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Speculation : within and about science.
 9780190615055, 0190615052

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SPECULATION

SPECULATION Within and About Science

PETER ACHINSTEIN

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1 Oxford University Press is a department of the University of Oxford. It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide. Oxford is a registered trade mark of Oxford University Press in the UK and certain other countries. Published in the United States of America by Oxford University Press 198 Madison Avenue, New York, NY 10016, United States of America. © Oxford University Press 2019 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, by license, or under terms agreed with the appropriate reproduction rights organization. Inquiries concerning reproduction outside the scope of the above should be sent to the Rights Department, Oxford University Press, at the address above. You must not circulate this work in any other form and you must impose this same condition on any acquirer. CIP data is on file at the Library of Congress ISBN 978–​0–​19–​061505–​5 9 8 7 6 5 4 3 2 1 Printed by Sheridan Books, Inc., United States of America

Draga Juditomnak

“Speculation” (mass noun): The forming of a theory or conjecture without firm evidence. —Oxford Living Dictionaries

CONTENTS

Preface Acknowledgments 1 . 2. 3. 4. 5.

6.

Scientific Speculation: A Pragmatic Approach The Complex Story of Simplicity: Ontological and Epistemic Speculations Non-​Epistemic Simplicity: Maxwell, Newton, and Speculation Holism vs. Particularism: An Evidential Debate (“Find the Ether”) The Ultimate Speculation: A “Theory of Everything” (What Is It, and Why Should We Want One?) Summing  Up Index

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216 262 273

PREFACE

Every problem has a solution, and every solution has a problem. That’s why there is speculation. It’s easier to do and has fewer problems. That’s also why, according to some scientists, philosophers speculate while scientists test and prove. Philosophical claims are often just too vague, too general, too abstract, and too numerous to be tested and proved. When they become more precise, less general, more concrete, and less numerous, they are candidates for scientific investigation. They become capable of verification. Therefore, according to some of the greatest defenders of science, scientists have no need to speculate, and should completely avoid such a loose and unregulated activity. This is not the only view about speculation that has been advocated by great thinkers. A contrasting one is that speculation is crucial when you are trying to come up with an explanation of a group of observed phenomena. For the activity to be scientific, however, it must be followed, as soon as possible, by an attempt to test and prove the speculation

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by experiment and observation. Proponents of this view say that the speculating stage should be subject to no rules or constraints whatever. Scientists should be given free license to invent even the wildest speculations. Rules and constraints enter in the testing stage. A third view is much more liberal than the other two. It agrees with the second view in saying that speculation is crucial and is not subject to rules and constraints, but it disagrees with views one and two about testing. It says that speculation is crucial in science especially in the absence of testing and proof—​indeed, when no tests have been made or even planned. It is an important way of finding fault with currently accepted theories, and it can lead to new ways of thinking that may turn out to be fruitful and even right. What shall we make of these contrasting positions? To answer this question and others to be raised, we first need to decide what a speculation is. Can this idea be defined in some reasonable way so that what counts as a speculation will match pretty well with claims that scientists and others have classified as speculations? This is no easy task. Even though there are philosophers and scientists who hold strong views about the value of speculating and about when, if ever, to do so, I find it surprising that they rarely attempt to define the concept about which they have such views. Or, if they do, they count as a speculation whatever fails to satisfy their favorite rules of scientific method. So, my first task will be to provide a clarifying definition that does not presuppose any one particular view of scientific method. Assuming that such a definition can be formulated, what attitude should be taken with regard to speculations so defined? Is speculating in science legitimate or not? If it is legitimate, is it subject to

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rules and constraints? Can speculations be evaluated even in the absence of proof? I will start with scientific speculations—​ones made by scientists about specific constituents of the physical world and the laws governing them, e.g., nineteenth-​ century speculations about the existence of light waves and an ether in which light is waving, and twentieth-​and twenty-​first-​ century speculations about the existence of strings vibrating in 10-​dimensional spacetime. Later, I  will argue in some detail that Newton’s law of gravity, despite his vehement claims to the contrary, was indeed a speculation. I will also consider much broader speculations made by scientists or philosophers, or both, about the physical world and methods to be used in finding out about that world. These include the claim that nature is simple and that simplicity is an epistemic virtue (claims made by Newton and Einstein in support of theories they propose); that scientific theories can only be confirmed “holistically” and not by establishing individual propositions within them (Whewell, Duhem, Quine); and that there is and must be a “Theory of Everything”—​a theory that can explain all phenomena by reference to fundamental laws governing the universe and fundamental objects in that universe (various physicists, especially string theorists, and various philosophers, especially those who preach a strong form of reductionism). These are all speculations, in a sense I will give to that term. That, I will suggest, is not enough to throw them out. But it is not enough to praise them, either. What attitude should we take toward speculations, and why? My answer will reject all three views mentioned above (“don’t speculate,” “speculate, but test,” and “speculate like mad even if you can’t test.”)

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I have contrasted speculation with proof. But “proof ” is too strong a term here because it suggests certainty. If speculations are understood simply as claims that have not been proved, too many scientific claims would be speculations. What scientists typically supply is evidence. And what they want, if they can get it, is evidence that provides a good reason to believe a claim they are making. If such evidence is lacking for a claim, then the latter might well be considered a speculation. At least that is the general idea of speculation I want to develop, make precise, and defend. To do so, I will need to talk about evidence itself, a concept I have examined in detail in other works.1 “Evidence,” I  argue, has several different senses, each of which can be defined by reference to a basic concept I call “potential evidence,” which I define using an objective epistemic concept of probability and a concept of “correct explanation,” which I also define.2 However, my purpose in the present work is not to develop or defend these concepts further but, rather, to use them to help us understand the idea of speculation, to show how speculations are to be evaluated as speculations, and to evaluate various “grand” and “less grand” speculations, including the ones mentioned above, that have been made by scientists and philosophers. For readers not familiar with my concepts and definitions of evidence and explanation, I will explain them briefly when they are introduced. William Whewell regarded speculation as crucial to science. The “tendencies of our speculative nature” lead the 1. See Peter Achinstein, The Book of Evidence (New York: Oxford University Press, 2001). 2.  See Peter Achinstein, The Nature of Explanation (New  York:  Oxford University Press, 1983).

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greatest scientists to produce the most important ideas. “Advances in knowledge,” he writes, “are not commonly made without the previous exercises of some boldness and license in guessing.”3 Yes, Whewell argues, speculations have to be proved, but that is a task in the “testing” stage of scientific practice. The first stage is discovering and proposing the ideas to be tested, which is not subject to constraints, he claims. The second stage, the testing one, requires those ideas to be proved or disproved. Is that all there is to it? If not, what else is there? James Clerk Maxwell, one of physics’ greatest speculators, held strong pragmatic views about how and when to speculate and how to evaluate speculations as such. He put them into practice when theorizing about electricity and molecules. In this book, I  will invoke some of Maxwell’s speculations in physics, particularly those about molecules, and his philosophical views about speculating. Like him, I  will take a pragmatic approach. (For what this means, and how such an approach works in the case of speculations, the reader is invited to keep reading.) Unlike Maxwell, Isaac Newton held a non-​pragmatic opinion about speculation in his “Rules for the Study of Natural Philosophy” and “General Scholium” in Book 3 of the Principia. Briefly expressed: Prove, never speculate! His practice, however, is somewhat different, as I will argue, even with respect to his greatest accomplishment, the law of gravity. Newton and Maxwell both engaged in speculation, and both defended important positions on the topic 3.  William Whewell, The Philosophy of the Inductive Sciences, Founded upon their History, 2 vols. (London: John W. Parker, 1840); parts of vol. 1, chap. 5, are reprinted in Peter Achinstein, Science Rules (Baltimore: Johns Hopkins University Press, 2004), 150–​167.

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that are well worth examining. Their views are among those that will be considered in determining what attitude we should take toward speculation. Unlike the suggestion at the beginning, I will argue that speculation is an essential part of science, not just philosophy, and it is not easy to do, or at least to do well. But, by contrast with those scientists and philosophers who are in favor of speculation and hold the second and third views noted earlier, it is not, nor should it be, done freely and without constraints.

ACKNOWLEDGMENTS

I am indebted to Justin Bledin, Richard Dawid, Steven Gimbel, Fred Kronz, and Richard Richards for reading the entire book or parts thereof and making important comments and criticisms. I also want to thank students in my Spring 2017 graduate seminar for their participation in the study and activity of speculating. That seminar included two who thankfully agreed to read proofs: Maegan Reese and Richard Teague; they did so with expertise. Finally, my deepest appreciation is to Isaac Newton and James Clerk Maxwell not only for their monumental speculations, but also for their clashing philosophical views about speculating.

SPECULATION

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✦ SCIENTIFIC SPECULATION A Pragmatic Approach Hypotheses, whether metaphysical or physical, or based on occult qualities, or mechanical, have no place in experimental philosophy. —​I s a a c  N e w t o n

I think that only daring speculation can lead us further, and not accumulation of facts. —​A l b e r t E i n s t e i n

1 .   I N T R O D U C T I O N During the history of science, controversies have emerged regarding the legitimacy of speculating in science. At the outset, I  will understand speculating as introducing assumptions without knowing that there is evidence for those assumptions. If there is evidence, the speculator does not know that. If there is no such evidence, the speculator may or may not know that. The speculator may even be introducing such assumptions implicitly without realizing that he is. In any of these cases (under certain conditions to be specified later), he is speculating. I will use the term “speculation” to refer both to the activity of speculating and to the product of that activity—​i.e., the assumptions themselves.

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Which meaning is intended should be clear from the context. In this chapter, I  propose to do three things:  first, to clarify and expand the initial characterization of speculation just given; second, to ask whether and under what conditions speculating in science is a legitimate activity; and third, assuming that speculating is or can be legitimate, to consider how, if at all, speculations are to be evaluated. Although philosophers and scientists have expressed strong and conflicting opinions on the subject of the second task, little has been written about the other two, particularly the first. In section 2, I offer three examples of speculations from the history of physics. In section 3, I introduce three influential contrasting views about whether and when speculating is legitimate in science. In sections 4 through 10, I focus on the basic definitional question, attempting to show exactly how the concept of speculation can be defined using various concepts of evidence—​my own and Bayesian ones. In section 11, I discuss and reject the three contrasting views about speculation presented in section 3. In sections 12 and 13, I  defend a different view—​a pragmatic one suggested by James Clerk Maxwell, one of the great speculators in physics, who had very interesting philosophical ideas about speculation.

2 .   T H R E E S P E C U L AT I O N S FROM PHYSICS Let me begin with three examples from the history of physics, together with claims of their detractors who reject or at least criticize them not because they are false or refuted but because they are speculations.

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a. Thomas Young’s Wave Theory of Light In 1802, Thomas Young published “On the Theory of Light and Colours,”1 in which he resuscitated the wave theory of light by introducing four basic assumptions: first, that a rare and highly elastic luminiferous ether pervades the universe; second, that a luminous body excites undulations in this ether; third, that the different colors depend on the frequency of the vibrations; fourth, that bodies attract this medium so that the medium accumulates within them and around them for short distances. With these and other assumptions, Young shows how to explain various observed properties of light. In 1803, Henry Brougham, a defender of the particle theory of light, wrote a scathing review of Young’s paper, in which he says: As this paper contains nothing which deserves the names either of experiment or discovery,  .  .  .  it is in fact destitute of every species of merit. . . . A discovery in mathematics, or a successful induction of facts, when once completed, cannot be too soon given to the world. But . . . an hypothesis is a work of fancy, useless in science, and fit only for the amusement of a vacant hour.2

Brougham defends the Newtonian particle theory of light on the grounds that it is inductively supported by experiments, and he rejects Young’s wave theory on the grounds that it is mere speculation.

1.  Thomas Young, “On the Theory of Light and Colours,” Philosophical Transactions of the Royal Society 92 (1802): 12–​48. 2. Henry Brougham, Edinburgh Review 1 (1803): 450, 455.

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b. William Thomson (Lord Kelvin): Baltimore Lectures on Molecules and the Wave Theory of Light In 1884, Sir William Thomson delivered a series of lectures at Johns Hopkins University on “molecular dynamics and the wave theory of light.” His aim was to provide a molecular interpretation for the luminiferous ether postulated by the wave theory. He assumes that there is an ether and that its properties can be described mechanically. He writes: It seems probable that the molecular theory of matter may be so far advanced sometime or other that we can understand an excessively fine-​grained structure and understand the luminiferous ether as differing from glass and water and metals in being very much more finely grained in its structure.3

He proceeds by offering various mechanical models of the ether to explain known optical phenomena, including rectilinear propagation, reflection, refraction, and dispersion. In his 1906 classic The Aim and Structure of Physical Theory,4 Pierre Duhem excoriates Thomson for presenting a disorderly series of contradictory models (as, he claims British minds, incapable of continental (meaning French) orderliness, are wont to do), for invoking occult causes, and for not producing a “system of principles, which aim to

3.  Reprinted in Robert Kargon and Peter Achinstein, eds., Kelvin’s Baltimore Lectures and Modern Theoretical Physics (Cambridge, MA: MIT Press, 1987), 14. 4. Pierre Duhem, The Aim and Structure of Physical Theory, trans. Philip P. Wiener (Princeton, NJ: Princeton University Press, 1954, 1982).

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represent as simply, as completely, and as exactly as possible a set of experimental laws” (p. 19). Duhem writes: The multiplicity and variety of the models proposed by Thomson to represent the constitution of matter does not astonish the French reader very long, for he very quickly recognizes that the great physicist has not claimed to be furnishing an explanation acceptable to reason, and that he has only wished to produce a work of imagination.5

Again, the complaint is that we have a theory, or set of them, that are pure speculations, and ones of the worst kind, since they lack order and simplicity.

c. String  Theory Characterized by some of its proponents as a “Theory of Everything,” it attempts to unify general relativity and quantum mechanics into a single framework by postulating that all the particles and forces of nature arise from strings that vibrate in 10-​dimensional spacetime (according to one prominent version) and are subject to a set of simple laws specified in the theory. The strings, which can be open with endpoints or closed loops, vibrate in different patterns giving rise to particles such as electrons and quarks. The major problem, or at least one of them, is that there are no experiments that show that strings and 10-​dimensional spacetime exist. The theory is generally regarded, especially by its critics, as being entirely speculative. Steven Weinberg,

5. Duhem, Aim and Structure, chap. 4, sec. 5.

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once an enthusiastic supporter of string theory (as the “final theory”) in 2015 writes: String theory is . . . very beautiful. It appears to be just barely consistent mathematically, so that its structure is not arbitrary, but largely fixed by the requirement of mathematical consistency. Thus it has the beauty of a rigid art form—​a sonnet or a sonata. Unfortunately, string theory has not yet led to any predictions that can be tested experimentally, and as a result theorists (at least most of us) are keeping an open mind as to whether the theory actually applies to the real world. It is this insistence on verification that we mostly miss in all the poetic students of nature, from Thales to Plato.6

As these examples illustrate, speculations are assumptions normally introduced in the course of activities such as explaining, unifying, predicting, or calculating. Young sought to explain, or at least to see whether it is possible to explain, known phenomena of light by a theory other than the particle theory. Kelvin was attempting to provide a molecular account of the ether, and in terms of this, to explain the known optical phenomena. String theorists want to explain and unify the four known fundamental forces and calculate the fundamental constants of nature. In the course of doing so, they introduce speculative assumptions. There are two sorts of speculations I want to distinguish. The first, and most common, are made by speculators who, without knowing that there is evidence (if there is), introduce assumptions under these conditions:  (a) They believe that the assumptions are either true, or close to the truth,

6. Steven Weinberg, To Explain the World (New York: Harper, 2015), 14.

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or possible candidates for truth that are worth considering. (b)  They introduce such assumptions when explaining, predicting, unifying, calculating, and the like, even if the assumptions in question turn out to be incorrect.7 I will call (a) and (b) “theorizing” conditions. Assumptions introduced, without knowing that there is evidence for them, but in a way satisfying these conditions, I  will call truth-​relevant speculations. They are represented by the three examples just given. In other cases, assumptions, without evidence, are introduced in the course of explaining, predicting, unifying, etc., but their introducers do not believe that they are true, or close to the truth, or even possible candidates for truth. Indeed, it is often believed that they are false and cannot be true. A good example, which I will discuss in section 12, is Maxwell’s imaginary fluid hypothesis introduced in his 1855 paper “On Faraday’s Lines of Force.” Here, to represent the electromagnetic field, Maxwell describes an incompressible fluid flowing through tubes of varying section. The fluid is not being proposed as something that exists or might exist. It is, as Maxwell says, purely imaginary. Its purpose is to provide a fluid analogue of the electromagnetic field that will help others to understand known electrical and magnetic laws by employing an analogy between these laws and ones governing an imaginary fluid. Another prominent example of this second type of speculation is atomic theory as viewed by some nineteenth-​ century positivists. They employed the assumptions of atomic theory not as ones they believed to be true, or close 7.  Anti-​ realists can substitute “empirically adequate” for “true” and “correct.” I don’t want to provide an account of speculation just for realists.

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to it, or as possible candidates for truth, but as fictions useful for explaining, predicting, and unifying certain observable phenomena.8 For them, as for Maxwell in the imaginary fluid case, no evidence is given for the truth of the assumptions introduced. Indeed, evidence is irrelevant, since truth is. I will call these truth-​irrelevant speculations. Both truth-​ relevant and truth-​ irrelevant speculations contain assumptions about objects and their behavior for which there is no known evidence. Both are introduced for purposes of explaining, predicting, and organizing phenomena.9 That is why I  call them both speculations. The 8. As with Maxwell’s incompressible fluid, the explanations are not meant to be causal. In Maxwell’s case, we explain, not what causes the phenomena but what they are, as well as unify them, by invoking an analogy between these phenomena and others, real or imagined (see section 12, this chapter). In the atomic case, according to some positivists, we explain not what causes—​e.g., Brownian motion—​but how the observed Brownian particles are moving. We explain that they are moving as if they are being randomly bombarded by molecules (without committing ourselves to the claim that they are being so bombarded). For my own account of explanation in general, and non-​causal explanation in particular, see Achinstein, Nature of Explanation. For a much more recent account of non-​causal explanations, see Marc Lange, Because without Cause: Non-​ Causal Explanations in Science and Mathematics (New  York:  Oxford University Press, 2016). 9.  There are non-​speculative cases when assumptions are introduced without knowing that there is evidence for them—​e.g., introducing an assumption known to be false in the course of giving a reductio argument, or in the course of giving an historical account of a discarded theory, or just to see whether it is consistent with what we know. But here the assumption does not satisfy “theorizing” condition (b), required for both truth-​relevant and truth-​irrelevant speculations. It is not introduced with the purpose of explaining, predicting, etc., but in the first case, just with the purpose of showing that it is false; in the second, just doing some history of science; and in the third just determining consistency. Nor, in such cases, does the assumption satisfy the “theorizing” condition (a) required

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difference between them stems from “theorizing” condition (a). Truth-​relevant speculations satisfy it, truth-​irrelevant speculations do not. However, both kinds are anathema to writers such as Brougham, who demands inductive proof based on experiment, and Duhem, who rejected atomic theory construed either realistically or as a useful fiction. According to their detractors, one must refrain from using both truth-​relevant and truth-​irrelevant speculations. In the former case, one is to do so until one determines that there is sufficient evidence to believe the assumptions, in which case they are no longer speculations. In the latter case, one is to find assumptions for which there is such evidence. By contrast, according to proponents such as Maxwell, speculations of both kinds are legitimate in science and can be evaluated. They do not need to be avoided or rejected simply on the grounds that they are speculations. My discussion of truth-​irrelevant speculations and how they are to be evaluated will appear in section 12. The main focus of this chapter will be on truth-​relevant speculations. Until section 12, when I  speak of speculations I  will mean just these. (Some readers, indeed, might prefer to restrict the term “speculation” to these, using a different term—​e.g., “imaginary construction”—​for truth-​irrelevant ones. Because of similarities just noted, I will continue to classify them both as speculations, while recognizing an important difference between them.) Truth-​relevant speculations have sparked the

for truth-​relevant speculations. It is not introduced with the idea that it is true, or close to the truth, or a candidate for truth worth considering. To be sure, in such cases the epistemic situation of the introducer may change, and the assumption may come to be treated by the introducer in a way satisfying (a) and/​or (b). But that is a different situation.

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most controversy among scientists and philosophers. I turn to three contrasting views about them next.

3 .   S P E C U L AT I O N C O N T R O V E R S I E S The conflicting views I have in mind are very conservative, moderate, and very liberal.

a. Very Conservative The idea can be simply expressed:  “don’t speculate.” I  will take this to mean: Don’t introduce an assumption into a scientific investigation, with the idea that it is or might be true or close to it, if you don’t know that there is evidence for it. Earlier we saw such a view expressed in Brougham’s response to Thomas Young’s speculations about light. Let me mention two other scientists who express this idea as part of their gen­ eral scientific methodology: Descartes and Newton, both of whom demand certainty when assumptions are introduced in scientific investigations. In his Rule 3 of “Rules for the Direction of the Mind,” Descartes writes, “we ought to investigate what we can clearly and evidently intuit or deduce with certainty, and not what other people have thought or what we ourselves conjecture. For knowledge can be obtained in no other way.”10 He continues:  those who, “on the basis of probable conjectures venture also to make assertions on obscure matters about which nothing is known, . . . gradually 10.  Reprinted in Peter Achinstein, ed., Science Rules (Baltimore:  Johns Hopkins University Press, 2004), 19.

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come to have complete faith in these assertions, indiscriminately mixing them up with others that are true and evident.” And in Rule 12, he writes: “If in the series of things to be examined we come across something which our intellect is unable to intuit sufficiently well, we must stop at that point, and refrain from the superfluous task of examining the remaining items.” Indeed, Descartes’ view is considerably stronger than “don’t speculate” (in the sense of speculation I briefly characterized earlier). His view of “evidence” requires proof with mathematical certainty. And it requires more than knowing that there is such a proof. It demands knowing what the proof is. Newton, at the end of the Principia, claims to have proved the law of gravity (not with the certainty of mathematical proof, but in his sense of empirically established: “deduced from the phenomena”). He admits, however, that he has “not yet assigned a cause to gravity”—​i.e., a reason why the law of gravity holds and has the consequences it does. He says he will not “feign” a hypothesis about this cause, “for whatever is not deduced from the phenomena must be called a hypoth­ esis, and hypotheses, whether metaphysical or physical, or based on occult qualities, or mechanical, have no place in experimental philosophy. In this experimental philosophy, propositions are deduced from the phenomena and are made general by induction.” Finally, when defenders of this “very conservative” view say “don’t speculate,” I will take them to mean at least that scientists should not make public their speculations. Perhaps they would allow scientists to indulge in speculation in private. (Descartes seems to disallow even that.) But, at a minimum, scientists should avoid publishing their speculations or communicating them in other ways to the scientific

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community, an injunction violated by Thomas Young, Lord Kelvin, and string theorists.

b. Moderate The slogan of this view is a modification of one expressed by President Reagan:  “Speculate, but verify.” In the mid-​ nineteenth century, William Whewell formulated the idea succinctly in this passage:  “advances in knowledge are not commonly made without the previous exercise of some boldness and license in guessing.”11 In the twentieth century, it was Karl Popper’s turn: According to the view that will be put forward here, the method of critically testing theories and selecting them according to the results of test, always proceeds on the following lines. From a new idea, put up tentatively, and not yet justified in any way—​an anticipation, a hypothesis, a theoretical system, or what you will—​conclusions are drawn by means of logical deduction.12

The general idea expressed by these and other so-​called hypothetico-​deductivists, is that the correct scientific procedure is to start with a speculation, which is then to be tested by deriving consequences from it, at least some of which can be established, or disproved, experimentally. Even if you do not know that there is evidence for h, you can introduce h

11.  William Whewell, chap.  5 from Philosophy of the Inductive Sciences, quoted in Achinstein, Science Rules, 155. 12. Karl Popper, The Logic of Scientific Discovery (New York: Basic Books, 1959), 32.

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into a scientific investigation as a (truth-​ relevant) speculation, provided you then proceed to test h to determine whether there is evidence that h. The only constraint Popper imposes on the speculation is that it be bold (e.g., speculating that Newton’s law of gravity holds for the entire universe, and not just for the solar system). Bolder speculations are easier to test and falsify. According to Whewell, scientists are usually capable of putting forth different speculations to explain a set of phenomena, and this is a good thing: “A facility in devising [different] hypotheses, therefore, is so far from being a fault in the intellectual character of a discoverer, that it is, in truth, a faculty indispensable to his task.”13 For these writers there are, then, no constraints on the character of the speculation, other than (for Popper) boldness, and (for Whewell) multiplicity. The constraints emerge in the testing stage, concerning which Whewell and Popper have significantly different views. Whewell believes that speculative theories can be verified to be true by showing that they exhibit “consilience” (they can explain and predict a range of different phenomena in addition to the ones that prompted the theories in the first place) and “coherence” (they contain assumptions that fit together, that are not ad-​hoc, etc., especially as new assumptions are added when new phenomena are discovered). Popper believes that speculative theories cannot be verified, only falsified, by deriving consequences from them that can be tested experimentally and shown to be false. If the speculative theory withstands such attempts to falsify it, all we can claim is that it is well-​tested, not that it is verified or true. But, for our purposes, the important claim for both 13. In Achinstein, Science Rules, 154.

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theorists is that speculation is not enough for science. There must be empirical testing. So, in practical terms, we might put it like this: If you want to do science, it is fine, even necessary, to speculate. But that must be followed by testing. Don’t publish your speculations without at least some progress in testing, even if that amounts only to saying how experiments should be designed.

c. Very Liberal The slogan here is “Speculate like mad, even if you cannot verify.” The most famous proponent of this idea is Paul Feyerabend, who proposes adopting a “principle of proliferation:  invent and elaborate theories which are inconsistent with the accepted point of view, even if the latter should happen to be highly confirmed and generally accepted . . . , such a principle would seem to be an essential part of any critical empiricism.”14 Feyerabend believes that introducing speculations, particularly ones that are incompatible with accepted theories, is the best way to “test” those theories critically by finding alternative explanations that might be better than those offered by the accepted theories. He places no restrictions on such speculations, other than that they be worked out and taken seriously. On his view, you may, and indeed are encouraged to, publish your speculations even when you have no idea how to test them empirically. Feyerabend would have awarded high marks to Thomas Young, Lord Kelvin, and string theorists for inventing and elaborating speculations about light waves, a mechanical ether, and strings, even if they produced no testable results, 14. Paul Feyerabend, “Against Method: Outline of an Anarchistic Theory of Knowledge,” reprinted in part in Achinstein, Science Rules, 377.

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or, indeed, even if they produced results incompatible with what are regarded as empirically established facts.15

4 .  W H AT C O U N T S A S   E V I D E N C E ? How the conflicting claims in the previous section are to be evaluated depends crucially on what is to count as evidence, since the characterization of speculation I have given so far does, too. We need to get clear about what concept or concepts of evidence we should use in understanding what it is to be a speculation, and what implications this will have for views, including the three above, about whether speculating is legitimate and how, if at all, speculations are to be evaluated. A standard Bayesian idea is that something is evidence for a hypothesis if and only if it increases the probability of the hypothesis; that is: (B) e is evidence that h if and only if p(h/​e) > p(h).16

15. I began the chapter with two quotes, one from Newton and one from Einstein. It is clear that Newton’s “official” view about speculation puts him in the very conservative camp. (His practice, as I will note in section 11, was somewhat different.) Where to put Einstein is less clear. Perhaps he should be placed somewhere between the “moderate” and “very liberal” camps, more toward the latter. Like Whewell, he believed that fundamental theories in physics “cannot be extracted from experience but must be freely invented.” But, unlike Whewell, he thought that theories cannot be empirically verified by showing that they explain and predict a range of phenomena. Theories are “underdetermined” by the evidence. (In ­chapter 3, I will discuss this underdetermination claim.) And as my initial Einstein quote suggests, and as Einstein in his actual practice confirmed, speculation is crucial even in the absence of empirical test or knowledge of how to test. 16. Many of those who write about evidence use the letter h for “hypoth­ esis.” I  will do so, too, but will also use the terms “hypothesis” and “assumption” interchangeably, and h for both.

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I will call this B-​(for Bayesian) evidence in what follows. Depending on what sort of Bayesian you are, probability here can be construed either subjectively or objectively. In the former case, we obtain a subjective concept of evidence; in the latter, an objective one. Elsewhere, using numerous counterexamples, I  have argued that definition (B), whether understood subjectively or objectively, provides neither a necessary nor a sufficient condition for evidence—​as the latter concept is employed in the sciences.17 I replace this concept with several others, the most basic of which I call “potential evidence.” It defines evidence using a concept of (objective epistemic) probability and a concept of explanation.18 The idea is that for e to be potential evidence that h, there must be a high probability (at least greater than ½) that, given e, there is an explanatory connection between h and e. There is an explanatory connection between h and e, which I  shall write as E(h,e), if and only if either h correctly explains why e is true, or e 17. Briefly, here is an example that questions the sufficiency of (B): The fact that I bought one ticket out of 1 million sold in a fair lottery is not evidence that I won, although it increases the probability. Here is an example against the necessity of (B): A patient takes medicine M to relieve symptoms S, where M works 95% of the time. Ten minutes later he takes medicine M′, which is 90% effective but has fewer side effects and destroys the efficacy of the first medicine. In this case, I claim that his taking M′ as he did is evidence that his symptoms will be relieved, even though the probability of relief has decreased. For a detailed discussion of these and other counterexamples, possible Bayesian replies to them, and my responses, see Achinstein, The Book of Evidence (New York: Oxford University Press, 2001), chap. 4. 18. Both concepts are explicated in the books cited in notes 8 and 17. For a discussion of the relevant concept of explanation, see ­chapter 4 in the present book.

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correctly explains why h is true, or some hypothesis correctly explains why both h and e are true. In what follows, I will call this and the related concepts I introduce A-​(Achinsteinian) evidence: (A) Potential Evidence:  Some fact e is potential evidence that h if and only if p(E(h,e)/​e) > ½; e is true; and e does not entail h.

The concept of probability involved (objective epistemic probability) measures the degree of reasonableness of believing a proposition. I claim that evidence, and hence reasonableness of belief, is a “threshold” concept with respect to probability; and that when the threshold has been passed, e provides a good reason to believe h—​where the degree of reasonableness increases with the degree of probability p(E(h,e)/​e). I will briefly mention three other concepts of evidence that are defined in terms of “potential evidence.” (A′) Veridical Evidence: Some fact e is veridical evidence that h if and only if e is potential evidence that h, h and e are both true, and in fact there is an explanatory connection between h and e.

Using (A′) we can define a concept of evidence that is relativized to the epistemic situation ES of some actual or potential agent: (A″) ES-​Evidence: Some fact e is ES-​evidence that h (relative to an epistemic situation ES) if e is true and anyone in ES is justified in believing that e is veridical evidence that h.

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An epistemic situation is a type of abstract situation in which one knows or believes that certain propositions are true, and one is not in a position to know that others are, even if such a situation does not in fact obtain for any person.19 Finally, as a counterpart to the Bayesian concept that is subjective, I offer this: (A′′′) Subjective Evidence: Some fact e is person P’s subjective evidence that h if and only if P believes that e is veridical evidence that h, and P’s reason for believing that h is true is that e is true.

An example of all four types of A-​evidence is given in note 20.20 The first three are objective concepts, in the sense that whether e is evidence that h does not depend on whether anyone in fact believes that e is evidence that h. In this sense, only the last, A′′′, is subjective. 19. A person in a given epistemic situation ES may not know that some propositions P1, . . . ,Pn believed in that situation are true. But if, on the basis of P1, . . . ,Pn, such a person is to be justified in believing that e is veridical evidence that h, then the person must be justified in believing P1,  .  .  .  ,Pn. For more on epistemic situations and ES-​evidence, see Achinstein, Book of Evidence, chap. 1. 20.  In 1883, Heinrich Hertz performed experiments on cathode rays in which he attempted to deflect them electrically. He was unable to do so, and concluded that they are not charged. Fourteen years later, J.  J. Thomson claimed that Hertz’s experiments were flawed because the air in the cathode tube used was not sufficiently evacuated, thus blocking any electrical effects. In Thomson’s experiments when greater evacuation was achieved, electrical effects were demonstrated. Hertz’s experimental results constituted his subjective evidence that cathode rays are not charged. They were also ES-​evidence for this hypothesis, since, given his epistemic situation in 1883, he was justified in believing that the results

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I much prefer the definitions supplied by the (As) to that supplied by (B). But since there are so many adherents to the Bayesian definition, I  will make reference to that as well as to the (As) in my discussion of scientific speculation. Let’s see how far we can get with either type of definition. Later, I  will show why, in order to offer a more complete definition of speculation, the basic Bayesian definition (B) needs to be upgraded in a way that makes it much closer to (A).

