1 Introduction

1. The Plan: Three Multiverse Proposals

I will discuss, in order, three different multiverse proposals. There will be one from philosophy, and two from physics. The philosophical proposal is about logically possible worlds. The first physical proposal is about the many worlds of the Everettian interpretation of quantum mechanics, and the second is about the bubble universes proposed by inflationary cosmology and string theory. For each proposal, I will explain it, and the reasons why people advocate it.

As one would expect, each proposal comes in various versions that have, in relation to each other, various advantages and disadvantages: in other words, features that are agreed, by at least some parties to the debate, to make the version in question more plausible or less plausible. To keep things simple (as befits an Introduction), I will, by and large, not try to formulate different versions, but instead focus on one version that is mainstream, at least in the uncontentious sense of having gotten plenty of attention, for and against, in the literature. But I should admit at the outset that each of these mainstream versions has been met in some quarters with incredulity, and even indignation. As we will see, here physics joins philosophy in being very controversial.

And as befits a philosophical introduction, I will, for each proposal, emphasize a philosophical question that it raises, which will shape my discussion of the later proposals. Each question will be a major philosophical problem—a problem which is unsolved: indeed, a problem about which I of course hope this book will prompt further effort.

So, there will be six chapters (including this one). The three main chapters, 3, 4, and 5, discuss my three multiverse proposals. Chapter 3 is about the philosophical multiverse, the logically possible worlds. Chapter 4 is about Everettian quantum mechanics, and chapter 5 is about the cosmological multiverse. But before these central chapters, I need to do some stage setting. In this chapter, I will describe how one assesses such proposals—or at least, how I propose to do so. This will largely be a matter of being wary of pitfalls and being self-conscious about one’s assumptions. In chapter 2, I will review those aspects of physics and philosophy from 1600 to 1900 that we will need in order to understand how, in both physics and philosophy, the ground was fertile by about 1970 for multiverse proposals. Then follow the three central chapters. In the final chapter, chapter 6, I review the relations between the multiverse proposals and conclude.

As a result of this plan, chapters 1, 2, and especially 3 are more about philosophy, while chapters 4 and 5 are more about physics. To a large extent, all five of these chapters can be read independently, so that a reader can follow their interests. The main exception is that chapter 5’s discussion of the cosmological multiverse, which will depend slightly on chapter 4’s explanation of Everettian quantum mechanics.

To give a glimpse of what follows, here is some more detail about the three proposals and the three questions they raise.

The first proposal I consider is from philosophy (chapter 3). It says that all the logically possible worlds—all the myriadly many ways that the universe could be, without contradiction—are equally real. We just happen to be in one of these worlds. (As I announced in this chapter’s preamble: here and throughout, world means, not a planet, but a cosmos or universe, throughout all of space and time.) The rationale for this proposal is that it gives the best account of a concept that is problematic but apparently indispensable, namely, the concept of possibility. For example, an everyday statement like “it might have rained today” (said on a dry day) is surely about an alternative way the world could be. So, to make sense of such statements being true, we surely need to countenance, i.e., accept as existing, the alternative ways the world could be other possible worlds.

Besides, there are several other concepts that are closely related to that of possibility (and equally problematic but apparently indispensable), which can be readily understood in terms of possible worlds. So much so that the arch-advocate of possible worlds, David Lewis, dubbed the possible worlds “a philosopher’s paradise.” (Although Lewis’ name is unknown to the general public, unlike, e.g., Bertrand Russell and Ludwig Wittgenstein, he is generally agreed by philosophers to be one of the greatest philosophers of the twentieth century. He died in 2001, at the age of 60.) Details of this paradise are in chapter 3. For now, I just note that one such related concept is that of a statement or proposition, i.e. the meaning of a sentence.

I call Lewis “the arch-advocate,” though the idea of a set of all the possible worlds goes back much further than the recent decades of philosophy (at least to Leibniz). I do so for two reasons. First, he defended his own version of the proposal with great clarity, imagination, and resourcefulness.

Second, his own version is, despite his fine defence, almost universally rejected by other philosophers. For Lewis proposes that the other worlds are, in their nature, just like the actual world. Thus, we all believe that the actual world consists (at least partly) of material objects that are, in the philosophical jargon, concrete rather than abstract, like a table, a rock, a molecule, or an animal, rather than, say, a number, a proposition, or an idea. Lewis argues that the other worlds are just as concrete as the actual world: they also consist (at least partly) of concrete material objects. This is a doctrine that almost all other philosophers, even those who endorse using possible worlds to address philosophical problems, find impossible to believe. They say: surely every non-actual possible world is in some way abstract, rather like a number or a proposition. So, in chapter 3, I will report this debate between Lewis (whose version is called “modal realism”) and other “more abstract” versions of the philosopher’s paradise.

