand, seems at least tractable, even though the exact nature of causation has perplexed philosophers and scientists since the beginning of philosophy and up to the present day. More specifically, at least with causation, and causal relations, the causes and the effects are both spatiotemporal. So even if there are issues having to do with that relation (cf. Russell 1912–13; Redhead 1990: 145–47; Torretti 1999: 133; Ladyman 2008: 753), the causes and the effects are at least within the same realm of things such that they can relate to each other (cf. Woodward 2003). But how do things that are spatiotemporal relate to things that are nonspatiotemporal? They cannot relate to each other as cause and effect do. In other words, they are not causally related. The nonspatiotemporal scale-relative parameters do not cause anything to happen. They explain why things are what they truly are and they can (perhaps) explain why two different regions of a spatiotemporal system are best understood as being two parts of a causal system, but the parameters themselves can have no causal-mechanical effects. For example, the law of gravity does not cause an apple to fall from a tree. The law only explains why the apple falls at the rate of acceleration that it does. But what is that explanatory relation? If not all explanations are casual-mechanical explanations, then what sort of explanatory relation is the relation between the nonspatiotemporal scale-relative parameters and the spatiotemporally extended complex dynamical systems? That question has been asked since Plato first proposed his theory of Forms as explanations for our perceptual world. Plato’s theory was, in fact, the first systematic theory of abstract objects in the history of Western thought (cf. Vlastos 1954: 340). And people throughout history who have rejected Plato’s theory have even pointed out that Plato himself was not able to explain that relation, which he called “participation” (cf. Plato’s Parmenides 129a–135c). Nevertheless, it would be nice to know what that explanatory relation is. Before trying to answer that question, though, it is important to emphasize the point that that question-turned-objection has been asked critically throughout history as if it applies only to Platonism. However, it actually applies to every theory that admits the existence of abstract entities. The classical Aristotelian admits such things. According to a classical Aristotelian, nonspatiotemporal

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universals, which exist in an incommensurate but lesser sense of existence, “belong to” or are “dependent on” the spatiotemporal things. But labeling the relation between the nonspatiotemporal and the spatiotemporal as one of “belonging” or “dependency” does not explain the relation any better. It just gives it another name. What is it, exactly, for a nonspatiotemporal universal to belong to or be dependent on a spatiotemporal particular? The classical Aristotelian tells us nothing. The most common contemporary way of thinking about universals or properties, on the other hand, is in terms of set theory. Socrates, for example, has the property of being human by being a member of the set of all humans. Socrates is a spatiotemporal thing and the set of all humans is an abstract thing, that is, a nonspatiotemporal thing, and the relation between them is that of set membership. “Being a member of ” is what the relation between them is called. But that label does not explain how they are related any better than Plato’s “participation” relation or Aristotle’s “belonging to” or “dependent on” relation. It is just another name for the same relation. Nominalists, given their denial of any nonspatiotemporal things or universals, do not have to worry about explaining the relation. But, they have worse problems: they cannot explain how spatiotemporal things can have anything in common and thereby cannot explain how scientists could come to have knowledge of those commonalities.9 Therefore, explaining the relation between spatiotemporal things and nonspatiotemporal things is everyone’s problem who is not a nominalist. That, of course, does not make the problem any less problematic. It just spreads the problem around, which is a comfort, though a small one. Nevertheless, despite its historic difficulty, I will now attempt to give an explanation of that important relation given what Platonism has at its disposal. Take, as a simple example of the relation, the relation between parabolaness and a particular parabola. Suppose that at the micron length scale there are graphite crystallites on a Cartesian plane in Euclidean space such that at the decimeter length scale the crystallites as a whole conform to the algebraic equation y = x2. If that is true, then the thing at the decimeter length scale is a parabola. The graphite crystallites at the micron length scale are not parabolas because y = x2 is not true of their structure, which is in fact hexagonal. And, it is also the case that the sum of those graphite crystallites is not a parabola. The sum of those graphite crystallites is just a multitude of crystallites. In order for it to be true that the plurality of crystallites is one parabola instead of merely one multitude of crystallites, the parameters by which we identify the different things have to be at different scales. A spatiotemporal parabola exists at a larger scale than the scale at which its spatiotemporal points exist. So far so good. Let us probe more deeply.

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The algebraic equation for parabola-ness, y = x2, refers to a nonspatiotemporal thing, that is, an abstract parameter, which is itself an abstract relation between two different kinds of quantities, specifically, the x-quantity and the y-quantity. The algebraic equation expresses the relation, a nonadditive one, between those two kinds of quantities, which is itself is another kind of quantity, that is, the kind of quantity whereby (a locus of points is such that) the distance to the focus, which is a point that is not part of the parabola, is the same quantity as the distance to the directix, which is a straight line also not part of the parabola. (Think of the focal point as the optimal place to put a light source in a convex mirror if one wants the mirror to have the best beam of light it can have and think of the directix as the x-axis or a fixed line on the closed side of the vertex). That third kind of quantity is what being a parabola is. That third kind of quantity is a particular kind of quantity that exists at a larger scale, or more coarse-grained scale, than the kinds of quantities that exist at smaller, or more fine-grained, scales to which it relates. The algebraic equation, then, explains the relation between those kinds of quantities that exist at different scales. The relation between those two kinds of quantities cannot be mere addition. If it were, there would not be a third distinct kind of quantity. To see why addition is not the right sort of relation between different kinds of quantities, take another very simple example: the nature of speed. Speed is a kind of quantity which is itself a specific relation between two other kinds of quantities, namely, spatial distance and temporal duration. The equation s = ∆d ∆t explains the relation between the quantities. Speed is not spatial distance plus temporal duration. If it were, then speed would not be another kind of quantity but would just be both spatial distance and temporal duration. For speed to be a (more complex) kind of quantity in addition to the two other (less complex) kinds of quantities to which it is related, the relation between the less complex kinds of quantities needs to be some nonadditive mathematical relation. So, the kinds of quantities at the smaller scale are related to each other in some nonadditive way such that that more complex kind of quantity is that additional kind of quantity at the larger scale. And these different kinds of quantities, according to Platonism, are what scientists aim to discover. In general, then, these more or less complex kinds of quantities are the scalerelative parameters, that is, the nonspatiotemporal things, that are the identities of the particular quantities, that is, the spatiotemporal things. Particular parabolas, specific speeds, particular cancerous tumors, and particular examples of evolution are truly parabolas, speeds, cancerous tumors, and examples of evolution because their particular scale-relative quantities are the same in structure as the structure the kind of quantity they are. For example,

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the 60 mph speed of a car, that is, its particular quantity of speed, has the same structure in its relation between the particular spatial length the car traveled, for example, 1 mile, and the particular temporal duration which it took to do so, for example, 1 minute, namely, a ratio, as the structure in the relation between of the kinds of quantities that the complex kind of quantity speed is, namely, spatial length divided by temporal duration. That, at last, is the explanatory relation for identity: when the spatiotemporal relation particular quantities have with each other, their spatiotemporal structure, is the same as the nonspatiotemporal relation their kinds of quantities have with each other, their nonspatiotemporal structure, then the latter is true of the former, or alternatively, the former exemplifies the latter. The nature of the relation, then, is structural. The physical structure of the particular quantities exemplifies the abstract structure of the kinds of quantities. The explanatory relation between them is that the complex abstract structure explains the identity (or nature) of the complex physical structure.10 For example, one could ask, why is this complex spatiotemporally extended dynamical system truly an instance of speed? The answer is that this is an instance of speed because the complex spatiotemporally extended dynamical system has a relation between its subsystems (specifically, its particular spatial distance and its particular temporal duration) that functionally relate to each other in the same nonadditive way that the kinds of quantities involved in speed (specifically, the scale-relative parameter for spatial distance and the scale-relative parameter for temporal duration), which is itself the scale-relative parameter for the kind of quantity speed is. One very important caveat here is that the identities of the spatiotemporal things, that is, the complex spatiotemporally extended dynamical systems, are not individual or unique identities. More specifically, the nonspatiotemporal things, the scale-relative parameters that identify what the spatiotemporal things truly are, apply one and the same identity to every spatiotemporal thing with the same structure. For example, every collection of points that are structured at a larger scale in conformity with y = x2 will have one and the same identity, namely, they will, every one of them, be a parabola. So, the identity of a nonspatiotemporal thing is only a sortal identity, that is, the kind of thing of which it is an example, and not a unique or personal identity. That seems sufficient to me since science does not aim to identify what this particular spatiotemporal thing is in itself, that is, its unique essence, but only what this sort of spatiotemporal thing is (cf. Enç 1986: 403–4). In other words, science does not aim to explain what I am essentially, if there be such a thing, but only to identify what I am relative to my

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being human, or my being white, or my being a bacteria culture, or my being 5’8”, or my being married, or my being male, or my being organic, or whatever else I truly am, none of which are ontologically more what I am as opposed to any of the others.11 Being able to correctly identify those spatiotemporally extended complex dynamic systems requires, therefore, that scientists discover the nonspatiotemporal scale-relative parameters for those spatiotemporal things, which they are, thankfully, doing.