5 .   T R U T H -​R E L E VA N T S P E C U L AT I O N S With these concepts of evidence in mind, I  return to the task of clarifying what it is to be a truth-​relevant speculation. In the case of such a speculation, a speculator P, without knowing that there is evidence for assumption h, introduces h under “theorizing” conditions (a) and (b) of section 2. In saying that P is speculating when introducing h under condition (a), I don’t mean that P believes true (or close to the truth, or a candidate for truth worth considering) just a conditional statement of the form “if h, then. . . .” I mean that he believes this with respect to h itself. Of course, the speculative assumption introduced may itself be a conditional

constituted veridical evidence. But because the experimental set-​up was flawed, unbeknownst to him, they constituted neither potential nor veridical evidence. By contrast, Thomson’s experimental results constituted evidence in all four of these senses for the hypothesis that cathode rays are electrically charged.

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whose antecedent is h. But then it is the entire conditional that is the speculation, not h by itself.21 If P introduces h in a way that satisfies the “theorizing” conditions (a) and (b), we might say that (Spec): h is a (truth-​relevant) speculation for P if and only if P does not know that there is evidence that h.

One way to know that there is evidence that h is to know what that evidence is and to know that it is evidence that h—​i.e., to know of some fact e that it is evidence that h. But it is also possible to know that there is evidence that h without knowing what that evidence is. If authoritative textbooks all tell me that that there is evidence for the existence of the top quark without telling me what that evidence is, and I introduce the assumption that the top quark exists and do so in a way that satisfies the “theorizing” conditions, then my assumption is not a speculation for me, since I know there is evidence for its existence. If you introduce a hypothesis h under the “theorizing” conditions, and you don’t know that there is evidence that

21.  What about “thought experiments,” understood as describable by conditionals whose antecedents will not be, or could not be, satisfied? Some are not speculations at all, since the thought experimenter knows there is evidence for the conditional expressing the thought experiment. An example is Newton’s thought experiment involving many moons revolving around the earth, the lowest of which barely grazes the highest mountains on the earth. Newton provides evidence that if such a moon did exist and lost its inertial motion, it would fall at the same rate of acceleration as bodies do near the earth (see c­ hapter 3). If Newton did not know that there is evidence for such a conditionally expressed thought experiment, then if he introduced it while “theorizing,” it would have been a truth-​relevant speculation.

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h, then if h is true you don’t know that it is. Speculating in this way entails lack of knowledge of the truth of the speculation. However, the converse is not true. If you introduce h under the “theorizing” conditions without knowing that h is true, it doesn’t follow that you are speculating, at least on the concept of speculation I am proposing, since you may know that there is evidence that h is true. On this concept, lack of knowledge that h is a necessary but not a sufficient condition for speculating that h. By extension, if you introduce h under the “theorizing” conditions, and unbeknownst to you h is false, the fact that h is false doesn’t make h a speculation for you, since you may know facts that you know to be evidence that h is true.22 A good deal more needs to be said about various ideas associated with (Spec). I will do so in the remainder of this section and the next two sections. In (Spec), h stands for an individual assumption. Now, as is the case with the three examples of speculations from physics at the beginning of this chapter, theories usually contain sets of assumptions, some of which may be speculations, some not. It is not my claim that each assumption in a speculative theory is necessarily a speculation. I have spoken of speculators introducing assumptions. As noted earlier, normally this is done in the course of “theorizing” activities such as explaining, predicting, 22. An example: Let e, which you know to be true, be that you own 95% of the tickets in a fair lottery. Let h be that you will win the lottery. Assume that e is (potential) evidence that h, and that you know this. Suppose that, unbeknownst to you, h is false, and you introduce h in the course of “theorizing,” doing so believing that h is true. Since you know that there is evidence that h—​indeed, very strong evidence—​you are not speculating, even though h is false.

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calculating, etc. But occasionally it is done with little if any “theorizing” on that occasion by writing them down and calling them “assumptions,” “speculations,” or “hypotheses” that the speculator believes to be true or possible and worth further investigation at some point. Newton does this in his Queries in the Opticks when he speculates about the particle nature of light, though even there he theorizes a bit by offering a few arguments against the rival wave theory. I will call both cases speculating while “theorizing,” even if the theorizing is intended for a future occasion. Among the speculations introduced in a theory consisting of many assumptions, some may be intended as literally true, some may be thought of as approximations with different degrees of closeness to the truth, while still others may be regarded as just possibilities worth considering. In ­chapter 3, I will argue that, despite Newton’s claims to the contrary, his law of gravity was a speculation, but one he believed to be literally true. His assumption that the only gravitational force acting to produce the orbit of a given planet was the gravitational force of the sun acting on the planet was also a speculation, but an assumption he regarded as only approximately true. And the speculation that “the center of the system of the world is at rest”—​which he explicitly classified as a speculation (or “hypothesis”)—​he perhaps regarded as a possibility. Whether speculations are introduced boldly with the idea that they are true, or more cautiously with the idea that that if not true they are close to it, or even more cautiously with the idea they are possibilities worth considering, does not affect their speculative status if the speculator does not know that there is evidence for them. What it does affect is the question “Evidence for what?” Evidence that h is a possibility, or that h is close to the truth, or that h is true will

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usually be different. If I introduce the assumption that h is a possibility—​meaning that it is not precluded by known laws or facts—​without knowing that there is evidence for the claim that it is not so precluded, then I am speculating when I claim that h is a possibility. Accordingly, we could modify (Spec) by introducing distinctions between types of speculations: speculating that h is true, speculating that h is close to the truth, speculating that h is a possibility, and perhaps others. But I will not do so. When some assumption h is classified as a speculation, the focus of the scientific community is normally on the truth of h, even if the speculator is introducing h only as a possibility. When Brougham criticized Young for producing a speculation (“a work of fancy”), it is not very convincing for Young to reply: “No I am not, I am only saying that the wave theory is a possibility, that it is consistent with Newtonian mechanics, and for that claim I can provide evidence.” Even if this reply correctly represents Young’s intentions, the main interest of scientists, including Brougham, is the question of whether the theory is true. Scientists want to know if there is evidence that light is a wave motion in the ether, not simply whether this is a possibility. So, in such cases I  will retain (Spec), and say that even if the speculative assumption h was introduced by P with the idea that it is a possibility, h is a speculation for P with respect to the truth of h, since P does not know that there is evidence that h is true. What about “closeness to truth”? Newton in defending Phenomenon 1 pertaining to the Keplerian motions of the moons of Jupiter introduces the assumption that the orbits of these moons are circular. The assumption itself is literally false, which Newton realized, but it is a good approximation. Since Newton had evidence that this is a good approximation,

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the latter claim was not a speculation for him. In view of such cases we could keep (Spec) as is but add another type of speculation for cases in which no evidence is known for “h is close to the truth.” Or we could simply retain (Spec) without adding other types, and understand “true” in a broad way to include “true or close to it.” I prefer the latter. There is a view about the introduction of speculations that I want to reject. It is based on a distinction that philosophers once regarded as important (perhaps some still do) between the “context of discovery” (when one first gets the idea of the hypothesis) and the “context of justification” (when one is attempting to test or defend it by providing evidence). Those wedded to this distinction claim that speculations appear in the first context, not the second. On the view I am defending, whether something is a speculation does not depend on whether it is introduced when one first gets the idea, or afterwards when one is (or is not) attempting to defend it. For speculations, what matters is only that they are introduced in the course of “theorizing” activities with the idea that they are truths or close to it, or at least possibilities worth considering. Finally, in accordance with (Spec), a “theorizing” assumption h introduced by P can be a speculation even if P does not believe that h is the sort of assumption for which evidence is possible. Assumption h might be regarded by P as “metaphysical,” or “theological,” or of some other sort for which there can be no evidence. In such a case, it follows trivially that P does not know that there is evidence that h, so that if P introduces h under the “theorizing” conditions, then h is a speculation for P. At the other extreme, what if P regards h as self-​evident, having and needing no evidence? Whether there are cases of self-​evident propositions having

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and needing no evidence is controversial. But if there are, and if P knows that h is one of them and “theorizes” using h, then, since P knows that h is “self-​evident,” and therefore true, I will say that P is not speculating.

6 .   E X A M P L E S T O   C L A R I F Y THE SCOPE OF (SPEC) The three examples of speculations noted in section 2—​ Young’s 1802 assumptions about the wave nature of light, Kelvin’s assumptions about the molecular nature of the ether, and string theory’s assumptions about strings and 10-​ dimensional spacetime—​all satisfy (Spec). Let me mention two other types of cases that will help to clarify the scope of (Spec). Case 1  Suppose that I  have read in a usually but not completely reliable newspaper that there is evidence that 10-​dimensional spacetime exists. And suppose the newspaper is right in saying this. Because the newspaper is not completely reliable, I do not know that there really is such evidence, though I have a good reason to believe there is. In accordance with (Spec), if, while “theorizing,” I  introduce the assumption that such a spacetime exists, I  am speculating. Case 2.  Suppose I  read in Science magazine, a very reliable source, that evidence for 10-​dimensional spacetime has been discovered, and I  use the assumption that 10-​dimensional spacetime exists in theorizing in a way that satisfies “theorizing” conditions (a) and (b). In fact, however,

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unlike Case 1, what Science magazine reports is false: what it took to be evidence is not so, and indeed no evidence exists. According to (Spec), when having read the article I  introduce the 10-​ dimensional spacetime assumption into my theorizing, I am speculating. I am justified in believing that there is evidence that 10-​dimensional spacetime exists, but in fact there is no such evidence, so I don’t know that there is. I believe I am not speculating, I am justified in so believing, but it turns out that I am speculating. In view of cases such as (1) and (2), the concept of speculation I have introduced is a strong one, since it rules something as a speculation in a situation in which the speculator has a good reason to believe there is evidence for the speculation but not enough to know that there is. This doesn’t imply that any assumption that I put forth while “theorizing” whose truth I don’t know is a speculation for me. That would be much too strong. It means only that any such assumption is a speculation if I don’t know that there is evidence for the assumption.23 So, if I assume that h is true, but don’t know that it is, h will not be a speculation for me if I know there is evidence that h. We might call this the “no knowledge of the existence of evidence” concept of speculation. A weaker concept might require only that, given my epistemic situation, I  am not justified in believing that there is evidence. If I am so justified, I would not be speculating. But suppose I am justified in believing that there is evidence that h, even though there is no such evidence. Then, on this 23. This has a range of possibilities, including cases in which e is true and I know that it is, and e is evidence that h, but I don’t know that e, or anything else I know to be true, is evidence that h.

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weaker concept of speculation, if I  “theorize” using h I  am not speculating. Under these circumstances, I am inclined to say that since there is no evidence that h, I am speculating, even though I think there is such evidence and even though I think that I am not speculating.24 I will continue to use the stronger “no knowledge” concept. If, like some scientists, you reject speculation, you are not rejecting the “theorizing” use of all assumptions whose truth you don’t know, but only the use of assumptions for which you don’t know that there is evidence. This permits speculations to cover a broad group of cases, ranging from simple hunches, where you have no idea whether there is evidence or even what would count as evidence, to cases in which in which you have good reason to think that something is (or that there is) evidence but don’t know that this is so.

7 .   R E L AT I V I Z AT I O N S In accordance with (Spec), an assumption h may be a speculation for one person but not another, depending on what the person knows or doesn’t know. But even if we focus on one theorizer and one assumption being introduced, we get different answers to the question “Is h a speculation for P?” depending on which concept of evidence is used. For the Bayesian concept, understood subjectively or objectively, if P knows that there is some e that increases the probability of h, then h is not a speculation for P.  This is pretty weak 24. This leaves open the question of what concept of evidence to employ, a question I will take up in the next section.

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fare, and I  will suggest strengthening it in a moment. My A-​ concepts of evidence yield different results depending on which concept is chosen. Veridical evidence A′, which requires the truth of h, classifies h as a speculation for “theorizer” P whenever h is false, even if P knows facts e that constitute evidence that h in the other A-​senses, and P is justified in believing that e also constitutes veridical evidence that h. This is perhaps too strong a sense of speculation. So, if we use one of my A-​concepts, I suggest either potential, or ES-​, or subjective evidence. All these can be used in connection with (Spec), but they will give somewhat different classifications for speculations. For example, Isaac Newton believed that the fact that (e) the planets lie on the same plane and rotate around the sun in the same direction is evidence that (h) God exists and designed it that way.25 (He claimed this because, he said, this can’t be due to “mechanical causes, since comets go freely into very eccentric orbits and into all parts of the heavens.”) Newton would have denied vehemently that he is speculating in this case, since he regarded h as “deduced from the phenomena.” Many would reject Newton’s claim that e is evidence that h, and say that when Newton introduces h to explain e, he is indeed speculating. When Newton claims that e is evidence that h he should be understood using the concept of subjective evidence. And his denial that he is speculating should be understood using the same concept of evidence in (Spec). In the subjective sense (one reflecting what he believed he was doing or intended to be doing), Newton was not speculating. 25.  Isaac Newton, The Principia:  Mathematical Principles of Natural Philosophy, trans. I. Bernard Cohen and Anne Whitman (Berkeley: University of California Press, 1999), Book 3, “General Scholium.”

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Newton’s critics who claim that he is speculating should be understood as using either the concept of ES-​evidence or potential evidence in (Spec).26 They are saying that in one or the other of these senses of evidence, Newton was indeed speculating (whether or not he believed he was). If speculation is to be defined in terms of evidence, or lack thereof, and if, as I  suppose, there are different concepts of evidence in use, then different classifications should be expected. For the sake of argument, I will suppose that those supporting one of the conflicting views regarding speculation noted in section 3—​either for it or against it—​would be for or against speculation defined in at least one, and perhaps all, of these ways. Now, two questions need to be addressed: (1) Using the Bayesian definition (B), how much increase in probability must e give to h so that P’s knowing that e is B-​evidence that h prevents h from being classified as a speculation for P? Alternatively, using my definitions supplied in the (As), how probable must it be that there is an explanatory connection between h and e, given e, so that knowing that e is A-​evidence that h prevents h from being classified as a speculation for P? (2) What sorts of considerations will increase the probability of an assumption h? Alternatively, what sorts of considerations will make it such that there is a high probability that there is an explanatory connection between h and e, given e? I will not attempt to give question (1) a detailed answer. We could talk about degrees of speculation, depending on how high the probabilities are. But let’s simplify the discussion, make things more precise, and set the bar reasonably 26. With ES-​evidence, the critics might say, their claim can be understood as relativized to their own epistemic situation, or indeed even to Newton’s.

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high by requiring that the probability involved be greater than ½. If we can suppose, as I do, that evidence must provide a good reason for believing a hypothesis, and that this requires that the evidence makes the hypothesis at least more probable than not, this will set a minimal standard for what is and is not a speculation. Assumption h is a speculation for you if you introduce h, under “theorizing” conditions, without knowing that there is evidence that provides a good reason for believing h. Using the Bayesian idea, we upgrade (Spec) and say this:  h is a speculation for person P, who introduces h (under “theorizing” conditions), if and only if P does not know that there is some fact that increases h’s probability so that the latter is greater than ½—​i.e., more likely than not. Using my definition of evidence, this upgrading idea is unnecessary, since my concepts of evidence require a probability greater than ½. It is question (2) that I regard as the central one. In the following section, l will look at various answers proposed to question (2). These answers are based on the use of an objective, rather than a subjective, concept of evidence, and hence of speculation. They propose ways of obtaining evidence that are supposed to hold no matter what particular individuals believe about what is evidence for what. This is not at all to reject the idea that there are subjective concepts of evidence (e.g., my subjective A-​concept, or the Bayesian one understood subjectively). Nor is it to reject the idea that there are subjective concepts of speculation (e.g., ones that accord with (Spec) in which evidence is understood in terms of my subjective A-​concept or in terms of a subjective Bayesian one). My claim is that there are objective ones as well, and that these are the most important and interesting ones, especially in understanding the controversies noted in section 3

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about the legitimacy of speculating and how speculations are to be evaluated. Later, on the basis of the answers proposed for question (2) I will argue that if an objective B-​concept is employed in understanding what it is to be a speculation, it will need to be augmented by incorporating an explanatory idea present in the A-​concepts. To simplify the discussion, the objective A-​concept I will focus on is potential evidence, since the others are defined using it. The question now is how to get objective evidence in one of these senses.

8 .  H O W T O   G E T E V I D E N C E The answers proposed by scientists and philosophers over the ages have varied considerably and have sparked lively debates. I  will begin with three historically influential, contrasting accounts:  Newtonian inductivism and two versions of hypothetico-​deductivism—​due to William Whewell and Peter Lipton—​ that introduce fairly strong conditions for obtaining evidence. Then I will turn to some weaker, but more controversial, accounts. It is not my claim that these exhaust the views of how to get evidence, in either an objective Bayesian sense or my own, only that they should suffice to give us a sufficiently broad basis for discussing the idea of speculation. I  will treat them as proposals for sufficient conditions for obtaining evidence, even though their defenders (in the first three cases) also regard them as necessary. 1.  Newtonian inductivism. Briefly, following Newton’s four rules of reasoning in the Principia, to get evidence for a causal law (such as Newton’s universal law of gravity), you

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attempt to establish that a cause satisfying certain conditions exists (in Newton’s case, that there is a gravitational force whose magnitude varies as the product of the masses of the bodies and inversely as the square of the distance between them), and that all objects of certain sorts (e.g., all bodies) satisfy a general law invoking that cause. For Newton, it suffices to establish that the cause exists by inferring that it does from the same observed effects it produces on various objects. And from these observed effects one infers, by induction, that all other objects of these sorts also satisfy the general law. This part of the argument Newton calls “analysis.” The second part, “synthesis,” consists in taking the law and showing how it can explain and predict phenomena other than the ones initially used to provide a causal-​ inductive argument to the law. Newton’s “Phenomena,” both the initial ones and those later explained, constitute evidence for the law.27 2.  Whewellian hypothetico-​deductivism. William Whewell offers a sophisticated version, according to which to show that e is evidence for a system of hypotheses H, you show that H explains e; that H predicts and explains new phenomena of a different sort that are later established to be the case by observation and experiment (“consilience”); and that the system of hypotheses is what he calls “coherent” and remains so over time as new phenomena are discovered. On this view,

27. For a discussion of Newton’s rules and his inductivism, see my Evidence and Method (New York: Oxford University Press, 2013), chap. 2. An interpretation of these rules, and a critical account of how he uses them to generate his law of gravity, will also be given in ­chapter 3 of the present book.

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e together with the successfully predicted and explained new phenomena constitute evidence for H.28 On both these influential accounts, if you want to obtain evidence for a hypothesis or system of hypotheses in the way each proposes, you must show more than simply that the hypothesis or system explains or entails some set of observed phenomena. For Whewell, you must show that it predicts and explains phenomena of different types, not just the sort you started with. For Newton, you need to do this as well, but also to provide a justified causal argument that the cause inferred exists and operates in a certain way, and a justified inductive argument that this can be extended to all bodies of certain sorts. Proponents of these accounts would claim that if you have satisfied the conditions they require, then the probability of the hypothesis or system will be increased (indeed, to the point of certainty), thus satisfying the Bayesian definition of evidence (B). Also, on these accounts, if you establish the hypothesis in the way proposed, you will have shown that there is a high probability of an explanatory connection between the hypothesis and the evidence, thus satisfying my concept of potential evidence, given by definition (A). The next account is similar to Whewell’s in certain respects, but weaker. 3.  Lipton’s “inference to the best explanation.”29 According to this account, to show that e is evidence for some hypothesis 28.  Whewell, Philosophy of the Inductive Sciences, chap.  5, reprinted in Achinstein, Science Rules. 29.  Peter Lipton, Inference to the Best Explanation, 2nd ed. (London: Routledge, 2004). The father of the doctrine and of the expression

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or system H, you show that H offers what Peter Lipton calls the “loveliest” explanation for e. For Lipton, the “loveliest” explanation is one that “would, if correct, be the most explanatory or provide the most understanding” of those explanations under consideration.30 For him, this means that it would be simple, unifying, and deep (however these are to be understood). This account does not require Whewellian “consilience” or Newtonian causal-​inductive reasoning. The last three accounts I will mention are weaker than those above. They are meant to provide only sufficient, but not necessary, conditions for obtaining evidence. And they are meant to provide sufficient conditions for obtaining at least some evidence for a hypothesis, not necessarily strong or conclusive evidence. 4.  Meta-​inductive evidence. The idea is that you can get evidence for a hypothesis if you can show that your hypothesis is of a certain general type and that other hypotheses of that gen­­­ eral type have been successful in the past. For example, in defense of his molecular-​kinetic theory of gases, Maxwell writes that it is a completely mechanical theory, and that (he claims) mechanical theories have worked well in astronomy and electricity. These facts would constitute evidence for the theory. 5.  “Only-​game-​in-​town” evidence. You can get evidence for a hypothesis h if you can show that h is the “only game in “inference to the best explanation” is Gilbert Harman, in “The Inference to the Best Explanation,” Philosophical Review 74 (1965): 519–​33. 30.  See Lipton, Inference to the Best Explanation, 58; also, Achinstein, Evidence and Method, 95.

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town” for explaining some set of phenomena e. It is the only hypothesis scientists have been able to come up with to explain e, after thinking about the matter, and rejecting known alternatives for various good reasons. Then the fact that it is the only game in town is some evidence in favor of it. 6.  Evidence from authority. You can get evidence for a hypothesis h by showing that the authorities or experts in the field relevant for h believe that h is true. The fact that the authorities believe h is evidence that h is true.31 Defenders of the first three accounts—​the Newtonian, the Whewellian, and the Liptonian ones—​maintain that if you satisfy the conditions they advocate, then, given e, you will have shown that it is highly probable that there is an explanatory connection between h and e, in which case you will have shown that e constitutes A-​evidence that h. For the sake of argument, let us also suppose that, according to all six of the accounts, if you satisfy the conditions they specify, you will show that e increases the probability of h so that the

31. Richard Dawid defends versions of views 4 and 5, but not 6. On his versions, evidence is not evidence for the truth, or even for the empirical adequacy of a hypothesis, but for what he calls its “viability.” A hypoth­ esis is viable relative to a given field, and to certain types of experiments that can be performed within that field, if it predicts the results of those experiments. He claims that with his restricted sense of evidence, meta-​ inductive evidence and “only-​game-​in-​town” evidence can provide evidence for “viability.” Among the meta-​inductive cases he has in mind are ones where the theory was the “only game in town.” If such theories have tended to be “viable,” then this fact counts as evidence for the viability of the particular “only-​game-​in-​town” theory. Richard Dawid, “The Significance of Non-​Empirical Confirmation,” in Why Trust a Theory? ed. Richard Dawid (Cambridge: Cambridge University Press, in press).

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latter becomes greater than ½ and e constitutes (upgraded) B-​evidence  for  h.

9 .  S P E C U L AT I O N A N D E V I D E N C E I characterized (truth-​relevant) speculating as introducing assumptions without knowing that there is evidence for those assumptions, and doing so under “theorizing” conditions I specified. In section 4, I supplied definitions for A-​and B-​ evidence, and using these, I offered a more precise account of what it is for an assumption to be a speculation for someone with respect to the truth of the hypothesis. These definitions generate somewhat different concepts of speculation. In section 8, I noted various views about how to obtain evidence that satisfies the definitions in section 4.  In what follows, I  examine these views in light of the concepts of evidence I have introduced. Let’s begin with the last three views:  “meta-​ inductive evidence,” “only-​ game-​ in-​ town evidence,” and “evidence from authority.” For the meta-​inductive case, let h be that gases are composed of spherical molecules that obey Newton’s laws (Maxwell’s first kinetic theory hypothesis—​ to be discussed in section 12). Let e be the fact that h is a mechanical hypothesis, and that (as Maxwell noted) mechanical hypotheses have been successful in astronomy and (he thought) electricity. But, using my A-​concept of “potential evidence,” it is not probable that, given e, there is an explanatory connection between h and e. (It is not probable that the reason gases are composed of spherical molecules is that mechanical hypotheses have been successful, or that the reason mechanical hypotheses have been successful

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is that gases are composed of spherical molecules, or that some hypothesis correctly explains both why gases are composed of spherical molecules and why mechanical hypotheses have been successful.32) Analogous claims are justified in the case of “only-​game-​in-​town” and “authoritative” evidence. What follows from this about speculation? If the A-​ definition of potential evidence is employed, and if you theorize using h and know that there are only “meta-​inductive facts” in favor of h, then h is a speculation for you. Matters get trickier in the case of “authoritative” and “only-​game-​in-​ town” facts in favor of h. Let’s start with the former. Suppose you know that the following is the case: e: The recognized authorities announce that they have discovered (potential) evidence that h is true, and that for this reason they believe that h is true, even though they do not announce what this evidence is.

Suppose that the evidence they have discovered really is potential evidence that h. Finally, suppose that these authorities are so good that you can rightly claim to know that such potential evidence for h exists, even though you don’t know what it is. If you use h in theorizing, then you are not speculating, since you know (from authority) that there is potential evidence that h. This is the case even though e is not potential evidence that h (it fails to satisfy the explanatory connection condition). So it is not that e is “authoritative” evidence for h. It is that, in this case at least, if you know that 32. This holds as well for meta-​inductive evidence of the sort Dawid has in mind. See note 31.

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the authoritative fact e is true, then you know there is (non-​ authoritative) potential evidence for h. On the other hand, suppose that that the evidence the authorities have in mind is not in fact potential evidence that h, though they believe it is, and perhaps, given their epistemic situation, they are even justified in doing so. Then, despite the fact that the authorities believe they have discovered potential evidence that h is true, they haven’t. And they, as well as you, are speculating (in a sense of (spec) employing potential evidence) when they and you use h in theorizing. So, in general, knowing the truth of an “authoritative” fact such as e is not sufficient to prevent h from being a speculation. Nor, for analogous reasons, is knowing that h is the “only game in town.” What happens if we use an objective Bayesian B-​concept of evidence (one that is upgraded to require that e is true and that e increase h’s objective probability so that the latter is greater than ½, but not to require satisfaction of the explanatory connection condition)? Such a Bayesian needs to argue first that meta-​inductive, “only-​game-​in-​town,” and authoritative facts do, or at least can, increase the probability of a hypothesis, so that they really do or can constitute (objective Bayesian) evidence.33 Next, he has to argue that

33. If the Bayesian insists on using subjective concepts of probability and evidence, then for any given individual, any of these facts can increase his degree of belief in a hypothesis, depending on the individual’s system of degrees of belief. The matter is entirely subjective, so long as his system of degrees of belief is probabilistically consistent. This will yield only a subjective concept of speculation, not an objective one. Again, my discussion is based on the claim that there are objective concepts of evidence and speculation as well, and that these are central in understanding the controversies over speculating.

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these kinds of facts can increase the probability of a hypoth­ esis sufficiently to make the probability greater than ½, so that the hypothesis is not a speculation (in an objective sense). Elsewhere I  have given arguments to show that at least “only-​game-​in-​town” facts fail to raise the probability of a hypothesis, so that they don’t even satisfy the Bayesian definition of evidence.34 Furthermore, even if the Bayesian can show that meta-​inductive facts can increase the probability that some theory of the type in question is true or viable, it doesn’t follow from this that the probability of the particular theory in question has increased. Maxwell argued from the success of mechanical theories in astronomy and electricity to the probable success (or the increase in probability) of some type of mechanical theory of gases. He did not claim that his particular theory of spherical molecules acting only by impact was probable, or that its probability was increased.35 “Authoritative” facts—​ones stating just that the authorities believe that h is true—​are subject to Laudan’s “pessimistic” induction:  “Authorities” (those deemed to be such) from Ptolemy to Aristotle to Newton to the present time have gotten it wrong so often that the only inference possible just from their success rate is that they will get it wrong again—​not that what they believe now is made more probable by the fact that they believe it.36 34. See Peter Achinstein, Particles and Waves (New York: Oxford University Press, 1991), chap. 9. 35.  It could be that the probability of Maxwell’s particular mechanical theory is zero, given what is known, even though the probability that some mechanical theory is true is greater than zero. 36. Larry Laudan, “A Confutation of Convergent Realism,” Philosophy of Science 48 (March 1981): 19–​49.

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However, for the sake of argument, suppose (contrary to what I have just claimed) that the fact that h is the “only game in town,” or that h is a theory of a type that has been successful, or that a vast majority of the authorities believe h, could raise the probability of h beyond ½. This would satisfy the upgraded objective Bayesian concept of evidence. And since the probability of h on e would be greater than ½, a necessary condition for potential evidence would be satisfied as well. However, the major claim I  want to make is this: So raising the probability of h, and thus making it reasonable to believe h, is not enough for what scientists want or should want of evidence. Even if h is the “only game in town,” even if h is a hypothesis of a general type that has been successful in other areas, even if the authorities believe h to be true, and even if these facts provide a good reason to believe the hypoth­esis, or a better reason than without them, when scientists seek evidence for h, they want something more. I turn to this next.

1 0 .   S C I E N T I F I C S P E C U L AT I O N Part of Newton’s evidence for his law of gravity (given in his “Phenomena,” Book 3) is that the planets in their orbits about the sun sweep out equal areas in equal times. For Newton, this is one among a set of facts that provide a good reason for believing the law of gravity is true. Now consider a Newtonian who says that the fact that the “incomparable Mr. Newton” believes the law of gravity to be true is a good reason to believe it is true. What scientists seek when they want evidence for a hypothesis is something along the lines offered by Newton, not by my imagined Newtonian. They want evidence

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that provides a reason why e or h is true, not just a reason to believe that one or both are true. Newton’s evidence is the sort scientists subscribing to the “mechanical philosophy” wanted because, they believed, it is based on a probable explanatory connection between e and h: probably the reason why the planets sweep out equal areas in equal times is that they are subject to a force governed by the law of gravity. My imagined Newtonian’s “evidence,” even if it gives a reason to believe Newton’s law, does not satisfy the condition that there is a probable explanatory connection between e and h. (It is not probable that the reason why the planets sweep out equal areas in equal times is that Newton believes this is true, or conversely.) My Newtonian’s reason is an authoritative one of the sort noted in section 8. Even if “only-​game-​in-​town” and meta-​inductive reasons, like authoritative ones, are or can be reasons to believe that a hypothesis is true, they are not reasons based on a probable explanatory connection between e and h. Now suppose that, given Newton’s “Phenomena,” the probability of an explanatory connection between these and his law of gravity is not very high, and that Newton did not know that there are other phenomena that would make it high.37 In accordance with my A-​concept of potential evidence, if Newton used the law of gravity in theorizing (which indeed he did, especially in showing how to explain the tides and other phenomena), he would then be speculating, since the “Phenomena” he cited would not be evidence for the law, and he didn’t know that there are other phenomena that would be. Suppose, further, that a follower of Newton uses the law in theorizing, believing that Newton has evidence 37. In ­chapter 4, I will suggest that this is indeed so.