This yields the philosophical question associated with this proposed multiverse. Though philosophy is, of course, a subject in which any question leads rapidly to several others, I choose to emphasize the obvious one: What exactly are these different “ways” that the universe could be? That is, what exactly is a possible world or a possibility?

In fact, we will see at the end of chapter 3 that the concrete/abstract distinction is not in good order. For it can be made precise in several different ways that cut across one another. This undermines the traditional idea that numbers, triangles, and the other entities mentioned in mathematics are abstract. And as a result, some have advocated the “Pythagorean” view that all of reality—the apparently concrete objects like a table, no less than the apparently abstract ones like a number—is mathematical. This leads to another multiverse proposal. For since there are, presumably, vastly many possible mathematical structures, reality being wholly mathematical would make for a mathematical multiverse. So, at the end of chapter 3, I will also discuss this proposal, albeit more briefly, as an epilogue to my assessment of the multiverse of possible worlds.

I turn to the two proposals from physics. They are from quantum theory and from cosmology.

Quantum theory is famous—one might say: notorious—for the conundrums about how to interpret it. Above all, there is the measurement problem. It arises from the fact that quantum theory attributes to the objects it successfully describes, e.g., atoms, a lack of definite properties; or in other words, it ascribes indefinite properties to them. For example, an object such as a particle that one expects to have a definite position gets attributed no definite position. (The buzzword here will be “superposition.”) One might accept this indefiniteness of properties for the unfamiliar and unvisualizable realm of microscopic objects like atoms. But the problem is that this indefiniteness of properties can be transmitted from the atomic realm to the everyday macroscopic realm, where such indefiniteness seems ludicrous. This is the measurement problem. It is summarized iconically by Schrödinger’s cat. In a famous paper in 1935, Schrödinger described how, in principle, an indefiniteness about a radioactive atom (viz. about whether it has decayed or not) could be transmitted by a quantum measurement apparatus, rendering a cat indefinite as to the property of being alive. That is, at the end of the process that Schrödinger describes, the cat is neither alive nor dead. And this indefiniteness is not due to the vagueness of our words “alive” and “dead,” but concerns the cat itself. It is somehow “in limbo.”

The second multiverse proposal (chapter 4) concerns how best to interpret quantum theory, and especially, how to solve the measurement problem. It was first suggested in 1957 by Hugh Everett. (Like the philosophers’ proposal, there are various versions in the subsequent literature. I will focus on one mainstream version developed in the last thirty years.) So, it is sometimes called the “Everettian interpretation” of quantum theory. But it is also often called the “many worlds interpretation.” For the idea is that there is a quantum state of the multiverse as a whole, and that this state encodes myriad different macroscopic worlds (sometimes called branches or realms), including the various macroscopic worlds that include (one each of) the various possible results of a quantum measurement process. So, in particular, for Schrödinger’s thought experiment, the quantum state at the end of the process encodes (at least) two macroscopic worlds. There is one, at least one, with a cat that is alive, and also at least one with a cat that is dead. Besides, and here is the punch line: all these macroscopic worlds are equally real.

As we will see, this proposal links back to the philosophers’ multiverse proposal, and it raises many conceptual, indeed, philosophical, questions. But I will emphasize one question: What is chance? Here, “chance” means objective probability, i.e., a probability that is made true by the subject matter concerned. Nowadays, a standard example is radioactivity (quite apart from Schrödinger’s mention of it in his thought experiment). For example, there is the chance of this uranium atom decaying in the next hour, and it has a particular numerical value. So, chance is contrasted with subjective probability, which refers to degrees of belief about a subject matter, e.g., my degree of belief that this horse will win the race. Such degrees of belief are made true by my state, not the horse’s. (For they are shown in my behaviour, for example, by what odds I would be willing to accept in a bet on the race.) As we will see, the nature of chance is a central aspect of the statement and the assessment of the many-worlds interpretation.

The third proposal (chapter 5) is from cosmology. The last sixty years have been a golden age for the science of cosmology. Our understanding of the structure and evolution of the universe has grown immeasurably. So, it is now an established fact that the universe we see, and see to be expanding, originated around 13.8 billion years ago in a very hot, dense fireball—which itself originated, perhaps, from a singularity of infinite density dubbed the “Big Bang.” However, since the early 1980s, cosmologists have also speculated (prompted by good empirical reasons) that very early on, there was a very brief period of rapidly-accelerating expansion called “inflation.”