5  Platonism Concerning Modal Truths One of the general ideas of Platonism, then, is that scientists at least aim to discover the nonspatiotemporal scale-relative parameters, which are the objects of scientific knowledge, that explain, that is, identify, the spatiotemporal things, which are the objects of their scientific experiments. But scientists do have further goals. They aim to explain not just what sort of thing this is or what sort of thing that is and why this sort of thing and that sort of thing are different from each other but also what a spatiotemporal thing could be and what a spatiotemporal thing could not be. For example, in addition to it being true that I am now sitting, it is also true, right now, that I could have been standing and it is also true that I could be standing in the future. Moreover, it is also true right now that I could not be flying. Since I am currently sitting, it is not true either that I am standing or that I am flying. Nevertheless, it does seem to be true that I could be standing. Further, it does seem to be true that I could not be flying. All of these banal truths are things that science should be able to explain. There are two issues here. First, what are these truths? That is, when we think about them or refer to them by means of our language, what are the objects of our thoughts or the references of our sentences? And second, why are these truths true? That is, what makes the objects of our thoughts or the references of our sentences be truths, as opposed to not? Let us call the actual spatiotemporal things, like my sitting at some place and time or my standing at some place and time, a non-modal truth. We have seen how science explains why things are the way they are, that is, the non-modal truths. And let us call the possible but not actual spatiotemporal things, like my possibly standing at some place and time or my possibly sitting at some place and time, a modal truth. Science should also be able to explain why spatiotemporal things could be a different way than they are. As we shall see, getting that explanation also helps us see how we can explain why some things not only do not exist, but also could not exist, as for example,

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a perpetual motion machine. How then, does Platonism explain how science accounts for modal truths? In the previous sections, I described Platonism concerning how science explains non-modal truths. If, for example, (1) Scott is sitting is a non-modal truth, then the scale-relative parameter for sitting, given by some differential equation, is true of the region of spacetime where the scalerelative parameter for being human, again given by some differential equation, is true. A Platonist thinks that scientists discover those scale-relative parameters, which explain the (sortal) identity of some region of spacetime, by reasoning about the experiments they perform, and by reasoning about the results of that reasoning (i.e., by doing mathematical analyses concerning experiments and then by doing more mathematical analyses based on the previous analyses). But in discovering these scale-relative parameters, scientists discover not only the identities of the spatiotemporal things, but also, at the same time, what the spatiotemporal things are not, that is, scientists discover the differences between the scale-relative parameters. For example, by reasoning about our experiences and experiments, we have discovered the scale-relative parameter for sitting, the scale-relative parameter for standing, and by so doing we come to understand that the scale-relative parameter for sitting is not the same thing as the scalerelative parameter for standing. To the extent we get that knowledge, to that extent we can differentiate sitting things from standing things. But further, it is also true that by reasoning about our experiences and experiments, scientists come to understand when these scale-relative parameters can and cannot be true of the same region of spacetime. For example, though my sitting does rule out my standing at the same time, my sitting does not rule out my being white, my being thirsty, my being healthy, my being 5’8”, or my being a good place for bacteria to grow. So, even though I could not be sitting and standing at the same time, I could be sitting and white at the same time. And I could be sitting and thirsty at the same time. In fact, sitting and standing could both be true of me if we are talking about the complete four-dimensional spacetime region that gets labeled “Scott.” But, we have discovered that sitting and standing cannot both be true of me if we are talking about a sufficiently narrow timeslice of that spacetime region. We have also discovered by reasoning about our experiences and experiments that flying could never be true of a human being such as myself. So then, in order to further fill out Platonism, I need to turn now to these modal truths. What are they?

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Consider the following modal truth: (3) Scott could be standing. What is (3)? Though I am not standing, it does seem true that I could be.12 So, if (3) is a truth, what truth is it? We have already explained above how the non-modal truth, that is, Scott’s sitting, is a spatiotemporally extended complex dynamical system. So does (3) require us also to admit that there is another thing besides Scott’s sitting, namely, Scott’s possibly standing. Is there a genuinely existing possible spatiotemporally extended complex dynamical system? If we admit that there is, then the number of things on our list of existent things will explode as there are infinitely many possible things that every spatiotemporal thing could be. (For example, see David Lewis’s concrete counterparts in his 1986 or Alvin Plantinga’s abstract states-of-affairs in his 1976.) If we need to do so in order to explain the objects of science, then we should do so. But if we can explain modal truths and what makes them true without having to do so, then we should take that more ontologically economical path. What, then, could these modal truths be? If we do not want (3) to be Scott’s possibly standing, that is, a genuinely existing possible spatiotemporally extended complex dynamical system, the best way to explain what modal truths, like (3), are, is to explain them away in terms of other things that do exist. Since a Platonist’s ontology includes only genuinely existing spatiotemporal things and genuinely existing nonspatiotemporal things, only those genuinely existing things can be the things to which the modal truths are reduced. First, a little background on a proper Platonist philosophy of language (cf. Berman 1994). What do names pick out? Plato argues in the Cratylus that any true name, including a proper name, is a tool, a means, for getting our minds into a direct two-place relation with the thing itself.13 So, when we use a true name, we do so transparently, that is, in order to have the real thing itself in mind, and not opaquely, that is, merely to have simplified images of those real things in mind. According to Plato then, true names are elliptical for whatever the spatiotemporal things of some region of spacetime are. (If our audience is unaware of a proper name, for example, George Smith, then we use a definite description, in the referring use and not the attributive use, such as the one in the corner with a champagne glass, where our aim is to get the thing itself in our hearer’s mind even if some or all of our descriptions are false of that thing.) And since we do not have an infallible grasp of whatever the things of some region of spacetime are, we do not, according to Plato, have an infallible grasp of what we are referring to when we use names. We may have

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some educated guesses, that is, some hypotheses, but none of these guesses are guaranteed to be true. So, what does the proper name in (3) pick out? According to the Platonist account of language in the previous paragraph, “Scott” would have to refer to all of the things of some region of spacetime. What are some of the things of this region of spacetime? If we are restricting that region to a timeslice of about one minute in temporal duration, then “Scott” refers to a spatiotemporal part of a human thing, a white thing, a 5’8” thing, a sitting thing, a spatiotemporal part of a married thing, and so on and so forth. From a Platonist point of view, none of the things in this region of spacetime are essential to this region, or, in other words, none of these things are ontologically more what this spacetime region is than any other. Each of these things is equally real. It may be the case that I and others, for various practical reasons, care more about some of the things in this region of spacetime as opposed to the others. And because we are humans, we humans tend to give proper names to things that are human. We could just as truly give proper names to white things, 5’8” things, and married things. But ontologically speaking, none of the things of this region of spacetime are any more fundamental to what “Scott” picks out than any of the others. The only condition for a name being true of some region of spacetime is that some scalerelative parameter, or what Plato called a “Form,” is true of it.14 Given that theory concerning the nature of names and what they refer to, then, what is the modal truth that I could be standing? First, the Platonist will say that the modal truth (3) has to be at least some of the things to which “Scott” refers. So, since “Scott” refers to whatever the things in that region of spacetime are, then (3) will at least include the human thing, the white thing, the 5’8” thing, the bacteria culture, the roughly 7 billion billion billion atomic things, and so on and so forth. But second, as we are assuming that the non-modal version of (3) is false, specifically, we are assuming that it is false that Scott is standing, we have to exclude the spatiotemporal sitting thing to which “Scott” in (3) in fact refers. In other words, since (3) is a truth, then (3) cannot have something truly false incorporated into it. And third, (3) will have to include some scalerelative parameter that could be true of that region of spacetime but is not. It is this last condition that gives the modal truth its modal character, even though the thing in question, the scale-relative parameter for standing, is not a possibly existing thing but a genuinely existing thing. It is just that that parameter is not true of some region of spacetime, but could be. So, (3) will be (i) the human thing, the white thing, the 5’8” thing, the roughly 7 billion billion billion atomic things, and so on and so forth, but (ii) not the sitting thing, and (iii) the

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nonspatiotemporal scale-relative parameter for standing. Therefore, (3) is in fact about me—this human thing here and now—and what could be true of me, that is, the nature of standing—but (3) excludes the thing that makes the non-modal version of (3) false—the sitting thing. As we see, nothing in that collection is a possible thing. Every thing in that collection is a genuinely existing thing. The spatiotemporal human thing genuinely exists and the nonspatiotemporal scalerelative parameter for standing genuinely exists. (The spatiotemporal sitting things also genuinely exists, but we are excluding that from what (3) is.) A modal truth, then, is an odd thing as it is a collection of things, both spatiotemporal and nonspatiotemporal. But that makes sense given that a modal truth is an odd thing! (3) is, then, a collection of genuinely existing non-modal things. (Bertrand Russell used a similar strategy in his theory of definite descriptions in his 1905 and his 1919: chapter XVI.) Just as an atheist might explain away the allegedly existing divine object of a theist’s beliefs in terms of genuinely existing social conditioning or some other such genuinely existing non-divine thing or things, the Platonist explains away the alleged genuinely existing possible thing apparently referred to in (3) in terms of genuinely existing spatiotemporal things and a genuinely existing nonspatiotemporal thing. So much, then, for what the modal truth (3) is. What, though, makes the modal truth (3) true? In other words, supposing that collection of genuinely existing things (the human thing, but not the sitting thing, and the scale-relative parameter for standing) is what constitutes a modal truth, what makes that modal truth true? The Platonist proposal is that what makes (3) true is the genuinely existing relation between the scale-relative parameter for standing and the particular scale-relative parameter true of that region of spacetime, specifically, the scale-relative parameter for being human. What relation is that? Given that all scale-relative parameters are mathematical equations of some sort or other, typically differential equations of one sort or another, the relation between these scale-relative parameters will be some more complex mathematical equation (or system of equations) that has a solution set (to be explained below). It is because those two parameters are mathematically related to each other that their both being exemplified in one region of spacetime is possible. Why, though, are the mathematical relations between the scale-relative parameter for standing and the scale-relative parameter for being human nonmodal? These relations are non-modal because the relations between them are not how the scale-relative parameters could be related to each other, but how the scale-relative parameters are related to each other. It is not that the scale-relative parameter for standing could be related to the scale-relative parameter for being

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human. Scientists have discovered that they are related to each other, partly by observing standing humans. Those observations have given them some evidence that there does exist, does genuinely exist, some real relation between being a human thing and being a standing thing (cf. Lewontin 2019: 97–8). For an easier way of thinking about all that, consider the natural numbers. The number 5 is mathematically related to many other numbers. It is mathematically related to the number 12 via the number 7 and the addition function. It is also mathematically related to the number 12 via the number 17 and the subtraction function. It is not that the number 5 could be related to the number 12 in these and many other ways, it is related to the number 12 in these specific ways and in many other specific ways. Another simple example is this: it is not the case that the pressure of a gas just could be related to the volume of a gas. These two different kinds of quantities are related in a specific way (as given by Boyle’s Law). Given an increase in the pressure of a gas (holding temperature and mass constant), its volume will decrease. Why? Because that is the way those two kinds of quantities are related (holding temperature and mass constant). We have discovered their mathematical relation P∝

1 V

partly by observing the relation particular pressures and volumes have with each other in dynamical systems and have thereby determined their mathematical relation, which holds between those two kinds of quantities of a gas. Just so, the scale-relative parameters for standing, sitting, and so forth are related in specific discoverable ways with the scale-relative parameter for being human. Why, though, do these actual mathematical relations between scale-relative parameters explain the modal nature of truths such as (3)? The reason that (3) seems to be about non-actual possibilities is that when we utter, write, or think (3), we are thinking about how the particular things actually in some region of spacetime could have been other than they are relative to the actual mathematical relations between some of the scale-relative parameters true of that region of spacetime and other scale-relative parameters not currently true of that same region of spacetime. So, what makes it true that I could be standing, though I am sitting, is that some of the scale-relative parameters true of the complex spatiotemporally extended dynamical system here-now have actual mathematical relations with other scale-relative parameters that are not true of this region of space but could be. What explains that these other scale-relative parameters that are not true of this region of spacetime but could be is that they