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that provides a good reason to believe the law, although this follower has no idea what this evidence is. His reason for believing the law to be true is authoritarian—​Mr. Newton believes it. Now we can see how an important difference between my objective concept of A-​evidence and the objective (and upgraded) Bayesian one makes an important difference concerning what counts as a speculation. According to the Bayesian, the follower of Newton would have evidence that the law of gravity is true (“Mr. Newton believes it,” which let us suppose raises the probability of the law to a number greater than 1/​2). So, on the upgraded Bayesian concept of evidence, the follower of Newton would not be speculating.38 By contrast, according to my A-​concept of evidence, the fact that Newton believes the law of gravity is not evidence that the law is true (because of the lack of a probable explanatory connection between the law’s being true and Newton’s believing it). So, under the present scenario, since Newton did not have A-​evidence that the law is true, our imagined follower of Newton would not know that there is evidence that the law is true, since his belief that it is true is based solely on the false assumption that Newton has evidence for the law. For him, as well as for Newton, the law would be a speculation, despite their protestations to the contrary. What remains from the list of “ways to obtain evidence” in section 8 are Newtonian inductivism, the Whewellian version of hypothetico–​deductivism, and Lipton’s “inference to the best explanation.” Unlike the other three, all of these 38. With an upgraded “subjective” Bayesian concept of evidence—​one that employs a subjective concept of evidence and requires that the subjective probability of h be increased by e so that it is greater than ½, but does not impose the explanation requirement—​we also get the result that the follower of Newton would not be speculating even if Newton was.

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accounts involve the idea of some explanatory connection between h and e—​e.g., that the reason that e is true is that h is. Of the “explanatory connection” accounts, I find Lipton’s the most problematic. Suppose you can show that a system of hypotheses H, if true, offers the “loveliest” explanation of phenomena reported in e. Have you shown that e constitutes either A-​or (upgraded) B-​evidence for H? And if so, have you shown that the evidence supplied is sufficiently strong so that H cannot be regarded as a speculation? Have you shown, e.g., that, given e, the probability of H, or the probability of an explanatory connection between H and e, is greater than ½? To do so, you have to show, at a minimum, that beauty tracks probable truth—​that the more beautiful a theory is, the more probable it is, and that if its beauty surpasses some threshold, its probability is sufficient for belief. Lipton simply assumes that this is so, without giving any argument.39 This does not mean that beauty is irrelevant in the assessment of a theory, only that, if it is a virtue, it is a non-​epistemic one: it does not, and should not, affect the reasonableness of believing a theory. Of the remaining two “explanatory connection” accounts, I  prefer the Newtonian to the Whewellian one. However, I  will not pursue this here.40 For the sake of argument, 39.  In Achinstein, Evidence and Method, 104–​10, I  examine possible arguments and reject them. In c­ hapters  2 and 3, I  will consider various arguments in favor of the claim that simplicity—​one of Lipton’s favorite types of beauty—​is an epistemic virtue. None of them succeeds. For a critical discussion of arguments for the more general claim that beauty tracks probable truth, see the article by Gregory Morgan and my reply in G. Morgan, ed., Philosophy of Science Matters: The Philosophy of Peter Achinstein (New York: Oxford University Press, 2011). 40.  For a critical discussion of Whewell, see Achinstein, Evidence and Method.

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I  will suppose that both Newtonian and Whewellian evidence e can make it highly probable that there is an explanatory connection between h and e (thus satisfying my A-​concept of potential evidence). If you have A-​evidence for h, then h is not a speculation for you. What is missing in “only-​game-​in-​town,” meta-​inductive, and authoritative “evidence” e (even if such “evidence” could make a hypoth­ esis (more) reasonable to believe), and what is present in Newtonian and Whewellian evidence, is the idea that e and h are (probably) explanatorily related. With this, we have what I call “evidence,” or perhaps, more accurately, “explanatory evidence.” Without it, we don’t. Explanatory evidence is what Brougham was demanding of Young’s wave theory of light, Duhem of Kelvin’s molecular theory of the ether, and Weinberg of string theory. These critics are claiming that the theories in question are speculations because their proponents lack such evidence. This explanatory idea is built into my concept of potential evidence, but it is not built into the Bayesian B-​concept, even if the latter is upgraded to require that e raise the probability of h to a point greater than ½. So, we can incorporate this idea into a Bayesian concept by saying that when one seeks explanatory B-​evidence for a hypothesis h, one seeks an e that increases the probability that there is an explanatory connection between h and e so that this probability is more than ½. That is, e is explanatory B-​evidence for h only if p(E(h,e)/​e) > p(E(h,e)), and p(E(h,e)/​e) > 1/​2.41

41. Since E(h,e) entails h, the usual Bayesian idea p(h/​e) > p(h) follows.

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If probability here is construed objectively, we obtain an objective concept of evidence. Now we have closed the gap very considerably between my concept of (“potential”) A-​ evidence and the Bayesian concept. The only important difference between my concept and explanatory B-​evidence (construed objectively) is that the latter requires that evidence increase the probability of an explanatory connection, the former does not.42 Finally, then, suppose that, in the course of a scientific investigation, P introduces an assumption h under previously noted “theorizing” conditions. Then, we can say that: (Scientific Spec): h is a (truth-​relevant) scientific speculation for P (with respect to the truth of h) if and only if P does not know that there is explanatory evidence that h (A-​evidence, or explanatory B-​evidence).43

Even if “meta-​inductive,” “only-​game-​in-​town,” and “authoritative” facts could raise the probability of a hypothesis and make it highly probable, these “facts” would not constitute explanatory evidence for the hypothesis. If these “facts” are the only ones known that make the hypothesis highly probable, and if it is not known that there are any others that do so and constitute A-​evidence or explanatory B-​evidence, then 42. For arguments against requiring that evidence increase this probability, see Achinstein, Book of Evidence, chap. 4. 43. This, of course, leaves open the question of what makes an investigation a “scientific” one—​a topic long debated. What I am saying is that however this is to be understood, whether or not an assumption introduced in such an investigation is a speculation depends on whether or not the speculator knows that explanatory evidence for it exists.

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the hypothesis, if introduced in a scientific investigation and believed to be true, is a scientific speculation. It is this concept of speculation—​(Scientific Spec)—​that I  utilize in what follows. I  will take it to be the concept in question when disputes occur about when, if at all, to introduce truth-​relevant speculations. It is the concept I will be employing in section 12, when I address the issue of how to evaluate such speculations.

1 1 .   S P E C U L AT I O N C O N T R O V E R S I E S REVISITED All the views in section 3 can be understood in terms of the concept of (Scientific Spec). Both Newton (espousing the “very conservative” view) and Whewell (the “moderate” one) are talking about evidence and speculation in an objective sense, not in a subjective one. Newton’s causal-​ inductive “Rules for the Study of Natural Philosophy” and Whewell’s “consilience” and “coherence” are supposed to yield evidence that is independent of any particular person’s beliefs about what counts as evidence.44 Moreover, both Newton and Whewell require “explanatory” evidence, since the proposition inferred from the evidence will explain that evidence and other phenomena as well. They are not talking about non-​ explanatory “evidence”—​ whether

44.  To be sure, a subjectivist about evidence could adopt Newtonian or Whewellian ideas by saying that e is evidence for him, but not necessarily for others, if and only if e and h satisfy Newtonian inductivism or Whewellian consilience and coherence. But this is not the position of Newton or Whewell. Their concepts of evidence are not tied to individuals.

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meta-​inductive, “only game in town,” or authoritarian. And both have in mind evidence that provides a good reason for believing a hypothesis, not just one that simply increases its probability. Using A-​or explanatory B-​evidence in defining speculation will yield the kind of activity that Newton opposes and Whewell supports. Feyerabend, a champion of the “very liberal” view that encourages unbridled speculation (“proliferation”) in the absence of evidence, presents no particular view of evidence or of how to get evidence. I will construe his self-​described “anarchist” view to encourage speculating where this at least includes speculation in the sense of (Scientific Spec). Understanding these conflicting claims using (Scientific Spec), how shall we respond to them? As for the “very conservative” view—​the view which Newton puts by saying “hypotheses have no place in experimental philosophy”—​ although both Newton and Descartes promulgate this idea in their official principles, they violate it in their practice. In the Principia, Newton introduces two propositions he himself calls “hypotheses.” (Hypothesis 1 is “the center of the system of the world is at rest.”45) And at the end of his book Opticks, there are speculations about the particle nature of light that are clearly hypotheses in his sense. Here, after offering empirical proofs of various laws of geometrical optics, he raises the question of what light is and offers a speculative hypothesis: “Are not the rays of light very small bodies emitted from shining substances? For such bodies will pass through uniform mediums in right lines without bending into the shadow, which is the nature of rays of

45. In Achinstein, Science Rules, 74.

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light.”46 These are Newtonian speculations in the sense given by (Scientific Spec). Descartes, as well, speculates in his Principles of Philosophy. After proving his general laws of motion (to his satisfaction)—​laws regarding inertial motion and motion after impact—​he introduces assumptions about the vortex motion of celestial bodies in the universe, saying “I will put forward everything that I am going to write [in what follows] just as a hypothesis.”47 He then proceeds to “suppose that all the matter constituting the visible world was originally divided by God into unsurpassably equal particles of medium size . . . that each turned round its own centre, so that they formed a fluid body, such as we take the heavens to be; and that many revolved together around various other points . . . and thus constituted as many different vortices as there now are stars in the world.” These also satisfy (Scientific Spec). Now, as these examples show, proof of a proposition or set of propositions about the behavior of some objects often leads to more questions about the nature of those objects and their behavior. It is natural for scientists to raise these questions and, when they do so, to think of possible answers. Refusing to do so is tantamount to stifling curiosity. How else could progress in science occur? Propositions don’t usually come to the mind proved, and even when and if they do, additional questions will come to mind, some of which, at least, are accompanied with answers that are not proved. This happened with both Descartes and Newton, and is part of both everyday and scientific thinking. Indeed, humans could

46. Isaac Newton, Opticks (New York: Dover Publications, 1979), 370. 47. Reprinted in Achinstein, Science Rules, 46.

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not survive without it. Despite pronouncements in their “official” methodologies to eschew speculations altogether, perhaps a more charitable interpretation of the positions of Newton and Descartes is this: Speculations are allowed, provided that they are clearly labeled as such, and provided they are not inferred to be true or probable on the grounds that, if true, they could explain, or help to explain, various known phenomena. If these conditions are met, why object to publicly communicating speculations, which in fact was done by both Newton and Descartes? What about the “moderate” position (“Speculate, but verify”) typically taken by hypothetico-​deductivists? There are several questions here. First, to raise a practical question, how long a period of time should be allowed between the speculation and the verification? Taking string theory as an example, and construing “verification” as providing (Newtonian or Whewellian) scientific evidence sufficient for belief, how long on the “moderate” view should string theorists be given to provide such verification of their theory—​10 years, 20 years, 100 years? Is the view simply that until there is verification, the speculation is not to be believed? Or is it that until at least there is some reasonable prospect or plan for verification, the theory should not be seriously pursued (developed, worked out, taught in the classroom) by scientists or even regarded as “scientific”? Or, as a practical question, is the answer a subjective one, to be decided by the interests, finances, and patience of individual scientists? More important, until it is tested, how, if at all, is a speculation to be evaluated? That is the main question I want to raise in the case of both the “moderate” view and Feyerabend’s “very liberal” one (“Speculate like mad”). Hypothetico-​ deductivists, as well as Feyerabendians,

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provide little information here. The “context of discovery,” where, according to hypothetico-​ deductivists, speculation is supposed to take place has few if any constraints placed upon it. Popper wants the speculations to be “bold.” Hypothetico-​deductivists want the speculations at least to be potential explanations of the data or potential solutions to the problems prompting the speculation. Feyerabend is more liberal than this. For him, a speculation can be inconsistent with the data and can even reject the problems prompting the speculation. A speculation, as such, is not subject to any standards of evaluation. I reject all three views, not only because scientists do and must speculate but also because, as I  will argue next, speculations can be evaluated in various ways other than by testing, and doing so is entirely appropriate. Giving “free rein to the imagination”—​a favorite slogan of hypothetico-​ deductivists and Feyerabendians—​sounds good, but isn’t always the best policy.

1 2 .  H O W S H O U L D S P E C U L AT I O N S B E E VA L UAT E D ? M A X W E L L’ S S P E C U L AT I V E S T R AT E G I E S The evaluations I have in mind—​ones satisfying (Scientific Spec)—​are not subject to universal standards that determine in general what is to count as a good speculation. They are subject to pragmatic standards that depend on the aims and epistemic situation of the speculator and the evaluator, which can vary from one scientist and context to another. To see how this is supposed to work in practice, I  will invoke

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the case of James Clerk Maxwell, a speculator par excellence, who had compelling philosophical ideas about speculating. My aim in what follows is not to present evaluations of Maxwell’s speculations but, rather, to show what Maxwell regarded, and reasonably so, as criteria that can be used in such evaluations. Beginning in 1855 and for more than twenty years, Maxwell made numerous speculations about electricity and molecules. Three are of particular concern to me in what follows, because they represent three different ways to speculate, and can be judged using different standards of evaluation. Maxwell himself had labels for these methods. The first he called an “exercise in mechanics”; the second, a “method of physical speculation”; and the third, a “method of physical analogy.” In the three examples I  mention, Maxwell begins with known phenomena that no established theory has explained, following which he introduces speculations, either truth-​relevant ones for which scientific evidence is unknown or insufficient or else truth-​irrelevant ones. Although the methods he employs are different, there are three very general aims he expresses that are common to all. One aim is to present a physical, rather than purely mathematical, way of understanding the known phenomena. Another is to proceed in a very precise way, using mathematics to present the physical ideas. A  third is to work out the speculation in considerable detail, drawing various consequences. Maxwell’s speculative methods represent different ways to accomplish these common aims, and the results are to be evaluated differently. In previous sections I have concentrated on truth-​relevant speculations. So I will begin with these.

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a. Exercise in Mechanics One type of speculation that Maxwell employs is illustrated by what he calls “an exercise in mechanics.” In 1860, in a groundbreaking work on the kinetic-​molecular theory of gases entitled “Illustrations of the Dynamical Theory of Gases,”48 Maxwell introduces a series of speculative assumptions. These include that gases are composed of spherical molecules that move with uniform velocity in straight lines, except when they strike each other or the sides of the container; that they obey Newtonian laws of dynamics; that they exert forces only at impact and not at a distance; and that they make perfectly elastic collisions. He then works out these assumptions mathematically so as to explain various known gaseous phenomena, and to derive new theoretical results, including his important distribution law for molecular velocities. Just before publishing the paper, Maxwell writes to Stokes in 1859 saying, I do not know how far such speculations may be found to agree with facts . . . , and at any rate as I found myself able and willing to deduce the laws of motion of systems of particles acting on each other only by impact, I have done so as an exercise in mechanics.49

Maxwell does not claim that the assumptions he makes are true or close to it. His aim in this paper is to see whether 48. W. D. Niven, ed., The Scientific Papers of James Clerk Maxwell, 2 vols. (New York: Dover, 1965), 1:377–​409. 49. Elizabeth Garber, Stephen G. Brush, and C. W. F. Everitt, eds., Maxwell on Molecules and Gases (Cambridge, MA: MIT Press, 1986), 279.

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a dynamical explanation of observed gaseous phenomena is even possible, that could be true, given what is known—​ one that invokes bodies in motion exerting forces subject to Newton’s laws. For this purpose, he employs a set of simplified assumptions about molecules constituting gases. His basic question in the paper is whether these assumptions about constituents of gases could be used to explain known gas laws and could be developed mathematically to yield some interesting theoretical claims about molecular motion. However, when Maxwell explicitly classifies his assumptions as speculations (as he does in the previous  quotation), he is thinking of them as being speculations with respect to truth, not possibility. They are (truth-​relevant) speculations that Maxwell introduces for explanatory purposes without knowing that there is evidence for the truth, or the closeness to truth, of the assumptions he introduces. How should such speculations be evaluated? This can be done from different perspectives, not just from the perspective of truth or evidence. One is purely historical, recognizing the significance of Maxwell’s speculations in the development of kinetic-​molecular theory. A different perspective, his own, is obtained by focusing on what he was trying to do when he introduced the speculative assumptions, viz. to see whether a molecular theory of gases is possible. This he did by showing how such a theory could offer mechanical explanations of pressure, volume, and temperature of gases and of known laws relating these and other properties. And he showed how such a theory could be extended by deriving consequences, such as his distribution law for molecular velocities, his most important new result. From this perspective, speculative assumptions are evaluated by considering whether and how well, if true, they would correctly explain various properties

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of, and laws governing, gases. For Maxwell, how well they would do so depends on whether they are worked out in considerable detail using mathematics, and whether they provide a physical and not merely a mathematical way to think about gases. Such a perspective was important during Maxwell’s time since, although there were substantially developed mechanical theories in other areas of physics and astronomy, this had not yet been accomplished for gases, at least not with the depth and precision that Maxwell demanded. To be sure, another perspective of evaluation is that of Newton:  Did Maxwell have any evidence for these assumptions? If not, he should have discarded them. Maxwell is urging a much more pragmatic approach. Speculations, like everything else, can be evaluated in different ways. From the Newtonian perspective of “proof ” or “deduction from the phenomena,” all speculations are bad. That perspective is supposed to be paramount and dwarf or even disallow others. If Maxwell had no evidence for his assumptions, he should not have speculated, at least not publicly. If he had evidence, it was not a speculation. But why should the Newtonian perspective be the only one from which to judge Maxwell’s speculations, especially since Newton himself violated the requirements of that perspective? Why not just label the assumptions as speculations, and say that the fact that they can explain known gas laws, and yield interesting new results, is not evidence or proof that they are correct? This, of course, is exactly what Maxwell did.

b. Physical Speculation In 1875, fifteen years after the publication of his first kinetic theory paper, Maxwell published “On the Dynamical

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Evidence of the Molecular Constitution of Bodies.”50 The paper contains various truth-​ relevant speculations about molecules, but Maxwell regarded his methodology as different from that in his “exercise in mechanics.” He calls it a “method of physical speculation,” and he writes: When examples of this method of physical speculation have been properly set forth and explained, we shall hear fewer complaints of the looseness of the reasoning of men of science, and the method of inductive philosophy will no longer be derided as mere guess-​work.51

Maxwell does not spell out the method, but illustrates its use in the paper itself. The method contains some elements present in his “exercise in mechanics,” but it adds a crucial component, which I call “independent warrant.” This consists of giving reasons for making the speculative assumptions in question, beyond simply that if one makes them then certain phenomena can be explained mechanically. Some of the reasons for some assumptions include appeals to experimental results and may rise to the level of what I have called scientific evidence for those assumptions. Some reasons do not rise to that level, including ones that appeal to the success of similar assumptions used in other domains and to the fundamentality and simplicity of some of the assumptions. Maxwell supplies reasons of all three sorts in the present paper. One claim he makes is that there is “experimental proof that bodies may be divided into parts so small that we cannot perceive them.” In this paper he does not say what 50. Niven, ed., Scientific Papers of James Clerk Maxwell, 2:418–​38. 51. Niven, ed., Scientific Papers of James Clerk Maxwell, 2:419.

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experiments he has in mind. But in his 1871 book Theory of Heat, he cites experiments showing that heat is not a substance (caloric) but a form of energy. (In all probability he has in mind experiments by Joule in the 1840s.) He proceeds to give empirical reasons why the energy must be kinetic rather than potential energy. And he concludes: The motion we call heat must therefore must be a motion of parts too small to be observed separately.  .  .  . We have now arrived at the conception of a body as consisting of a great many parts, each of which is in motion. We shall call any one of these parts a molecule of the substance.52

Maxwell seems to believe that he has explanatory evidence at least for the claim that molecules in motion exist in bodies. Since he uses the expression “experimental proof,” he appears to regard this evidence as sufficient to justify believing that they do. He also provides an empirical reason for thinking that the molecules satisfy a general virial equation derived by Clausius from classical mechanics as applied to a system of particles constrained to move in a limited region of space, and whose velocities can fluctuate within certain limits. The reason is that this equation works for macroscopic bodies in an enclosure. This may not rise to the level of explanatory evidence, let  alone proof, but he thinks it provides at least some empirical reason for supposing the equation works for unobservable molecules in an enclosure as well. Before introducing the Clausius equation, Maxwell makes the important general assumption that molecules in

52.  James Clerk Maxwell, Theory of Heat (New  York:  Dover, 2001), 304–​305.

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an enclosure are mechanical systems subject to Newtonian laws. Part of his reason for this assumption is methodological, having to do with the fundamentality of mechanical explanations. He writes: When a physical phenomenon can be completely described as a change in the configuration and motion of a material system, the dynamical explanation of that phenomenon is said to be complete. We cannot conceive any further explanation to be either necessary, desirable, or possible, for as soon as we know what is meant by the words configuration, motion, mass and force, we see that the ideas which they represent are so elementary that they cannot be explained by means of anything else.53

Another part of the reason Maxwell offers for assuming that molecules are subject to mechanical laws is that such laws have been successful in astronomy and (he thinks) electrical science. The claims of fundamentality and historical success for mechanical principles are nowhere near proof of, or scientific evidence for, the truth of the assumptions Maxwell makes about molecules. But they are among the reasons he offers for making the kind of assumptions about molecules that he does. Maxwell clearly regards the theory he develops as a speculation (he uses the term “physical speculation”). And it is one in accordance with the objective ideas in (Scientific Spec), since even though he thinks he has “experimental proof ” for some assumptions, for others he does not. In the latter case, he has reasons for introducing such assumptions, working them out, and trying to develop

53. Niven, ed., Scientific Papers of James Clerk Maxwell, 2:418.

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experiments that could confirm them. But he does not have, or know that there is, explanatory evidence for them. Again we can evaluate his speculations from the perspective of his epistemic situation and the questions he was raising. We can ask whether, given his epistemic situation, he was justified in concluding that he had explanatory evidence for certain assumptions, and whether the reasons he offered for other assumptions, even if they did not rise to the level of explanatory evidence, were good ones, and how good they were. And, as in the case of the earlier 1860 paper, we can also provide non-​epistemic evaluations—​e.g., ones pertaining to the historical importance of his results.54

c. Physical Analogy Finally, I  turn to a truth-​irrelevant speculation. In 1855, Maxwell published a paper, “On Faraday’s Lines of Force,”55 in which he imagines the existence of an incompressible fluid flowing through tubes of varying section. His aim in developing this idea is to construct a physical analogue of electric and magnetic fields. In the electrical case, the velocity of the imaginary fluid at a given point represents the electrical force at that point, and the direction of flow in the tube represents the direction of the force. Particles of electricity are represented in the analogue as sources and sinks of fluid, and the electrical potential as the pressure of the fluid. Coulomb’s law, according to which the electrical force on a particle a 54. The idea of different perspectives, both epistemic and non-​epistemic, from which to evaluate a theory will appear again in c­ hapter 4, in my discussion of the holism–​particularism debate. 55. Niven, ed., Scientific Papers of James Clerk Maxwell, 1:155–​229.

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distance r from the particle varies as 1/​r2, is represented by the law that the velocity of the fluid at a distance r from the source of fluid varies as 1/​r2. The bulk of Maxwell’s 75-​page paper is spent working out this analogy mathematically by showing how to derive equations governing the imaginary fluid that are analogues of ones governing electrical and magnetic fields. Why is Maxwell proceeding in this way? He wants to understand and unify a range of known electrical and magnetic phenomena. He notes that one way to do so is to explain why they occur by introducing a hypothesis that provides a physical cause for these phenomena. But he has no such physical hypothesis to offer. In its place he wants to introduce a different way to understand and unify the phenomena—​a way that explains not why they occur but what they are, without providing a cause. One way to do the latter is to describe the known phenomena using concepts that are to be applied more or less literally to the phenomena—​e.g., describing known electrical phenomena using concepts such as charged particle, force, and motion. Another way is to draw an analogy between these phenomena, so described, and some others that are known or can be described. In Maxwell’s time, fluids were much better known than electrical phenomena. So, thinking of electricity as being like a fluid, and charged particles as being like sources and sinks of fluid, and of the electric force at a point as being like the velocity of that fluid at a point might help one to understand what electrical phenomena are without understanding why they occur. This is so, even though the fluid in question doesn’t exist. Now, some analogies involve truth-​relevant speculations in the sense that I have defined. For example, in an article on molecules in the Encyclopaedia Britannica, Maxwell draws an

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analogy between molecules in a gas and bees in a swarm: they are similar in some of their motions. This involves a truth-​ relevant speculation. Maxwell is introducing an assumption about the existence and behavior of molecules with the idea that molecules exist and behave like bees in a swarm, without knowing whether there is sufficient evidence for the claim that molecules exist or for the claim that they behave like bees in a swarm. Other analogies, such as the one in his 1855 paper, involve speculations that are not truth-​relevant. Here, Maxwell is talking about something that does not (and could not) exist: his imaginary fluid. He is introducing a range of assumptions about that fluid, without the idea that these assumptions are or might be true—​indeed, with the idea that they cannot be true. Maxwell is in effect making up a story about an imaginary fluid, one that is not to be taken as true but one that will serve, he hopes, as a useful analogy for understanding what electrical phenomena are. This analogue story is a truth-​irrelevant speculation. Viewed in this way, Maxwell’s story is like a biblical story (under some pragmatic interpretations of the Bible). The “characters” in the story (the imaginary fluid; Cain and Abel) are not being claimed to exist. But in both cases, the behavior of certain things that are real and that we know about can be understood by analogy with the behavior of the “characters” in the story. How is such a speculation to be evaluated? Here, big differences emerge between those such as Maxwell, who take a pragmatic view, and those such as Descartes, Newton, Brougham, and Duhem, who, at least in their official methodologies, take a non-​pragmatic view of any explanatory assumptions introduced in a scientific investigation. From the latter perspective, you evaluate solely on the basis of what you regard as an ideal and how close the theorizing

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in question has come to satisfying that ideal. The Newtonian ideal is to introduce an assumption that is true and to establish its truth by causal-​inductive reasoning from observed phenomena. From this perspective, Maxwell’s physical analogy is a nonstarter. Using words that Brougham, a devout Newtonian, employs against Young’s speculation about the wave nature of light, it is “a work of fancy, useless in science . . . fit only for the amusement of a vacant hour.” From Maxwell’s point of view, the question is whether the imaginary fluid analogy provides a non-​causal physical way of understanding and unifying certain electrical and magnetic phenomena for which no causal explanation has yet been discovered; a way that is worked out mathematically; and, most important, a way that may help others, including physicists, in understanding and unifying the phenomena. This is a pragmatic perspective because it says that if you can’t get what you and others might regard as ideal (e.g., a true theory experimentally verified that causally explains and unifies electrical and magnetic phenomena), do what you can that will be useful (in this case, provide a physical analogy that will help explain and unify the phenomena in a non-​causal way). From this perspective, you evaluate the speculation, in part at least, by seeing whether it is or was in fact useful in producing the kind of understanding sought. Here, it should not be surprising, I adopt Maxwell’s pragmatism: To conduct the operations of science in a perfectly legitimate manner, by means of methodized experiments and strict demonstration, requires a strategic skill which we must not look for, even among those to whom science is most indebted for original observations and fertile suggestions. It does not detract from the merit of the pioneers of science that their

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advances, being made on unknown ground, are often cut off, for a time, from that system of communications with an established base of operations, which is the only security for any permanent extension of science.56

When you are so “cut off,” Maxwell proposes that you proceed to speculate in various ways, “on unknown ground,” including with the use of physical analogies such as his imaginary fluid one.57

1 3 .   B E P R A G M AT I C All three strong positions on speculation discussed in sections 3 and 11 make a bold claim about standards to be used in evaluating a speculation. All three hold that considered as a speculation, and not as something for which there is explanatory evidence, there are no such standards. On the (“official”) Newtonian view, scientists should not speculate at all. The only standards of evaluation are ones used in determining whether there is explanatory evidence for the truth of a hypothesis. On both the “moderate” and “very liberal” views, there are few if any constraints imposed on speculations. (Proof is a different matter.) What I  am claiming is that there are legitimate ways to evaluate a speculation—​as a speculation—​independent of standards requiring explanatory evidence. And different perspectives are possible for such an evaluation: ones 56. Niven, ed., Scientific Papers of James Clerk Maxwell, 2:420. 57.  For more details on Maxwell’s speculative strategies, see Achinstein, Evidence and Method, chap. 4.

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pertaining to the speculator, with his knowledge and interests; and ones pertaining to an evaluator with different knowledge and interests. It is one thing to evaluate Maxwell’s imaginary fluid analogue from his perspective in 1855, when no confirmed electromagnetic theory was known that would unify and explain observable electrical and magnetic phenomena in physical terms. It is another to evaluate his account from our twenty-​first-​century perspective. If we were to engage in constructing an imaginary physical analogue for electrical and magnetic phenomena, even if it were somewhat different from the one Maxwell was imagining, perhaps we would deserve Brougham’s epithet “a work of fancy, useless in science.” My view is pragmatic because it allows speculations to be introduced with different purposes and different epistemic and non-​epistemic situations in mind, and it allows an evaluation of those speculations based on those purposes and situations. In section 2, I  noted that Duhem criticized Kelvin’s speculations about the molecular nature of the ether as being a “work of imagination,” not “acceptable to reason.” Duhem also criticized both Kelvin and Maxwell for theorizing in physical rather than in purely abstract mathematical terms. He called this type of mentality “British,” and he clearly thought it was inferior to the abstract “continental” (or “French”) mind. Theorizing, whether speculative or not, should always be done in the “continental” style, he thought. (Whether this perspective is reasonable is another matter!) Maxwell, too, recognized that there are different sorts of scientific minds: some minds . . . can go on contemplating with satisfaction pure quantities presented to the eye by symbols, and to the mind in a form which none but mathematicians can conceive.

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But there are others that require that these quantities be represented physically. He concludes: For the sake of persons of these different types, scientific truth should be presented in different forms, and should be regarded as equally scientific, whether it appears in the robust form and the vivid colouring of a physical illustration or in the tenuity and paleness of a symbolic expression.58

Maxwell himself strongly preferred physical explana­ tions and sought to provide mechanical ones in his theorizing because he regarded them as fundamental. But he recognized that there are other ways to theorize that can be just as good or better for certain minds. There are other, legitimate perspectives from which to theorize and evaluate the result. As far as speculation itself is concerned, yes, it would be great to have “methodized experiments and strict demonstration.” But the “pioneers of science” (including J.C.M.) are often “cut off, for a time” from methodized experiments and strict demonstration. Their “advances, being made, on unknown ground,” are speculative, but advances nonetheless. Finally, if you are a pragmatist, and you want to provide “methodized experiments and strict demonstration,” how long do you wait? For a pragmatist that is mostly a practical question, the answer to which depends on your interests, your temperament, your time, and your money. It also depends on how likely it is that such experiments can be performed and when, given what is known. Suppose, however, that for some empirical reasons—​say, energies required for proper 58. Niven, ed., Scientific Papers of James Clerk Maxwell, 2:220.

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detection are not and may never be achievable (perhaps string theory), or signals from objects postulated can never reach us (multiverse theory)—​methodized experiments and strict demonstration will never be possible. Suppose, that is, that there will be no known evidence sufficient to justify belief in the speculation. Should you just give up? Should you stop speculating? Newtonians following the official party line will say:  “Of course. Speculations, especially those that will always remain so, ‘have no place in experimental philosophy.’ ” Pragmatists, however, in the spirit of Maxwell’s first paper on molecules, can say, “Not so fast. Here is a way the world might be, even if neither I  nor anyone else can present evidence sufficiently strong to believe in the existence of molecules (or strings, or multiverses, or whatever speculative entities are postulated), indeed perhaps even if there never will be such evidence. If, for that reason, you choose to stop working on, or even considering, the theory introduced, that is your pragmatic choice. If you reply that this is not science, my response will again be Maxwellian: Not so fast. Science encompasses many activities, including speculation. Hopefully, the latter will lead to testing, but it may not. From a pragmatic viewpoint one can evaluate a speculation without necessarily testing it. You don’t have to know how to test the speculation for it to be a good one, or even good science. And, perhaps in the most extreme cases, if you have reasons to suppose that it is not testable and will not become so, you may still be able to give reasons, whether epistemic or non-​epistemic, for making the speculation, even if these do not amount to evidence sufficient to believe it. Such reasons can be evaluated from a pragmatic scientific perspective.”