It is this conjectured inflationary epoch that leads to the multiverse proposal. For the conjectured mechanism driving inflation also yields countless bubbles, or pockets, “domains” (so called) that branch off from all the material that then expanded to become the observable universe which we now see. And each of these domains would itself expand and become a universe. So, each of the countless bubbles (pockets, domains) is a universe, and the whole collection is a multiverse.

As we will see in chapter 5, there are two main sources of this multiverse proposal. The first source, in the early 1980s, was what came to be called “fine-tuning.” For the cosmological theory developed in the 1980s to be adequate, the value of certain physical quantities (such as a measure of how dense the matter in the universe is) had to be “just so.” That is, their exact numerical value was theoretically constrained to many decimal places. For example, the quantity about matter-density was constrained to sixteen decimal places: for the theory to be adequate, its value could differ from 1 by at most 10^-16. This is a minuscule difference, i.e., a very tight constraint. For 10^-16 is approximately the ratio between the width of a human hair (viz. a tenth of a millimetre) and the average distance between Earth and Mars (viz. 225 million kilometres)! In the early 1980s, cosmologists realized that this glaring conundrum—why should there be such fine-tuning?—could be resolved if there was, very soon after the Big Bang, a very brief period of rapidly-accelerating expansion. Roughly speaking, such a period made these quantities’ values generic rather than exquisitely fine-tuned. But this speculation, for all its merits as an explanation of the quantities’ values, prompts the question: What could be the mechanism of this brief accelerating expansion?

Here enters the second source: string theory. This is a speculative physical theory (developed from the mid-1980s onwards) that aims to reconcile quantum theory with Einstein’s general relativity, which is our best theory of gravity. It suggests not only a mechanism, but also one that generates countless bubble (pocket, domain) universes. Besides, these bubble universes will, in general, differ from one another regarding the value of physical quantities, such as the speed of light or the electric charge of an electron, that we normally call “constants of nature,” since we find them to be constant across the whole observable universe. So, the cosmological multiverse, as elaborated using string theory, envisages a variety in the values of these so-called constants.

Again, this proposal (of which, again, there are many versions) links back to the previous ones and raises many questions, including philosophical ones. Of these, I will emphasize the question that is most directly suggested by the conundrum of exquisite fine-tuning: What counts as an explanation?

So, that is the overall plan of the book. In short, there will be three multiverse proposals and three associated questions. But throughout the book, I will also discuss how various themes that the book downplays fit in, such as (i) the proposal for a Pythagorean or mathematical multiverse, and (ii) the philosophical justification of induction.

2. What Do I Believe?

So much by way of a prospectus. You will want to know—maybe to gauge my sanity, before deciding whether to read what follows—where I stand on these speculations.

I began this chapter by saying I believe that I have always lived in one world. Of course, that could be so, even while there are many other worlds. It could even be so, while there are many other worlds, and also, we can have some knowledge of them; or at least, we have some warranted beliefs about them. So you will want to press the question: do I believe there are such worlds?

To cut a long story very short: My answer is “Yes, No, and Maybe.” (Needless to say, my reasons about all three proposals will be less than conclusive.) That is, I believe in the philosophical multiverse, though not in Lewis’ modal realist version with its “concrete” worlds. But I do not believe in quantum theory’s Everettian multiverse. And for the cosmological multiverse, I say, as the film producer Sam Goldwyn is meant to have done: “a definite Maybe.”

In chapter 6, I will discuss these verdicts in more detail, in the light of the evidence and arguments we will by then have in hand. But for the moment, I want to emphasize two points. The first is about what I mean by “belief.” The second is about what my beliefs imply for you, the reader. This will require a longer discussion, which is in the next section.

First: here and throughout the book, I use the word “believe” in an everyday sense: a belief is a conviction on which I am willing to bet a great deal, even my life. We all make these kinds of bets all the time. I believe the plane will fly safely, so I get on it without worrying. Agreed, some people have their doubts about planes. But the same point is made, even more vividly, by even more humdrum examples. As I walk across the room, I believe the floor will continue to support me; as I eat the bread, I believe it will not poison me. And so on. Agreed: we all have, for many propositions, degrees of belief that fall short of conviction. Recall the example above, of my degree of belief (subjective probability) that this horse will win the race. But for most of this book, we can set subjective probabilities aside, and so take belief to involve a subjective probability so close to 1 (100%) that the difference is negligible. Hence, my word above, “conviction.”

So, I intend my beliefs as reported above—“Yes, No, and Maybe”—in this everyday sense. But stated so briefly, they are also “merely autobiographical.” They just report that after surveying the evidence and arguments as well as I can, I cannot believe this, while I could believe that.