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have actual genuinely existing mathematical relations with some, but not all, of the scale-relative parameters that are true of that region of spacetime. With respect to (3), then, the actual relation involved will at least be the actual mathematical relation between the (complex) scale-relative parameter for being human and the (complex) scale-relative parameter for standing. Scientists are currently working on discovering the scale-relative parameter for being human and they are also working on discovering the scale-relative parameter for standing, that is, the scale-relative parameter for being in an orthostatic state. The former is exceedingly complex and we are very far from having it figured out. The latter is less complex and therefore we have a much better grasp on its details. The scale-relative parameter for standing has something to do with when the resultants of the forces and the torques acting on the human complex spatiotemporally extended dynamical system are zero. Figuring out what has to be happening in that complex dynamical system, which is a human being, for standing to occur is being studied by all sorts of scientists, including physical therapists. They are working on the nature of the mathematical relation between those two different scale-relative parameters. If (3) is true, then there is a solution set for that more complex mathematical equation, that is, the one that nonadditively relates those two less complex mathematical equations. If (3) is not true, then there is not a solution set for that more complex equation, and hence, we find out that there is no more complex equation non-additively relating those two less complex equations. I now turn to the latter idea, namely, how science explains how some alleged “things” could not happen. Consider, then, the following different sort of modal truth: (4) Scott could not be flying. As we said before, (4) is a truth. It is true that I could not be flying. That is true. But when we think about that truth, what are we thinking about? If we do not want (4) to be this: Scott’s impossibly flying, that is, a genuinely existing impossible spatiotemporally extended complex dynamical system, which we would rather not have to believe genuinely exists, the best way to explain what negative modal truths, like (4), are is to explain them away in terms of other things that do exist, similar to how we explained modal truths away in terms of other non-modal things. Moreover, since this modal truth is a negative modal truth, (4) will have to be truly something other than what a positive truth would have been. Let me explain. Consider, as an analogy, the activity of archery. And specifically, focus on what it is to miss the target in archery. If it is possible to miss the target, then we have

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to be able to explain what missing the target is. And, according to Platonism, in order to explain what missing the target genuinely is, we have to explain it only in terms of things that do in fact exist. For example, we could explain what missing the target genuinely is as (i) the location the arrow in fact landed, that is, in the grass, (ii) the difference between being located in the grass and being located on the target, and (iii) the nature of archery as determined by its goal, that is, arrows landing on targets. (i), (ii), and (iii) are all things and together are what a miss is. A miss is neither the successful hitting of something that does not exist (since things that do not exist are nothing at all) nor the same in kind as the kind of thing hitting a target is. Of course, if the nature of archery is the loosing of arrows regardless of whether or not they hit anything, then a miss would be the same kind of thing as a hit is. But in that case, the failure to loose one’s arrow, say, because it falls off the bow, would then be what needs to be explained differently and not the missing of the target. And in that case, a Platonist would say, the arrow’s falling off the bow would not be the same in kind as the kind of thing an arrow’s being loosed is. The nature of archery, according to a Platonist, is a functionally interdependent set of scale-relative parameters. If that set of functionally interdependent scalerelative parameters are different, then the identity of the things involved in that activity would be objectively different. With respect to negative truths, then, they will be analogous to missing the target in archery. How so? The idea will be that negative truths—both modal and non-modal—refer to genuinely existing things other than the things the negative truths are ostensibly about. For example, if it is non-modally true that I am not standing, then that truth is really about things other than my standing, for example, my sitting. And what makes that negative truth true is that the scale-relative parameter for standing is not true of the region of spacetime where it is true that I am sitting. But a negative modal truth, such as (4), is more complicated. It is more complicated because it is not just that some scalerelative parameter is not true of some region of spacetime. It is more than that. The idea is that some scale-relative parameter could not be true of some region of spacetime. But in order to say that some scale-relative parameter could not be true of some region of spacetime, one has to bring in the relations between scale-relative parameters. The reason why the scale-relative parameter for flying could not be true of this region of spacetime, that is, the spacetime region where I am sitting, is that the scale-relative parameter for flying does not have the right sort of mathematical relation with the scale-relative parameter for being human. The reason that humans could not be flying is due to the lack of the right relation

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between the scale-relative parameter for being human and the scale-relative parameter for flying. But let me back up and take it step by step. Given a Platonist theory concerning the nature of names and what they refer to, to what does (4) refer? First, the Platonist will say that the modal truth (4) has to be at least some of the things to which “Scott” refers. So, since “Scott” refers to whatever the things in that region of spacetime are, then (4) will at least include the human thing, the white thing, the 5’8” thing, the bacteria culture, the roughly 7 billion billion billion atomic things, the sitting thing, and so on and so forth. But, second, since (4) is a negative truth, specifically, it is not the case that Scott could be flying, we have to include at least one scale-relative parameter that is not in the right sort of mathematical relation with flying, for example, the scale-relative parameter for being human. And third, (4) will have to include the scale-relative parameter for flying. So, (4) will be (i) the human thing, the white thing, the 5’8” thing, the roughly 7 billion billion billion atomic things, and so on and so forth, (ii) at least one scale-relative parameter that is not mathematically related in the right way with flying, for example, the scale-relative parameter for being human, and (iii) the nonspatiotemporal scale-relative parameter for flying. Therefore, (4) is in fact about me—this human thing here and now—and what could not be true of me, that is, the nature of flying. As we see, nothing in that collection is an impossible thing. Every thing in that collection is an actual thing. The spatiotemporal human thing is a genuinely existing thing and the nonspatiotemporal scale-relative parameters that are not mathematically related to the scale-relative parameter for flying, for example, the scale-relative parameter for being human and the scale-relative parameter for flying are all genuinely existing things. What then, makes (4) be a true collection? What makes the spatiotemporal human thing, the nonspatiotemporal scale-relative parameters that are not mathematically related to the scale-relative parameter for flying (e.g., the scalerelative parameter for being human, and the scale-relative parameter for flying) a true collection? What makes it true that I could not be flying is that some scale-relative parameter that does not have a solution set with the scale-relative parameter for flying is true of this region of spacetime. That is why (4) is true. Which scale-relative parameter is that? The scale-relative parameter for being human. What explains why the scale-relative parameter for flying is not only not true of this region of spacetime, but could not be true of this region of spacetime, is that the scale-relative parameter for flying is not mathematically related in the right way with some of the scale-relative parameters that are true of that region of spacetime, in this case, the scale-relative parameter for being human.

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In case another example helps, consider, again, the thought here as it relates to the natural numbers. As we said, the number 5 is mathematically related to many other numbers. But it is not related to those other numbers in every way. There are some mathematical relations the number 5 does not have with other numbers. For example, 5 ≠ 6. Identity is a mathematical relation that the numbers 5 and 6 do not have with each other. All of the relations they do have with each other are different than that one. Suppose, for example, we are playing a game of musical chairs. If there are 5 chairs when the music stops, then it true that (4*)

all 6 of us could not sit down on our own chair.

The number 6 is in fact mathematically related to the number 5 by way of the number 1 and the subtraction function. The relevant relation required, though, in order to make it true that all 6 of us could sit down on those 5 chairs is the identity relation, that is, the number 6 would have to be identical to the number 5 in order for it to be possible for a 1-1 mapping of people to chairs. But the identity relation is not the relation the numbers 6 and 5 have with each other. Since they are not related in that way, (4*) is true. Or again, take the relation the quantities of pressure and volume have with each other in a gas. Suppose some gas, say in the air in the tire of a car, has the gauge pressure of 35 psi and a volume of 4 cubic feet. The mathematical relation between the pressure and the volume of a gas was discovered about 350 years ago and is, as we said, called “Boyle’s Law.” Again, as these two different kinds of quantities are inversely related to each other: P∝

1 V

If the amount of air and its temperature in the tire is held constant, then the air in the tire could only have a higher pressure if the volume of the air in the tire was lower. Likewise, the air in the tire could only have a higher volume if the pressure of the air in the tire was lower. Given Boyle’s Law, we know that P1V1 = P2V2. So, if we want to increase the pressure of the air in the tire from 35 psi to 40 psi, without increasing the amount of the air by pumping in more, we would have to compress the tire such that its volume would be 3.5 cubic feet instead of 4 cubic feet. And if we want to increase the volume of the air in the tire from 4 cubic feet to 5 cubic feet, again without changing the amount of air in the tire, we would have to stretch the tire such that its pressure would be 28 psi instead of 35 psi. So, it is true that

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(3*)

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the tire’s air pressure could be 28 psi.