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1 4 .   A   P R E V I E W O F   C O M I N G AT T R A C T I O N S So far my examples of speculations have all been ones introduced by scientists making specific claims about items in the world and laws governing them. They are recognizably “scientific,” whether they are “truth-​relevant” or “truth-​irrelevant.” Now I  want to extend the discussion to much more general and abstract speculations introduced by philosophers, scientists, or both, about the world and about methods for gaining scientific knowledge about the world. I will call them “philosophical.” Suppose that in the course of a “philosophical” investigation (however broadly that is to be understood), the investigator P introduces an assumption h under “theorizing” conditions (i.e., in the course of explaining, etc., and with the idea that it is true, or close to the truth, or a worthy truth contender). Then, using the account of (Scientific Spec) given in section 10 as a template, we can say that h is a truth-​relevant “philosophical” speculation for P if and only if P does not know that there is explanatory evidence that h. The speculations I  will consider are ones made within or about science. They are important, if only because they have been assumed and promoted by philosophers and scientists who believe that doing so is central to the pursuit and understanding of science. Usually those who introduce these speculations give reasons in favor of them, as Maxwell did for his speculative kinetic-​molecular theory. Perhaps some of those who present these reasons believe they are strong enough to satisfy the requirements of A-​or explanatory B-​evidence. But even if these reasons do not satisfy such requirements (I will argue that they do not), and

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even if the champions of these speculations admit that they are speculations, the reasons they do offer in support of them can be evaluated in philosophical cases, as well as in scientific ones. The speculations I will examine are concerned with three topics:  simplicity, holism, and a “Theory of Everything.” With respect to the first, there are speculations claiming that the world is simple, that simplicity is a guide to truth, that scientists must aim to provide simple theories, and that even if the world is not simple, scientists must presuppose that it is to do science. With respect to the second, there are speculations that scientific theories can only be supported “holistically,” not by establishing individual parts, and that in the absence of such holistic support, theories cannot be evaluated. With respect to the third, there are speculations claiming that there exists a “Theory of Everything,” and that even if it has not yet been found, it needs to be found in order for scientists to be able to make the world completely intelligible. In the next four chapters, I will discuss these and related speculations. They are grand and exciting speculations, or at least are considered so by their proponents. Some of these speculations are argued for by those who make them, by offering either epistemic reasons for believing they are true or non-​epistemic ones for believing that they need to be assumed to do science. Some are assumed without argument. My aim is to convince you to reject them. I do so, not because they are speculations but because, even considered as speculations, the arguments that have been presented in their favor by their proponents, as well as other possible arguments I will try to construct, do not deserve high marks. These speculations, although believed by many, have little, if any, support and do not need to be made in order to engage in, or understand, science.

2

✦ THE COMPLEX STORY OF SIMPLICITY Ontological and Epistemic Speculations Simplicity is the ultimate sophistication. — ​L e o n a r d o d a   V i n c i

Simplicity: The last refuge of a scoundrel (with apologies to Samuel Johnson)

1 .   I N T R O D U C T I O N Some of the greatest scientists, including Newton and Einstein, invoke simplicity in defense of a theory they are promoting. Einstein writes that he cannot define simplicity, but that he recognizes it when he sees it.1 Newton also does not attempt to define simplicity, and I think it is fair to say that he, too, believed that he could recognize it when he saw it. Perhaps these scientists refrained from a definition since there are too many different kinds of simplicity, or respects in 1.  Paul Arthur Schilpp, ed., Albert Einstein:  Philosopher-​Scientist (New York: Tudor Publishing, 1951), 23.

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which something can be simple—​or by contrast, complex—​ to be usefully characterized by a single definition. There is simplicity with respect to the number of different types of entities postulated by a theory; the complexity of these entities (are they basic or do they have parts?); the number of different types of causes that produce the behavior of these entities; the number of different laws postulated that govern those causes; the complexity of these laws and the calculations required to apply them; and so on. Perhaps a gen­ eral definition of simplicity can be found that will cover all these and other types of simplicity or ways in which things can be simple. Following the example set by Newton and Einstein, I will not attempt such a task. I seriously doubt that a useful definition can be given. My question is different:  What role or roles is simplicity supposed to play according to scientists who invoke it, and can it do so? In describing such roles, scientists and philosophers make various claims about simplicity, including that nature itself is simple; that simplicity is an epistemic virtue that provides a basis for believing that a theory is true; that it is the aim of science to produce simple theories; that in order to do science one must presuppose that nature is simple; and that scientific theories are always underdetermined by empirical evidence, so that simplicity must be invoked in choosing a scientific theory. In this chapter and the next, I propose to consider these claims and the reasons that scientists and philosophers offer or might offer for them. I will argue that, despite what scientists and philosophers say, these claims about simplicity are (truth-​ relevant) speculations. They are introduced in the course of theorizing and believed to be true by their champions, without

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knowing that there is evidence for them—​at least not evidence that provides a good reason for believing them. But even considered as speculations, they should not receive high marks. In some cases no reasons, evidential or otherwise, are given for them, while in others the reasons given, both evidential and non-​evidential, are very dubious. The speculations I  have mentioned have serious problems, and should not be, and need not be, made to do or understand science. The virtue of simplicity, I will maintain, is not that it provides an ontological or epistemic guide to the way the world is or a necessary presupposition for science. It doesn’t. Its virtue is mainly pragmatic—​one that has to do with practical aims that can vary from one context to another. Moreover, simplicity frequently conflicts with virtues such as truth or empirical adequacy. When it does, whether to choose simplicity on the one hand or truth (or empirical adequacy) on the other is decided on pragmatic grounds. These ideas will be explained, expanded, and defended in the present chapter and the one that follows. It will turn out that simplicity is no simple matter. Two preliminary points should be made. First, scientists and philosophers who invoke simplicity usually apply the concept to abstract objects such as theories, laws, hypotheses, and explanations. But some of them apply it also to the world itself, or parts of it. I will do so as well, when they do. Second, simplicity enthusiasts, especially contemporary ones, invoke simplicity as a criterion of what they call “theory-​ choice.” But “theory-​choice” is a vague expression: choice for what? One might choose a theory for a variety of different purposes including working on it, promoting it, using it to make calculations, and explaining its historical importance.

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Whether simplicity is relevant in any of these “choices” depends on the purpose for which it is “chosen” and the context in question. Defenders of simplicity, I think, have in mind something else, viz. “choosing to believe,” or if one rejects the idea that one can choose to believe, just “believe,” neither of which is to be understood as choosing for some purpose or other. The claim would then be this: the simplicity of a theory is a good reason, or among the good reasons, for believing a theory to be true, or empirically adequate (in one or more of the senses of the latter expression I will note in section 2). This is just one of the claims about simplicity that I examine in what follows.

2 .   C L A I M S A B O U T   S I M P L I C I T Y Those who invoke simplicity make at least one and usually more of the following bold claims.

a. An Ontological Claim Nature is simple.

In Book 3 of the Principia, Newton presents his proof of the law of gravity. In doing so, he first introduces four methodological “Rules for the Study of Natural Philosophy” that he will appeal to in the proof. The first three rules he justifies by appeal to the claim that nature is simple. Rule 1: “No more causes of natural things should be admitted than are both true and sufficient to explain their phenomena.” He defends this by writing: “For nature is simple and does not indulge

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in the luxury of superfluous causes.”2 Rule 2: “Therefore, the causes assigned to natural effects of the same kind must be, so far as possible, the same.” He begins Rule 2 with “therefore,” since he takes this rule to follow from Rule 1, which is based on simplicity. Rule 3: “The qualities of bodies that cannot be intended and remitted and that belong to all bodies on which experiments can be made should be taken as qualities of all bodies universally.” This he defends by saying “nature is always simple and ever consonant with itself.” Albert Einstein, in a Herbert Spencer lecture in 1933, appeals to simplicity when he claims that “the axiomatic foundation of theoretical physics cannot be extracted from experience but must be freely invented.”3 In this “free invention,” scientists choose the simplest theory. Why? He writes: “Our experience hitherto justifies us in trusting that nature is the realization of the simplest that is mathematically conceivable.” There are different ways to construe what Einstein is claiming, and perhaps he is making more than one claim. On one interpretation, the claim, as with Newton, is that nature is simple—​at least with respect to mathematically expressible truths. 2. See also Newton’s letter to Leibniz, October 16, 1693, in which Newton rejects a vortex theory to explain the orbits of the planets in favor of his own gravitational one. He writes:  “since all phenomena of the heavens and of the sea follow precisely, so far as I  am aware, from nothing but gravity acting in accordance with the laws described by me; and since nature is very simple, I  have myself concluded that all other causes are to be rejected.” In Andrew Janiak, ed., Isaac Newton: Philosophical Writings (Cambridge: Cambridge University Press, 2004), 108–​109. 3. Albert Einstein, “On the Method of Theoretical Physics, Philosophy of Science 1 (1934):  163–​69. For a very good account of Einstein’s philosophy of science, see Don A. Howard, “Einstein’s Philosophy of Science,” in Stanford Encyclopedia of Philosophy, ed. Edward N. Zalta, https://​plato. stanford.edu.

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b. An Epistemological Claim If a theory is compatible with the available evidence, then its simplicity provides a good epistemic reason for believing that the theory is true or that it is empirically adequate.4

“Empirically adequate” is van Fraassen’s expression.5 He uses it to mean that the theory is compatible not just with observed phenomena but with all observable phenomena.6 However, in what follows, I  allow for various weaker interpretations of claim (b). According to one, the claim would be that simplicity provides an important epistemic basis for believing that a theory will be compatible with, or even more strongly, supported by, experiments and observations that have been and will be made.7 I will use the term “empirical adequacy” to cover various cases. You can defend a version of claim (b) by defending one of these positions. Whatever the position, 4.  You may believe that there are epistemic criteria in addition to compatibility with available evidence and simplicity (e.g., explanatory depth, unifying power, coherence). If so, you may believe that any one of these, in addition to evidential compatibility, will also provide a good epistemic reason for belief. Or you may believe that when these, or some of them, occur together, they provide such a reason. Newton and Einstein focus on simplicity, and so will I. For the sake of discussion, I will understand the epistemic claim as saying that, in offering an epistemic defense of a theory, at least one of the important criteria relevant for such a defense is the theory’s simplicity. 5.  Bas van Fraassen, The Scientific Image (Oxford:  Oxford University Press, 1980). 6.  Van Fraassen believes that simplicity is a non-​epistemic virtue of a theory, and so it does not provide a basis for believing the theory true or empirically adequate. He rejects claim (b). 7.  This is, or comes close to, Richard Dawid’s sense of “viable.” See ­chapter 1, note 31.

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however, the claim that a theory is empirically adequate is to be understood as making a stronger claim than simply that a theory is compatible with, or supported by, all experiments and observations that have been made. Both Newton and Einstein (at least on one interpretation) support some version of claim (b). For them, it seems to follow from the ontological claim that nature itself is simple. Newton’s Rule 1 tells you not to infer multiple causes when one will suffice to explain the phenomena. Why? Because “nature is simple and does not indulge in the luxury of superfluous causes.” I  would understand the “and” here as meaning “in the sense that.” The idea is that since nature is simple in the sense that it does not contain redundant causes, when you infer a cause of phenomena you are not justified in believing that two or more causes produce the phenomena if one by itself could do so. This is a version of Ockham’s razor. Newton’s (inductive) Rule 3 tells you that you can make an inference from the fact that all observable bodies have qualities that cannot be intended and remitted to the conclusion that all bodies have those qualities.8 Why? Because “nature is simple and ever consonant with itself.” The idea is that since nature is simple in the sense that the laws governing it are universal and not different in different parts, you are justified in inferring that all bodies in nature satisfy a law if all observable ones do. This is a version of the “uniformity of nature” principle. For Einstein, you cannot “extract” the “axiomatic foundation of theoretical physics” from experience alone. You need to invoke simplicity. And, on the present interpretation, 8. See Achinstein, Evidence and Method, 48–​49, for a comment on the “intended and remitted” clause.

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you are justified in doing so because nature itself is simple in the sense that it is “the realization of the simplest that is mathematically conceivable.”

c. An Underdetermination Claim Scientific theories are underdetermined by the evidence. In order to choose a theory to believe or accept, you must do so on the basis of simplicity:  choose the simplest theory compatible with the evidence.

There are two ways to understand this claim, one epistemic and one not. On the epistemic interpretation, simplicity is itself an epistemic virtue. Experimental and observational evidence will never by itself be sufficient to believe a theory, since there will always be competing theories compatible with this evidence. But if one of these theories is the simplest, then the fact that it is renders that theory worthy of belief (as true, or empirically adequate). This interpretation makes the underdetermination thesis a version of the epistemological claim (b). On the second version, the claim is that epistemic grounds are never sufficient to believe a theory, but we do need to choose a theory to work on, promote, use for predictions and calculations, compare with others, or, more generally, to “take seriously.” We do so invoking simplicity as a criterion of choice. We are frequently in this position with regard to things other than theories with respect to which we have choices. I am on an airplane with two books I have chosen at random, and I have no reason to think that one is better than the other or that I will enjoy one more than the other. I choose the one with the simplest prose, not because I  think it is better or that I  will enjoy it more but because

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I  want to read something and I  can finish the simpler one more quickly on the trip. An underdetermination claim is present in Duhem and Einstein. Einstein, I believe, subscribes to the epistemic version, and Duhem to the non-​epistemic one, at least with respect to truth, although he believes that producing simple theories is an aim of science.

d. A Presupposition  Claim When engaging in scientific activity, particularly theorizing, you must presuppose three things:  (i) that the world is intelligible, which, on the present view, implies that it satisfies some standard of simplicity; (ii) that since this is so, everything can be correctly explained by a simple theory that is true or empirically adequate; and (iii) that simplicity in a theory provides an important epistemic basis for believing the theory is true or empirically adequate.

Thomas Nagel writes: Science is driven by the assumption that nature is intelligible. . . . So when we prefer one explanation of the same data to another because it is simpler and makes fewer arbitrary assumptions, that is not just an aesthetic preference; it is because we think that the explanation that gives greater understanding is more likely to be true, just for that reason.9

Einstein and Infeld write: “Without the belief in the inner harmony [and simplicity] of our world there could be no science.”10 9. Thomas Nagel, Mind and Cosmos (New York: Oxford University Press, 2012),  16–​17. 10.  Albert Einstein and Leopold Infeld, The Evolution of Physics (Cambridge: Cambridge University Press, 1938).

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I shall understand the presupposition claim as implying not that the world is simple (claim (a)), or that simplicity in a theory provides an important epistemic basis for believing the theory is true or empirically adequate (claim (b)), or that everything can be correctly explained by a simple theory that is true or empirically adequate, but that if you engage in scientific theorizing, then you do presuppose that these claims are true. The very practice of science is based on these assumptions.

e. “Aim of Science” Claim The aim of science, or at least one central aim, is, or should be, to provide true or empirically adequate theories that will represent and/​or explain the observable facts in the simplest way.

Such a view was expressed by Duhem (whom Einstein read) and by Einstein himself. Duhem:  A physical theory  .  .  .  is a system of mathematical propositions, deduced from a small number of principles, which aim to represent as simply, as completely, and as exactly as possible a set of experimental laws.11 Einstein:  .  .  .  the pre-​eminent goal of science [is] that of encompassing a maximum of empirical contents through logical deduction with a minimum of hypotheses or axioms.12

To be sure, there are factors in addition to simplicity demanded by these scientists. For both, the theoretical

11. Reprinted in Achinstein, Science Rules, 269. 12.  Albert Einstein, Ideas and Opinions (New  York:  Bonanza Books, 1954), 238.

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representations must be compatible with the experimental laws. But simplicity in the representation is, or should be, a crucial aim for each. One could in principle hold an “aim of science” view of simplicity as well as an ontological, epistemological, and presupposition view—​as did Einstein. But one could also defend an “aim of science” view without adopting the other three. Following what I think is Duhem’s position, one could say that the aim of science should be to represent the observable facts in the simplest way possible, without also claiming that nature itself is always simple or that the simpler the theory, the more one is justified in inferring that it is true or empirically adequate, or even that scientific activity presupposes the truth of the ontological and epistemic claims.

f. A “Scientific Virtue” Claim Simplicity is a non-​epistemic scientific virtue that is worthy of having for its own sake.

This claim, which is fairly minimal, does not entail or presuppose any of the previous ones. It is simply that simplicity is a virtue of a scientific theory—​perhaps one of a number of such virtues (including unifying power, depth, exactness)—​ valuable when it is present, but not necessary or sufficient for a theory to be a good one. And it is not a virtue that adds to the credibility of a theory. Such a view is, or is close to, one defended by van Fraassen: When a theory is advocated, it is praised for many features other than empirical adequacy and strength:  it is said to be mathematically elegant, simple, of great scope, complete in certain respects; also of wonderful use in unifying our account

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of hitherto disparate phenomena, and most of all explanatory. These are specifically human concerns, a function of our interests and pleasures, which make some theories more valuable or appealing to us than others. Values of this sort, however, provide reasons for using a theory, or contemplating it, whether or not we think it true, and cannot rationally guide our epistemic attitudes and decisions.13

g. A Pragmatic  Claim Simplicity is a pragmatic virtue.

Theories that are simpler in certain respects—​that make fewer assumptions, postulate fewer or less complex entities, have simpler equations, etc.—​are easier to use for various purposes, including explanation, prediction, calculation, and communication. And, very important, they are easier to develop further. They are excellent starting points from which to create more sophisticated and perhaps more complex ideas. This view can be held without holding any of the others. I think that van Fraassen, with his talk of values that satisfy both “our interests and pleasures,” could reasonably be said to hold not only an aesthetic view but a pragmatic one as well. Einstein’s claims about simplicity might also be interpreted in this pragmatic mode. Recall his famous remark that theories “cannot be extracted from experience but must be freely invented,” and that by using the simplest mathematical ideas we can discover “the concepts and the laws connecting them with each other, which furnish the key to the understanding of natural phenomena.” Perhaps the claim 13. Van Fraassen, The Scientific Image, 87.

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is a pragmatic, heuristic one to the effect that since theories are not dictated to us by experience, we need to invent them, and in doing so, we should start with simple ideas mathematically expressed before we develop more complex ones. We are justified in doing so, not because nature itself is simple, and not because simplicity provides an important epistemic basis for inferring truth or empirical adequacy, but because, historically speaking, this pragmatic way of proceeding has been successful. Successful in what way? Starting with simple theories and developing them in more complex ways has led to more complex theories that are better supported by experimental results than are the simple ones with which we begin. Whether or not this is all that Einstein is saying about the role of simplicity, I shall assume it is at least a part. Later I  will show how James Clerk Maxwell is committed to the pragmatic claim, but not to any of the others. With the exception of the first two claims, one could make any of these seven claims about simplicity without being committed to the others. The boldest, and historically the most important, are the ontological claim (a)  and the epistemological one (b). In the present chapter, I  examine these, leaving the remainder for ­chapter 3.

3 .  N AT U R E I S   S I M P L E My first response to this claim, made by both Newton and Einstein, is to say that it is vague. I say this not because these scientists fail to provide a definition of simplicity. Let us grant, with both Newton and Einstein, that we recognize it when we see it, without a definition. The claim is vague because there are different respects in which nature could be simple,

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and even if we specify these various respects, we need to say which ones are applicable to nature. All of them? Some, but not others? They don’t all march together. The set of laws governing certain phenomena might be mathematically simple while at the same time being complex because there are so many different laws. Newton, after claiming that nature is simple, goes on to indicate two respects (“Ockham’s razor” with regard to causes, and “uniformity of nature” with regard to laws). Einstein invokes mathematical simplicity. Are there others, or are these the only respects in which nature is simple? The ontological claim needs more specificity:  In what way(s) is nature simple and in what way(s) not? Moreover, presumably simplicity is subject to degrees or at least to “more or less.” If so, and if nature is claimed to be simple in some particular respect—​say, mathematically speaking—​how simple is it being claimed to be in that respect? Suppose we construct some scale of mathematical simplicity, so that a circular orbit of a planet is simpler than an elliptical one—​indeed, the simplest one possible, given that the planets move around the sun. Or suppose our scale is such that that a linear path of a molecule is simpler than some zigzag one—​indeed, the simplest one possible, given that molecules in a gas are in motion. Is the claim that nature is simple (together with the true assumption that the planets move in some closed orbit around the sun) supposed to entail, or make it likely, that planetary orbits are circular? Is the claim that nature is simple (together with the true assumption that molecules in a gas are in motion, not stationary) supposed to entail, or make it likely, that molecular paths are straight ones? If so, then the claim that nature is simple (in the respects specified) is false, or likely to be, since these consequences are false.

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Perhaps the claim that nature is simple, when this is applied to planetary orbits or molecular paths, is to be understood as saying that whatever in fact the planetary orbits and molecular paths are, they are simple ones, even if they are not the simplest possible. Now we have made the claim even vaguer, but still clear enough to be challenged. Because of perturbations caused by forces exerted by other planets, the planetary orbits are by no means simple; the same applies to the paths of gas molecules, due to the presence of non-​contact intermolecular forces. Of course, we can idealize, ignore these forces, and say what the orbits and paths would be like if these forces did not exist. Doing so, we would obtain orbits and paths that are mathematically much simpler. But this idealization falls more squarely into what I have called the pragmatic view of simplicity rather than the ontological one. For certain pragmatic purposes, it may be useful to idealize and represent (parts of) nature as simple in certain respects. We can then say how close this representation is to nature. But nature itself is not idealized. There are two more complications I will mention. First, the same fact about nature can be described in different ways, even ones that are logically or mathematically equivalent, one of which is much simpler than another. The shape of a petaled flower (called a polar rose) can be described by a simple equation expressed using polar coordinates, or by a much more complex equation expressed using rectangular coordinates. Is the shape itself simple or complex? It would seem that if we want to talk about the simplicity of nature, we would need to relativize this to a description or representation: under one description or representation, some aspect of nature is simple, under another, it may be complex. Second, nature may be simple at one “level” but not at another. For example, some claim that nature is simple at

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the most fundamental level. At this level there are “atoms” with no parts (hence, they are simple), and they are subject to simple fundamental laws that have no further explanation. At nonfundamental levels, nature gets quite complicated. Such a view is held by some reductionists, particularly those who favor the idea of a “Theory of Everything” (TOE).14 Another possibility is that nature is simple, or at least is representable as such, at some macro levels, but not at corresponding micro levels. The ideal gas law, which works well within certain ranges of temperature, is much simpler than virial equations that invoke underlying molecular forces. Accordingly, when we give even a slight push and poke at the vague but simple claim that nature is simple, we end up with a claim that is still vague, but now complex: in certain respects, under certain descriptions, and at some levels, but perhaps not others, nature has some measure of simplicity; in other respects, under some descriptions, and at other levels, perhaps less and in some perhaps none. Or more simply, for certain purposes, nature, or parts of it, can be represented in ways that have some measure of simplicity. Despite its vagueness, let us suppose that this resulting claim is still clear enough so that we can ask the following about it: How do we know that nature is simple—​in whatever ways, or amounts, or representations, or levels, it is? My answer is a “nonglobal” or “localist” one:  the only way to know this is to do science itself and make particular judgments about particular simplicities or complexities. Given his evidence concerning the observed motions of the planets and their moons, Newton, we might suppose, was

14. In ­chapter 5, I will examine the very idea of a TOE.

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justified in believing that one force of gravity, not many, was operating on both celestial and terrestrial bodies; and that this force is an inverse-​square force, not some mathematically more complex one.15 In the case of the motions in question and the forces and laws governing this motion, Newton, we might say, was justified in believing that nature is simple. (In what follows, I will simplify the discussion by supposing that the simplicity label is assigned to the feature of nature under the representation given to it by the scientist in question or under one that is explicit or implicit in the context.) Given what was known about gaseous behavior, Maxwell was justified in believing that although the ideal gas law is a simple equation of state that works well within certain ranges, it is not an accurate one in general; a much more complex virial equation is much more accurate. In the case of the relationships between the pressure, volume, and temperature of gases, Maxwell was justified in believing that nature, represented more accurately, is not so simple. Nothing very interesting follows globally from individual cases such as these. In certain cases, we find that nature is, or is representable as, simple; in other cases, it is not. How might a “globalist” respond?

4 .   A   G L O B A L I S T R E S P O N S E Suppose a globalist admits that we can and do make local simplicity claims of the sort I have mentioned. He may reply that these are just the data from which, in the spirit of science 15.  I  say “we might suppose” because, in ­chapter  3, I  will question this supposition.

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and philosophy, we can and should generalize. For example, we might say that although certain features of nature are complex, for the most part and to a considerable degree, nature is simple or is representable as such in a fairly accurate way. Or at least we should generalize and say something like this:  at certain levels, under certain descriptions, and with respect to some features, nature is simple—​where the levels, descriptions, and features are formulated in ways that have some generality to them and do not refer just to particular cases, such as the motions of terrestrial and celestial bodies or the relationships between pressure, volume, and temperature of a gas. How might such a claim be defended? Since Newton and Einstein make “global” rather than “local” claims about simplicity, how do they defend their claims? Newton offers no defense at all in the rules.16 Einstein writes that “our experience hitherto justifies us in trusting that 16.  In his theological writings, he attributes the simplicity of the world to God:  “It is the perfection of God’s works that they are all done with the greatest simplicity. He is the God of order and not of confusion.” (See Elliott Sober, Ockham’s Razors [Cambridge: Cambridge University Press, 2015], 35.) In the General Scholium at the end of the Principia, Newton offers what he regards as an empirical design argument for God’s existence:  the known planets lie on the same plane and revolve in the same direction around the sun. This is not required by mechanical laws, since the comets, which also revolve around the sun, have much freer orbits. But the planetary motions in question are too orderly to occur by chance. He concludes that “this most elegant system of the sun, planets, and comets could not have arisen without the design and dominion of an intelligent and powerful being.” A few sentences later, he writes that God is “omnipotent” and that he “rules all things.” So Newton seems to be arguing from the claim that God is responsible for orderly planetary motions that have no mechanical causes (orbits on same plane in same direction) to the claim that God is responsible for orderly planetary motions that do have mechanical causes (Keplerian motions of the planets), to the claim that God is responsible for even less orderly motions (comets), to the claim that God is

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nature is the realization of the simplest that is mathematically conceivable.” This suggests a defense of the claim that nature is simple (at least with respect to mathematical simplicity) on inductive grounds:  theories that are mathematically simple have generally been successful. Since an even more general inductive argument will appear in sections 5 to 7 when I discuss the epistemological role of simplicity, I will postpone a discussion of it until then. Whatever one’s views on its validity, however, neither Newton nor Einstein is in a position to give such an argument. To inductively justify the claim that nature is simple, in the sense of having laws that are uniformly applicable, rather than applicable to some parts of nature but not others, Newton would need to use some version of his inductive Rule 3. But he justifies Rule 3 by appeal to the claim that “nature is always simple and ever consonant with itself.” For him, an inductive argument for the claim that nature is simple would be a circular argument. Similarly, to justify the claim that nature is simple in the sense that it doesn’t contain “redundant” causes, Newton would need to appeal to his causal Rule 1.  But, again, this would be circular, since he justifies Rule 1 by appeal to the fact that nature is simple. What about Einstein? If he is indeed defending the claim that nature is simple, he cannot do so inductively by appeal to the empirical success of simple theories and the lack of such success in complex theories. His claim is that responsible for everything. These are very bold inductive generalizations, indeed! But they still don’t get him to the simplicity of the world, since God could also be responsible for complex phenomena that may (or may not) be subject to complex causes and laws. Newton needs an additional premise that he does not “deduce from the phenomena,” viz. since all the works created by God are perfect, they are simple. This is basically the theological or metaphysical assumption quoted at the beginning of this note.

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experience by itself (including presumably observing the success of simple theories) cannot justify a grand conclusion about the world, such as nature is simple. There are other conflicting hypotheses about the world compatible with the success of simple theories. To defend the claim that nature is simple on the empirical grounds that simple theories have been successful would be insufficient for Einstein, since empirical grounds alone are insufficient for such a defense. But what other way is there for Einstein? It might be replied that the claim that nature is simple can be defended in an empirical way that is non-​inductive, and non-​causal, viz. by appeal to what is called “inference to the best explanation” (IBE). The basic idea, introduced by Harman,17 and developed much further by Lipton,18 is that the best explanation of the fact that the simple theories we have studied have been empirically more successful than the complex ones (assuming they have) is that nature is simple. And from the fact that this is the best explanation, it follows that nature is (probably) simple. But this argument is inconclusive as it stands, since it needs to be established that it is the simplicity of the world, rather than something else (including selection bias in our sample), that is indeed the best explanation of the success of simple theories. As Harman notes, “in general there will be several hypotheses which might explain the evidence, so one must be able to reject all such alternative hypotheses before one is warranted in making the inference.”19 17. Gilbert Harman, “The Inference to the Best Explanation,” 88–​95. 18.  Peter Lipton, Inference to the Best Explanation, 2nd ed. (London: Routledge, 2004). 19. Harman, “Inference to the Best Explanation,” 89.

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There is a deeper issue here. What are the criteria for the “best explanation”? Both Harman and Lipton appeal to simplicity, among other criteria.20 So, focusing just on the criterion of simplicity, which is central to both Harman and Lipton, the question to be raised is this: How is one to infer the (probable) truth of a hypothesis (as IBE theorists do) from the fact that it is the simplest? If an appeal is made to the fact that nature itself is simple, then the response should be: How do you know that? If the answer is that we know this because, using IBE, that is the simplest explanation of the past success of simple theories, then the argument is circular. We are using IBE to defend the claim that nature is simple, where our use of IBE presupposes that nature is simple. Suppose, then, that the use of IBE is not based on the ontological assumption that nature is simple. How, then, are we supposed to justify an inference from simplicity of a hypoth­ esis or theory to its (probable) truth? Harman and Lipton offer no argument, but just assume it. Can an epistemological argument be constructed? For the answer we must turn to the aforementioned epistemological claim about simplicity.

5 .  A N E P I S T E M O L O G I C A L   C L A I M Epistemological Claim: If a theory is compatible with available evidence, then its simplicity provides a good epistemic reason

20.  Harman writes:  “There is, of course, a problem about how one is to judge that one hypothesis is sufficiently better than another hypothesis. Presumably such a judgment will be based on considerations such as which hypothesis is simpler, which is more plausible, which explains more, which is less ad hoc, and so forth” (89).

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for believing that the theory is true or that it is empirically adequate (in one or more of the senses I have noted).

Can this be defended whether or not nature itself is simple? Since the epistemic claim is so important from a scientific perspective, I  will spend the most time with it. Can it be defended without assuming the truth of the ontological claim, and if so how? In the present section I will examine a historical argument, and in sections 6 to 9, various probabilistic ones. I have noted that nature might be considered simple in various respects, and not so in others. The same holds for theories about nature. However, in what follows I  will idealize (or simplify) by supposing that even though a theory can be simple in certain respects, degrees, and formulations while complex in others, we are dealing with theories that are simple in enough respects and degrees and with respect to some canonical formulation to be classified as just plain simple; the same will be supposed for complex theories. My general response to the Epistemological Claim will be to reject it. The fact that a theory is simple may be very desirable, but it is no reason whatever to believe it is true. An appeal to it may be made in the course of an argument to a conclusion, but that appeal does no epistemic work. In ­chapter 3, I will argue for this claim in my discussion of Newton’s argument for gravity. But before getting to that point, in the remainder of this chapter I will look at ways the Epistemological Claim might be defended. William Whewell makes this historical observation: “we have to notice a distinction which is found to prevail in the progress of true and of false theories. In the former class all additional suppositions tend to simplicity and harmony. . . .

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In false theories the contrary is the case.”21 Whewell seems to be saying here that true theories, as they evolve over time, tend to be simple and false ones, as they evolve, tend to be complex. If a historical argument is to be produced to defend the claim that simplicity is an epistemic virtue, we need to reverse this order. We need to argue from the simplicity of a theory to its truth or empirical adequacy, rather than the other way around. Now, as Whewell notes, theories themselves—​ i.e., their content—​can change over time in response to new data. They can start out simple, and end up complex owing to the addition of new complicating assumptions. Let me initially simplify the situation by considering just the central and distinctive assumptions of a theory and by supposing that these don’t change, or if they do, they change in a way that doesn’t affect their simplicity or complexity. Let’s try an inductive argument. We start with the idea that if we look at the historical facts, simple theories have been much more “empirically successful” than complex ones. Their predictions, explanations, calculations, etc., have been better experimentally confirmed than those of complex theories. To isolate the power of simplicity, let us suppose that both the simple and the complex theories we are considering are roughly equal with respect to other virtues that might conceivably be regarded as epistemic, but that among these, the simple theories have been much more experimentally successful than the complex ones. And to avoid the problem of different formulations of the same theory, some simple, some more complex, we can idealize by supposing that if there are such 21.  Whewell, Philosophy of the Inductive Sciences, chap.  5, reprinted in Achinstein, Science Rules, 162–​63.