3. What Should You Believe?

This leads to the second point. Being “merely autobiographical,” these verdicts should have little weight with you, the reader. While I am happy to tell you straight up what I believe, you should, and of course, will, make up your own mind. You may well reach more positive conclusions about these multiverse proposals than I have. For as we will see, much deeper thinkers than I have believed in a multiverse and made an extended case for the multiverse they believe in. I only hope that my survey of the evidence and arguments is open-minded and clear-headed enough to give you good material for reaching your own conclusions.

The reason you and I may differ is that in the current state of knowledge and combining the insights of both physics and philosophy, it is impossible to now know for sure about any of the three multiverse proposals. Thus, I do not give my Yes and No, respectively, to the first two multiverse proposals, on the basis of some evidence or argument that I take to be irrefutable or “knock-down.” Indeed, I doubt that we could get such irrefutable evidence or arguments, either for or against these proposals.

Within philosophy, this situation—of admitting that while one finds some evidence or argument cogent, and even persuasive, it is not conclusive or irrefutable—is, of course, familiar. It is also to be expected. For philosophy is by its nature controversial. Since the problems it addresses are abstract and general, it is difficult to pinpoint what evidence or considerations would definitively solve them. (Or if one prefers to think of philosophy as asking questions: it is hard to pinpoint what evidence or considerations would provide a definitive answer.)

Of course, to say that philosophical problems are abstract and general makes it sound like mathematics, or perhaps physics. But there is a difference. Philosophical problems are also about concepts that are either not completely precise and/or are contested, i.e., rejected as bad concepts by some people. (Here, “bad” means, roughly speaking, “useless and even misleading,” e.g., because the concept has a mistaken presupposition.) This is obvious for concepts that are the focus of moral and political philosophy, such as freedom, responsibility, equality, justice, class, and just war. For example, someone might reject the concept of political equality, in the sense that they maintain its only role is to mislead: namely, the ruling elite use it as a slogan to deceive the ruled that they have a say in how politics and the government are run.

But as we will discuss, imprecision and being contested are similarly features of concepts that are a focus of philosophy of science, and so of this book—even within its discussion of the multiverse proposals from the less controversial discipline of physics.

For example, think of the concepts in the three questions that I listed as being raised by the three multiverse proposals: namely, possibility, chance, and explanation. Each of these concepts is not precise, and even when they are made precise, philosophers disagree over claims involving them; and some philosophers reject the concept (even once made precise) as bad. Besides, we shall see that these concepts are linked to several other such concepts, concepts that are apparently valuable for making philosophical sense of science, but are not completely precise and/or are contested. Two examples are the concept of a law of nature and the concept of causation, both of which we will return to.

So, for any problem whose formulation uses an imprecise and perhaps even contested concept, it is inevitably controversial how we should assess proposed solutions to the problem. For there will be no prior agreement on the kinds of evidence, either empirical or conceptual, to which a solution should be answerable. And as I said, this is as expected—it’s all in a day’s work—in philosophy.

Agreed, physics is, by and large, far less controversial than philosophy. Its concepts are more precise and less contested, and so its problems are better defined. And so also are the kinds of evidence to which a proposed solution in physics is answerable.

But obviously, for physics’ two multiverse proposals, these contrasts with philosophy fall away. The Everettian multiverse is one proposal of several in the debate about the best way to interpret quantum theory. That debate still rages, with a mixture of empirical and conceptual reasons for and against the various proposals. So, assessing the Everettian multiverse is as controversial as most of philosophy.

The cosmological multiverse is also controversial, though for rather different reasons. It is not, in the first instance, an interpretative proposal in the way that the Everettian multiverse is. So, one would expect the empirical evidence, or indeed conceptual considerations, that would count for or against the proposal to be easier to state, i.e., to be better defined and easier for different people to agree on. But any relevant empirical evidence is fearfully hard to get, as, of course, one would expect, since the proposal is precisely that there are universes other than—beyond—all that we can directly observe. It is also hard to agree on the relevant conceptual considerations that would weigh one way or the other. For as we will see, the proposal raises interpretative, and therefore controversial, issues, even though it is not primarily an interpretative proposal. One cluster of such issues relates to the fact that it turns out to be closely related to the debate about the best way to interpret quantum theory. (Hence, it is clearest to postpone discussing it until after the Everettian multiverse.)

So, in short, my personal assessments of the three proposals, “Yes, No, and Maybe,” will be tentative. I do not urge them as definitive. For we must recognize that different people are likely to disagree about how to weigh the various pieces of evidence and lines of argument, not least because they may disagree about the usefulness of the concepts through which the evidence or argument is formulated.