Given that the tire’s air pressure is not 28 psi, what makes (3*) true is the actual mathematical relation between the pressure and volume of a gas such that relative to the actual air pressure and volume of the tire here-now, namely, 35 psi and 4 cubic feet, the tire could have had a pressure of 28 psi if, given Boyle’s Law, its volume were 3.5 cubic feet instead. On the other hand, it could not be the case that (holding the mass and temperature constant) we could increase both the pressure and volume of the air in the tire. Why? We could never do that because the scale-relative parameter for the pressure of a gas and the scale-relative parameter for the volume of a gas do not have that sort of relation with each other, specifically, they do not vary directly with each other. As it turns out, they in fact vary only indirectly with each other. So, it is true that we could not increase both the pressure and volume of the air in a tire (holding the mass and temperature of that gas constant). It is Boyle’s Law, that is, the genuinely existing mathematical relation between the pressure and volume of a gas, which scientists discovered, that makes it true that we cannot make the pressure and volume both increase proportionally. In general then, the explanations for modal truths are the genuinely existing specific mathematical relations, or lack thereof, between the different scale-relative parameters. One of the key aspects of a Platonist explanation of modality, in general, is that Platonists reject what philosophers call “Humean independence.” Humean independence is the idea that there are no necessary connections between independently existing entities. Since a Platonist thinks that the spatiotemporal part of reality is not constituted by independently existing entities and that all of the scale-relative parameters are mathematically connected with each other (cf. Plato’s Theaetetus 201d–210b and esp. Sophist 251a–260a), what is possible and what is not possible is more restricted than what is logically possible. Logical possibility, as it is usually discussed by philosophers, assumes Humean independence and so, flying humans would be logically possible. Since a Platonist denies Humean independence, what is possible is restricted to the mathematical relations there in fact are between the scale-relative parameters. So, if the scalerelative parameter for being human is mathematically related in the relevant way only to scale-relative parameters other than the scale-relative parameter for flying, there could not be any flying humans. On the other hand, if the scalerelative parameters for being human and flying are in fact mathematically related in the relevant way, then depending on the nature of that relation, there could be flying humans. For example, if the scale-relative parameters for being

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human and flying are related to each other via the scale-relative parameter for artificial flight, then there could be flying humans in that way, for example, by being in an airplane. The main point, though, is that modal truths, no matter how expressed, are all to be explained by the non-modal genuinely existing mathematical relations between the scale-relative parameters.15

6  Laws of Nature It should be clear from the preceding section that a Platonist will think that laws of nature are the mathematical relations between the scale-relative parameters. Scientific research, therefore, whether it be physics, chemistry, biology, psychology, sociology, economics, ecology, or astrophysics, aims to discover the scale-relative parameters relevant to the subject matter at hand, together with the relations between those scale-relative parameters. And since these laws, that is, these functionally related scale-relative parameters, are themselves just more complex scale-relative parameters, laws of nature are just scale-relative parameters that are more complex than the scale-relative parameters that they mathematically integrate. In other words, the functional interdependence of particular scale-relative parameters is a more complex scale-relative parameter than the scale-relative parameters which functionally relate to each other. Philosophers, and physicists, however, more often than not think of the laws of nature as contingently true. In other words, they think that it is possible that the laws of nature, which explain and are true of the spatiotemporal world we find ourselves in, could have been different than they in fact are. Why? The ultimate reason philosophers have, which physicists likely rely on, for the view that the laws of nature are possibly other than what they in fact are is that it is logically possible for the laws to be different than they are. But what is required for something to be logically possible? In classical logics, something is logically possible if it does not entail a contradiction. So, while it is true that the pressure exerted by a gas (with a fixed mass and temperature) is inversely proportional to the volume it occupies, the relation between the pressure and volume of a gas could have been directly proportional instead, that is, their varying directly does not entail a contradiction. They happen to have an inverse relation, given the laws of nature true of our world. But if those laws were different, then those kinds of quantities, the pressure and volume of a gas, could have had a different relation with each other. There is nothing logically inconsistent in that. And so, just as it is logically possible for these kinds of quantities to have a different relation with

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each other than they do, it is logically possible for every law of nature, that is, every relation between different kinds of quantities, to be different than they are. And therefore, because it is logically possible for the laws of nature to be different than they are, it is possible without qualification for the laws of nature to be different than they are. I shall now explain why the Platonist position defended in this book is committed to the idea that it is not really possible for the laws of nature to be different than they are, even if it is logically possible for them to be different. Philosophers (and physicists) who claim that the laws of nature are really only contingently true are making an important mistake about the nature of possibility. The mistake is in thinking that the fundamental kind of possibility is logical possibility, as opposed to scientific possibility. The reason that philosophers (and the physicists who think about the issue at all) think that is this: since the logical notion of possibility is the least restrictive one, logical possibility is the fundamental notion of possibility. So, if we want to know whether something is possible or not, that is, fundamentally possible, and not just possible relative to the laws of nature, which is a more restrictive notion, then logical possibility is what tells us what is, fundamentally, that is, at bottom really, possible. However, the study of logic is not the sort of study that aims at discovering what is fundamentally, that is, really, true. Classical formal logics are supposed to help us differentiate between good and bad structures of reasoning, but with a special constraint: they have to be neutral as regards the truth or falsity of the claims being made within those structures. If the formal logical structures discovered were not neutral as regards all matters of fact, then logic could not be used to adjudicate the arguments used within every subject matter impartially, since logic would itself have commitments that might conflict with one of the protagonists within the field in question. It is precisely because formal logics do not take a stand on the truth or falsity of any claims that it can be used to evaluate every argument no matter what its subject matter. The fundamental idea of formal logic, then, is that good arguments, that is, valid arguments, are ones in which the truth of the premises guarantee the truth of the conclusion just based upon the purely formal relations between the premises and the conclusion and never upon the factual relations between the assertions and the world. Here is the problem though: if we use logic, which claims to be neutral as regards all matters of fact and real existence to discover whether it is possible, that is, whether it is in fact possible, for the laws of nature to be different, then we are trying to get more out of logic than it can provide. Logic can tell us whether it is logically possible for the laws of nature to be different, that is, whether we can, from logical considerations alone, assert a different set of laws. But it does not tell

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us whether those logically possible different laws are truly possible or not. Logic is not a descriptive inquiry into the truth concerning some specific aspect of reality. Logic is a prescriptive or normative inquiry into how one ought to reason. At a minimum,16 one ought to reason in such a way so as not to contradict oneself. But if logic at most only tells us about how we ought to reason, then logic delivers recommendations about good reasoning and not true descriptions of reality. As such, logic is epistemological in nature and not metaphysical or scientific. Logical possibility, then, gives us the widest possible constraint on what is reasonable to believe, but not the widest possible constraint on what is truly possible. In order to get the widest possible constraint on what is truly possible, we need a descriptive science that is about what is true and not a normative inquiry that is neutral as regards what is true. Einstein put it well: “Propositions arrived at by purely logical means are completely empty as regards reality (1934: 14).” For example, if you ask me whether it is possible for a thing to travel faster than the speed of light, and I tell you that it is logically possible, that is, no contradiction follows from assuming it to be true, I will have skirted the question you asked. You had wanted to know if it is possible, that is, really possible. In other words, you were not asking me if it is irrational to believe that something can travel faster than the speed of light. It is not logically contradictory to believe such things. But knowing that it is not logically contradictory to believe it is only to know something negative. You had wanted to know something positive: Can something really, truly, in fact, travel faster than the speed of light? What determines whether that is really possible is not merely whether asserting it entails a contradiction or not. Finding out that something does not entail a contradiction tells you, at best, only that, for all we know, it is not impossible, but not that it is possible (cf. Seddon 1972; van Inwagen 1998). On the other hand, what determines whether or not something really is possible depends on the kind of thing it is. So, something is possible if, and only if, the relevant kinds of complex quantities involved in the kind of thing that it is have in fact that relation with each other. For example, if we are asking if it is really possible for something to travel faster than the speed of light, we need to ask that question relative to the kinds of quantities involved. And what are those? Well, they are energy, mass, and velocity. According to the Special Theory of Relativity, the relation between these three kinds of quantities is this: Ek = m0 (g − 1) c 2 =

m0c 2 1−

2

v c2

− m0c 2

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If that is truly the relation between these three different kinds of quantities, as our best science tells us, then no spatiotemporal thing can travel faster than the speed of light.17 For it to be really possible that something travels faster than the speed of light, there would have to be a specific relation between mass, energy, and velocity other than the one that is true, as far as we know, of those three different kinds of quantities. Given that our best guess is that there is not that different relation between them, it is not really possible for any spatiotemporal thing to travel faster than the speed of light, even if it is logically possible.18 But the question at hand is this: Could the mathematical relation between energy, mass, and velocity be different than it is? Logic might be able to tell us that, for all we know, it is not impossible that it is. But is it really possible for it to be different? If the laws of nature can really be different than what they in fact are, what makes it true that the laws of nature could truly be different? Something has to make it true, if it is true that the laws of nature could really be different than they in fact are. The usual answer is that logical considerations make it true. However, as I have just argued, since logic is neutral as regards all matters of fact and real existence, logical considerations cannot make claims about what is really possible true. Again, at best, all logical considerations can do is say that, for all we know, it is not impossible that the laws of nature could really be different than they are. But that was not what we wanted to know. We wanted to know this: What makes it true (if it is true) that the laws of nature could really be different than they are? Thankfully, some physicists have put forward a guess as to how to answer that question, for example, Max Tegmark (2008, 2014). Suppose, then, there exist mathematical meta-laws that constrain the possible range of laws, which would function as the scientific laws of a maximally continuous spatiotemporal world, then we could make sense of how it can be true that the laws of our universe could be different than they are. These actual mathematical meta-laws would be the things that make it true that our universe’s laws could have been different. If so, though, these meta-laws would then be the genuine laws of nature and the effective laws, that is, the ones that we thought were the laws of nature but are not, could then truly be possibly other than they are. If the real laws of nature are these meta-laws, then Platonists would have to concede that the effective laws which explain our spatiotemporal world are in fact only contingently true. But in that case, the Platonist would then just re-state the position as this: the laws of nature, properly understood as these meta-laws, could not have been other than what they are. The Platonist position is this:

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whatever ultimately explains our spatiotemporal world, be it the effective laws we thought were the laws of nature or the meta-laws which are, ex hypothesi, the laws of nature, cannot truly be other than what they are.19 Such a view might be best thought of as a Pythagorean version of Platonism. And we just might find out that it is true. But if so, then these mathematical meta-laws would be the ultimate laws of reality and not possibly other than what they are. On the other hand, if there are not these mathematical meta-laws, then there is nothing that makes it true that the laws of our universe could have been different than they are. So, it would not be true that they could have been different than they are. That is not to say that the laws of our universe are necessarily what they are. It is just to say that they are not possibly other than what they in fact are. Necessity and possibility have a specific relation to each other in logic, that is, they are interdefinable. As we are not asking whether it is logically possible for the laws of nature to be different than they are (or whether it is logically necessary that the laws of nature be what they are), but whether it is really possible for the laws of nature to be different than they are, finding out that it is not possible for them to be different does not make it true that the laws of nature are necessary. The idea of scientific necessity is foreign to science.20 There are just scientific truths. We can use some of those scientific truths, the laws of nature, to explain what is possible and what is not possible, that is, what is scientifically possible and what is not scientifically possible. Scientific possibility is a way of indicating which kinds of spatiotemporal things, that is, what kinds of complex dynamical systems, are spatiotemporally possible. And what makes that true, that is, scientifically true, is that the laws of nature are what they are. And though it is true that the laws of nature could not be other than what they are, that does not make it true that the laws are necessarily what they are. But regardless of whether or not there are those mathematical meta-laws, since we live in this universe, it is plausible to assert that we do not really know that the laws which explain our universe are not possibly other than what they are.21 It is possible that the physical constants that we have discovered could have been other than what we have discovered them to be had the very early start of our universe been different. But even if that is the case, the (yet to be discovered) laws, which explain why that early quantum fluctuating system locked in the physical constants it did, would themselves be that which ultimately explains our universe. Even stochastic laws, that is, probabilistic laws, explain dynamical systems. On the other hand, it is also plausible to assert that the laws of nature change over time.22 But again, if they do, their changes would be explainable, according to Platonism, via whatever meta-laws ultimately explain how those