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formulations, there is some widely accepted canonical formulation with respect to which questions about simplicity and complexity will be considered. Also, we need to avoid “selection” bias. Suppose, e.g., that simpler theories are easier to test and, if needed, to modify in light of new experiments; but when scientists testing complex theories find an experimental problem, they give up more easily and abandon the search for a solution. So let us suppose that the theories we select in both the simple class and the complex one have been thoroughly tested and (to simplify even further) either generally confirmed or disconfirmed. Now, we need to ask the question: Confirmed when? If we are to judge the empirical success of theories and use this as a basis for an epistemic claim about simplicity, then we must use experimental data available to us, not just to those during the time the theory was proposed and favored. On this basis, many of the theories once considered highly confirmed are no longer considered so. If we were to make an induction from just the fact that the “temporary” success rate of simple theories has been higher than the “temporary” success rate of complex theories, that induction could at best be only to the conclusion that simpler theories in the future will probably have a better temporary success rate than complex ones. But champions of the Epistemological Claim want a much stronger conclusion than that. Let’s see what we can do.

6 .  R E F I N E D I N D U C T I V E A R G U M E N T From a set of past and current theories that have been proposed and well tested, we select two groups. The first

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contains simple theories (simple in one or more respects) that were at least temporarily empirically successful. The other contains temporarily successful theories that are complex or at least not particularly simple. Immediately, we are confronted with the Laudan “pessimistic induction” problem:  historically, if judged by today’s evidence, most proposed theories, simple or not, temporarily successful or not, have turned out to be empirically unsuccessful, given today’s evidence, to the degree that many are regarded as just plain false.22 Even so, perhaps the simple ones have a better success rate than the complex ones. To be very generous, suppose that historically 20% of the simple theories that were temporarily empirically successful remain so now, and that 80% do not. And suppose that only 10% of complex theories that were temporarily empirically successful remain so now, while 90% do not. (Lacking a measure of “success,” these assumptions are admittedly vague, but perhaps clear enough to formulate the argument.) Finally, let us also suppose that we are concerned only with theories in which other potentially epistemic qualities are pretty much equal. Using these historical data as the basis for an inductive conclusion, we might say that the probability that a simple theory that is temporarily empirically successful will remain empirically successful is twice that of a temporarily empirically successful complex theory (20% vs. 10%). So, indeed, we might conclude that, other things being equal, a temporarily successful simple theory has twice the chance of being empirically adequate, or perhaps even true, that a temporarily 22. Larry Laudan, “A Confutation of Convergent Realism,” Philosophy of Science 48 (March 1981): 19–​49.

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successful complex one has. (“Empirical adequacy” is to be understood as going well beyond “temporary empirical success.”) We need a stronger conclusion than this to defend the Epistemological Claim. We need to argue that the simplicity of a theory compatible with the data is a good epistemic reason for believing that the theory is true or empirically adequate. But if 80% of the simple, temporarily empirically successful theories have turned out to be empirically unsuccessful, given our present data, then although simplicity increases the chance of empirical adequacy and doubles the chance of empirical adequacy over complexity, it is not a very good historical reason for believing in the empirical adequacy or the truth of simple theories generally. Inductions here, as Laudan says, are “pessimistic.” Using this sort of induction, simplicity will be a poor indicator of truth or empirical adequacy. Even worse, what frequently happens to a simple theory is that it gets more complex as it becomes more fully developed. Its simplicity at the outset is often achieved by neglecting certain factors whose inclusion would make the theory more empirically successful at the price of more complexity. The ideal gas law is simple, but it neglects intermolecular forces, and as a result its empirical success is limited. If we introduce a virial equation, we get broader empirical success but more complexity. Newton’s theory of gravity is simple if we use it to explain the orbit of a planet as a two-​ body problem, neglecting the forces of other planets. But then we lose some empirical accuracy. If we introduce other forces acting, we get more empirical success, but also more complexity (indeed, too much for computational purposes). There are several equations giving the energy density of an

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oscillator at a given temperature:  the Rayleigh-​Jeans equation, the Wien equation, and the Planck equation. The first fails in the high-​frequency region of black body radiation, the second at low frequencies. The Planck equation gives better results for all frequencies, but it is a good deal more complex than the other two. An even more important reason why a theory that started out simple gets more complex over time is that new experimental results force such a change. Think of the history of the atomic theory from the mid-​nineteenth century to the present. At first, simple atoms without structure are postulated subject to laws of classical mechanics. This yields fairly good results in explaining and predicting certain properties of gases and liquids. Then, as a result of experiments, such as those of J.  J. Thomson on cathode rays, electrons are discovered, and are claimed by Thomson to be the sole constituents of atoms (the “plum pudding” model). Then other constituents of atoms are discovered, and the laws governing these constituents are no longer conceived to be classical ones, but quantum ones, making the atomic picture much more complex. Indeed, on the basis of an induction, one might conclude that the probability is very high that, as new phenomena are discovered, a simple theory with some temporary empirical success will turn into, or be replaced by, a more complex one with much more (at least) temporary empirical success. If this happens more frequently than a simple theory’s remaining simple over time, then an inductive defense of the epistemic claim for simplicity becomes very dubious. So does an inductive defense of the ontological claim that nature itself is simple.

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7 .   A   B AY E S I A N R E P LY:   E V I D E N C E A Bayesian who accepts the concept of B-​evidence given in ­chapter  1 will reply that if simplicity raises the probability of truth or empirical adequacy at all, then, no matter what the absolute probability is, the fact that simpler theories have been more successful than more complex ones counts as evidence for the truth or empirical adequacy of a simple theory. So simplicity is indeed an epistemic virtue. And that is all the Bayesian wants to say. To this I offer three replies. First, the defender of B-​evidence needs to be reminded that the inductive argument presented is entirely hypothetical. It is based on a speculative assumption for which no evidence has been offered, viz. that simpler theories have had a sustained empirical success rate that is better than that of complex ones. The most that the Bayesian can say is that if this is so, it is evidence for the continued empirical success of simple theories. But this is a big “if,” especially in view of the fact that in order to retain empirical success, many simple theories have to be modified or replaced by more complex assumptions Second, as noted in c­ hapter  1, I  reject this Bayesian B-​ concept in favor of my A-​concepts because, among other reasons, the former is much too weak to capture a basic idea that I regard as important for evidence, viz. the idea of providing a good reason to believe. Increasing the probability of a hypothesis need not provide any reason to believe a hypoth­ esis. If I play golf, the probability of my being killed by lightning increases. But this by itself is not evidence that I will be—​it is not a good reason to believe this—​since the probability is so tiny. (According to the New  York Times Magazine, June 18,

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1995, in 1993, 24.5 million golfers played nearly 500 million rounds; one golfer died via lightning.) This is important because the Epistemological Claim for simplicity says that the simplicity of a theory compatible with the available evidence is a good reason to believe the theory is true or empirically adequate. A defender of B-​evidence will need to modify that claim considerably and say only that the simplicity of a theory increases its probability. The Epistemological Claim under discussion doesn’t follow from that. Third, on my A-​concepts of evidence, as well as on the (much-​ improved) concept of explanatory B-​ evidence of ­chapter 1, section 10, for e to be evidence that h, there must be a high probability of an explanatory connection between h and e, given e. But that is not satisfied by appeals to historical facts about the success of simple theories. Consider, as an example, J. J. Thomson’s hypothesis in 1897: (h) Cathode rays are negatively charged particles.

For the sake of argument, let us accept the idea that (e) h is a simple theory about cathode rays, and simple theories have had a good success rate.

On my concept of (potential) evidence, as well as that of explanatory B-​evidence, it is not the case that e is evidence that h. It is not at all probable that, given e, there is an explanatory connection between h and e. It is not probable, given e, that cathode rays are negatively charged particles because this is a simple theory about cathode rays and simple theories have had a good success rate; or that h is a simple theory and simple theories have had a good success rate because

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cathode rays are negatively charged particles; or that some fact explains both h and e. What does count as evidence for (h), or did for Thomson, was the fact that (e′) Cathode rays are deflected toward a positively charged plate.23

Given e′, which was demonstrated in Thomson’s experiments, and given other background information known at the time, the probability is high that there is an explanatory connection between h and e′ (the probability is high that cathode rays are deflected toward a positively charged plate because cathode rays are negatively charged particles). On my account of evidence, or that of the explanatory B-​concept, e′ is (explanatory) evidence that h, but the “historical” e is not. As I noted in c­ hapter 1, however, epistemic reasons for believing the truth of a hypothesis are sometimes proposed that are not explanatory. And they may be good reasons. For example, the fact that the third Cavendish Professor of Physics at Cambridge (Thomson) believed h to be true (even before he conducted his experiments) might be a good reason (before the experiments) to believe that h is true. In the present case, however, the alleged historical fact about the success of simple theories in claim e is a speculation, not something established or even shown to be probable. Perhaps, then, the Epistemological Claim at the beginning of section 5 can be defended without invoking a dubious historical argument from the success of simple theories. Can 23.  For a historical and philosophical account of this episode, see Achinstein, Book of Evidence, chap. 1.

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one show in some other way that the simplicity of a theory makes it probable, or even that it increases its probability?

8 .  W I L L A M O R E G E N E R A L A PPE A L TO PROBA BI L I T Y S H O W T H E E P I S T E M I C VA L U E OF SIMPLICITY? Let’s start with a simple formulation of Bayes’ theorem: p (h/e ) =

p (h ) × p (e /h ) p (e )



On the left, p(h/​e), the “posterior” probability, represents the probability of the hypothesis h given the evidence e. On the right, p(h), the “prior probability,” represents the probability of h independently of the information e. The expression p(e/​h), the “likelihood,” represents the probability of information e, on the assumption that h is true. And p(e) represents the prior probability of the information e. There are two ways that the simplicity of h could affect the posterior probability of h: by affecting the prior probability of h or by affecting the likelihood (or, of course, both). In this section I will discuss simplicity and prior probability. In section 9, I will turn to simplicity and likelihood. Let us suppose that we have two conflicting hypotheses, h1 and h2. And let us also suppose that both hypotheses entail the evidence e, so that the “likelihood” of each hypothesis is the same, viz., 1. In this case, the posterior probability of each will be equal to the prior probability of the hypothesis in question divided by the prior probability of e. Now suppose

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that h1 has a higher prior probability than h2. Then, since the prior probability of e is the same in both cases, and since the likelihood of each hypothesis is 1, it follows from Bayes’ theorem that p(h1/​e) > p(h2/​e). Now let’s introduce simplicity. Suppose that if one hypothesis is simpler than another, then it has a higher prior probability. That is, suppose that if h1 is simpler than h2, then p(h1) > p(h2). Then on simplicity grounds alone, it follows that p(h1/​e) > p(h2/​e). Now, if we construe probability in an epistemic way—​as measuring some notion of reasonable belief—​then using probability, we show that simplicity is indeed an epistemic virtue. We show that if two conflicting hypotheses each entail e, then, given e, it is more reasonable to believe the simpler hypothesis than the more complex one. Admittedly, this by itself is not sufficient to make e evidence that h—​in the sense of A-​evidence or explanatory B-​evidence. Nor is it strong enough to make it reasonable to believe the simpler hypothesis. But simplicity will provide a basis for comparing the believability of hypotheses. It will be of some epistemic value. The crucial question, then, is why we should assign h1 a higher prior than h2 on grounds of simplicity. The answer varies depending on your interpretation of probability. If you are a subjective Bayesian, you can assign prior probabilities any way you like, for any reason whatever, so long as your entire system of probabilities, prior and posterior, is “coherent”—​that is, so long as all your probability assignments do not violate the formal rules of mathematical probability. “Coherence” in your set of probabilities (your “degrees of belief ”) is both necessary and sufficient for your set of beliefs to be reasonable, according to the Bayesian. So, if you want to assign higher prior probabilities to simpler hypotheses, you

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are free to do so, so long as you satisfy coherence. You may have reasons for assigning higher priors to simple hypotheses, including the belief that nature is simple, but they are your reasons, and it does not follow that others should do the same. Except for coherence, it is entirely subjective. This view should be distinguished from the pragmatic claim that I will discuss later—​the claim that simplicity is a pragmatic virtue, one that can make a theory easier to use. Like subjective probabilities, this can vary from one person to another. But the pragmatic claim is not an epistemic one. It does not say that if one theory is simpler to use than a competitor, then the probability of that theory, subjective or otherwise, is higher that of the competitor. I  won’t pursue a subjective probability account of simplicity, because it essentially abandons the attempt to justify simplicity as an epistemic virtue—​at least as a universal objective epistemic one that most simplicity enthusiasts want, including Newton and Einstein. In effect, it says that it can be a virtue or not, depending on your subjective beliefs. What I  will ask is how an objectivist about probability can justify the claim that simpler theories have a higher prior probability. This will vary, depending on what sort of probability objectivist you are. If you are a frequentist or a propensity theorist, then the question of simplicity doesn’t arise. You don’t assign probabilities to hypotheses, but to types or classes of events in a sequence or to propensities in the world. And these probabilities are not in any very direct way epistemic, unless you add some postulate relating frequency or propensity probabilities to epistemic ones.24 Asking whether 24.  David Lewis does that. See his “A subjectivist’s Guide to Objective Chances, in Studies in Inductive Logic and Probability, vol. 2, ed. Richard Jeffrey (Berkeley: University of California Press, 1981), 263–​93.

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string theory is more probable, and therefore more believable, than the standard model because it is simpler cannot be answered by the frequentist whose definition of probability is not applicable to theories. So let’s concentrate on objective probability theories that are explicitly epistemic. These are of two sorts: empirical (e.g., my own objective epistemic theory25 ) and a priori (e.g., Carnap’s). With the former, prior probabilities are, in general, empirical.26 Referring to Bayes’ theorem, p(h) is the probability of h independently of e. It is not the probability of h independently of everything. So, e.g., if h is that Sally has disease D, and e is that Sally has symptoms S, then one empirical way to interpret p(h) is as a number determined at least in part by the empirically established “base rate” of disease D in the general population. Now, suppose we make the very broad claim that that, for any hypothesis h that assigns a property to an individual, the simplicity of h gives h a higher prior probability than does the “base rate” of that property in the general population by itself. How is that to be justified empirically? The only way I can see is by empirically establishing that: (i) nature is simple, or (ii) simple theories have turned out to be more empirically successful than complex ones. But claims (i) and (ii) are just the ones I have been questioning and found wanting so far. It will not do to invoke objective empirical priors based in part on claims about the simplicity of nature, or the success of simple theories, unless you can empirically justify those claims. 25. In Achinstein, Book of Evidence, chap. 5. 26. I say “in general,” since there will be a priori probability assignments, specifically ones in which the probabilities are “definitional.” For example, the probability of heads with a fair coin is ½ because that is part of the definition of a “fair coin.”

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So let’s try a view of prior probability according to which it will be an a priori fact, not an empirical one, that simpler theories have higher prior probabilities than more complex ones. The best exponent of such a viewpoint is Carnap.27 For him, probabilities are to be determined by reference to a “linguistic framework” that contains a fundamental vocabulary, rules of inference, and probability axioms that include, but go well beyond, the usual axioms of probability. There are many different possible linguistic frameworks, with different prior probabilities assigned. In some frameworks, simple hypotheses will have much higher prior probabilities than complex ones, in others, less so (and there are even frameworks in which simplicity plays no role whatever). Once a linguistic framework has been chosen, then, for Carnap, it is an a priori fact what prior probability an hypoth­ esis will have. For example, suppose we have a linguistic framework containing just one property term P, and two names a and b. There are four possible basic states of a world describable in such a framework: Both a and b have P; a has P but b does not; a does not have P but b does; and neither a nor b has P. These, Carnap calls “state-​descriptions” (they describe possible states of the world that our linguistic framework can represent). Now, we are to assign prior probabilities to these state-​descriptions, subject to the standard rules of probability. How shall we do so in such a way that these rules are satisfied? There are an infinite number of ways. One that Carnap particularly likes (he calls it c*) is to assign equal priors to the 27.  Rudolf Carnap, Logical Foundations of Probability, 2nd ed. (Chicago:  University of Chicago Press, 1962), and The Continuum of Inductive Methods (Chicago: University of Chicago Press, 1952).

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state-​descriptions in which both a and b have P and in which both a and b lack P. Without going into the mathematical details, the assignment of priors will be such that both these state-​descriptions will have a prior probability of 1/​3, whereas the two state-​descriptions in which P is present in one item and lacking in the other will each have a prior of 1/​6. Now, in one respect, the two favored state-​descriptions are simpler than the others. In both, everything is uniform—​everything either has P or lacks it; whereas in the others, one thing has P while the other lacks it. The former represent simpler possible worlds than the latter. They are more uniform. What is the justification for assigning priors in such a way that simpler hypotheses have higher priors than complex ones? There are two ways to deal with this question. One is to treat it as what Carnap calls an “internal” question, which is to be answered by reference to the rules governing the framework. The other is to treat it as an “external” question—​one to be answered by indicating why those rules rather than others were chosen. Treated as an internal question, Carnap’s answer is that this is just a stipulation, or convention, needed to formulate the most fundamental rules of the linguistic framework. Within the framework there is no argument to be given for formulating the fundamental priors one way rather than another. As an internal question in the example above we can ask what the prior probability is of the state-​ description in which both a and b have P. The answer to this is determined a priori by appeal to the rules of that framework. Similarly, we can determine a priori by computation and appeal to the rules whether in general simple hypotheses have higher priors than complex ones. If they do, and if we interpret probabilities epistemically as providing a basis for (degrees) of rational belief, which Carnap allows, then we

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get the a priori result that simplicity is an epistemic virtue. But if we ask why the rules are set up this way rather than some other—​why, e.g., the simpler hypothesis “everything has P” has a higher prior than the more complex hypothesis “one thing has P and one thing lacks it”—​that is an external question to be answered pragmatically in terms of ease of use and familiarity or aesthetically in terms of the elegance of the system. External questions cannot be answered empirically or by a priori calculation. For Carnap, then, you can build a probability system so that simple hypotheses will have significantly higher priors than complex ones. You can also build a probability system so that simple hypotheses will have only modestly higher priors than complex ones, or even ones in which the priors are the same. But the only justification you can have for using one system rather than another is pragmatic or aesthetic, not epistemic. In short, using probability you can represent the claim that simplicity is an epistemic virtue by assigning higher priors to simpler hypotheses. But this does not suffice to justify such an assignment, either empirically or a priori.

9 .   S O B E R , L I K E L I H O O D , AND SIMPLICITY There is another way that simplicity might be introduced into Bayes’ theorem, viz. through the “likelihood” factor, p(e/​h), the probability of the evidence e, given the hypothesis h. Can the simplicity of a hypothesis h somehow increase likelihood? Not if h entails the evidence e, whether h is simple or not. In that case p(e/​h) = 1, and no increase is possible. So let us take

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a case in which p(e/​h) is less than one. Elliott Sober provides an example, where likelihoods are empirically determined.28 Susan, who goes to the lake each day for a week, sees a red sailboat each day. Let e be that the sailboat she sees each day is red. There are two hypotheses, h1 and h7; h1 says that the same sailboat was on the lake each day that Susan was there and no other boat was; h7 says that 7 different sailboats were on the lake during this week, one each day. Now, Sober makes the assumption that 10% of the boats that use that lake are red, so that the probability that a boat is red, given that it uses the lake, is 1/​10. He also makes the assumption that if a boat is on the lake, then the probability is close to 1 (I will say it is 1) that Susan sees it and its color. Now, let us determine the likelihood of each hypothesis, h1 and h7: p(e/​h1) = 1/​10, since if the same boat were there each day (h1), then (assuming that boats don’t change color overnight) the probability that the boat she sees each day will be red, is just the probability that a boat using the lake is red, viz. 1/​10. But the likelihood of h7—​i.e., p(e/​h7), will not be equal to 1/​10. This is because the events in this case, unlike the former one, are probabilistically independent. Given that it is the same boat each day, the probability that it will have a different color the next day is zero. But if there are seven different boats, then the probability of whatever boat is there each day being red is just the probability of a boat using the lake being red multiplied by itself 7 times—​i.e., (1/​10)7, a pretty tiny number. But since h1 postulates one boat producing the sightings, while h7 postulates 7 different ones, one each day, h1 is much simpler than h7 (at least according

28. Sober, Ockham’s Razors, chap. 2.

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to Sober’s argument). Here, then, we have a case in which we express this simplicity by means of the likelihood, rather than the prior. Taking this even further than Sober does, suppose we can assign equal priors to h1 and h7, so that it is just as probable that the same boat was on the lake each day as that 7 different boats were on the lake, one per day. (Imagine that in half the weeks the same boat is present each day, and in half the weeks 7 boats are present, one per day.) Then, from Bayes’ theorem, and the likelihoods just mentioned, we can conclude that the posterior probability p(h1/​e) is much greater than the posterior probability p(h7/​e), since p(e) is the same in both calculations. In such a case, it might be concluded, a difference in simplicity of the hypotheses makes a big difference to the (posterior) probabilities of these hypotheses, given the evidence e. Let us agree that, in these cases, the simpler hypothesis has the higher likelihood and posterior probability. But is simplicity really doing the work here? No, what is doing the work is the fact that one hypothesis, h7, makes the probability of getting a red sighting on a given day independent of the probability of a red sighting on another day. Given h7, the probability of e is the probability of a red sighting on Monday times the probability of a red sighting on Tuesday, etc. By contrast, this is not so if we assume h1: given h1, that the boat is the same each day, the probability of a red sighting on any or all days is just the probability of that boat’s being red. To bring this out, let us change the example a bit. We keep h1, understanding it to be that one and the same boat was sailing each day and that boat had the same color each day. Now consider h2: two different boats with the same color were sailing during the 7-​day period, each one on alternate

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days. Now by the reasoning above, p(e/​h1) = p(e/​h2) = 1/​10, since with both h1 and h2, the boat sailing will be the same color each day, and, given this, the probability that it will be red is 1/​10, by hypothesis. So the likelihoods of these two conflicting hypotheses are the same. Now, since h1 postulates one boat and h2 postulates two boats, h1 is simpler than h2 (in accordance with Sober’s idea). But this fact does not change the likelihoods at all. Even if h1 is simpler than h2, that fact does no epistemic work here. Indeed, if we suppose in addition that in three-​quarters of all the weeks there are two boats of the same color on the lake and in one-​quarter there is one boat and it has the same color, then we get these priors:  p(h1)  =  ¼; p(h2)  =  ¾. In such a case, the posterior probability of h2 will be three times that of h1, even though h1 is simpler than h2. A different idea Sober introduces is based on a statistical theorem proved by Hirotugu Akaike, which gives a gen­eral formula for determining an unbiased estimate of a model’s predictive accuracy.29 The general idea might be put like this: You have obtained some data points from some unknown source of data and you want to connect these points by a curve. A model gives you a way to do so. The question is how to select an unbiased model with the most predictive accuracy. Akaike’s theorem yields a way to do so based in part on simplicity: the fewer the number of adjustable parameters in the model, the better the model. The problem is that the theorem is of very limited use. First, it is restricted to cases in which the data are produced by the same unknown source. In the real world, we may not know whether the source is the same. (If

29. Sober, Ockham’s Razors, 131–​35.

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lots of bullet holes are produced in a target and our measuring device gives us the positions of some of them, we may or may not know whether they were produced by the same gun or same shooter.) Second, it is restricted because it is not applicable to cases involving predictions about future data outside the range of the data obtained. Third, it is restricted to cases in which models are being compared, one of which is true. These are major restrictions for the usual tasks of science. Finally, Sober makes the following claim: “there are three parsimony paradigms that explain how the simplicity of a theory can be relevant to saying what the world is like.”30 The first consists of the claim that “sometimes simpler theories have higher [prior] probabilities.” The second is the claim that “sometimes simpler theories are better supported by the observations.” The third is that “sometimes the simplicity of a model is relevant to estimating its predictive accuracy.” The first, he tells us, is illustrated by the advice to young doctors that “when you hear hoof beats, think horses not zebras,” since horses are more common. The second is illustrated by the case in which a single cause for a group of similar events is inferred rather than a more complex group of independent separate causes. The third is illustrated by the use of Akaike’s theorem. Since I  have noted the very restricted applicability of the latter in the previous paragraph, let me comment here on Sober’s first two “paradigms.” In both cases the epistemic work is being done not by simplicity but by empirical evidence. It is because horses are much more common than zebras, not because of simplicity, that it is more probable that 30. Elliott Sober, “Why Is Simpler Better?,” Aeon Essays, May 2016. I thank Michael Roche for alerting me to this reference and discussing it with me.

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the hoof beats are those of a horse than that they are those of a zebra. (In African grasslands, the reverse is the case.) Similarly, to infer a common cause, rather than multiple independent causes, in a group of people with broken legs in an orthopedic surgeon’s waiting room would be empirically rash, even if one common cause is simpler than many. We infer a common cause in such a case only if we have evidence that points in that direction (e.g., these people were involved in the same accident). In both the horse and the broken leg examples, it is empirical information, not simplicity, that justifies an inference to the “simpler” hypothesis. Sober is right in saying that sometimes simpler theories have higher prior and posterior probabilities. But what he needs to demonstrate—​which his examples do not—​is that these higher probabilities are due to simplicity.31 31.  Sober may reply that even if what really matters in the cases I  have mentioned is empirical evidence, if simplicity is usually present when and only when confirming empirical evidence is, then simplicity is a sign of truth. (See Sober, Ockham’s Razors, 149.) He writes: “These remarks about “really” really leave me cold. They are like saying that barometer readings aren’t evidence of storms, since what really matters to whether a storm will occur is the barometric pressure.” My reply: Of course the falling barometer is evidence of an impending storm even though it doesn’t cause it. It is evidence, I  would claim, because, given the falling barometer, it is probable that there is an explanatory connection between this and the impending storm. (It is probable that that the falling atmospheric pressure explains both the storm and the falling barometer reading.) But Sober has not shown that, e.g., given the fact that monotheism is a simple hypothesis (much simpler than polytheism), it is probable that there is an explanatory connection between this fact and the truth of monotheism (from which it would follow that it is probable that one god exists). Even if Sober does not buy my A-​concept of evidence, to pursue the reply above he would need to show that simplicity is usually present when and only when empirical evidence is. But this is a highly dubious claim, since, as I have illustrated earlier, there is frequently strong evidence for highly complex hypotheses.

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1 0 .   A   N O N -​P R O B A B I L I S T I C A PRIORI VIEW I turn to a view according to which simplicity is “built into” the very concept of inductive reasoning. Reasoning inductively just is reasoning to the simplest hypothesis compatible with the evidence. This is what it means to reason inductively. The idea can also be expressed using a more standard definition of induction, according to which if from the fact that all observed As are Bs you infer that all As are Bs, you are making an inductive inference. Some inductive inferences are valid, some are not. You are making a valid inductive inference if and only if the hypothesis that all As are Bs is the simplest one compatible with all your data. That is part of the meaning of “valid induction.” This view is just too simple to be true. To begin with, your sample of As observed may be much too small or too unvaried to justify an inference to the hypothesis that all As are Bs, even if that hypothesis is the simplest one compatible with the data. The As may have been selected in a way biased toward being B. This can be so even if all the observed As are Bs. And whether the size, variation, or methods of selection are adequate is a matter to be determined empirically, not a priori, depending on the nature of the As and Bs in question. For J. J. Thomson in 1897, a few experiments showing that cathode rays are attracted to a positively charged plate was sufficient to justify his general claim that cathode rays are negatively charged. For pollsters in 2016, showing that the majority of the people in their poll said they would vote for Hillary Clinton was not enough to justify the claim that Hillary would win—​it depends on the size, variation, and location of the sample, and on the degree of commitment of

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those sampled. In these cases, one evaluates the strength of the inference by reference to empirical facts about the case, not by an appeal to simplicity. An a priorist may reply by saying, “Yes, in cases of these sorts, empirical factors enter into determining whether the inductive inference is justified. But so does simplicity, and that is a priori.” Suppose the election pollsters did a very good job:  the size, variation, location, and commitment of those sampled are empirically impeccable. And suppose, given their impeccable polling, done say two weeks prior to the election, they concluded that Hillary would win by a margin of at least 5 points. Let’s say that was the simplest hypothesis given the polling and all other information available at the time. Now, there were more complex hypotheses that were also compatible with the data—​e.g., that the director of the FBI would announce a further investigation of Hillary, and that the Russians would hack into the computers of the DNC, which would cause Hillary to lose. We have, then, two competing hypotheses, each of which is compatible with all the well-​gathered information. On the present viewpoint, the pollsters were supposed to say that the inference to the “Hillary wins” hypothesis was justified and the “FBI–​Russian hack–​Hillary loses” hypothesis was not, because the former was the simplest one compatible with the data and the latter is too complex. My response is that simplicity has nothing to do with it. The reason is that two weeks prior to the election, the pollsters had no evidence at all for the more complex hypoth­ esis and a lot of evidence for the simpler one. Yes, both hypotheses are “compatible” with the polling evidence two weeks prior to the election. But this is “logical” compatibility. There is no contradiction in conjoining either hypothesis

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with the polling results. But given the information available at that time, the polling results constituted evidence for the “Hillary wins” hypothesis and none for the “FBI–​Russian hack–​Hillary loses” one. Simplicity is irrelevant. So let’s change the case a little to give simplicity a chance. Let us change the “Hillary wins” hypothesis in a way that makes it more comparable to the rival I  have introduced. The hypothesis is now “No FBI–​No Russian hack–​Hillary wins.” I will suppose that this hypothesis is simpler than the “FBI–​Russian hack–​Hillary loses” hypothesis because the latter introduces external causes that will interfere with the outcome, while the former denies the existence of such external causes. Now, suppose that two weeks prior to the election, the polling results were dead-​even and that no other empirical information was obtained that favored one candidate over the other or that provided evidence for or against the FBI–​Russian hack idea. We might even suppose that the experts put the probability of the FBI–​Russian hack idea at 50%, since they learned that Director James Comey of the FBI and President Vladimir Putin are, surprisingly, in collusion and will flip a coin in deciding whether to reopen the investigation of Hillary and to hack the DNC. Should the pollsters have said:  “Well, the fact that the new hypothesis involving Hillary winning is simpler than the hypothesis involving Hillary losing makes the former more believable than the latter. It is ‘a priori evidence’ for the former hypoth­ esis.” No, under these circumstances the pollsters should say: “Yes, one hypothesis is simpler than the other, but there is no evidence favoring one rather than the other. There is no more reason to believe one rather than the other. So, suspend belief or, if you are a betting person, assign the same odds for both hypotheses.”

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1 1 .  S I M P L I C I T Y A S   A N E P I S T E M I C S T R AT E G Y Finally, I will consider a view according to which simplicity should be understood as part of a strategy for modifying theories as new data emerge. If such a strategy can be demonstrated most likely to eventually lead to the truth in a maximally effective way, then simplicity is shown to be an epistemic virtue. At least that is the claim. An idea of this sort was suggested years ago by Hans Reichenbach,32 and more recently by Kevin Kelly.33 For Reichenbach, the aim of induction is to infer the probability of certain types of events, which for him means inferring the limit of the relative frequency of events of that type in an infinite sequence of such events. Reichenbach advocates using the “straight rule” of induction for this purpose. This rule is to infer that the limit of the relative frequency of a type of event E in an infinite series of events is the same as the observed relative frequency of events of type E in that series. In short, infer that the “population” will match the observed “sample.” Reichenbach’s famous justification for this rule (his “justification of induction”) is that if you continue to use this straight rule, and if there is a limit, then as you observe more and more events in the series, there will come a point after which the observed relative frequency of Es will be, and stay, within any desired margin of the correct limit of the relative frequency. In other words, if 32. Hans Reichenbach, Experience and Prediction (Chicago: University of Chicago Press, 1938). 33.  Kevin Kelly, “Simplicity, Truth, and Probability,” Research Showcase @ Carnegie Mellon University.