Besides, it seems too much to hope that all such disagreements could be resolved in principle, by arranging some resolutely open-minded exchange of opinions that was allowed to last “as long as it takes”. If, in order to resolve such a disagreement, you were to lock “the jury” in a room with coffee and refreshments and let them out only when they agree—argh, the jury might never come out. Agreed, some such disagreements might be thus resolved. For example, a conflicting assessment of some specific line of argument might be shown to turn on people using different versions of some controversial concept, such as explanation. But I doubt that all can be thus resolved.

To be clear, this is not a bland or indifferent agnosticism. I agree that it would be good—indeed, wonderful—to know whether any of the three proposals is true. Or if knowledge is not to be had, at least to have conclusive reasons for belief, one way or the other. But we must recognize that enquiry about these proposals is both inconclusive and fallible (as it is also, no doubt, for many topics). For these multiverse proposals, the best we can do is to marshal the available evidence, both empirical and conceptual, and to try to be open-minded and clear-headed in assessing the proposals.

4. What Would You Risk? Confidence vs. Caution

I have just delivered a right-minded sermon about what one might call “cognitive modesty.” The summary is: we should accept that our views are tentative, not conclusive; that even the concepts with which we formulate our views may be contested by other people; and that maybe some of our disagreements with them could not be resolved by an open-minded exchange of opinions, no matter how long we allow the exchange to go on.

But there is another aspect of cognitive modesty that I should also register and extol. It arises from the fact that people differ in their attitude to risk, i.e., in how willing they are to take a risk. We will see that these attitudes influence people’s views, especially about the topics of this book.

We are all familiar with the fact that what is an unacceptably large risk to one person can be a tolerably low, or even negligible, risk to another. We are also all familiar with the fact that, although to some extent one can urge reasons on someone to change their attitude to risk, beyond a certain point, such attitudes are a matter of basic temperament, and one cannot expect reasons to change the person’s attitude.

The same goes, say I, for enquiry. People differ in their attitude to risk in enquiry, just as much as in action. It is just that in enquiry, the risk is of error or false belief, rather than of some traumatic event. (Of course, false belief can engender traumatic events.) So, each of us, when pursuing abstract and general questions that cannot be easily settled by some well-defined body of evidence, takes a stance about how tolerant, or how averse, we are to ending up with a false belief. (Of course, the falsity may seem harmless as regards our personal safety and well-being, just because the topic of the belief lies so far from practical matters.)

Of course, this stance is almost never a matter of a decision being made consciously. Did anyone, even a philosopher, ever say to themselves: “I hereby decide that I am too cautious, too averse to having a false belief, to either endorse or reject this philosophical proposition (about, say, a multiverse proposal)—I must remain entirely agnostic?” I doubt it. Nevertheless, each of us, when we engage with philosophical debates, in particular the debates in this book, thereby endorses, or rejects, or at least assesses various philosophical propositions. And we thereby adopt some stance, in the spectrum from tolerance to aversion, about the risk of false belief.

I believe that, like the everyday examples of attitudes to risks about actions, this stance is ultimately a matter of temperament. And this is even so for beliefs whose topic is far removed from practical matters, such as philosophical beliefs.

Like the everyday examples, your stance can be changed, to some extent, by reasons. Other people engaged in the same philosophical debate, i.e., assessing the same philosophical propositions as you, can offer you reasons to change your stance. Thus, they might say to you: “You should be more willing to endorse this proposition about the multiverse, because your background philosophical beliefs about possibility (or about explanation or whatnot) make it more plausible.” Or they might say: “your background beliefs are such that, even if it is false, this would cause little damage to—force only a minor revision of—your other philosophical beliefs.” (These examples show that the reasons urged for being less risk-averse can concern either a specific proposition or the coherence of the pattern of one’s beliefs. The same point applies to reasons for being more risk-averse.)

But I maintain that beyond a certain point, such reasons cannot persuade. Your stance cannot be wholly determined by discursive reasoning, i.e., by reasons that can be put in a discourse of words and arguments. It is ultimately a matter of what I would call “intellectual temperament.” So, when reason falls short in this way, the most that can be reasonably asked of you is that you should be self-conscious about this matter of temperament. And a fortiori, you should not be dogmatic about it: You should not proclaim that it is the only stance that is defensible or rational.

Because a person’s attitude to the risk of false belief, as shaped by reasons and by their individual temperament, will play a role in the position they take in various debates throughout this book, it will be convenient for us to have a label for the two main attitudes: risk-tolerance and risk-aversion. I label these respective attitudes “confident” and “cautious.” (Another possible label is “ambitious” vs. “modest.”)