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intra-universe “effective laws” can, possibly, change. And if so, again, the ultimate explanation of our universe would be those meta-laws that do not themselves change. The guiding hypothesis here is that the sciences, other than the alleged science of logic, tell us what is spatiotemporally possible, and so, what is scientifically possible is what is really possible. Physics tells us what kinds of physical dynamical systems could be spatiotemporally exemplified. Chemistry tells us what kinds of chemical dynamical systems could be spatiotemporally exemplified. Biology tells us what kinds of biological dynamical systems could be spatiotemporally exemplified. Psychology tells us what kinds of psychological dynamical systems could be spatiotemporally exemplified. Economics tells us what kinds of economic dynamical systems could be spatiotemporally exemplified. Sociology tells us what kinds of sociological dynamical systems could be spatiotemporally exemplified. And so on for every science. They each do so by discovering the scale-relative parameters that are true of those restricted regions of spacetime. The relations between those parameters, which are discovered by the scientists working in these fields, explain the possible changes in those systems. In other words, the laws discovered by the scientists working in these fields explain what changes in those systems are really possible.

7 Conclusion We have now seen how Platonism explains the objects of science. According to Platonism, the objects of scientific knowledge are the nonspatiotemporal mindindependent fully existing scale-relative parameters that identify and explain the spatiotemporally extended complex dynamical systems, which are themselves the objects of scientific experiments. In previous chapters, I argued that other explanations for the objects of scientific knowledge are inadequate in various ways. If those arguments are correct, then physicists, chemists, biologists, psychologists, sociologists, ecologists, and astrophysicists are all aiming to get objective knowledge of the scale-relative parameters that identify and explain the spatiotemporally extended complex dynamical physical, chemical, biological, psychological, sociological, ecological, and astronomical systems. Moreover, the relations between the nonspatiotemporal scale-relative parameters explain why it is scientifically possible for particular regions of spacetime to be different than they are and why it is scientifically impossible for particular regions of spacetime to be different than they are.

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I have argued in this book, then, that Platonism is the best explanation of the objects of science as compared with nominalism, contemporary Aristotelianism, constructivism, and classical Aristotelianism. But one thing that I have not addressed, except in passing in Chapter 4, and which is possibly the most obvious objection to Platonism, is the worry one might have about how science itself could embrace a commitment to nonspatiotemporal things. After all, science seems to be about what is spatiotemporal and seems focused on experiments concerning what is spatiotemporal. It is usually thought that it is the nonnaturalist, that is, the one who is not scientific, who believes in things that are not spatiotemporal. Would not explaining anything about science having to do with nonspatiotemporal things just be antithetical to science? Surprisingly, that objection or worry is perhaps the easiest one to answer.23 A Platonist will say that given that scientists use their reason to think about the experiments they perform, they get the nonspatiotemporal things in mind by means of that reasoning.24 For example, when one infers from many experiences, controlled or not, to a generalization about what will, in general, happen in the future or what did happen in the past, the vast majority of these events will never be experienced by anyone. For example, suppose we see every day, for weeks, months, and years without exception, sunshine beginning at our eastern horizon and ending at our western horizon. Based on those experiences, we infer both that it will continue to do the same in the future even after we are no longer able to experience it and that it was happening the same way in the past even before we were able to experience it. Is that inference guaranteed to be correct? That is, does our inference guarantee that it was always that way and that it will always be that way? Of course not. But our reasoning about those experiences does put those future and past non-experienced happenings in our minds, not as experiences, that is, not as something that we experience, but instead, the actual events themselves. Or when Mendel infers from the thousands of examples of pea plants he carefully produced, which had the same proportion of tall to short plants, that the same proportion of tall to short plants will likely be produced in the future if he maintains the same procedures, whether he does the producing or not, he has all those related and unexperienced plants in mind by means of that inference. Those are just two examples of inductive reasoning, that is, inferring what we would likely see, in general, from what we have seen, in particular. Another example of how reasoning can get something unseen in mind would be that of a detective, as illustrated by Sir Arthur Conan Doyle’s Sherlock Holmes. When Holmes infers, for example, that someone did a criminal act by

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reasoning about what best explains the evidence he finds, he has someone, he knows not who, in mind, namely, the person who is actually responsible for the criminal act. Once he figures out who the someone is that he has been thinking about, namely, Professor Moriarty, say, he then comes to know who, that is, what thing, he had been thinking about all along. Or when Mendel infers from seeing the thousands of examples of pea plants, which produced the same proportion of tall to short plants, to an explanation for that pattern, namely, that there are genes which combine, that is, function, in ways relative to some of those genes being functionally dominant and some being functionally recessive. Mendel inferred that if things such as genes do exist, and genes combine in specific ways, then that would explain why he sees what he sees. So, although he does not see the genes, when he infers that if they existed that would explain what he does see, he gets something unobserved in mind by means of that inference. Those would be two examples of abductive reasoning, that is, inferring the existence of an unseen thing, an explanation for what we are seeing.25 Both of these types of nondeductive inferences, inductive and abductive, are risky inferences. Neither one of them guarantees that if the premises are true, then the conclusion is true. Our observations of where the sunshine starts to appear each day could be correct even if some day down the road, the sunshine no longer appears each day at the eastern horizon (say, if, the earth changes its rotation or if the earth leaves orbit or when the sun burns out). And even if the observations of the pea plants are correct, there could be a better explanation of why we keep getting the same proportion of tall to short plants. Nevertheless, those inferences can in fact be correct, even if they are not guaranteed to be correct. If so, then we do get those unseen things in mind by virtue of our reasoning when it is in fact correct. Knowing when our reasoning is correct, of course, is the hard part. And that is the job of science, not logic. If there are in fact genes, for example, then Mendel’s inference was correct. If there are not, then his inference was incorrect. However, the preceding might seem objectionable because even if we never see the future experiences or past experiences or the person who committed the crime or the genes, they are observable. That is, they can be observed. The explanatory things the Platonist requires are not, in principle, observable! That is quite correct. Nonspatiotemporal things are not, in principle, observable, as they cannot, for instance, reflect any wavelengths of visible light. But, so goes the objection, that is the part of Platonism that seems particularly unscientific. Why would any scientist consent to believing in things that are not in principle observable?

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The Platonist would respond that the unobserved genes (in Mendel’s time, anyway) only explain the observed pattern of pea plant production if the spatiotemporal genes, which are observable, are the sort or kind of thing that they are. That is, it is only because the particular genes exemplify the abstract structure that they do can they be identified as the cause of that effect. What Mendel discovered by means of his reasoning about his observations was not those particular genes in those particular pea plants, though those particular genes in those particular pea plants do constitute the evidence for what he discovered. What Mendel discovered, and what is an object of scientific knowledge, was the kind of thing genes are, that is, the abstract structure or scale-relative parameter, which explains why we see the patterns of pea plant behavior that we see. If there exist things that exemplify the specific kinds of functional roles Mendel reasoned were needed, things with recessive and dominate functionalities, then we will see examples of the specific kinds of effects we do in fact see. And since, as I have argued in this book, kinds are best thought of as nonspatiotemporal scale-relative parameters, Mendel simply used human reasoning to get those nonspatiotemporal things in mind, as does every scientist in every field whatever. Nothing mystical or mysterious at all. We human beings, then, use our reason to get unobserved and unobservable things in our minds. Just as the objects of perception are the things in the world, so are the objects of thought. We can see dangerous objects in the world and we can think about those same things and reason about how best to avoid those objects. If the arguments of this book are correct, then in addition to spatiotemporal objects, there also exist nonspatiotemporal objects. If so, then we can have the latter in mind as well, even though we cannot perceive them, again, due to our ability to reason. We make inductive or abductive inferences about the things we will see in the future or the things that best explain what we have seen in the past. Our inferences put those unobserved or unobservable things in our minds. We do not know what those things are, which we have in mind, just by introspection, but we have those unobserved or unobservable things in mind nonetheless. And through careful research involving further observations and still more reasoning, including mathematical reasoning, we sometimes confirm that our initial reasoning that such things exist was correct. Of course, whether we confirm that our initial reasoning was correct or not, if we did in fact make the correct inference, whether we know it to be correct or not, then we did get those unobserved things or that unobservable thing in mind, that is, we did discover them or it. Peter Higgs, for example, came to have an unobservable

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kind of boson in mind in 1964 due to his (and others’) reasoning about how best to explain why particles have the mass they do and then came to know, in 2012, after all those years of research by many people, that his reasoning was in fact correct and that that kind of particle does in fact exist. The evidence collected at CERN and the careful reasoning about it confirmed that that inference was correct: there does in fact exist an unobservable nonspatiotemporal kind of particle that explains why any spatiotemporal particle has the mass it does and which we call “the Higgs boson.” Therefore, if Platonism is the best explanation of the objects required for the possibility of scientific knowledge, because all of the other explanations fail for one reason or another, then we are justified in believing in the existence of nonspatiotemporal things, in addition to the spatiotemproal things, that are mind-independent exist in the same full sense of existence as those spatiotemporal things. What could be more scientific or naturalistic than a commitment to the existence of something science needs in order to be possible? In conclusion, then, when we reason about our experiences in order to understand them and when scientists use reason in order to understand their experiments, what we and what scientists come to have in mind when using reason correctly are the nonspatiotemporal and, in principle, unobservable entities Plato first hypothesized as existing 2,400 years ago, which he argued were needed for the existence of science. Surprising conclusion, no doubt. But, as I hope to have shown, the core of his idea turns out to be arguably true.