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you continue to use the inductive straight rule to infer limits, and if there is a limit, your inferences will eventually get as close as you like to the true limit. As Reichenbach himself noted, however, there are infinitely many inductive rules about which the same can be said. Let m/​n be the observed relative frequency of an event of type E at a point n in the sequence. Consider some function f(n) which is such that as n approaches infinity, f(n) approaches 0. Consider rules of inference of the form: If the observed relative frequency of E is m/​n, then infer that the limit of the relative frequency of E is (m/​n) + f(n).34

This yields an infinite set of “inductive” rules, each of which will permit your series of inferences to “converge” to the correct limit, if one exists, but each of which will yield different predictions about the limit along the way. The straight rule is the special case in which f(n) = 0 for all n. Why choose this special case, as Reichenbach does? Well, you might say, the straight rule is the simplest: it doesn’t add a “corrective” factor to the observed relative frequency. But then the question arises:  Is this epistemic 34. This will violate the probability calculus, since it will yield probabilities greater than 1. (For example, let the observed relative frequency m/​n be 1.) We need a “corrective” factor that avoids this outcome. Carnap presents one for his logical-​epistemic concept. He is concerned with the probability that the next item in a series will have a property P, given the relative frequency of Ps in the sample. He constructs a class of probability functions in which this probability is a weighted mean between the relative frequency and what he calls a “logical” factor, which can vary with the language in question. All these functions will converge to the observed relative frequency of Ps as the sample gets larger and larger. See his The Continuum of Inductive Methods.

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simplicity, or is it merely pragmatic? That is, is the choice of the simpler “straight rule” based on an assumption such as: the continued use of the straight rule is likely to lead to the correct limit faster than the others? Or is the choice of the straight rule based on convenience? Reichenbach’s response sends a mixed message. He admits that choosing some corrective factor f(n) other than 0 could hasten the convergence to the correct limit. But it could also delay the convergence; and he adds, “we know nothing about the two possibilities.” So, he concludes, choosing f(n) = 0—​i.e., the straight rule—​ is to choose “the value of the smallest risk; any other determination may worsen the convergence. This is a practical reason for preferring the inductive principle.”35 The claim that the simple straight rule gives the “smallest risk” suggests an epistemic defense of this simple rule over other, more complex convergent rules. But Reichenbach also claims that the fact that it gives the smallest risk is a practical reason for choosing the rule. Perhaps, then, it is supposed to give both an epistemic and a practical reason. The main problem I have with Reichenbach’s approach is this:  Suppose you choose the corrective factor f(n)  =  0, 35. Reichenbach, Experience and Prediction, 355. This appeal to a “principle of ignorance” I  find unconvincing. Is he assuming a priori that by choosing f(n) to be greater than 0 it is just as probable that you will delay convergence as it is that you will hasten it? Why isn’t this true also of choosing f(n) = 0? In any case, appeal to a priori probabilities should be anathema to one such as Reichenbach, who seeks to develop an empirical concept of probability. Also, to measure “risk” you need to talk not just about the value or disvalue of the possible outcome, but in addition about the probability of that outcome. But Reichenbach cannot be measuring “risk” in terms of probability without circularity, since he is telling us how to determine probabilities in terms of some inductive rule of inference. How else is “risk” to be measured?

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saying that it is the simplest choice. And suppose, following Reichenbach, you argue that if you continue to use this simple straight rule to infer probabilities, then as more and more evidence is gathered, your simple inductive conclusions about the probability of some type of event will at some point converge to the correct probability, assuming there is a limit to the series. Finally, suppose you claim that this is both an epistemic and a practical reason for using the simple straight rule. Is this enough to show that simplicity is an epistemic virtue? If so, it is a far cry from the original Epistemological Claim or even to the substantially modified Bayesian version. Let me say why. To confine our attention just to inductive inferences of the sort Reichenbach is concerned with, suppose, using the simple straight rule, I make an inductive inference from the fact that the observed relative frequency of type E events is m/​n to the claim that the limit of the relative frequency is m/​n. Reichenbach is not telling me that the fact that I  am using his simple straight rule to infer this when I have determined that m/​n of the observed members of the series are of type E provides a good reason, whether epistemic or practical, to believe that my conclusion is correct—​that the limit of the relative frequency is m/​n. Nor is he telling me that the fact that I am using his straight rule to infer this constitutes a better reason than before. What he is telling me is that if I continue to use this strategy of following the simplest inductive rule, and if there is a true conclusion of the sort I am seeking, then eventually I will arrive at a conclusion that is as close to the true one as I would like. Furthermore, I will never know whether there is a true conclusion here (i.e., whether there is a limit of the relative frequency), and if there is, whether I  have reached a point of convergence. Finally,

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he is telling me that (practically or epistemically speaking) continuing to follow the straight rule is better at getting to a point of convergence, if there is one, than continuing to follow more complex rules. This defense of simplicity provides little if any reason for Newton to appeal to simplicity in making his inference to the law of gravity. It would be telling Newton: “Well, Sir Isaac, simplicity cannot justify making the inference you did—​i.e., inferring that all bodies obey the law of gravity on the grounds that all the ones that have been observed do. (Simplicity cannot justify inferring that the limit of the relative frequency of bodies that obey the law of gravity is 1, from the fact that the observed relative frequency is 1.) But as you observe more and more bodies, and continue to make inferences from the observed relative frequency to the limit of that frequency using the simple straight rule, then, if there is a limit of relative frequency here, you will eventually get closer and closer to it, and do so in a better manner than with more complex rules, although you will never know if there is a limit, or when you have reached a point of convergence.” I think Sir Isaac would be unimpressed, and with good reason. He wants simplicity to justify the inference he in fact made—​which Reichenbach does not do—​not a strategy to continue to make such inferences. Kevin Kelly offers an epistemic justification for simplicity that is similar in certain respects. Like Reichenbach, Kelly is concerned with situations in which you are receiving new empirical data over time, and you are inferring and modifying hypotheses that go well beyond the data. In the light of new data, how should you do so? Kelly provides a formal strategy that proceeds in the simplest way. It minimizes the number of revisions or retractions you make

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on your road to truth. And he claims that the formal account of simplicity he provides is epistemic, not pragmatic, because “retraction-​minimalization (i.e., optimally direct pursuit of the truth) is part of what it means for an inductive inference procedure to be truth-​conducive, so retractions are a properly epistemic consideration.”36 Without examining the formal details, suffice it to say that Kelly, like Reichenbach, does not provide an epistemic role for simplicity of the sort I have been discussing. To do so, it needs to be shown that the fact that a theory is simple provides a good reason for believing it is true or empirically adequate (or at least a better reason than without that fact). But even for Kelly, the fact that some modification of a theory in the light of new data is simple, or the simplest one possible, does not by itself give you any reason for believing that it is true. He admits that his simplicity strategy “cannot point at or indicate the true theory in the short run and . . . alternative methods [could] have converged to the truth eventually.”37 What Newton, Einstein, and other epistemic simplicity theorists want, or at least need, is an epistemic justification not for continuing to modify theories in the simplest way in the light of new data but for taking the simplicity of a particular theory to be at least some epistemic reason to believe it to be true or empirically adequate.38

36. Kelly, “Simplicity, Truth, and Probability,” 22. 37. Kelly, “Simplicity, Truth, and Probability,” 21. 38.  For a criticism along these lines, see S. Fitzpatrick, “Kelly on Ockham’s Razor and Truth-​Finding Efficiency,” Philosophy of Science 80 (2013): 298–​309.

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1 2 .   C O N C L U S I O N S In this chapter, I have examined two important claims about simplicity. One is that nature is simple, and the other is that simplicity is an epistemic virtue. “Global” arguments for the claim that nature is simple are either nonexistent or are unconvincing. I  favor “non-​global” arguments, but these will show only that in certain respects, and to a certain extent, nature is (representable as) simple, and in other respects and to a certain extent nature is (representable as) complex. This can be supported by scientific investigation of parts of nature, not by metaphysical, theological, or even empirical speculations about the totality of nature. Similarly, I  reject “global” arguments in favor of the claim that simplicity is an epistemic virtue—​arguments that appeal to the historical success of simple theories, or to concepts of evidence, or to assumptions about prior probabilities or likelihoods. If you are not justified in making an inference to your hypothesis from the available empirical evidence, then either you don’t have enough evidence or you don’t have the right kind of evidence. What you need is not simplicity but more or better evidence. To be sure, when you don’t have sufficiently good evidence you can always invoke the simplicity of the hypoth­ esis. This may cause you and others to come to believe the hypothesis. (To misquote Samuel Johnson, “Simplicity [as an epistemic defense] is the last refuge of a scoundrel.”) But then you still don’t have sufficiently good evidence for your belief; you just have a simple hypothesis, which you may regard as a good thing for other reasons. On the other hand, if you are justified in making an inference to your hypothesis from the available evidence, then you don’t need simplicity at all for this purpose.

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You may reply that simplicity does carry at least a little epistemic weight, especially in those cases in which you have some empirical evidence that is almost but not quite enough to make you justified in believing the hypothesis. An appeal to simplicity will just be enough to bring you over the hump epistemically. Suppose that a drug company has tested a drug for reducing certain symptoms. The company has tested it on groups of patients with those symptoms and so far has had good results. But suppose the groups tested are almost but not quite large or varied enough to justify the inference to the conclusion that the drug is effective, although the preliminary results are promising. Now, suppose also that the hypothesis that the drug is effective in reducing symptoms is simpler than competing hypotheses being considered—​e.g., that it is not the drug that is producing the reduction in symptoms but a set of other things, any one of which could reduce the symptoms and at least one of which was operating in each of the cases in which the patient had reduced symptoms. The drug company then invokes the simplicity of its hypothesis in its report. If the groups tested are almost but not quite large or varied enough to justify the inference to the hypoth­ esis that the drug is effective, should an appeal to simplicity do the job? The FDA would, I hope, reject this idea. What the drug company needs in order to show the effectiveness of the drug is to produce more tests—​on larger and more varied patients. Simplicity here should carry no epistemic weight. Only empirical evidence—​results of testing—​will. My reply is similar in the case of the weaker Bayesian idea that simplicity increases the (epistemic) probability of a hypothesis and thus counts as Bayesian B-​evidence for it. Suppose, as in the example above, that the groups tested are almost but not quite large or varied enough to justify the

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inference to the conclusion that the drug is effective. The FDA demands stronger evidence for approval. If the drug company replies that the simplicity of the hypothesis makes the evidence stronger, the FDA should reject that response. Again, what is wanted is more testing.

3

✦ NON-​EPISTEMIC SIMPLICITY Maxwell, Newton, and Speculation

IN SECTIONS 1 TO 3 of the present chapter I  turn to four

speculative views about simplicity that do not assert that nature is simple or that the simplicity of a theory provides epistemic grounds for belief. These include: (i) that theories are underdetermined by evidence, and so must be selected on the basis of simplicity; (ii) that in conducting their inquiries, scientists must presuppose that nature is simple; (iii) that it is the aim of science to present theories that are simple; and (iv) that simplicity is a scientific virtue worthy of having for its own sake. Each of these views, I argue, has serious problems. In section 4, I consider the idea that simplicity is a pragmatic virtue. This I take to be its most important role, one that I illustrate by showing its use in various speculations made by Maxwell in developing his molecular-​kinetic theory of gases. In the remainder of the chapter I consider Newton’s use of simplicity in his argument for the law of gravity. Despite the fact that Newton appeals to simplicity in this argument, I argue that these appeals carry no ontological or epistemic

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weight, only a pragmatic one, and that the law, contrary to Newton’s claim, was a speculation, albeit a grand one.

1 .   U N D E R D E T E R M I N AT I O N Underdetermination Claim: Scientific theories are under­ determined by the evidence. In order to choose a theory you must do so on the basis of simplicity:  choose the simplest theory compatible with the evidence.

This quite popular idea is that if we just look at the results of experiments and observations, these will be compatible with various conflicting theories that we have or might construct. So if we are to choose a theory, we must do so using some criterion in addition to empirical evidence. Simplicity is that criterion. There are two ways to understand the Underdetermination Claim, depending on the purpose of the “choice” in question. If we are choosing a theory for non-​epistemic reasons—​ e.g., to explain its historical importance or its fundamental ideas—​then simplicity is usually irrelevant. If we understand the “choice” as an epistemic one (choose to believe, or just believe), then the question becomes:  If a theory is underdetermined by the evidence, why should we believe the theory (i.e., believe it to be true or empirically adequate) if it is the simplest one compatible with the evidence? In such a situation, why is simplicity relevant for belief? The only possible answer is that simplicity is an epistemic virtue, that it provides an important epistemic basis for believing that the theory is true or empirically adequate (whether or not this idea is based on the claim that “nature is simple”). But this is

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just the epistemic (or ontological) claim that I challenged in the previous chapter, so I will not pursue it further. Perhaps, then, the Underdetermination Claim should be understood as making a pragmatic assertion to the effect that since theories are in fact underdetermined by the evidence, and since scientists do need to choose some theory to work on, test, promote, utilize to make calculations, etc., they should choose the simplest theory for such purposes, even if simplicity is not a sign of truth. I will challenge this claim by questioning the assumption it is based on, viz. that theories are underdetermined by the evidence. What exactly does this assumption mean? Here are two possibilities: (i) Empirical evidence by itself can never establish a theory with certainty, although it can make its probability high. (ii) No matter what the available empirical evidence, it is never sufficient by itself to make a theory more probable than not, or more probable than every competitor. Claim (i) is easier to deal with. If the empirical evidence can make the probability of a theory high (or, using my concept of A-​evidence, if, given the evidence, there can be a high probability of an explanatory connection between the evidence and the theory), then even if this probability is not 1, it can be reasonable to believe the theory. Evidence need not be conclusive to make a hypothesis reasonable to believe. The fact that I own 95% of the tickets in a fair lottery is a very good reason to believe I will win, but not a conclusive reason. What argument, then, can be given for claim (ii)? To take a simple example, suppose that a coin, drawn randomly from a coin machine in my grocery store, has been tossed in a fair manner 1,000 times and has landed heads roughly 50% of the time. Shouldn’t this count as strong evidence that the

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coin is physically unbiased and that it will continue to land heads about 50% of the time if tossed? Shouldn’t it make it at least more probable than not that this will be case, and hence more probable than any competitor? You might reply, “No, there are various alternative hypotheses that are also compatible with the available evidence—​ e.g., that the coin is physically biased toward heads, not unbiased, but it is under the control of the Mafia, which makes it land heads approximately 50% of the time just during the first 1,000 tosses; or that the coin is physically biased toward heads in such a way that, in the long run, it will land heads 90% of the time, and the experimental result we got is just a matter of chance (after all, the probability of getting such a result with a 90% biased coin, though tiny, is not zero).” Evidence about the results of the first 1,000 tosses does not rule out these conflicting hypotheses. If we choose the “physically unbiased” hypothesis over the “biased” ones, we cannot be doing so on the basis of this evidence. There must be some other basis for this choice—​e.g., simplicity. Simplicity is the sort of non-​evidential criterion that must be appealed to in selecting what hypothesis to choose to work on, promote, and so forth. Evidence is never sufficient for this purpose. My response: “Yes, such competing hypotheses are ‘consistent’ with the data so far, in the logical sense of consistency:  there is no logical contradiction in conjoining the data with either of the two ‘bias’ hypotheses. But there is no evidence that either of these alternative hypotheses is true—​none that would give these alternatives any significant probability. And there is considerable evidence that makes it very probable that the ‘no physical bias’ hypothesis

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is true: look at how and where the coin was selected, the way it was tossed, the way coins are normally manufactured, the fact that while the Mafia may be in involved in casinos, it generally doesn’t get involved with coin machines in grocery stores, and, of course, the results of the tosses.” This sort of reply is given by Newton in his Rule 4, in response to Descartes’ attempt to crush or at least weaken inductive arguments generally by invoking alternative possible explanations of the data.1 If you are going to crush or weaken my evidence-​based claim that the coin is physically unbiased by presenting other possibilities, you need to introduce evidence for these alternatives. Merely concocting some alternative explanation is not providing such evidence. The “alternative explanation” argument works only when there is either no evidence in favor of a preferred hypothesis or the evidence is pretty weak, or when there is at least equally good evidence in favor of the alternative.

2 .   U N D E R D E T E R M I N I S T R E S P O N S E S A champion of underdetermination may respond by saying that alternative explanations needn’t be specifically invoked or even known. The mere possibility of such explanations, whether known or not, is sufficient to show that evidence by itself is not enough to establish or even confirm a hypothesis. John Stuart Mill employs a “possible alternative

1.  Newton’s Rule 4:  In experimental philosophy, propositions gathered from phenomena by induction should be considered either exactly or very nearly true notwithstanding any contrary hypotheses, until yet other phenomena make such propositions either more exact or liable to exceptions.

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explanation” argument in claiming that the nineteenth-​ century wave theory of light, and particularly the hypothesis that there is a luminiferous ether, should not be regarded as “probably true” on the grounds that it “accounts for all the known phenomena,” including experimental results involving diffraction and interference. Mill argues that there are “probably many others [other competing hypotheses] which are equally possible, but which, for want of anything analogous in our experience, our minds are unfitted to conceive.”2 Mill objects not by providing an alternative explanation but simply by saying there probably are ones that we can’t even conceive of. Whether this argument carries any weight depends on what Mill means by speaking of explanations that are “equally possible.” If he means that there are optical theories supported at least as well as the wave theory is by diffraction, interference, and other experimental results (however “support” is to be understood), then the following question needs to be raised: Q: How does Mill know this? What evidence does he have?

One answer is: he doesn’t know this because he has no evidence. The only way to know this is to produce such an alternative and to show that it is supported as well as the wave theory is by the experiments. One who gives this answer is saying (following Newton): “Put up or shut up!” That is, if you are going to use the “alternative (or competing) explanation”

2. John Stuart Mill, “A System of Logic, Book 3,” reprinted in Achinstein, Science Rules, 223.

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argument, then (a) give me an alternative explanation, and (b) show me how it is supported by the experiments.3 A different answer to (Q)  is to say that Mill does have evidence, viz. historical evidence. The history of science (the “pessimistic induction”) shows that in most cases, including that of the wave theory itself, theories that were supported by the evidence available turned out later to be refuted by new data and replaced by conflicting theories, in the light of new data. So, Mill has historical inductive evidence for his claim that there are, or probably are, competing optical theories that are or will be supported at least as well as, if not better than, the wave theory in mid-​nineteenth century, and hence that the wave theory is either probably false or at best no more likely to be true than not.4 Is this answer to (Q) reasonable? Let the hypothesis be: h: There exists a luminiferous ether.

The “pessimistic induction” does not provide evidence in one of my A-​senses (or in the explanatory B-​sense) against h. It is not the case that, given the historical fact that most theories have turned out false, there is probably an explanatory connection between that fact and the fact that the ether does not exist. If Mill were to claim that he has A-​evidence that the ether probably does not exist, then, following Newton, I would say: “Let him produce it; don’t cite history.” In fact, of 3.  See Philip Kitcher, The Advancement of Science (New  York:  Oxford University Press, 1993), 154. 4. See P. Kyle Stanford, Exceeding Our Grasp (New York: Oxford University Press, 2006).

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course, Mill does not give a historical, or any other, argument that he takes to provide evidence against the existence of the ether. His central claim is that there is no known evidence for its existence. By saying that there probably are alternative hypotheses that are “equally possible,” I would understand Mill to mean simply that there probably are alternatives that are logically consistent with the experimental data and which, if they were true, would correctly explain those data. But, he is saying, the fact that a hypothesis, if true, would correctly explain some data is no reason whatever to conclude that those data provide evidence for that hypothesis. The Mafia hypothesis in section 1, if true, would correctly explain the results of the coin tossing. But unless there is evidence that the Mafia is involved, the experimental results provide no evidence for the Mafia hypothesis. Indeed, this is Mill’s own objection against Whewell’s version of hypothetico-​deductivism. In order to show that observed phenomena provide evidence for a hypothesis, you need to show more than that the hypothesis, if true, would explain those phenomena. You must provide (causal-​inductive) evidence in support of the claim that the entities and laws cited in the hypothesis exist and are sufficient to produce those phenomena. Accordingly, Mill’s “competing hypothesis” objection might best be put like this: Suppose there is evidence e for a hypothesis h (e.g., causal-​inductive evidence that goes beyond simply e’s being logically consistent with h). Then, if there were some alternative hypothesis h′ that, if true, would explain e, that fact would not refute or weaken the claim that e is evidence that h. Put this way, the objection doesn’t claim that there are, or probably are, alternative hypotheses that explain e. It is a conditional claim that amounts to what Newton

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says in his Rule 4:  If there are “contrary hypotheses” to h, they do not refute or weaken inductive evidence for h unless they have inductive evidence of their own. So understood, the “competing hypothesis” objection does not establish underdetermination. The only time invoking a competing hypothesis h′ will serve to show that the original hypothesis h is not supported by e is when the “support” for h simply amounts to its explaining e. It might be suggested that the way to generate underdetermination is to combine three ideas, each of which may be lurking in the minds of those who preach the doctrine: (a) a hypothetico-​deductive view of evidence (the thesis that a set of observed phenomena constitutes evidence for a system of hypotheses if and only if this system deductively explains those phenomena); (b)  an existence claim about competing hypotheses (the thesis that for any system of hypotheses that deductively explains the observed phenomena, there exists a competing system of hypotheses that does, too); and (c) a claim about evidence (if e is evidence for some system of hypotheses H, then e cannot be evidence for H′, where H′ is incompatible with H). Suppose, then, that H represents some system of hypotheses, and that H deductively explains a set O of observed phenomena, so that, in accordance with (a), set O constitutes evidence for H. Now in accordance with (b), there is a competing system of hypotheses H′ that also deductively explains O. Since H and H′ are incompatible, by (c) the observed phenomena, even though deductively explained by both H and H′ cannot be evidence for either. Since this is so for any system of hypotheses H, it might be claimed, underdetermination is born! No observed phenomena can be evidence for any hypothesis.

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This doesn’t yield underdetermination, only a contradiction. The three ideas together are inconsistent. Suppose that H deductively explains O. Then, by (a), O is evidence that H. But if, in addition, (b) and (c) hold, then O cannot be evidence that H. Of these three ideas, I can accept only (c). Indeed, (c) is entailed by my concepts of potential, veridical, and ES-​evidence (as well as by the upgraded and explanatory Bayesian concepts in c­ hapter  1), since all these require probabilities greater than ½ for e to be evidence that h. Claim (a) I reject because, in accordance with my A-​concepts of evidence (as well as all the Bayesian ones I have noted), e can be evidence that h even if h does not deductively explain e. Indeed, entailment of e by h, whether or not this is explanatory, is neither a necessary nor a sufficient condition for e to be evidence that h. Claim (b), the existence claim about competitors, I  find dubious for the same reason Newton does:  Don’t give me possibilities; give me reasons to think that for every system of hypotheses that deductively explains the observed phenomena there exists a competitor that does, too. (This is particularly important if, like Whewell, you demand that the competing system, as well as the original one, deductively explain phenomena of different kinds (“consilience”) and that the assumptions of the explanation satisfy “coherence”5). But even if you can give reasons to think that for any system of hypotheses there are competitors of these sorts, your

5. Whewell claimed that if your theory explains known phenomena and satisfies consilience and coherence, it will have no competitors that do the same. He was mistaken about that. (For an example, see ­chapter 4, section 4.) Even so, it doesn’t follow that for any theory that satisfies Whewell’s conditions there will be a competitor that does, too.

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argument won’t work unless you accept (a), a hypothetico-​ deductive view of evidence, which I, and Bayesians, do not. For me and for those Bayesians who require probability greater than ½ for evidence, you need to show this:  in accordance with our concepts of evidence, for any set of beliefs H for which there is evidence e, there is an incompatible set of beliefs H′ for which e is also evidence. But you can’t show that, because of our probability requirements for evidence. Finally, then, if you are an underdeterminist, there are two positions you could take with regard to simplicity. On both positions, you could say that theories are underdetermined by evidence, in the sense that no matter what the evidence, it does not give a sufficient reason to believe the theory. According to the first position, simplicity is an epistemic virtue, so that if a theory is simple (or the simplest of the competitors), then the evidence plus simplicity give a good reason to believe the theory. According to the second position, simplicity is not an epistemic virtue. Since theories are underdetermined by the evidence, and since simplicity is not an epistemic virtue (nor are any other criteria such as explanatory power, unification, and so forth), you are never epistemically justified in believing a theory. (At best you are only pragmatically justified in using it for certain purposes.) The former position requires accepting a claim I  rejected in ­chapter 2, viz. that simplicity is an epistemic virtue. The latter lands you in the position of epistemic skepticism. Both consequences are avoided by utilizing an A-​or B-​explanatory concept of evidence and rejecting underdetermination of the sort I have been considering.

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3 .  P R E S U P P O S I T I O N , A I M O F SCIENCE, SCIENTIFIC VIRTUE I will consider these three claims about simplicity together. Presupposition Claim:  When engaging in scientific activity, particularly theorizing, you must presuppose three things: (i) that the world is intelligible, and therefore simple; (ii) that since this is so, everything can be correctly explained by a simple theory that is true or empirically adequate; and (iii) that simplicity in a theory provides an important epistemic basis for believing the theory is true or empirically adequate. Aim-​of-​Science Claim:  The aim of science, or at least one central aim, is, or should be, to provide true or empirically adequate theories that will represent and/​or explain the observable facts in the simplest way. Scientific Virtue Claim: Simplicity is a non-​epistemic scientific virtue worthy of having for its own sake.

In the Presupposition Claim, I will understand “intelligible” to mean “intelligible to us” (or to scientists).6 I will also understand “correctly explained by a simple theory that is true or empirically adequate” in such a way that we can obtain sufficient evidence to justify a belief that the simple theory is true or empirically adequate. Also, I will understand the Presupposition Claim to be saying that even if there are 6.  In ­chapter  1, I  also spoke about a non-​relativized concept of “intelligible,” having to do with the universe being ordered in some way, even if we cannot understand the order. In the present claim, the relativized concept is the appropriate one.

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complex aspects of nature, scientific activity presupposes that everything can be explained by a simple theory (not necessarily the same theory for all phenomena) that is true or empirically adequate. The Presupposition Claim, then, is that when you engage in scientific activity, particularly theorizing, you must make the three assumptions noted in the claim. Let us suppose that there are scientists who do in fact make such assumptions. The Presupposition Claim says that they must do so. Why must they? The “standard model” in particle physics, one of the most empirically well-​confirmed theories in physics, postulates various subatomic particles subject to four basic forces: electromagnetic, strong and weak nuclear forces, and gravity. In addition there are constants specifying the masses of particles and the strength of the forces. The latter are to be determined experimentally. Now, string theorists seek a theory (indeed, a “Theory of Everything”) that correctly and simply explains why there are these four forces and how they are related (and in so doing, unifies them), why the constants have the values they do, and many other things as well—​a theory that can be subject to empirical testing. Let us assume that at least some string theorists do presuppose that there is such a correct, simple, and empirically confirmable explanation and that it will be supplied by string theory. The question is whether such a presupposition is necessary. As a string theorist, you might hope that there exists such a theory, you might hope it is string theory, or if not, you might attempt to find such a theory, and you might admire such a theory if it is ever discovered—​but do you have to presuppose that one exists? Perhaps there is no such theory—​i.e., no correct simple (or even complex) explanation to be had (at least an explanation of the sort scientists seek, viz. one postulating more basic

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laws, particles, and forces than the standard model does). Perhaps it is a matter of chance that the four basic forces exist or that the constants have the values they do, so that no explanation of the kind sought exists. You can raise the questions “Why do the four forces exist?,” “Can they be unified?,” and “Why are the constants what they are?,” and search for answers, without presupposing, assuming, or believing that there are correct answers of the kind being sought. You can remain agnostic: “I don’t know whether there are simple (or complex) correct answers to the questions I am asking, but I am raising the questions to find out whether there are, and if so, what they are.” This attitude is not contradictory or otherwise impossible to maintain.7 Even Brian Greene, one of the staunchest supporters of string theory, takes such an attitude to be possible. Discussing string theory, he writes: Maybe we will have to accept that after reaching the deepest possible level of understanding science can offer, there will nevertheless be aspects of the universe that remain unexplained. Maybe we will have to accept that certain features of the universe are the way they are because of happenstance, accident, or divine choice.8

Turning now to the Aim-​of-​Science and Scientific Virtue claims, we can agree that simplicity is a condition scientists often aim to satisfy in their theories. Some think of it as an aesthetic virtue: the simpler the theory (in one or more ways), the more beautiful it is. Whether or not you associate 7.  In ­chapter  5, I  will offer more specific objections to the idea that theorizing presupposes the existence of a simple “Theory of Everything.” 8. Brian Greene, The Elegant Universe (New York: Norton, 2003), 385.

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simplicity with beauty, the claim is (1)  that the aim of science, or at least one of the aims, is to represent and explain in the simplest way, and that this is so since (2) simplicity is a scientific virtue worth having for its own sake.9 Without rejecting either (1) or (2), we need to recognize two complicating factors. The first is noted in ­chapter 1. The same theory can usually be formulated in different equivalent or nonequivalent ways, some simpler than others. Which way to formulate the theory depends on pragmatic factors: For what purposes are we using a particular formulation? Even if there are simpler formulations, a more complex one may be more valuable for our purposes, or vice versa. So, even if, in some very general way, one of the aims of science is to produce simple theories and explanations, and even if, in some very general way, simplicity is a scientific virtue worthy of having for its own sake, in applying these global maxims to particular cases, pragmatic issues loom important. Second, when we apply claims (1) and (2) to the evaluation of particular theories, we need to recognize a tension between simplicity, on the one hand, and truth or empirical adequacy, on the other.10 This tension affects how one represents or explains observable facts. Often, the simpler the explanation or representation, the less accurate it is. Following Newton, you can explain why the planets revolve around the sun in the orbits they do by representing this as

9. Of course, I am construing (2) in a non-​epistemic way. Those who believe that simplicity, or more generally, beauty, is an epistemic virtue are invited to reread ­chapter 2 . 10. See Nancy Cartwright, How the Laws of Physics Lie (Oxford: Oxford University Press, 1983) for a discussion of the tension between explanatory power and truth.

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a two-​body problem involving just the sun, the planet, and the gravitational force between them. This will yield elliptical orbits. But it is not fully accurate, since you are ignoring gravitational forces from other planets, which yield perturbations. Following classical thermodynamics, you can explain certain behavior of gases representing this as a macro problem involving pressure, volume, and temperature, and invoking the ideal gas law pV = RT. Or, because that law is not accurate at high pressures or low temperatures, you can invoke one or another more accurate, but complex, virial equation that introduces intermolecular forces and volumes (e.g., van der Waals’ equation p + a/​V2 [(V – ​b)] = RT, or much more complex ones that are even more accurate). If you want to accept the Aim-​of-​Science Claim and satisfy both truth or empirical adequacy, on the one hand, and simplicity, on the other, what do you do? There is no universal answer. It is a pragmatic issue that depends on the aims of the explainer and the needs of the intended audience. In some situations, accuracy is all important at the expense of simplicity: one wants to develop a formula that introduces as many of the contributing factors as possible and gets closer to the truth than simpler formulas. In other situations, one wants to simplify the picture as much as possible and ignore many, if not all, these complicating factors. There is no unique right way here. There is also a tension between some respects in which a theory can be simple and other such respects—​e.g., between mathematical simplicity and “comprehensiveness.” This can be illustrated by invoking the two examples just given. If you want an equation of state relating pressure, volume, and temperature that is mathematically simple, choose the ideal gas law, recognizing that it holds only for a limited range of

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pressures and temperatures. If you want an equation of state that is more comprehensive in the sense that it applies to a greater range of pressures and temperatures, choose a virial equation, recognizing that it is mathematically (and ontologically) more complex. If you want to explain the orbit of a planet in a mathematically simple way, represent the situation as a two-​body problem. If you want to represent the situation in a more comprehensive way so that a single representation covers more of the forces that are acting, represent it as a many-​body problem, which makes the mathematics too complex to solve. My response to the Scientific Virtue Claim is similar. Yes, simplicity is, or can be, a scientific virtue worth having for its own sake, but in evaluating a theory, it is frequently trumped by other considerations, and it is frequently valued not for its own sake but for its practical value. What about the grander idea of a “Theory of Everything” that is simple “in all respects”? If such a thing were possible, wouldn’t it be valuable for its own sake? Wouldn’t it be like a Shakespearean sonnet or a Beethoven sonata?11 Wouldn’t it be a beautiful thing to behold? Yes, it would be.12 We could evaluate theories on the basis of simplicity (or, more generally, of beauty). We could say that string theory is better than the standard model because, or in the sense that, it is simpler: it postulates only one type of entity—​ strings—​ whereas the standard model has a zoo of basic entities, and it unites the four fundamental forces, whereas the standard model does not. (Of

11. See the quote by Steven Weinberg on sonnets in ­chapter 1, p. 6. 12. Whether such a theory could actually be used is another matter, which will be discussed in ­chapter 5, .