Besides, this discussion of one’s attitude to the risk of false belief—confidence vs. caution—can be generalized. Hitherto, I discussed the topic simply in terms of whether a belief is true or false, without distinguishing whether the proposition believed is (i) “mildly” or “merely” false in that, though it is false, all the concepts it involves are correct, or at least are concepts that the agent herself does not reject or contest; or (ii) “more sickly” false, or wrong-headed, in that some of the concepts it involves are rejected or contested, at least by the agent herself.

But we must allow for (ii). That is, we must allow that someone might be cautious about using a concept, whatever claim is then made using it, and so they will be tempted to reject it. So, one can be cautious about a concept, as well as about a claim or proposition. In subsequent chapters, we will see several examples of philosophers and physicists (including myself, and maybe you, the reader) being cautious about, or definitely rejecting, some concept or other.

For the moment, let me give an example of this distinction between (i) and (ii) by considering the broad enterprise of “making sense” of physical science. Think of how physicists go about their business. They invent general theories; they specialize them in various ways with models and approximations; and they do experiments to help improve the theories, models, and approximations. Now, let us ask: does making sense of this overall enterprise need the concept of a law of nature? Of course, “law of nature” is vague, and different advocates will make it precise in different ways. But the main idea is that a law of nature is an especially informative proposition about how the natural world “works”: a proposition that is true, but which can be unknown, or even unformulated, by us humans. Some philosophers accept this concept (making it precise in one way or another). And some even say that it is a central goal of physics, or of all of science, to discover laws of nature.

But the point here is: a person might reject the very concept of a law of nature. That is, a person might reject the idea of a true and especially informative proposition about nature, especially such a proposition that is not yet formulated, but nevertheless said to be the goal of enquiry. They might say it is an illusion, a will of the wisp. So, according to this view, we can, and should make sense of the overall enterprise of physics—the theorizing, modelling, approximating and experimenting—without ever invoking the idea of a law of nature, in any precise version. Using my jargon of “confident” vs. “cautious,” such a person and such a view is cautious. (Chapter 3 will return to this example.)

Again, I should come clean about my own attitudes, my own position in the spectrum from confidence to caution. In later chapters, I will give details in the context of each discussion. But to try to be honest and clear-headed about my intellectual temperament, let me say in advance. Broadly speaking, about the dozen or so contested (usually philosophical) concepts that arise in multiverse proposals, I am inclined to be confident, i.e., accepting, of concepts that are proposed in physics, logic, or metaphysics. Examples of such concepts include the quantum state of the universe, logical necessity, possible world, and supervenience. But I am inclined to be cautious, i.e., rejecting, about concepts proposed in epistemology and methodology. Examples of such concepts include the idea of a law of nature and the idea of explanation.

I should also say that for several philosophical issues, my views are close to David Hume’s. This will be most evident in the stage-setting chapter 2, especially its sections 4 and 5, and, to a lesser extent, in chapter 3. But I think my assessments of the Everettian and cosmological multiverses, in chapters 4 and 5, are largely independent of my Humean sympathies.

So, as the book proceeds, it may be useful to you, the reader, to know that these are my tendencies. But again, this report of my intellectual temperament is “merely autobiographical.” So, do not let them have undue weight. As I said above, each of us must, in the end, decide our position for ourselves.

5. Beware the Beguiling Power of Words

I have just followed my sermon about “cognitive modesty” with an admission of the role of intellectual temperament, and a confession of my own temperament. I turn to giving a warning about how confusing words can be.

The warning is this. Once one has a word to use, one readily falls into thinking that it represents a concept in good order: that one understands, or can explain, something, though often one doesn’t understand and cannot explain anything. This warning is, of course, of a piece with my previous point that a person may reject a concept as bad because it’s misleading (recall the example of rejecting the concept of political equality because it is only the elite’s tool for duping those they rule).

This is a time-honoured warning. Sometimes, it is expressed as a joke. In Molière’s play, The Hypochondriac, the target of the joke is doctors who give a learned label, suggestive of understanding, to something they do not understand at all. When asked to explain why opium induces sleep, they answer in a learned tone of voice—as if they knew something—that opium has a “dormitive virtue.” (Here, derived from Latin, “virtue” means “causal power,” so that “dormitive virtue” means “tendency to induce sleep,” and the doctors’ answer merely repeats the question.)

This warning also occurs in some great philosophical texts. Since the next chapter will discuss the natural philosophers, i.e., philosophers-cum-physicists, of the seventeenth century, let us enjoy the prose of one such author, John Locke, in a famous passage.