8 Implications If the arguments I have made in this book are correct, then some obvious and less obvious implications follow. First, obviously, if the objects of scientific knowledge are nonspatiotemporal, then given that they are not spatial, they cannot be located anywhere. So, we cannot ask: Where are they? But second, given that they are not temporal, neither can they change nor can they have been created nor can they be destroyed. So, we cannot ask, well, who made them? They are not such that they could have been made. They just are. Spatiotemporal things, on the other hand, given that they are spatial can be located somewhere and given that they are temporal can change and can cometo-be and pass-away. They are a kind of thing where those questions could be appropriate to ask. Of course, the upshot of those first two implications is that

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every scientifically possible nonspatiotemporal kind of thing exists (no where and no when) whether it is exemplified spatiotemporally or not. For example, the nonspatiotemporal nature of AIDS exists (no where and no when) regardless of whether anyone ever suffers from it. Tragically, millions of people have and are suffering from it and due to that, we are aware of it and are working to prevent it, and manage or cure it. But even before anyone ever contracted it, AIDS existed. Generalizing from that, there are likely thousands, which is a low estimate no doubt, of kinds of diseases that exist (no where and no when) of which we will never (hopefully) ever become aware because no one will ever suffer from them. That would be all to the good. Nevertheless, as long as those kinds of diseases are biologically possible, then those kinds of diseases exist. Clearly, Platonism countenances the existence of many more kinds of things than we will ever come to know and many more kinds of things than will ever be exemplified. But as I argued in Chapter 3, such is required for the nature of science to do its work. Third, and more sweeping, if, as I argued in Chapter 4, constructivism is in fact incoherent, then it cannot be a good explanation about any of the truths in any domain. If that is correct, then not only is it incorrect about the objects of science, but it is also not correct about the objects of social scientific knowledge or the objects of humanistic knowledge. In other words, just as physicists discover the mind-independent nonspatiotemporal natures of the kind of thing a Higgs boson is and the kind of thing an electron is, chemists discover the mind-independent nonspatiotemporal natures of the kind of thing hydrogen is and the kind of thing bonding is, biologists discover the mind-independent nonspatiotemporal natures of the kind of thing cancer is and the kind of thing a gene is, it is also the case that economists discover the mind-independent nonspatiotemporal natures of the kind of thing a market is and the kind of thing a business cycle is, and sociologists discover the mindindependent nonspatiotemporal natures of the kind of thing a class is and the kind of thing a culture is, and ethicists discover the mind-independent natures of the kind of thing goodness and/or rightness is, and aestheticians discover the mind-independent natures of the kind of thing art is and the kind of thing beauty is. The reason that the third implication seems so surprising is that it would seem obvious that things involving human beings, such as art, morality, society, and economics, could not be mind-independent as they depend on us! However, as I argued in Chapter 4, the fact that we are necessary for manifesting certain structures does not entail that we ultimately determine what is true about those

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kinds of structures. At most, what is ultimately up to us is whether or not we do manifest or exemplify a kind of mind-independent nonspatiotemporal economic, societal, ethical, or artistic structure. We can exemplify or manifest a kind of mind-independent spatiotemporally extended dynamical system only if the scale-relative parameters relevant to that kind of system are in fact functionally interdependent, that is, mathematically related. If they are not in fact functionally interdependent, then we cannot manifest that kind of spatiotemporally extended system whereby those different objective variables do in fact function together as a system. Discovering which societal features, that is, variables or parameters, can in fact function interdependently is what people in the social sciences and humanities are trying to figure out, whether they realize it or not, just as in the natural sciences. It is just that the subject matters of the social sciences and the humanities are far more complex; that is, they have many more functionally interdependent variables, such that it makes it that much harder to figure out. Being able to see that one is making progress in one’s research requires one to measure those vastly more complex spatiotemporally extended dynamical systems. But even though it is much harder to measure, it is not impossible. In other words, though it is true that there will not exist any beautiful sculptures unless we sculpt them, or ethically good lives unless we live them, or egalitarian societal structures unless we construct them, or democratic political systems unless we adopt them, or socialist economic systems unless we put them in place, or even names of things unless we name them, the natures of those kinds of things are not created or constructed by us. We discover, after reasoning about the various ways things have gone with other humans in the past, that it would be in fact better for us if we organized our lives this kind of way as opposed to that kind of way. We discovered that this way of organizing our collective lives is in fact better than that way. But those two different ways of organizing our collective lives are two different kinds of societal structures. And so, what we have discovered is that this kind of societal structure is better for our collective lives than that kind of societal structure. We did not create those two different kinds of societal structures. We just created examples of them, or we looked at other people who did, and we reasoned about their experiences and how their lives went and then concluded that one of them is in fact better for humans than the other and that is why it is best for us to go down this path as opposed to that path. The same explanation would be the case for kinds of economic systems, kinds of patterns of behavior that we want to identify as being ethically good or bad, and kinds of patterns of creative expression that we want to identify as

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being aesthetically beautiful or ugly. I will leave for another place a discussion of the details of how that works for aesthetics and ethics, but the main idea is this: whatever is true in any domain of interest will ultimately be true, and be best explained by, the mind-independent nonspatiotemporal fully existing things scientists pursue every day in their work and which we, less rigorously, use to think about and understand our experiences all of our lives.

Appendix

Do any nonspatiotemporal entities exist?

Yes

No

Are the nonspatiotemporal entities mindindependent?

Yes

Do any universals exist?

No

Yes

Realism

Constructivism

Is 'being' univocal?

Whose Mental Activity?

Yes

Platonism

Contemporary Aristotelianism

No

Classical Aristotelianism

God's

Ours

Mine

Theological Voluntarism

Cultural Relativism

Existentialism

No

Nominalism

Notes Chapter 1 1 Penner 1987 is that book and it is the basis for how I think it best to interpret Plato’s dialogues. As this book is not about interpretation, but just about its consequences for theoretical concerns, I will not defend his interpretation. My goal here is just to defend in contemporary terms, what I have been convinced are, the ideas that follow from that interpretation. 2 Though Plato accepts these three contrasts in his middle-period dialogues, he wisely rejects the first of the three contrasts in his later dialogues and relies only on the second and third of the contrasts. I will henceforth not mention the first contrast as part of any argument. I include it here only because it is used by Plato, until he realizes his mistake in the Theaetetus in doing so. 3 Besides all of Plato’s middle and later dialogues, see also Aristotle’s Posterior Analytics I.8.75b21-30, I.24.85b16-22, I.30, I.31, I.33, for his clearest presentation of those commitments. 4 There is good reason to think that these inferences are not best explained by contentindependent mechanisms—that is, as most philosophers think of them, for example, in terms of logic—but by content-dependent mechanisms—that is, as evolutionary psychologists think of them, for example, in terms of domain-specific biological neural circuits. The importance of this difference will be discussed in Chapter 2. 5 For a defense of the identification of moral goodness with prudential goodness, see Berman (2014).

Chapter 2 1 See the opening paragraph of Quine (1948) for a succinct example of this! 2 But see Fales (1990) for an argument to the contrary. 3 “Science at its best is the search for commonalities, regularities, principles, and universalities that transcend and underlie the structure and behavior of any particular individual constituent, whether it be a quark, a galaxy, an electron, a cell, an airplane, a computer, a person, or a city” (West [2017: 269]). 4 Many have pointed this out, but the first was Plato in his Theaetetus in his discussion of Heracleitean flux at 179c–183e.

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5 I say “realistic” because it does not seem really possible for an organism to have as many receptors as there are things in existence. And even it is granted that under the assumption that we only need to have receptors for a subset of all the things there such that there will be countless many things that exist that we will not be able to have experiences, it is still the case that we will not have, realistically, enough receptors to be able to help us survive given the environment within which we live. 6 See Levinson (2006) for a good argument against taking tropes seriously. I do, briefly, talk about this theory in Chapter 3 on pages 64–65. 7 However, the class nominalist would immediately backtrack and say that these collections, or groupings, or classes, do not really exist in addition to the particulars themselves. All there is to these classes is the particulars. So, there does not exist a class of red things in addition to all the red things there are. All there is to the class of red things is just the red things themselves (Lewis 1983: 343–44; confirmed by Armstrong 2001: 79). 8 The class nominalist’s view is more complex as it countenances not just all the red things there are, were, and will be, but also all the red things that exist in every possible world. 9 Lewis’s “best system” theory of laws of nature does not answer this worry because it still gives no explanation of how scientists can even begin to collect the “collections of truths” if none of the individual truths have any thing in common with each other in order to be compared with other “collections of truths” to see which of them is the best system, as evaluated by their simplicity and strength. His version of nominalism needs to be supplemented by something else, for example, resemblance between individual truths or particulars. 10 The contemporary Aristotelian disputes this claim. We shall examine it in detail in the next chapter. 11 Simons correctly identifies the idea of “internal relations,” which nominalists and trope theorists often employ, as the same gambit as the idea that particulars brutely resemble each other, and therefore, I will not discuss that idea separately. 12 Simons 1994, a nominalist, seems to admit, science, and not “armchair philosophy” will discover what “kinds of trope” there are (p. 569; my italics).