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course, string theory complicates the matter by postulating 10 dimensions of spacetime.) We could say that the biblical explanation of the origin of the universe and the development of life is better than the amalgamated cosmological-​ biochemical-​Darwinian one because, or in the sense that, it is simpler: one God did it all. But scientists want much more, and some are happy with much less. Scientists want truth or empirical adequacy, and they also want understanding. Depending on the theory, these can conflict in various ways with the desire for simplicity for its own sake, since what standards of truth, empirical adequacy, and understanding are appropriate to employ involves pragmatic considerations that can be independent of simplicity “for its own sake.” Despite its simplicity, these days the biblical explanation of the origin of the universe is not regarded highly by scientists, not just because there is a better confirmed theory but also because they claim there is no credible evidence for the truth of the biblical explanation, and because that explanation does not provide the kind of understanding they demand, including an empirically supported mechanism that describes how God did it, whether or not that mechanism is simple or complex.

4 .   P R A G M AT I C S I M P L I C I T Y A N D M A X W E L L’ S “ E X E R C I S E I N M E C HA N IC S” Pragmatic Claim: Simplicity is a pragmatic virtue.

Theories that are simpler in certain respects—​that make fewer assumptions, postulate fewer different types of entities, have

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simpler equations than theories that are more complex—​are easier to use for various purposes, including explanation, prediction, calculation, and communication. And, very importantly, they are easier to develop further. They are excellent starting points from which to create more sophisticated and perhaps more complex ideas. As I noted earlier, you can hold such a view about simplicity without holding any of the other six views. Or, you can hold this view together with any or all of the other six. But since I reject the first four claims, I recommend that you accept the Pragmatic Claim, and that you understand the Aim-​of-​Science and Scientific Virtue Claims in such a way that they incorporate the ideas in the Pragmatic Claim. Unlike some simplicity enthusiasts, I  regard the pragmatic virtue of simplicity as the most important one. Partly, I  do so because I  reject ontological and epistemological virtues that have been attributed to it by champions of simplicity. Partly, I do so because even though truth or empirical adequacy are virtues as well, pragmatic considerations are relevant for determining what standards of truth or empirical adequacy to require. But my main reason for defending simplicity as a pragmatic virtue is that I regard it as an important one in presenting, developing, and applying theories to solve questions about actual phenomena. I will illustrate this with a case in which simplicity plays a crucial pragmatic role. In ­ chapter  1, I  introduced three speculations that James Clerk Maxwell developed. My reason for discussing Maxwell there was to illustrate the point that different kinds of speculations are possible, and different ways of evaluating them are appropriate. Here, I return to the 1860 paper, not because it is a speculation but because it is one

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in which simplicity plays an important non-​ epistemic, pragmatic role. Maxwell begins the paper, as follows: So many of the properties of matter, especially when in the gaseous form, can be deduced from the hypothesis that their minute parts are in rapid motion, the velocity increasing with the temperature, that the precise nature of this motion becomes a subject of rational curiosity.13

In order to see whether and how many of the known properties of gases can be explained in terms of the motions of their “minute parts” (the hypothetical molecules), Maxwell makes a series of assumptions about these parts and their motions, including that gases are composed of spherical molecules; that these molecules move in straight lines except when they strike each other and the sides of their container; that they exert forces only at impact and not at a distance; and that they make perfectly elastic collisions (the total kinetic energy before collision is the same after). He offers no evidence for these assumptions. Indeed, a year before publication, he writes to Stokes saying that he is making these assumptions “before we know whether there be any molecules.” In ­ chapter  1, I  quoted a passage from Maxwell in which he emphasizes the important role of mechanical explanations—​ones in which phenomena are explained in terms of bodies in motion subject to forces governed by laws of dynamics. In his 1860 paper, the question for Maxwell is whether a mechanical explanation of known gaseous behav­ ior is even possible, not whether the particular mechanical 13. Niven, ed., The Scientific Papers of James Clerk Maxwell, 1:377.

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assumptions he introduces in the paper are true or probable. For this purpose, it suffices to introduce simple ones—​for example, that the molecules are spherical, rather than odd-​ shaped; that they travel in straight lines, rather than in some more complex path; and that the only forces they are subject to are contact forces, rather than more complex forces that act at a distance. These assumptions are easier to express and develop mathematically than more complex ones. (In later papers he revises these in various ways, e.g., by allowing noncontact forces that are both attractive and repulsive.) The strategy in this paper is to see how far he can get with a set of simple assumptions—​ones that are “ontologically” simple (spherical molecules all of the same mass, subject to only one kind of force) and mathematically simple (e.g., in deriving his velocity distribution law, he assumes that the directional components of velocity of a molecule are independent, thus simplifying probability calculations). He is certainly not claiming that the simplicity of his assumptions makes it likely, or more likely, that they are true or close to the truth. His use of simplicity here is entirely pragmatic: by introducing simple assumptions, rather than more complex ones, he can more readily see where they lead (30 out of 32 pages of his paper are spent deriving answers to mechanical questions about these molecules). If the simple assumptions work out reasonably well in some cases but not so well in others, he can try more complex ones later. That is exactly what happened. From his simple assumptions he derived the ideal gas law relating pressure, volume, and temperature of a gas, and he explained known deviations from the law at low temperatures and high densities. But he also got some results that were not so happy, particularly specific heat ratios that were too far

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from observed values. In a later paper in 1865, he replaces the contact force repulsion idea with a more complex action at a distance idea and with more complex attractive and repulsive forces. And in 1875, he begins not with his simple 1860 assumptions but with a very complex virial equation relating the pressure, volume, and temperature of a gas to the total kinetic energy of the molecules in the container of gas, the force of attraction or repulsion between molecules, and the distance between molecules. This equation he takes from Rudolf Clausius, who derived it from classical mechanics for observable particles constrained to move in a limited region of space. In short, Maxwell chose to make simple assumptions in 1860, not because he thought that simple assumptions are more likely to be true than complex ones, or because he presupposed that nature is simple, or because as a physicist he aimed to produce simple theories, or because he valued simplicity for its own sake. He chose to make simple assumptions because they are easier to develop and see where they lead in his attempt to provide a mechanical theory of gases. This, I am claiming, is the main function of simplicity—​an important one, often ignored or belittled by those who believe it serves a “higher” function.

5 .   N E W T O N ’ S S I M P L I C I T Y-​B A S E D A R G U M E N T F O R   G R AV I T Y In the final part of this chapter I return to Newton, who had strong views about simplicity and put them to use in his argument for universal gravity. His argument is based on the assumption that nature is simple, and that simplicity is an

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epistemic guide to truth. If simplicity is doing any real ontological or epistemic work, one would expect to find it here. My question in this section and the next is this: Despite the fact that Newton explicitly invokes simplicity in his argument, is it carrying any real ontological or epistemic weight? My answer will be: hardly any. In section 8, I present a different way to interpret Newton’s simplicity-​based rules. It is a pragmatic one that does not assign any ontological or epistemological role to simplicity. Newton invokes simplicity in his argument for the law of gravity when he employs his first, second, and third “Rules for the study of natural philosophy” in the proof of gravity. The first rule (“No more causes of natural things should be admitted than are both true and sufficient to explain their phenomena”), Newton defends by saying that “nature is simple and does not indulge in the luxury of superfluous causes.” The second rule (“Therefore, the causes assigned to natural effects of the same kind must be, so far as possible, the same”), Newton regards as following from his simplicity-​ based Rule 1. The third rule (“Those qualities of bodies that cannot be intended and remitted and that belong to all bodies on which experiments can be made should be taken as qualities of all bodies universally”), Newton defends by saying “nature is always simple and ever consonant with itself.” There is a fourth rule that Newton invokes in his argument for gravity that is not defended by appeal to simplicity, or in any way, for that matter. (Rule 4: “In experimental philosophy propositions gathered from phenomena by induction should be considered either exactly or very nearly true notwithstanding any contrary hypotheses, until yet other phenomena make such propositions either more exact or liable to exceptions.”) However, in effect, what Newton is

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saying in Rule 4 is that if you have followed the simplicity-​ based inductive Rule 3 (and I  would add, the simplicity-​ based causal Rules 1 and 2), then the satisfaction of these rules justifies your claiming the truth or approximate truth of the causal law you have inferred, until new phenomena are discovered that can change the picture. So, even here simplicity seems to play a role in determining whether you are justified in claiming truth for your causal-​inductive law. My question is this: When Newton uses these simplicity-​ based rules in arguing for his law of gravity, do they in fact carry much, if any, weight? At the beginning of Book 3 of the Principia, after stating these rules, Newton introduces a set of six “Phenomena.” These are facts pertaining to the motions of the known planets and their moons that Newton takes to have been established by astronomical observations. They claim, in effect, that all the known planets and their moons obey Kepler’s second and third laws of motion: in their orbits a line drawn to them from the orbited body sweeps out equal areas in equal times, and the square of their periods of revolution is proportional to the cube of their distances from the orbited body. Newton follows the six “Phenomena” with a set of what he calls “propositions” (or “theorems”) that he derives from the “Phenomena,” his three laws of motion in Book 1, and theorems that follow from the latter. The first, second, and third of the propositions in Book 3 pertain to the forces operating on the moons of Jupiter and Saturn, on the known planets, and on our moon:  they are all central forces (produced by a central body about which they rotate), and they are all inverse-​square forces. Proposition 4 says: “the moon gravitates toward the earth and by the force of gravity is always drawn back from rectilinear motion and kept in its orbit.” Proposition 5 makes a corresponding claim

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for the satellites of Jupiter and Saturn (with respect to Jupiter and Saturn) and for the planets (with respect to the sun). Proposition 6 asserts that all bodies gravitate toward each of the planets and that at any distance that a body is from a planet, the weight (or “heaviness”) of that body toward the planet is proportional to the mass of the body. Proposition 7 says: “Gravity exists in all bodies universally and is proportional to the quantity of matter [mass] in each.” Proposition 7, together with the earlier derived idea that the force is an inverse-​square one, gives us Newton’s law of gravity. Where does Newton invoke the simplicity-​based rules in his argument for universal gravity? Not at all in his argument for the first three propositions, which claim that the forces acting to keep the moons of Saturn and Jupiter and the planets in their orbits are central inverse-​square forces. This proposition he derives, without appeal to his simplicity rules, from the “Phenomena” he cites at the beginning of Book 3 and from theorems he has proved in Book 1, using his three laws of motion. The simplicity-​based rules (at least the first and second) are invoked for the first time in his argument in the discussion of proposition 4. Let’s look at this. Here, Newton wants to show not simply that the force keeping our moon in its orbit about the earth and the force causing unsupported bodies near the earth to fall toward the earth are both central inverse-​square forces but that they are the same force. There is one force here, not two—​i.e., the force in both cases is governed by the same law. This he argues for by introducing empirically determined measurements of the mean distance of our moon from the earth, the circumference of the earth, and the mean time the moon takes to make one revolution. From these he calculates the acceleration the moon would have near the earth if it were deprived of its

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inertial motion and fell toward the earth. (Newton calculates this to be 15 1/​2 Paris feet; one Paris foot is 0.9383 feet.) The magnitude of this acceleration is exactly the same as that of bodies near the earth falling toward the earth. From the fact that the magnitudes of the accelerations produced by these two forces are the same, and since he has already shown that the forces are both central, inverse-​square, and directed toward the center of the earth, he concludes that “the force by which the moon is kept in its orbit . . . is that very force which we generally call gravity.” This is, or should be, enough to convince us empirically that the forces are identical. To be sure, in reaching the “one force, not two” conclusion, Newton explicitly cites the simplicity-​based Rules 1 and 2. But if simplicity were providing any real basis for the inference to the same force, why doesn’t he invoke it earlier, before he gets to the moon argument? Using Rule 2 (“the causes assigned to natural effects of the same kind must be, so far as possible, the same”), why, in propositions 1, 2, and 3, doesn’t he argue from the fact that the forces operating on the known planets and their satellites keeping them in their orbits are central inverse-​square forces to the (simple) conclusion that the same force (“the same cause”) is operating in all these cases? After all, the effects of these forces that he notes in the “Phenomena” are the same (effects satisfying Kepler’s second and third laws). If simplicity is capable of doing genuine epistemic work, why wait until the moon argument, in proposition 4, to invoke it? Using his Rule 2, wouldn’t it be sufficient to argue from the fact that the observed Keplerian motions of the planets and their satellites are the same to the conclusion that there is one force producing these effects, not many? In fact, Rule 2 mandates that he should do so. It does not say that (in accordance with simplicity) from effects of the

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same kind, you may infer the same cause. It tells you something you must do, “so far as possible.” Newton appears to violate this rule, or at least to ignore it, in his discussions of propositions 1, 2, and 3, since here he assigns causes (viz. central inverse-​square forces) to effects of the same kind (effects described in his “Phenomena”) without assigning the same cause (universal gravity). Perhaps he thought that the observed effects in question described in propositions 1, 2, and 3 were not yet sufficient to invoke Rule 2 (to use Newton’s expression in Rule 2, it was not yet “possible” to make the inference). He needed more effects, and ones that are even more convincing, particularly the effects involving the moon’s acceleration toward the earth and the acceleration of falling bodies near the earth. Why are the latter effects more convincing? The answer has nothing to do with simplicity. The answer has to do with empirically determining a critically important new effect: the magnitude of the acceleration produced by the force exerted on the moon by the earth. Newton writes: For if gravity [on the earth] were different from this force [on the moon] then bodies making for the earth by both forces acting together would descend twice as fast and in the space of one second would by falling describe 30 1/​6 Paris feet, entirely contrary to experience.14

The latter empirical defense is important to Newton because it shows that if the forces acting on such bodies were different 14.  Victor Di Fate stresses this in his excellent chapter, “Achinstein’s Newtonian Empiricism,” in Philosophy of Science Matters: The Philosophy of Peter Achinstein, ed. Gregory J. Morgan (New York: Oxford University Press, 2011), 44–​58.

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forces, then bodies falling toward the earth would fall with a different acceleration than observed bodies do. More generally, if there are, among the observed common effects, some that would be otherwise if the causes were different ones, then at least some of the observed effects would be “contrary to experience.” But then what is driving the inference to one cause rather than several different ones is not the simplicity of one cause rather than many but the set of observed common effects, particularly those of the kind just noted. It is not that Newton is arguing for one force here because one force is simpler than two. In this passage, he is arguing for the existence of one force rather than two on the grounds that if there were two, then the combined accelerative effects of these forces would be incompatible with what is observed.

6 .  S I M P L I C I T Y A N D N E W T O N ’ S PROPOSITIONS 5 AND 6 Newton also invokes one or more of his rules in his discussion of propositions 5 and 6. (Proposition 7 makes no reference to the rules.) Proposition 5 claims that the moons of Jupiter gravitate toward Jupiter, the moons of Saturn gravitate toward Saturn, and the known planets gravitate toward the sun, and by the force of their gravity they are always drawn back from rectilinear motions and kept in curvilinear orbits. He defends this claim by saying that the observed motions of these bodies are phenomena of the same kind as the revolution of the moon about the earth, and therefore (by Rule 2) depend on causes of the same kind, especially since it has been proved that the forces on which those revolutions depend are directed toward

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the centers of Jupiter, Saturn, and the sun and decrease according to the same ratio and law (in receding from Jupiter, Saturn, and the sun) as the force of gravity (in receding from the earth).15

And in a Scholium at the end of his discussion of proposition 5, he writes: Hitherto we have called “centripetal” that force by which celestial bodies are kept in their orbits. It is now established that this force is gravity, and therefore we shall call it gravity from now on. For the cause of the centripetal force by which the moon is kept in its orbit ought to be extended to all the planets, by Rules 1, 2, and 4.

In these two passages from the discussion of proposition 5, Newton appeals to the simplicity-​based Rule 2 (in the first and second passage) and to the simplicity-​based Rule 1 and to Rule 4 (in the second passage), which is indirectly simplicity based. So, is simplicity driving these inferences? This is a tougher question. In both passages he refers to his previous discussion in the moon argument, in which he concluded that the force keeping the moon in its orbit is the very same force as that producing accelerations of bodies near the earth. Now, in defense of the claim that there is a single force keeping the planets in their orbits around the sun and the moons of Jupiter and Saturn in their orbits around 15. Here, Newton speaks of “causes of the same kind,” while in Rule 2 he speaks of causes as being “the same.” It is clear that when he uses the former expression, he means the latter. From observed motions of the same kind we are to infer the same cause. In this case, we are to infer that it is the same gravitational force operating on each of the planets, not different forces that obey different laws.

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these planets—​viz. (universal) gravity—​he appeals to the fact that certain observed effects of this putative force are the same (Keplerian motions), and to the fact that the observed rate of accelerations of bodies falling toward the earth is the same as that of the moon falling toward the earth. It looks like there is a very big leap here from what is observed to the claim that there is one force of gravity operating. After all, although he has calculations of accelerations in the moon argument, he has no such calculations in the case of the moons of Jupiter and Saturn toward these planets, and of the planets with respect to the sun. So, you might say, Newton needs help here from his simplicity-​based Rules 1 and 2.  Given that he does infer a cause in each case (an inverse-​square force of attraction), from the fact that the effects observed in all these cases are “of the same kind,” in virtue of his claim (in the discussion of Rule 1) that “nature is simple and does not indulge in the luxury of superfluous causes,” and in virtue of Rule 2, he must infer that the cause is the same. He needs to invoke Rules 1 and 2 because the observed effects by themselves aren’t sufficient to justify such an inference. They may be sufficient to justify an inference to an inverse-​square force in each case, but not to the claim that there is one force operating, rather than many. For that you need simplicity, or so it might be thought. But if this is what is really going on, then, as I asked before, why not invoke Rules 1 and 2 before he embarks on the moon argument? Why not say that since “nature is simple and does not indulge in the luxury of superfluous causes,” and since the observed Keplerian motions of the planets and their moons are “of the same kind,” and since I have assigned a cause in each case (viz. an inverse-​square central force), in

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accordance with Rule 2, I  must conclude that there is one force here, not many? This, of course, he does not do. He invokes Rules 1 and 2 only when he has what he takes to be enough of the right kind of effects to do so. So, we have a dilemma. Either Newton, at some point, has effects of the right kind to make the inference (ones that show empirically that there are not different forces acting, as in the moon argument) or he doesn’t. If he does, then simplicity becomes irrelevant. If he doesn’t, then why does he wait to appeal to simplicity? Just invoke simplicity as soon as you get some common effects and make your inference to one cause. Newton doesn’t do that, either, presumably because he doesn’t yet have enough of the right kind of effects. In either case, it is the presence or absence of the right kind of observed effects that is driving or preventing the inference. If Newton does not have the right kind of observed effects to make the inference that the same force is operating in all these cases, then we should say: “Sir Isaac, find them! Don’t substitute simplicity for evidence.” The same applies to his simplicity-​based Rule 3, which he invokes in corollary 2 of proposition 6.  Proposition 6 asserts: “All bodies gravitate toward each of the planets, and at any given distance from the center of any one planet the weight of any body whatever is proportional to the quantity of matter [mass] which the body contains.” Corollary 6 states:  “All bodies universally that are on or near the earth are heavy [or gravitate] toward the earth, and the weights of all bodies that are equally distant from the center of the earth are as the quantities of matter [mass] in them. This is a quality of all bodies on which experiments can be performed and therefore by Rule 3 is to be affirmed of all bodies universally.” (This is the first time Newton actually invokes Rule 3.)

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One of the most important parts of proposition 6 and of corollary 3 is the claim that the weight of any body is proportional to its mass. This Newton defends by experiments he performed on pendulums made of different materials but with bobs of the same weight. There is no mention of any of the rules here, but these experiments presumably allow Newton to infer at least the second clause in corollary 6, viz. that the weights of all bodies equally distant from the center of the earth are proportional to the masses of the bodies. Similarly, in extending this result to the planets and their moons, Newton proceeds by giving empirical reasons for this conclusion, not appeals to simplicity. For example, Further, that the weights of Jupiter and its satellites toward the sun are proportional to the quantities of their matter is evident from the extremely regular motion of the satellites, according to Book I, Prop.  65, Cor. 3.  For if some of these were more strongly attracted toward the sun in proportion to the quantity of the matter than the rest, the motions of the satellites (according to Book I, Prop. 65, Cor. 2) would be perturbed by that inequality of attractions [which does not happen].

Newton repeats the same argument for the satellites of Saturn. It is only in corollary 2 of proposition 6 that Newton appeals explicitly to his simplicity-​based inductive Rule 3, when he generalizes this idea to all bodies. But why does he wait so long to do so? If Rule 3 is capable of doing any work, then why not invoke it right after his experimental results with pendulums on the earth? Presumably, the reason is that he needs more experimental or observational results, particularly pertaining to the motions of the planets and their moons, to make the inference justified. But then it is those results that are really driving the inference, not simplicity. If

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it were simplicity, then he could have stopped after the pendulum experiments and made the bold inference about all bodies. Newton reaches proposition 7, which asserts that “gravity exists in all bodies universally and is proportional to the quantity of matter [mass] in each.” This, together with previously proved propositions about the inverse-​square nature of the force required to keep the planets and their satellites in their orbits, where the latter is generalized to all bodies, yields Newton’s law of gravity. The forces involved all obey the same law, which relates the magnitude of the force to the masses of the bodies and to the inverse-​square distance between them. He argues, in effect, that since all the bodies in question are subject to the same force law, there is one force operating, not many. The latter is true, not because one force is simpler than many but because he has shown, or claims that he has, that the law holds universally. In his argument for proposition 7, there is no mention of the simplicity-​based rules at all. I conclude that even though Newton on several occasions invokes simplicity or, rather, simplicity-​based rules, in his complex argument for the law of gravity, this is doing no real epistemic work. What is doing the epistemic work are his appeals to results of experiments and observations—​what Newton calls the “Phenomena”—​and his calculations from these, together with theorems that follow from his laws of motion.

7 .   T H R E E O B J E C T I O N S Objection 1:  Induction and Simplicity. Even if simplicity is doing no real work in his argument for one cause rather than many, simplicity is important in his grand generalization to

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gravity “in all bodies universally” in proposition 7.  For this generalization he needs his inductive Rule 3, even though he does not mention it. How else could he make the generalization? And Rule 3 Newton explicitly justifies by saying that “nature is always simple and ever consonant with itself.” Objection 2:  Appeal to Alternative Hypotheses. Given the experimental and observational evidence Newton invokes, it could be the case that there are several forces operating whose resultant is what Newton calls the gravitational force. Or, it could be that even if Newton’s law of gravity holds in our solar system, it doesn’t operate beyond that. The reason Newton chooses the possibility he does is that it is the simplest one. Objection 3: Newton is speculating. If what I have said in the previous section is right, and if in fact Newton does not have enough experimental evidence to justify an inference from the phenomena to his law of gravity, then Newton is speculating. He is introducing “hypotheses” without being able to “deduce them from the phenomena.” If so, this goes against what Newton himself claims. Although, he admits, he cannot deduce the cause of gravity from the phenomena, he claims that he can deduce the law of gravity. It is not a speculation.16

My reply to objection 1 is to agree that Newton is making an inductive argument here, but to question whether any such argument is to be justified by appeal to the simplicity of nature, or to the general epistemic power of simplicity. Indeed, in the next section I offer a pragmatic interpretation of Newton’s rules that avoids treating them as rules 16. More exactly, the objection is that it is a speculation in which the latter is understood in terms of ES-​evidence or potential evidence. It is not a speculation only in the “subjective evidence” sense, since Newton did believe that the facts in question were veridical evidence for his law. (See ­chapter 1, section 6, for a discussion of these different senses.)

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based on the assumption that nature is simple, or that simplicity provides an epistemic basis for believing in the truth or empirical adequacy of a theory or hypothesis. Elsewhere I have argued for the claim that inductions are to be defended “locally” by appeal to the particular facts cited (e.g., by appeal to Newton’s “Phenomena,” to his laws of motion, and to propositions derivable from these), rather than by appeal to general claims about the “consonance” of the universe or about the validity in general of inductive arguments.17 My reply to objection 2 is to repeat Newton’s own reply to objections of this sort in his Rule 4 and the brief discussion of it, which I quoted in section 1: In experimental philosophy, propositions gathered from phenomena by induction should be considered either exactly or very nearly true notwithstanding any contrary hypotheses, until yet other phenomena make such propositions either more exact or liable to exceptions. This rule should be followed so that argument based on induction may not be nullified by hypotheses.

Newton is saying that if you have made an induction from the phenomena, as he claims he has with the law of gravity, then the fact that you can imagine a contrary hypothesis does not count at all against the induction. Of course, if 17.  Achinstein, Evidence and Method, chap.  3. I  don’t claim originality for this idea, since it was expressed in the nineteenth century by William Whewell (in his critique of Newton’s rules), and much more recently in excellent papers by John Norton (“A Little Survey of Induction,” in Scientific Evidence, ed. Peter Achinstein [Baltimore: Johns Hopkins University Press, 2005], 9–​34), and by Di Fate (“Achinstein’s Newtonian Empiricism,” in Philosophy of Science Matters, The Philosophy of Peter Achinstein,  44–​58).

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new phenomena are discovered, the situation can change. Perhaps your inductive conclusion will need to be modified or even rejected; and, if that happens, perhaps new phenomena will be discovered on the basis of which a contrary hypothesis can be defended. But if no such phenomena are available, the existence of alternative possibilities casts no doubt on your inductive conclusion. Newton is not saying here that if two hypotheses explain the phenomena, choose the simplest one. He is saying that you should regard as true, or nearly so, a proposition that is properly induced from the phenomena, even if it is incompatible with a contrary hypothesis, so long as the contrary one has not been induced from the phenomena. I have defended this type of response in section 2. Objection 3 is the most important of these objections. My reply is to accept it! I  accept the idea that Newton is speculating at certain points in the argument. For example, although he has empirical calculations of how fast our moon would accelerate toward the earth if it suddenly lost its inertial motion, he has no calculations of how fast the moons of Jupiter and Saturn would accelerate toward those planets, or how fast the planets would accelerate toward the sun if their inertial motions were to cease. Even without such calculations, he writes: For the revolutions of the circumjovial planets [the moons of Jupiter] about Jupiter, of the circumsaturnian planets about Saturn, and of Mercury and Venus about the sun are phenomena of the same kind as the revolution of the moon about the earth, and therefore (by [simplicity-​based] Rule 2) depend on causes of the same kind, especially since it has been proved that the forces on which those revolutions depend are . . . [central inverse-​square forces].

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From his calculations of the acceleration of our moon toward the earth, Newton, invoking his simplicity-​based Rule 2, infers that calculations on the accelerative rates of other moons and other planets would show, e.g., that if a moon of Jupiter were to fall toward Jupiter, at a point near Jupiter it would fall at the same rate of acceleration as any unsupported body near Jupiter would fall toward Jupiter. Just as happens with our moon, he is inferring that there is one force here, not two. Now, a critic might say to Newton: “Sir Isaac, I need more empirical argument here. You are inferring something about the moons of Jupiter from information about our moon. Indeed, you are making a very grand generalization about all the planets that is based on calculations of our moon. Let’s concede that you have shown that the forces involved in all these cases are central inverse-​square forces. But you haven’t yet shown that they are the same force; they could be different forces that combine to produce twice the effect of either. You show they are not different forces in the case of our moon. But unless you can produce such calculations for other bodies as well, you are just speculating. And my reason for saying you are speculating, albeit grandly, is that at this point in your argument you invoke your dogmas about simplicity—​that nature is simple and does not indulge in the luxury of superfluous causes, and that nature is simple and ever consonant with itself. You don’t have sufficient experimental evidence to believe them. If you had, you would give it.” I am inclined to agree with such a critic. Newton’s move here, and one later when he generalizes his full law to all bodies in the universe, should, I  think, be viewed as bold

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speculations.18 But that, I  would claim, is not necessarily a criticism of them, viewed as speculations. Assuming they are, what Newton should have said is that he has evidence sufficient to believe that the forces responsible for other lunar, planetary, and terrestrial motions involving “falling” bodies are all central inverse-​square forces. But that they are all the same force, and that this same force operates throughout the universe is not yet established. Yes, it is a simpler hypoth­ esis than one that postulates many different forces. That it is simpler can well be a pragmatic reason for pursuing it. But that it is simpler is not evidence that the universal law of gravity is true. If we take this stand, then what Newton should have done is what he did in his defense of his particle theory of light in the Opticks. There, he introduces his particle theory as a “query” rather than as a proposition “deduced from the phenomena.” He does so because although he can give a few empirical reasons why (he thinks) the particle theory is better than the wave theory, he cannot provide experimental evidence for it. He can only suggest it as a serious possibility. In the case of gravity, although he could provide evidence for parts of his law, he could not provide sufficient evidence to believe that there is just one force of gravity and that it operates throughout the universe. He presents some empirical reasons for believing these things, but these don’t rise to the standards required for evidence sufficient to believe. Yes, it is a speculation, perhaps one that only a genius like Newton could make. But, as was the case with Maxwell’s 18. In a sense of “speculation” defined using ES-​or potential evidence; see note 16, this chapter.

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molecular speculations in kinetic theory, it is a speculation for which some empirical reasons are given, and which deserves the highest marks from various perspectives, including its unification of celestial and terrestrial phenomena, its successful predictions, its mathematical rigor, and its enormous influence.

8 .   A   P R A G M AT I C I N T E R P R E TAT I O N OF N E W TON ’ S  RU L E S Finally, I return to Newton’s rules and offer a pragmatic interpretation of them that avoids treating them as rules based on the assumption that nature is simple, or that simplicity provides an epistemic basis for believing in the truth or empirical adequacy of a theory. It is not my claim that Newton himself understood the rules in this way. But I believe that, understood in the manner I will suggest, the rules are reasonable ones and reflect many, though by no means all, of Newton’s ideas. I will understand the rules not as rules of inference but as rules of strategy that tell you how to go about defending a causal law.19 Newton’s stated aim in the Principia is to “discover the forces of nature from the phenomena of motions and then to demonstrate the other phenomena from these forces.” This aim has two parts, first to discover the forces from observed phenomena, and second to show how these forces can be used to explain other phenomena. The first part Newton calls “analysis,” the second, “synthesis.” The rules are rules of strategy for accomplishing the first part. Before 19. See Achinstein, Evidence and Method,  66–​78.