Locke, in the “Epistle to the Reader,” at the start of his An Essay Concerning Human Understanding (1690), praises the contemporary great physicists (as we would now call them), Huygens and Newton. He sees himself as an under-labourer to them, who can help by doing what one might call “conceptual housekeeping,” and, in particular, by seeing through beguiling words. Thus, he writes:

The commonwealth of learning is not at this time without master-builders, whose mighty designs, in advancing the sciences, will leave lasting monuments to the admiration of posterity: but every one must not hope to be a Boyle or a Sydenham; and in an age that produces such masters as the great Huygenius and the incomparable Mr. Newton, with some others of that strain, it is ambition enough to be employed as an under-labourer in clearing the ground a little, and removing some of the rubbish that lies in the way to knowledge; which certainly had been very much more advanced in the world, if the endeavours of ingenious and industrious men had not been much cumbered with the learned but frivolous use of uncouth, affected, or unintelligible terms, introduced into the sciences, and there made an art of . . . Vague and insignificant forms of speech, and abuse of language, have so long passed for mysteries of science . . . that it will not be easy to persuade either those who speak or those who hear them, that they are but the covers of ignorance, and hindrance of true knowledge. . . . Few are apt to think they are deceived in the use of words; or that the language of the sect they are of has any faults in it . . .

By the way, similar sentiments, also famous, can be found in Francis Bacon, who warns against the danger of being misled by what he calls the “idols of the marketplace”: i.e., false ideas engendered by human communication and abuse of language. He also warns against three other idols (i.e., sources of false ideas). Roughly speaking, they are (i) universal human tendencies, such as relying uncritically on perception and jumping to conclusions (called “idols of the tribe,” where “tribe” means humankind); (ii) idiosyncratic or communal prejudices and other deficiencies of judgment (called “idols of the den,” where “den” refers to a benighted community, as in the allegory of the cave in Plato’s Republic); (iii) being misled by abstract, general, and high-falutin’ theories (called “idols of the theatre,” where “theatre” connotes a fantastical representation).

In short, we have been warned . . .

6. Can We Be Sure That We Are in the Same Universe?

Finally, let me broach a teasing question: If there is a multiverse, how can we be sure that we are in the same universe? In particular, how can I, as I write this book, be sure that you, the reader, are in the same universe as me?

Of course, this question is more pressing for advocates of a multiverse than for agnostics. But it needs to be addressed. For if the answer is “in a multiverse, the reader of my book might be in a different universe from me,” then writing a book becomes a curious enterprise, especially if most (the vast majority?) of the readers are not in the author’s universe. And the worry is, of course, not just about writing and reading, or speaking and hearing, or communication in general. It seems that in a multiverse, there could be all sorts of “disconcerting” causal processes from one universe to another: for example, with objects disappearing from one universe and appearing in another. (Science fiction makes great play with these ideas, with the channels between universes called “portals” and “wormholes.”)

But rest assured. We will see (especially in Chapter 6.2) that on the three multiverse proposals, I will consider, causal processes between objects, events, or states of affairs in different universes are either downright impossible or very rare and arcane, because they require very special circumstances.

So, the overall situation about whether you and I, as reader and writer, are in the same universe is as follows. Agreed, any or all of these multiverse proposals may be very weird, and/or very hard to believe, and/or plain false. But even if such a proposal is true, at least there is nothing problematic about an advocate of such a proposal believing that you, dear reader, are in the same universe as them (and as me). And accordingly, they write their books . . .

7. Notes and Further Reading

The subsequent chapters give more detailed suggestions for further reading. Here, I will do just four things.

1. I advertise some internet resources.

2. I list three other books about the idea of a multiverse in general.

3. I list two academic but introductory books about topics at the interface of philosophy and physics, other than the multiverse.

4. I add a little to the “sermon” about philosophical method that I gave in sections 3, 4, and 5.

7.1 Internet Resources

There are some excellent internet resources for philosophy in general, philosophy of science, and physics. Below are some you may want to consult.

• For philosophy generally, The Stanford Encyclopedia of Philosophy, edited by Edward N. Zalta, is an outstanding resource. It contains many authoritative entries in the philosophy of science, including extensive coverage of the philosophy of physics. It is freely available at: https://plato.stanford.edu/
• Another major reference work is The Routledge Encyclopedia of Philosophy, edited by Edward Craig. This encyclopedia also includes many high-quality entries relevant to philosophy of science and physics, but access requires a subscription: https://www.rep.routledge.com

In addition to encyclopedic resources, there are electronic archives that host individual research and expository articles in both physics and philosophy.