Chapter 3 1 Some contemporary Aristotelians, like Lowe, admit tropes into their ontology while some, like Armstrong, do not. 2 Perhaps no one accepts this weak version. But when explicating just what the principle of instantiation is, one cannot assume from the start that universals exist “timelessly.” I think that this weak version is the natural first idea of someone who

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3

4 5 6 7

Notes

might be tempted by the principle of instantiation. It may not be one’s considered view, especially in light of the difficulty I shall presently raise for it. But I think it is important to consider this version here, at least for completeness. For the record, this version of the principle would be consistent with what Lowe (2006: chapter 3) calls “rigid existential dependence.” Though this assumes something controversial, namely, that the objects of scientific knowledge have to be changeless, it should not be controversial among realists, whether Aristotelian or Platonic. Lowe (2006: chapter 3) calls this “non-rigid existential dependence.” Marenda, Orlandini, and Micheletti (2018) is just one recent example of such research, but there are countless others. Again, we shall get into more details about these relations in Chapter 6, as it does seem odd to say that the lack of a universal makes some claim true. There are other reasons people have nowadays for being Aristotelian than just the ones I have laid out concerning universals. Contemporary philosophers who view themselves as Aristotelian might have been motivated to adopt Aristotelianism instead due to how they see Aristotelianism as being the best explanation of the mind-body problem (e.g., Ryle [1949], Putnam [1975], and Nussbaum [1984]), or being the best explanation of causation (e.g., Marmodoro [2017]), or being the best explanation of biology (e.g., Austin [2017]). In other words, they may not see the issues we have discussed concerning the nature of universals as being central or even relevant to what seems right to them in Aristotelianism. To them I say this: as long as what you find explanatorily useful in Aristotle or in Aristotelianism does not ultimately require that spatiotemporal universals exist or that there is more than one sense of existence or that spatiotemporal particulars are essentially just one thing, that is, what Aristotelians call a substance, as opposed to being accidentally or contingently what they are, then nothing you are using in your explanation is particularly Aristotelian as opposed to Platonic. Rather, what you are finding useful is just the same realism that both Plato and Aristotle share. In other words, Plato and Aristotle have more in common than not. They are both realists, that is, they both reject nominalism and constructivism. Aristotle, in many areas, is just giving a more detailed account about the same subjects, which Plato initiated. They differ on the logical status of being—Plato thinks that there is a genus of being and Aristotle denied any such genus—and they differ on whether spatiotemporal things had essences—Aristotle thinks that they do have essences and Plato denies that they do. Therefore, if someone thinks that the soul or mind exists in a different and lesser sense of existence than human being as a whole does, then that explanation will not ultimately be best as it unfortunately commits itself to an incoherent foundation, as we will see in Chapter 5. On the other hand, if someone thinks that causation is best explained in terms of agent causation, since both Plato and Aristotle accepted that same theory—Aristotle just explicating it in far more

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detail—the contemporary philosopher who adopts that view is not necessarily being more Aristotelian than Platonic. If agent causation is false, as I think it arguably is, then both Plato and Aristotle share being wrong about the nature of causation (pace Lowe 2008). However, since I am not defending everything Plato argued for but just his account of the objects of science, that is, knowledge, I can let go his errant view on causation if it is not essential to his view on the objects of science, which it is not. Regardless of that, though, and in summary, as long as the contemporary self-described Aristotelian does not require that universals are spatiotemporal or that they, or anything, do not exist in a lesser sense of existence than anything else, or that spatiotemporal particulars are not substances, then I do not see any incompatibility with their preferred explanation of whatever they are explicating and the Platonism that I am arguing for in this book. On the other hand, if they do require in their explanations that there are spatiotemporal universals or that something exists in a lesser sense of existence or that there are substances, then their preferred explanations would fall prey to the objections I have raised in this chapter as well as the ones I shall raise in Chapter 5—against there being different senses of existence—and Chapter 6—against there being substances. 8 Medievals referred to Aristotle’s idea as “the analogy of being,” but they were mistaken to think that Aristotle thought of the different senses of “being” as being analogous to each other. He is very clear in his Nicomachean Ethics at I.6.1096b27-8 that analogy is a different sort of relation than the pros hen relation he uses to explain how being is equivocal.

Chapter 4 1 I am thinking of reasoning broadly. So, not just as deductive sorts of inferences but also as nondeductive inferences as well, in fact, centrally. I am thinking of inductive and abductive sorts of inferences as the most central forms of reasoning scientists engage in when discovering the nonspatiotemporal commonalities between spatiotemporal things. 2 I will not be discussing theological voluntarism as a possible explanation in this chapter even though I do think it too suffers from the same bootstrap problem as the rest and is, therefore, theoretically incoherent as well. Seeing exactly why grounding scientific truths on God’s ultimately arbitrary will is not going to work would take us too far afield. 3 Let us assume that we are talking about some time in 2015, that is, when there was at least some degree of democratic institutions still functioning properly. 4 My colleague in Saint Louis University’s History Department, Lorrie Glover, tells me, though this is controversial, she thinks that the Founding Framers thought that (DTA) was true by nature and not true due to their “mutual pledge.”

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5 The traffic laws example was explained using a deontological framework. But a consequentialist framework would have worked just as well. Instead of explaining why I ought to drive on the right-hand side of the road because someone with the legitimate right to make commands is commanding me to do so, the consequentialist will say that I ought to drive on the right-hand side of the road because it will produce better outcomes for me (and us) than if I drive on whatever side I feel like at every time. Picking the right-hand side or picking the left-hand side will produce less fender-benders and deaths than not picking just one side and sticking to it. So, there is nothing intrinsically better about picking the right-hand side or the left-hand side of the road, as long as we pick one of them. Therefore, our agreement is truly good not just because we picked it, that is, made an agreement. Our agreement is truly good because of its real consequences, namely, preserving our lives and our cars. The idea is the same: something else in addition to an agreement or mental activity is required for the agreement or mental activity to be true. 6 So-called “if-then-ism” does not obviate the claim here, as people have argued that it does in the philosophy of mathematics, starting with Russell (1903) and most recently with Dorr (2008). The idea in the main body is that these “if-then” statements refer to mind-independent relations between kinds of things. We will be talking about these real relations in Chapter 6. With respect to (DTA), though, it would be referring to the mind-independent relation, that is, the natural political law, between the kind of thing agreement is and the kind of thing political authority is, just as we could express natural physical laws as relations between kinds of things, as, for example, between the kind of thing mass is and the kind of thing force is in Newton’s Second Law, if something has this much mass, then it will have that much force.

Chapter 5 1 Penner (1987) is very influential in my thinking on the first five and that helped me see the sixth one when I came across it in conversation with James Bohman, a colleague of mine who was a student of Thomas McCarthy and Jürgen Habermas. 2 Though I did not discuss them, perhaps two of the most famous uses of classical Aristotelianism were in the twentieth century by philosophers who used it to solve important logical and semantic paradoxes. Bertrand Russell’s “Theory of Logical Types,” as a way of solving Russell’s Paradox, which strikes at the core of classical formal logic, and Tarski’s notion that truth and falsity never apply to the same level of discourse, thereby solving the Liar’s Paradox, among other semantic paradoxes, were extraordinarily influential (cf. Penner 1987: Clarification VI and passim.). Gottlob Frege also seems to employ classical Aristotelianism in his distinction between “objects” and “concepts” (cf. Geach and Black 1960: 21–41, 42–55, 107–16).

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3 Jason Turner, a self-described ontological pluralist, responded in personal correspondence in the same way as Russell to the objection that his view is selfreferentially incoherent.

Chapter 6 1 I am not asking: What is the visual inscription, or the auditory utterance, or the mental thought token? These things are all symbols or images of something else. Instead, the question here is: What is (1) an image of? How images refer to other things, or how symbols stand for other things, is not an issue I can take up here. 2 Mike McCarthy, the head coach of the Green Bay Packers in 2016, said this: “So, yes, it’s what drives how you’re going to sort out your 46 [active players], the pressure you may put on the other side of the ball or the pressure they might put on us based on their injuries. So all of that is put into a formula. I have a general formula, I have basically a different equation for every game that I’ve ever called, on trying to create opportunities for certain players. So you try to hit those targets” (Press conference, October 22, 2016). 3 Lewes instructively differentiates “resultants”—or compound motions—from “emergents”—or complex motion—in this way: “[Take] the orbit of a planet—the resultant of its tangential direction and its direction towards the sun—every student learns that the resultant motion of two impressed forces is the diagonal of those directions which the body would take were each force separately applied. Every resultant is either a sum or a difference of the co-operant forces; their sum, when their directions are the same—their difference, when their directions are contrary. Further, every resultant is clearly traceable in its components, because these are homogeneous and commensurable. It is otherwise with emergents, when, instead of adding measurable motion to measurable motion, or things of one kind to other individuals of their kind, there is co-operation of things of unlike kinds. Add heat to heat, and there is a measurable resultant; but add heat to different substances, and you get various effects, qualitatively unlike: expansion of one, liquefaction of a second, crystallisation of a third, decomposition of a fourth; and when the senstive nerves of the skin are acted on, the effect is still more dissimilar. Here we have emergents, simply because in each case there as been a different co-operant; and in most of these cases we are unable to trace the process of coalescence. The emergent is unlike its components in so far as these are incommensurable, and it cannot be reduced either to their sum or to their difference. But on the other hand, it is like its components, or, more strictly speaking, it is these: nothing can be more like the coalescence of the components than the emergent which is their coalescence. Unlike as water is to oxygen or hydrogen separately, or to both when uncombined, nothing can be more like water than their combination, which is water. We may

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be ignorant of the process which each passes through in quitting the gaseous to assume the watery state, but we know with absolute certainty that the water has emerged from this process. To fill up this gap in our knowledge by the word ‘power,’ or ‘casual link,’ is illusory. Some day, perhaps, we shall be able to express the unseen process in a mathematical formula; till then we must regard the water as an emergent” (Lewes 1875: 413–14). 4 This is just one of the many theories now under consideration. I am considering this one only for the purpose of illustration. The same point could be applied to any of the other explanations, including the one where there are multiple spacetime continua within one universe or the one where there are multiple universes (as in the multiverse solution to the measurement problem in quantum mechanics). 5 For example, the partial differential equation for the Higgs boson is: 2

 v2  L = ( D mj )D m j − mh2 jj −  / 2v 2 2 

6 A plaque on Bascom Hall, a building on the campus of the University of WisconsinMadison, where I did my PhD in philosophy, had this quotation on it: “Whatever may be the limitations which trammel inquiry elsewhere, we believe that the great state University of Wisconsin should ever encourage that continual and fearless sifting and winnowing by which alone the truth can be found.” 7 That is, the differential equations that explain the dynamical systems at each scale are mathematically related to each other. Figuring out those mathematical relations is the work of a few scientists who work on the periphery of each scientific discipline, that is, who do the interdisciplinary scientific work. See Batterman (2001) for an extremely helpful description of that work. 8 For some skepticism about whether this is even possible, see Torretti (1999: 133). 9 Again, as Geoffrey West puts it: “Science at its best is the search for commonalities, regularities, principles, and universalities that transcend and underlie the structure and behavior of any particular individual constituent, whether it be a quark, a galaxy, an electron, a cell, an airplane, a computer, a person, or a city (2017: 269).” 10 As Eran Tal puts it: “A key insight of measurement theory is that the empirically significant aspects of a given mathematical structure are those that mirror relevant relations among the objects being measured. . . . This mirroring, or mapping, of relations between objects and mathematical entities constitutes a measuring scale . . . [which] are usually thought of as isomorphisms or homomorphisms between objects and mathematical entities” (2017: 9, emphasis in the original). 11 If an individual or personal identity is wanted, then the complete set of contingently related scale-relative parameters true of whatever region of spacetime one is interested in constitutes that identity. But there is no science of that. At best, it would merely be a list which together uniquely corresponds to that region. For an alternative approach using the machinery of formal logic, see Ladyman, Linnebo, and Pettigrew (2012).