• For physics, the principal archive is arXiv: https://arxiv.org. Relevant sections include “Physics,” “History and Philosophy of Physics” (a subsection), “General Relativity and Quantum Cosmology,” and “Quantum Physics.”
• For philosophy of science, the main archive is maintained by the University of Pittsburgh: http://philsci-archive.pitt.edu

All of these archives allow searching by author, title, subject area, and related criteria, and they contain both published papers and preprints.

7.2 Books on the Multiverse

A rigorous academic treatment of the cosmological multiverse (the topic of chapter 5), with additional discussion of the Everettian and philosophical multiverses, can be found in :

• S. Friederich. Multiverse Theories: A Philosophical Perspective (Cambridge University Press, 2021).
  https://www.cambridge.org/core/books/multiverse-theories/68CE18BE78DE31550C67855107A57942

Several widely read popular books by physicists also discuss multiverse ideas in detail. Two particularly influential examples are:

• Tegmark, Max. Our Mathematical Universe (Knopf, 2014), which advocates various forms of the multiverse, both physical and philosophical.
• Hossenfelder, Sabine. Lost in Math (Basic Books, 2018), which offers a sustained critique of multiverse proposals in physics, along with criticism of several other recent trends in the field.

I have reviewed both of these books and stand by the assessments offered there. Although the present book does not reproduce the substance of those extended reviews, some overlap with later chapters is unavoidable. The reviews are most conveniently available via the Pittsburgh philosophy of science archive at:

• https://philsci-archive.pitt.edu/10760/
• https://philsci-archive.pitt.edu/15724/

7.3 Further Reading in the Philosophy of Physics

Beyond the multiverse, there are many topics at the interface of philosophy and physics, and a number of accessible academic introductions that survey them. Two especially strong examples are:

• Wallace, David. Philosophy of Physics (Oxford University Press, 2021). This volume is part of the Very Short Introduction series, which includes many related titles.
• Huggett, Nick. Everywhere and Everywhen (Oxford University Press, 2010), available online at: https://academic.oup.com/book/9556?searchresult=1

7.4 Final Reflections on Philosophical Method

I think my view, in sections 3, 4, and 5, of philosophy and its method is very widespread in academic philosophy. After all, hardly anyone would disagree that in debates involving concepts that are not precisely defined and are perhaps contentious, one cannot expect conclusive arguments; and so the best we can do is try to assess all the evidence and arguments in an open-minded way—and beware of the beguiling power of words. But three further comments may interest philosopher readers.

First, I wrote throughout in an “objectivist” manner. I presupposed that there are truths about the concepts of interest, even though the concepts are not precisely defined. (More precisely: there are truths about those concepts one does not reject as bad; cf. section 3.) Or, in other words, I assumed that philosophy addresses genuine questions or problems that have a correct answer or solution. I stand by this. I agree that even if the concepts were made precise (perhaps in an arbitrary stipulative way), the truths would remain fearfully hard to know, just because the concepts are multiply connected with other concepts, in an open sea of both empirical and conceptual considerations. But in the face of this, we must not get disheartened about the validity of our enquiry. We must not let the difficulty of the problems prompt a failure of nerve.

Second, in sections 3, 4, and 5, I for the most part combined the sorts of evidence one can get from science and philosophy. I combined in a single phrase, such as “empirical and conceptual considerations” or “evidence and arguments,” the contingent facts we might learn from the sciences, and the apparently necessary (non-contingent or analytic) facts we might learn by analyzing our concepts (by “armchair reflection,” in the traditional image of philosophy). So let me here be more explicit. I do indeed think that empirical science and philosophy are continuous with one another, in that both are about—and should attend assiduously to—both sorts of considerations. In philosophy, this view is very much associated with Quine. But one can endorse it without also joining him (in his essay “Two Dogmas of Empiricism,” 1951) in denying the validity of the analytic-synthetic distinction. In fact, I do not join him in the denial. I endorse the distinction—and Putnam’s diagnosis (in his essay “The Analytic and the Synthetic,” 1962) of the grain of truth in Quine’s view. Incidentally, this diagnosis is prefigured in Kemeny's insightful review of Quine in the Journal of Symbolic Logic in 1952.

My third comment is more programmatic. My view of philosophy and its method (and indeed, my acceptance of the analytic-synthetic distinction) is reminiscent of that great influence on analytic philosophy, David Hume. Thus, recall my comment at the end of section 4. In particular, I should announce now that in chapters 2 and 3, I will endorse his scepticism about the idea of necessity in nature and thereby, his modest and low-key conception of the sort of explanation and understanding of nature that empirical science, indeed all of human enquiry, can provide us with.