Notes

173

12 Unless I state otherwise, I am only trying to explain modal truths where the nonmodal version of that truth is false, that is, conditionals that are contrary to the facts or what philosophers call “counterfactuals,” for short. 13 False names, along with falsity in general, have a different explanation than true names, along with truth in general, as Platonism is committed to disjunctivism. See Berman (1994, 1996, 2013). 14 Therefore, I have many true names. For example, “human” is true of this region of spacetime if one is trying to differentiate the human thing from other nonhuman animal things, “animal” is true of this region of spacetime if one is trying to differentiate the animal thing from other nonanimal living things, “living thing” is true of this region of spacetime if one is trying to differentiate the living thing from other nonliving things, and so on and so forth. “Scott” would be true of this region of spacetime as well if one is trying to differentiate me from other members of my family, but that is irrelevant to science, unless one is trying to differentiate me from my sister, given the nature of what it is to be the sort of thing a brother is. But that concern is, again, with sortal identity and not personal identity, which does not matter to the scientific enterprise. 15 This is what Plato has in mind, I think, concerning what he calls “the interweaving of the Forms” in the Sophist and other late dialogues. 16 Dialetheists aside, who maintain that there can be true contradictions, and for which Paraconsistent Logics were developed, will not be considered here. 17 If v = c, then the denominator will be 0, making the entity in question have infinite mass/energy. 18 Though even their logical possibility might be doubted. Perhaps logic might only be able to tell us, at best, what is really impossible. (Again, see Seddon 1972; van Inwagen 1998.) 19 This point is parallel to how Max Tegmark (2008, 2014) talks about a “Level IV” multiverse. Ignoring what he calls a “Level I” multiverse, that is, a plurality of universes all with the same laws and constants but beyond each others’ event horizons and ignoring what he calls a “Level II” multiverse, that is, a plurality of universes with the same laws but different constants and ignoring what he calls a “Level III” multiverse, that is, the Everettian “many-worlds” interpretation of quantum mechanics which would also have the same laws operating in every world, but not ignoring what he calls a “Level IV” multiverse, that is, a plurality of universes that are each a Gödel-complete mathematical structure and which allows for differing laws, Tegmark denies that there can be a Level V multiverse as the Level IV multiverse is the ultimate foundation, that is, explanation. 20 Though I would prefer to affirm what Bigelow and Pargetter (1991) is doing, as it is, like this book, an argument for Platonism, it unfortunately explains Platonism in terms of logic and not terms of mathematics. Hence, their claim that Platonism can explain necessity in science is misdirected as there is no necessity in science.

174 21 22 23 24

Notes

See Steven Weinberg’s work. See Lee Smolin’s work. This answer was briefly mentioned at the end of Chapter 4 on pages 101–102. I do not think that we need any special sort of mental faculty pace Gödel (1944) who argued that we need a special sort of “intuition” for thinking about abstract objects. Whatever reason is is sufficient. 25 As discussed earlier in this chapter, there are two different sorts of explanations one could infer is the best explanation of some phenomena: a causal-mechanical explanation or an identity explanation. The inference by Mendel is an example of the latter, whereas if one inferred that the best explanation of someone’s getting lung cancer is that they smoked for forty years, then that would be an example of the former.

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Index abstraction  101–2 abstract things  13–14, 21–5, 28, 46, 49, 54–5, 58–9, 76–8, 81–4, 101–2, 137–40, 160, 174 n.24 aesthetics  18, 82, 100, 164 Aristotle medieval misinterpretation  2, 5–6, 11–13, 51, 53 vs. Plato  2, 5–6, 15–17, 79–80, 103, 105–7, 129–30, 137–8, 166 n.3, 168–9 n.7 being, senses of  8, 15–17, 78–80, 103, 105–23, 135, 168–9 n.7 biology  1–2, 18, 49, 70, 73, 76, 83, 128, 152, 157, 162, 166 n.4, 168 n.7 bootstrap problem  14–15, 95–100 Boyle’s Law  146, 150–1 brute  39, 42, 46–50, 55, 57 causation causes  15, 29–32, 110, 132–7, 160, 168–9 n.7, 174 n.25 as evidence  11, 22–7, 65–71, 77, 89–90, 100–1 chemistry  1–2, 18, 65–70, 73, 76, 152, 157, 162 classical Aristotelianism  12, 15–17, 59, 79–80, 84, 103–23, 137–8, 158, 165, 168–9 n.7, 170 n.2 complex dynamical systems  18, 124–37, 140–7, 156–7, 163, 172 n.7 concepts  13–14, 81–102, 123 concrete  25, 28, 32, 143 constructivism  13–15, 18, 59, 81–103, 123, 158, 162, 168 n.7 contemporary Aristotelianism  12–13, 15, 51, 53–79, 115, 123, 133, 158, 165, 167 n.10, 167 nn.1–2, 168 nn.3–4, 168–9 n.7 cultural relativism  86, 90, 165

dependence in general  2, 5–7, 58–61, 67–9, 74, 105, 138, 166 n.4, 167 n.2, 168 n.4 mind–independence in particular  2, 8, 13–14, 81–103 differential equations  126–8, 135–6, 142, 145, 172 n.5, 172 n.7 dualism  15–16, 110 economics  1–2, 9, 13, 18, 152, 157, 162, 163 emergence  6, 171 n.3 essentialism  18, 105, 130, 133, 140, 144, 168–9 n.7 ethics  18, 82, 100, 113, 116, 163–4 evolution by natural selection  42, 49, 84–5, 139, 166 n.4 existentialism  86, 165 explanation  2, 4, 6, 11–12, 16–17, 24–5, 28, 33, 36, 41–57, 63–5, 69, 71, 77–9, 82–6, 100–3, 105–22, 132–41, 151, 157–9, 163–4, 167 n.9, 168–9 n.7, 172 n.4, 173 n.13, 173 n.19, 174 n.25 extensional objects  107, 112–14 foundationalism  46–9, 111 function  16, 34, 109, 111, 115, 125–62 heap  17, 55, 70–2, 78, 108–10, 118, 126 Higgs boson  1, 9–11, 13, 62–4, 81, 160–2, 172 n.5 identity  7, 11–12, 16–17, 21, 34, 36, 42, 44–6, 84–9, 101, 110, 124, 130–50, 157, 160, 163, 172 nn.10–11, 173 n.14, 174 n.25 independence in general  58–61, 67–9, 74, 105, 120–6, 151, 166 n.4 mind independence in particular  2, 8, 14, 81–103, 105, 135, 157, 164, 170 n.5

182 intensional objects  107, 112–14 interdependence  128–31, 148, 152 Kantian  14–16, 86–90, 94, 113–15 language  119–22, 141, 143–4 laws  11, 64, 96–9, 152–7, 167 n.9, 169–70 n.3 levels of reality  6, 70, 107, 118–19, 122 lock  40–4, 50 logic  152–6 Logical Positivism  116–17 logical types  107, 120, 170 n.2

Index Plato  1–7, 79, 110, 123, 137–8, 143–4, 161, 166 nn.2–3, 168–9 n.7, 173 n.15 Platonic participation relation  137–8 Platonism  2, 7–8, 17, 123–64, 165 playground ball  3, 21, 30–2, 45, 54–6 possibility  23, 30, 32, 42, 56, 66, 86, 94, 151–6, 173 n.18 principle of instantiation  60–78, 167 n.2 prudential goodness  16, 166 n.5 quantities  69–72, 125, 135, 139–40, 146, 150, 152–5

Mendel, Gregor  48, 54, 65–6, 69, 158–60, 174 n.25 mental states  14–15, 59, 78, 81–103 mind-brain identity  15–16, 110–11 modal truths  141–52, 173 n.12 moral goodness  16, 113–14, 166 n.5

reasoning  9–10, 30–1, 46–9, 54, 65, 101–2, 158–61, 169 n.1, 174 n.25 reduction  32–5, 38, 41, 69–73, 143, 171 n.3 regress  107, 111–15 regulative principle  16, 113–17

natural kinds  8, 37, 67, 74, 85, 107, 115–22, 146, 150, 162 necessity  156, 173 n.20 neo-Kantian  15, 16, 90, 94, 113–15 nominalism  11–12, 15, 19–51, 54–7, 81, 83–4, 105, 107–8, 123, 138, 158, 165, 167 nn.7–9, 168 n.7 non-modal truths  141–8, 152, 173 n.12

scales of measurement  18, 72, 125–52, 157, 160, 163, 172 n.7 science  1, 7, 9, 23, 25, 49, 50, 81–2, 101–2, 125, 142, 153–4, 158–64, 169 n.1 self-referential incoherence  17, 106, 116–18, 121–2, 171 n.3 sensory receptors  29–31, 43–5, 167 n.5 slippery slope arguments  71–2 sociology  1–2, 18, 70, 73, 127, 152, 157, 162 spatiotemporalism  9–13 structure  84–95, 134–40, 160–3, 166 n.3, 172 nn.9–10 substances  6, 16–17, 73, 83, 105, 115, 117, 123, 130, 133, 168–9 n.7

ontological commitments  2, 4, 6, 11–17, 43, 47–51, 55, 57–63, 69, 76, 79–80, 84, 87, 94, 103, 105–8, 114–16, 119, 122, 153, 158–9, 166 n.3, 168 n.7, 173 n.13 ontological status  5, 105–22 ontology  9–17, 19, 22–5, 28, 33, 36, 60, 107–8, 143, 167 n.1 parameters  134–52, 157, 160, 163, 172 n.11 parts  6–7, 12–13, 17, 31, 37–8, 42, 55, 57, 73–8, 83, 92, 109–10, 126, 133–4, 137, 143 perception  9, 32–56, 78, 81–2, 84, 94, 102, 107–8, 123, 160 physics  1–2, 18, 66, 70, 72–3, 125, 152, 157

Theological Voluntarism  165, 169 n.2 tropes  32, 54–5, 58–9, 167 n.6, 167 n.1 truth  89–103, 124–61 TT-principle  91–5 universals  2, 5–7, 11–13, 16–17, 22–8, 46, 50–1, 53–70, 72–9, 83–4, 86–7, 101–3, 105–15, 117, 119, 122, 123, 135, 138, 167 n.2, 168–9 n.7, 172 n.9