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saying how the rules are pragmatic, here is how I  suggest interpreting (or re-​interpreting) them. 1.  Given that your aim is to establish a general causal law on the basis of observed phenomena, you will need to introduce a cause or causes of those phenomena. When you do so, try to determine empirically whether the cause or causes exist (e.g., whether there are centripetal forces exerted by the sun on the planets and the earth on the moon); whether these causes are different or the same (e.g., whether these centripetal forces are really one force or different ones); and whether these causes are sufficient to explain the phenomena or whether others are needed as well. This strategic rule does not tell you what cause(s) to infer; that is an empirical matter. It does not tell you to infer the simplest cause because nature is simple. It just tells you to make sure that you don’t infer causes that play no role in producing the phenomena. If you violate the latter, then it is not that you are violating the simplicity of nature but, rather, that you are introducing inoperative causes. 2.  When you introduce a cause or causes for a given phenomenon, try (“so far as possible”) to assign those causes to other phenomena of the same kind. This means trying to determine empirically whether such an assignment is warranted by those phenomena. For example, if it has been empirically established that the fact that the acceleration of unsupported bodies toward the earth is caused by an inverse-​ square force of attraction exerted by the earth, try to determine empirically how our moon orbiting the earth would accelerate toward the earth if it suddenly lost its inertial motion—​in order to see whether the same cause could be assigned to both motions. To do this, we do not assume that

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nature is simple, or that simplicity is a sign of truth, even if we agree that the hypothesis that one force is acting here is simpler than the hypothesis that the forces acting here are not the same. 3.  Given that you are trying to establish a law governing the cause(s) introduced, you will need to generalize. If you have empirically established that some causal property holds for all the bodies you have observed, then try to generalize this to all bodies, or if exceptions are discovered, try to generalize to some restricted class of bodies. The generalization you make is to be justified empirically by reference to what sort of bodies, and how many, were selected for observation, what else is known about such bodies, how the observations were made, and so forth. It is not to be justified by assuming that “nature is always simple and ever consonant with itself.” 4.  If you have followed rules 1 to 3 in an empirically defensible way, and have arrived at a causal law, then you may infer that the law is true or approximately true. You are justified in doing so until phenomena are discovered that cast doubt on the law as it stands. Rules 1 to 3 tell you what you should try to do if you want to establish a causal law. Rule 4 tells you that if you have followed rules 1 to 3, and have done so (and not merely tried to do so) in an empirically defensible way, then you are justified in inferring the truth or approximate truth of any law you have arrived at. If you infer a cause of certain phenomena without sufficient empirical argument that the cause exists and does in fact produce the phenomena, or if you have generalized the cause you have inferred to other cases without having

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observed sufficiently many and varied instances, then you are not justified in inferring the law. The fact that you have made a causal inference or an inductive one does not count at all in favor of the truth or probability of your conclusion. Nor does it count that you have tried to make an inference that is empirically warranted. It depends entirely on whether the causal or inductive inference is empirically warranted. The causal-​inductive rules 1 to 3 themselves do not provide an epistemic justification for believing the conclusion. They tell you what general types of inferences you will need to make from the phenomena, but having made those inferences, they don’t tell you whether the particular inferences you have made are epistemically justified. That is a scientific question, not a methodological one. Using my concepts of evidence, that you have followed rules 1 to 3 does not constitute objective (potential, ES-​, or veridical) evidence for your conclusion. But if you have followed rules 1 to 3 in an empirically defensible way, relative to your epistemic situation, then you do have ES-​evidence for the conclusion, and you are justified in believing that you have veridical evidence for it. Whether you do have veridical evidence depends as well on the way the world is. I have spoken of an inference as being “empirically warranted” or “empirically defensible.” How is that to be determined, except by appeal to rules? And if the latter are Newton’s rules, either in my formulation or his, all of this becomes circular. My response is that determining whether inferences are empirically warranted or defensible is an empirical and a local matter, not subject to general a priori causal or inductive rules that tell you what you can or should reasonably infer from what. As John Stuart Mill—​a champion of induction—​noted, whether an inductive inference

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from “all observed As are Bs” to “all As are Bs” is empirically warranted depends on, and varies with, the nature of the As and Bs in question, the size and variety of the sample of observed As, how the sample was selected for observation, and so forth—​all empirical matters. Saying simply that the nature of the As and Bs, and the size, variety, and the method of selection of the sample should be “appropriate” to make the inference is both vague and circular. When we assess Newton’s inference to the claim that the force causing bodies to fall toward the earth is the same force as that which causes the moon to fall toward the earth, we do so by examining the calculations and empirical laws he is using in proposition 4 (the moon argument). Even though Newton himself invokes his simplicity-​based Rules 1 and 2, these are really doing no epistemic work. If they were, as I have argued in sections 5 and 6, he could have used them earlier to reach his conclusion about one gravitational force, which he does not do. What justifies the inference is not simplicity, or simplicity-​ based rules of inference but, rather, empirical considerations of the sort I noted. Newton’s rules, in my formulation, might be criticized as being rather trivial. They say, in effect:  make causal and inductive inferences from observed phenomena, so long as you are empirically justified in doing so. It is a bit like giving the following rule of strategy to a chess player:  checkmate your opponent’s king when you can—​without telling the chess player how to do so. (Indeed, William Whewell, a severe critic of Newton’s rules, but not his physics, invoked this sort of criticism.) I believe Newton would reply, and rightly so, that the rules, even in my formulation, are not so trivial. Newton was concerned to distinguish his methodology from two

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others of which he was very critical. One was Descartes’ rationalist methodology (as expressed, e.g., in his “Rules for the Direction of the Mind”). The other was hypothetico-​ deductivism of a sort practiced by Christiaan Huygens. In response to Descartes’ idea that you defend a law of nature by showing how it follows deductively from a priori intuitions—​ basic self-​evident propositions (such as “all bodies are extended in space”) that cannot be doubted—​Newton replied that it cannot be done:  “The extension of bodies is known to us only through our senses,” not by some a priori “intuition.” In response to the hypothetico-​deductivist idea that it suffices to defend a law, such as the law of gravity, by showing that it explains and predicts observed phenomena (which Newton called “synthesis”), Newton replies that you need to show more. You need to argue empirically from the phenomena that the cause of those phenomena is gravity, and not something else, and that this cause can be generalized to all bodies. (This he called “analysis.”) In what way are these rules pragmatic? They are so in the sense that they tell you what you should try to do if you have a certain end in mind: if you want to defend a causal law, at least one that is not derivable from other established causal laws, then you should try to make a causal inference to the existence of the cause from the observed phenomena, and you should try to generalize this by appealing to a range of other observed cases. Other methods, such as Cartesian rationalism and hypothetico-​deductivism, will not suffice to defend the law in a way that provides a justification for believing it. But in this sense, aren’t Newton’s rules, as he formulated them, pragmatic as well? Don’t they also tell you how to try to defend a causal law? If so what’s the difference?

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The answer is that, in my formulation, the rules are merely pragmatic, while in Newton’s formulation, they are supposed to be epistemic as well. Because Newton believes that nature is simple, and because he bases his Rules 1–​3 on that assumption, he can appeal to the rules themselves as providing a crucial part of the justification for believing the inferred causal law:  it is because “nature is simple and does not indulge in the luxury of superfluous causes” that, from the facts about the moon introduced in the “moon argument,” and from facts about how bodies fall to the earth, Newton can invoke his Rule 2 to infer that the force keeping the moon in its orbit is the same force as that producing falling bodies on the earth. On my interpretation, if you follow the rules above, you are not justified in believing the conclusion you reach—​unless you have followed the rules in an empirically justified way, which the rules themselves don’t tell you how to do. If you follow Newton’s original rules, then, he claims, you are justified in believing the conclusion. In the present formulation of Newton’s rules, simplicity plays no ontological or epistemic role. In using these rules, you do not have to assume that nature is simple or that simpler theories are more likely to be true than complex theories. To be sure, when you introduce causes, you should try to find out whether the causes you introduce are or are not the same. But whether they are or are not the same is not established, or made more likely, by appeal to the fact that one cause is simpler than two, but only by appeal to whether observed effects are or are not the same. When you try to generalize your results in the form of a law, that law is not established or made more likely by appeal to the fact that one general law is simpler than many less general ones, but

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only by appeal to the numbers and kinds of observed cases in which the law holds. You may want your law to be simple for various reasons. One way Newton’s law of gravity is simple is that it unifies both celestial and terrestrial motion: one law suffices, not many different ones. Unification is something physicists love. But that it is simple in this unifying way does not establish or add to its credibility. It establishes or adds to its desirability. Finally, as noted earlier, you may have followed rules 1 to 3 as I have formulated them, and reached a causal-​inductive conclusion without being epistemically justified in believing the conclusion, despite your best efforts. If so, and if you have no other arguments for the conclusion that provide a sufficient epistemic basis either, then that conclusion is a speculation for you (in a sense of speculation understood in terms of ES-​evidence). I  suggest that Newton’s argument can be understood as one that follows the pragmatically formulated rules I propose, even though his argument does not provide a sufficient empirical basis for someone in his epistemic situation to believe the law of gravity in its most general form. What it does do is provide reasons for someone in that epistemic situation to pursue the law, take it seriously, and try to find additional evidence for it—​in short, reasons to try to turn a speculation into an empirically established proposition—​one that is “deduced from phenomena.”

4

✦ HOLISM VS. PARTICULARISM An Evidential Debate (“Find the Ether”)

“EVIDENTIAL HOLISM,” AS I  WILL CALL IT, is the view that individual (“isolated”) hypotheses do not receive evidential support—​that only whole systems or groups of hypotheses do. By contrast, what I  shall call “evidential particularism” is the view that individual (“isolated”) hypotheses can receive evidential support, whether or not they are part of an entire system of hypotheses. These are bare-​boned descriptions of the two positions, and each needs spelling out. This can be done in various ways, yielding different versions of the basic views. Here, I will examine one important version of each. The version of evidential particularism I  explore is advocated by John Stuart Mill.1 By contrast, the version of evidential holism I am interested in is not so clearly attributable to anyone

1.  John Stuart Mill, A System of Logic, Book 3, reprinted in part in Achinstein, Science Rules, 173–​233.

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in particular, but is suggested in the writings of Whewell,2 Duhem,3 and Quine.4 The views I  present here are bold and brassy. Each has important implications for what is to count as evidence for a scientific theory. Both, I  will argue, are (truth-​ relevant) speculations, in the sense I  characterized in ­ chapter  1.5 Their proponents may believe they have evidence for these speculations, but they do not, at least none sufficient to make them reasonable to believe. Even considered as speculations, however, they have their problems. Those supporting each view make various assumptions for which either no argument is offered or one that is very dubious. In place of each of these positions, I  present one that rejects holism completely and defends a type of particularism that is pragmatic and, I think, much richer than that suggested by Mill. Perhaps my version of particularism will still be a speculation. But if it is, I want to claim it is better defended than the versions of holism and particularism I will consider.

1 .   E V I D E N T I A L PA R T I C U L A R I S M : M I L L’ S D E D U C T I V E   M E T H O D In formulating his “deductive method,” Mill makes it clear that he is concerned with situations in which we are trying 2.  Whewell, Philosophy of the Inductive Sciences, chap.  5, reprinted in Achinstein, Science Rules, 150–​67. 3.  Pierre Duhem, The Aim and Structure of Physical Theory (Princeton, NJ: Princeton University Press, 1954, 1982). 4. W. V. Quine, “Two Dogmas of Empiricism,” in his From a Logical Point of View (Cambridge, MA: Harvard University Press, 1953). 5. This is a sense defined in terms of potential or ES-​evidence.

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to understand what he calls “complex phenomena.” These are ones in which not just one cause and a law governing it are involved but various causes are operating, governed by different laws, where these causes combine to produce effects of some type or types. How should one proceed to establish the causes and laws in such cases? Mill’s “deductive method” provides the answer. It consists of three parts, all of which are necessary. The first part contains what Mill calls “inductive” inferences to general types of causes and laws governing them, using his famous “canons” of causal reasoning to do so. For Mill, each type of cause and causal law introduced needs to be defended empirically by causal-​inductive reasoning involving the presence or absence of observed effects, or derived from other causal laws that are so defended. The second part of the method, which Mill calls “ratiocination,” involves combining the various causes and causal laws governing the causes introduced and calculating the consequences that follow deductively from the combination. Among these deductive consequences, it is hoped, will be ones that can be verified by experiment and observation. If they are so verified—​the third part of Mill’s deductive method (“verification”)—​then the entire system of causes and laws employed is inductively and deductively verified, and can be used to explain the complex phenomena that prompted the investigation. Mill’s deductive method is, in essence, a combination of what Newton calls “analysis” and “synthesis.” Analysis consists in making causal and inductive inferences from observed “phenomena” to the causes of these phenomena and the laws governing them (see ­chapters 1 and 3). Synthesis consists in mathematically deriving, and thereby explaining, consequences from this set of causes and laws, among which will be ones that can be tested experimentally, and then testing

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those consequences. Both Mill and Newton distinguish the method they advocate from the “method of hypothesis” or “hypothetico-​deductivism.” As Mill notes, the method of hypothesis omits the first step—​the causal-​inductive argument to each cause and law—​and uses only ratiocination and verification. Advocates of the method of hypothesis claim, while Mill denies, that if ratiocination from a set of unsupported hypotheses leads to experimentally verified consequences, then not only are these verified consequences explained by the set of hypotheses but also they provide evidence for the set of hypotheses used to generate them. How exactly is Mill’s deductive method committed to “evidential particularism”? It is so because for each cause and law introduced it requires a causal-​inductive argument from observed phenomena. (Or else it requires deduction from other laws so inferred.) To be sure, it also requires that testable consequences derived from, and explained by, the combination of causes and laws introduced be empirically verified. But the latter by itself is not sufficient for verification of the system of laws introduced. Each cause and law in that system must be individually established (Mill’s “inductive” step; Newton’s “analysis”). Let me put this more broadly in evidential terms. Suppose we want to obtain evidence for a set of hypotheses H. Mill is operating with a strong sense of “evidence,” one which is such that if e is evidence that h, then e provides a good reason to believe h.6 Moreover, in his discussion of the 6.  Mill speaks of “ascertaining” or “proving,” though he recognizes that this does not produce the certainty of mathematics. For him, it is empirical and probabilistic. Although it is probabilistic, it requires something much stronger than increase in probability (Bayesian B-​evidence).

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“deductive method,” he is concerned with evidence for a set of hypotheses H that will provide a good reason for believing the entire set. In order to do so, we must obtain evidence for each hypothesis in H. Let ei be evidence for the individual hypothesis hi in the set H. Then, on the view I am attributing to Mill, as well as to Newton, there is evidence for the system H if and only if (a) for each hypothesis hi in the system H, there is evidence ei which is not necessarily evidence for the entire system H; and (b) consequences derived from and explained by the system are verified. This is the version of evidential particularism I will consider. A lot depends on how the concept of evidence is itself to be construed. Before turning to this, however, I will construct a version of evidential holism, which is suggested to me by writings of Quine, Duhem, and Whewell. I say “suggested” because these writings do not spell out the doctrine in as complete a manner as I  would like. After formulating this doctrine, in order to bring out a central difference between particularism and holism, I will invoke an example discussed by both Whewell and Mill—​the nineteenth-​century wave theory of light. This will help us to focus on the basic issues.

2 .   E V I D E N T I A L H O L I S M :   D U H E M , QUINE, WHEWELL Quine’s pithy summary of the doctrine is well known: “our statements about the external world face the tribunal of sense experience not individually but only as a corporate body.”7

7. Quine, “Two Dogmas of Empiricism,” 41.

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Duhem, the most famous exponent of the view, summarizes it more expansively: In sum, the physicist can never subject an isolated hypothesis to experimental test, but only a whole group of hypotheses. . . . We have gone a long way from the conception of the experimental method held by persons unfamiliar with its actual functioning. People generally think that each one of the hypotheses employed in physics can be taken in isolation, checked by experiment, and then, when many varied tests have established its validity, given a definitive place in the system of physics. In reality, this is not the case. . . . Physical science is a system that must be taken as a whole.8

A few pages earlier, Duhem explains the doctrine by showing how evidence disconfirms a hypothesis: A physicist decides to demonstrate the inaccuracy of a proposition; in order to deduce from this proposition and institute the experiment which is to show whether the phenomenon is or is not produced, in order to interpret the results of this experiment and establish that the predicted phenomenon is not produced, he does not confine himself to making use of the proposition in question; he makes use also of a whole group of theories accepted by him as beyond dispute. The prediction of the phenomenon, whose nonproduction is to cut off debate, does not derive from the proposition challenged if taken by itself, but from the proposition at issue joined to that whole group of theories; if the predicted phenomenon is not produced, not only is the proposition questioned at fault, but so is the whole theoretical scaffolding used by the physicist. The only thing the experiment teaches us is that among the propositions used to predict the phenomenon and to establish 8. Duhem, Aim and Structure of Physical Theory, 187.

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whether it would be produced, there is at least one error; but where the error lies is just what it does not tell us. The physicist may declare that the error is contained in exactly the proposition he wishes to refute, but is he sure that it is not in another proposition? If he is, he accepts implicitly the accuracy of all the other propositions he has used, and the validity of his conclusion is as great as the validity of his confidence.9

In the first quotation, Duhem formulates the idea that only a theoretical system as a whole is tested, not an isolated proposition within that system. In the second quotation, he spells this out for testing that involves disconfirming evidence. His general view is that you obtain evidence, whether confirming or disconfirming, only for a theoretical system, not for an individual statement within that system. And you obtain such evidence by deriving consequences (“predictions”) from this system and determining by experiment and observation whether these obtain. If they do, then they constitute confirming evidence for the theory as a whole. If they don’t, they constitute disconfirming evidence for the theory as a whole. Unlike Duhem and Quine, William Whewell, whose doctrine of evidence I summarized in ­chapter 1, does not explicitly endorse a holist position. But this, I think, is the most reasonable way to understand his view. For him, some fact or set of facts e is evidence for some H only if H not only explains e but also explains and predicts facts of types different from e (“consilience”), and only if, as H develops over time and new or revised assumptions are made in the light of new observations, the revisions “tend to simplicity and harmony” (“coherence”). Whewell clearly has in mind here a system of hypotheses H, 9. Duhem, Aim and Structure of Physical Theory, 185.

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rather than an individual one. (His two favorite examples are Newtonian mechanics and the wave theory of light.) And his criterion of “coherence” involves groups of hypotheses that “run together” (his phrase) in giving explanations of phenomena. When these phenomena are explained by a theory that is consilient and coherent, they constitute evidence that provides a good reason for believing the theory, or even stronger, evidence that establishes or proves it. Now, let me formulate a general holistic doctrine suggested by these ideas. Suppose we seek to obtain evidence that provides a good reason for believing a set or system of hypotheses H. In order to do so, we need to derive consequences from this set that can be subjected to experimental test. These consequences are ones explained or predicted by H. In general, they are derivable not from just one hypothesis in H but from many, if not all of them, in H—​from the whole system H. These consequences, when confirmed or disconfirmed by experiment and observation, provide evidence sufficiently strong to accept or reject the whole system H, not isolated parts of it. By contrast, suppose we seek to obtain evidence for a single (“isolated”) hypothesis h. How can we do so? On the present holistic view, we can do so only by deriving testable consequences from h and determining by experiment and observation whether they are true. But, the holist insists, in general in order to derive testable consequences from h, you will need to add further assumptions to h—​e.g., laws governing the entities postulated in h, assumptions about the instruments used in testing the consequences, and many others. Therefore, what you are testing by means of these consequences is the entire set of assumptions used to generate them, not any individual assumption in that set.

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Why doesn’t the holist add that if e is evidence for the set H, then e is evidence for each hypothesis in H? The holist doesn’t want to do that because that destroys the holist’s central idea that it is only systems, not individual hypotheses, that receive confirming or disconfirming evidence. Adding the present idea would turn the doctrine into a type of particularism. More important, the holist, at least in my version of him, wants to restrict the idea of evidence for (or against) a theory to tested consequences derivable from the theory itself. But adding the idea that if e is evidence for a system H and if H contains, or otherwise entails, a hypothesis h, then e is evidence for h, is to accept what Hempel called the “special consequence condition.” And this is a considerable departure from the holist’s idea of evidence for h as something derivable from h itself. (e could be derivable from h, and h could entail h′, without its being the case that e is derivable from h′).

3 .  T H E WAV E T H E O R Y O F   L I G H T AND THE LUMINIFEROUS ETHER The debate between holists and particularists is not a purely philosophical one bereft of practical consequences for scientific activity. On the contrary, it has important consequences for what does and does not need to be tested. To show this, let me turn to a prominent example in mid-​nineteenth-​century physics debated by Mill, the particularist, and Whewell, the holist, viz. the wave theory of light.10 10. For a summary of a few basic assumptions of this theory, see c­ hapter 1, section 1.

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Whewell defends the wave theory of light against the particle theory on the grounds that it is “consilient” (it explains and successfully predicts a range of different optical phenomena, not just ones such as diffraction that were initially used in reviving the Huygensian wave theory at the beginning of the nineteenth century).11 Furthermore, Whewell claims, it is “coherent” (as the theory changes over time to accommodate new phenomena, the revisions “tend to simplicity and harmony” and avoidance of ad hoc hypotheses). By contrast, Mill argues that Whewell’s criteria are not sufficient to establish the wave theory, or even to make it probable. He focuses on one central supposition of this theory, viz. that by analogy with water in the case of water waves, and with air in the case of sound, there exists a substance, the ether, that is waving. Mill writes: At present, however, this supposition cannot be looked upon as more than a conjecture; the existence of the ether still rests on the possibility of deducing from its assumed laws a considerable number of actual phenomena; and this evidence I cannot regard as conclusive, because we cannot have, in the case of such an hypothesis, the assurance that if the hypothesis be false it must lead to results at variance with the true facts. Accordingly, most thinkers of any degree of sobriety allow, that an hypothesis of this kind is not to be received as probably true because it accounts for all the known phenomena, since this is a condition sometimes fulfilled tolerably well by two conflicting hypotheses, while there are probably many others which are equally possible, but which, for want of anything analogous in our experience, our minds

11.  For a fuller discussion of the Mill-​Whewell debate and the wave vs. particle theories, see Achinstein, Particles and Waves.

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are unfitted to conceive. But it seems to be thought that an hypothesis of the sort in question is entitled to a more favourable reception, if, besides accounting for all the facts previously known, it has led to the anticipation and prediction of others which experience afterwards verified; as the undulatory [wave] theory of light led to the prediction, subsequently realized by experiment, that two luminous rays might meet each other in such a manner as to produce darkness [destructive interference]. Such predictions and their fulfillment are, indeed, well calculated to impress the uninformed. . . . If the laws of the propagation of light accord with those of the vibrations of an elastic fluid [the hypothetical ether] in as many respects as is necessary to make the hypoth­ esis a correct expression of all or most of the phenomena known at the time, it is nothing strange that they should accord with each other in one respect more. Though twenty such coincidences should occur, they would not prove the reality of the undulatory ether.12

The assumption of the existence of light-​bearing (“luminiferous”) ether is a central one in the wave theory. What Whewell is saying, and Mill is denying, is that this assumption by itself is not subject to experimental test. Only the entire wave theory is. If that theory as a whole—​ether and all—​ can successfully explain and predict different phenomena and satisfy “coherence,” then the theory as a whole can be regarded as proved or at least highly probable. There is no such thing as proving or showing probable a particular assumption within that theory. What Mill, the particularist, is 12. In Achinstein, Science Rules, 223. Earlier (­chapter 3, section 2) I focused on Mill’s claim that there are probably many other conflicting theories that are “equally possible.” My focus now is on his particularist claim that to empirically establish the theory you must establish each assumption in it.

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saying is that you can’t regard the theory as a whole as proved or shown to be probable without showing that each assumption within that theory is proved or probable. For Mill, the wave theory is a speculation. Moreover, he is saying, you cannot show that the theory as a whole is proved or probable, and hence not a mere speculation, simply by showing that it satisfies “consilience” and “coherence.” Mill’s particularism, then, leads him to say that in order to prove the wave theory, or to show that it is probable, you need to show that the ether exists. For Mill, in mid-​nineteenth century, there is serious scientific work to be done in establishing the wave theory or showing that it is probable: Find the ether. For Whewell, in mid-​nineteenth century, there is no such work. The wave theory is established. Indeed, Whewell claims this, even on the basis of “consilience” alone. Citing his two favorite theories, Newton’s theory of gravity and the wave theory of light, Whewell writes: The theory of universal gravitation and of the undulatory theory of light, are, indeed, full of examples of this Consilience of Inductions.  .  .  . No example can be pointed out, in the whole history of science, so far as I am aware, in which this Consilience of Inductions has given testimony in favour of an hypothesis afterwards discovered to be false.13

In short, Mill’s particularism and Whewell’s holism generate very different conceptions of what the wave theorist can and must do to establish the theory or show it to be probable. 13. In Achinstein, Science Rules, 161–​62.

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4 .  W H AT L I E S B E H I N D T H E D E B AT E : DIFFERENT VIEWS AB OU T EVIDENCE On the particularist view, you can have evidence for individual hypotheses, and you can have evidence for a set of hypotheses, but only if you have evidence for each hypoth­ esis in the set. On the holist view, you can have evidence for the set but not evidence for any particular hypothesis in the set. So the question is:  What sense of “evidence” is being employed in each view? Both the holist and the particularist, of the sorts I  am considering, invoke a concept of explanation in their views of evidence. For both, e is evidence for a set of hypotheses H only if there is some kind of explanatory connection between H and e. Now, one way—​perhaps the only way—​to generate a holistic doctrine is to understand “explains” in a deductive way, according to which a set of hypotheses H potentially explain e only if H deductively entails e. (On this view, for H to correctly explain e, the hypotheses in H must be true.) And if H potentially explains e, then e is evidence that H. (In Whewell’s more sophisticated version, if H deductively explains e, then e is evidence that H, provided that the set H is “consilient” and “coherent.”) Now, the present holist, who understands “explains” in a deductive way, wants to deal with a set of hypotheses H in which each hypothesis is necessary to derive the results described in e. He doesn’t want to say that if H explains e, then so does H conjoined with any arbitrary statement H′. Yet if H entails e, then so does the conjunction H & H′. Indeed, in Hempel’s “deductive-​nomological” model of explanation, it is required that for a set of hypotheses to potentially explain

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some phenomena e, each member of the set must be necessary for the deduction. So, on the corresponding deductive-​ explanatory view of evidence, e is evidence for the set H only if all the hypotheses in H together deductively entail e and no subset in H does. In general, however, even when deductively irrelevant hypotheses have been pruned from the set H, many hypotheses will remain, each of which is necessary to derive e. On the present view, then, we generate evidential holism, since e is derivable only from the entire set, not from any individual hypothesis or subset of them. One problem here is that the deductive account of explanation, whether Hempel’s or Whewell’s more demanding one (requiring “consilience” and “coherence”), is subject to serious counterexamples. These show that the requirements for an explanation proposed by these accounts are neither necessary nor sufficient. (See section 6 below, for examples.) A potentially more serious problem pertains to the central idea of defining “evidence” in such a way that if the set of hypotheses H potentially explains some established phenomena e, then e is evidence that H. Another way of putting this central idea is that if H, if true, correctly explains e, then e is evidence that H. The problem, which arises whether or not “explains” is understood in a deductive way, is how to respond to the “competing explanation” (or “competing hypoth­ esis”) objection noted in c­ hapter 3, section 2. Suppose that H, if true, would correctly explain e. In general, the objection goes, there are competing sets of hypotheses which, if they were true, would correctly explain e. Yet it would seem absurd to say that e is evidence for each of these competing sets. Whether the objection is valid or not depends on what else can be said about the original and alternative explanations. When Newton confronts this objection in his discussion of

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Rule 4, his reply is that if your theory has proper causal and inductive support (that accords with his Rules 1–​3), and if the competing theory has no such support, then the fact that there is a competing theory does not, in his terms, “nullify” the causal and inductive support for the original. Whewell, as Mill notes, omits this causal-​inductive requirement. So, Whewell is subject to the “competing explanation” objection in this form: if your theory H, if true, correctly explains e, then, if there is a competitor H′ that, if true, would also correctly explain e, then e cannot be evidence that h, at least not evidence sufficient to believe h. To this, Whewell might respond that when, in addition to deductive explanation, we require consilience and coherence, we rule out competing hypotheses. That is, if H is a set of hypotheses, and if these hypotheses together entail a set of observational claims e, and if H is consilient and coherent, then if the claims in e are true, the fact that they are is evidence that H. This will be so, since under these conditions there will be no other competing set of hypotheses with the same advantages. To this we might respond:  How does Whewell know this? He doesn’t even give an argument! Perhaps Whewell didn’t know about, or live long enough to know about, competing versions of the nineteenth-​century wave theory, and particularly versions of the ether, that were championed. One invokes a continuous ether, another an ether composed of discrete particles. In an article on the ether, Maxwell says that it might be thought that the fact that the ether is elastic and compressible is a proof that the medium [the ether] is composed of separate parts having void spaces between them. But [Maxwell

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continues] there is nothing inconsistent with experience in supposing elasticity or compressibility to be properties of every portion, however small, into which the medium can be conceived to be divided, in which case the medium would be strictly continuous.14

These versions of the wave theory, though conflicting, explain lots of different optical phenomena (including rectilinear propagation, reflection, refraction, diffraction, interference, etc.) known during the nineteenth century. Indeed, there are at least three versions of the wave theory:  one postulates a continuous ether, one postulates a discontinuous ether, and one postulates an ether but makes no claim about continuity or discontinuity. Now, these three versions of the wave theory are all committed to the idea that the ether, whether continuous or discontinuous, is a substance subject to mechanical, Newtonian laws. They are compatible with the optical phenomena known during this period (before the Michaelson-​Morley experiments in 1887). And they are reasonably consilient and coherent in their explanations of those optical phenomena. Are we to conclude that, although two of the three are incompatible with each other, the known optical phenomena constitute evidence for all three? Here, I think, we confront a damaging form of Mill’s competing-​hypothesis objection. (“Damaging forms” of the objection are ones applied to cases in which we have two or more competing theories, each compatible with the known phenomena, where all anyone defending one of

14. Niven, ed., The Scientific Papers of James Clerk Maxwell, 2:774. Maxwell himself favored the discrete version. So did Kelvin (Kargon and Achinstein, Kelvin’s Baltimore Lectures, 10ff.). Green and Cauchy favored homogeneity.

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these competitors can say is that his theory, if true, correctly explains the phenomena, even adding that his theory is consilient and coherent.) If we seek to employ an explanatory concept of evidence, avoid both the competing-​hypothesis objection (in damaging forms), as well as the problems facing a deductive account of explanation, and try to settle the holism–​particularism debate, we need to look elsewhere. I  shall do so by using one of the explanatory concepts of evidence introduced in ­chapter  1, viz. (potential) A-​evidence,15 which I  defined as follows: e is (potential) A-​evidence that h if and only if it is more probable than not that, given e, there is an explanatory connection between h and e (p(E(h,e)/​e) > ½); e is true; e does not entail h.

This definition avoids the competing hypothesis objection, since if p(E(h,e)/​e) > ½, then for any competing hypothesis h′, p(E(h′,e)/​e) < ½. This definition, I  will show, employs a concept of correct explanation that avoids the standard counterexamples to deductive accounts of correct explanation. The important question is whether the definition can be used to support holism, particularism, or neither. The answer must await section 8. The definition above appeals to the idea of an explanatory connection. As indicated in c­ hapter  1, there is such a connection between h and e if and only if h correctly explains

15.  This is the most basic of the A-​ concepts. The other A-​ concepts (ES-​, veridical) are defined in terms of it. Explanatory B-​evidence requires A-​evidence plus the condition that e increase the probability of an explanatory connection between h and e.

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why e is true; or e correctly explains why h is true; or some hypothesis correctly explains why both e and h are true. But now we need to dig deeper and provide an account of a “correct explanation” that allows us to address the holism–​ particularism debate and avoids problems with deductive accounts of explanation.16

5 .   C O R R E C T E X P L A N AT I O N To proceed, I  will introduce the idea of content. Consider sentences such as: (1) The reason John got sick is that he ate contaminated fish. (2) The penalty for trespassing is that the person convicted will be drawn and quartered.

These sentences contain content-​nouns (in italics) together with that-​clauses (or more generally nominals) that give content to the noun. They can be used in forming what I  call content-​giving sentences such as the two above. Contrast these sentences with the following: (3)  The reason John got sick is easy to grasp. (4)  The penalty for trespassing is cruel and unusual.

These sentences do not say what the reason or the penalty is. They do not give a content to the noun in question. Sentence 16. Those familiar with my previous work on “correct explanation” in The Nature of Explanation may wish to briefly review material in sections 5–​7 of this chapter or turn directly to section 8.

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(1), but not sentence (3), contains an answer to the question “Why did John get sick?” by giving the reason. Sentence (2), but not sentence (4), contains an answer to the question “What is the penalty?” by giving the penalty. I will say that sentence (1) is a content-​giving sentence with respect to the question “Why did John get sick?” And sentence (2) is a content-​giving sentence with respect to the question “What is the penalty for trespassing?” A question such as “Why did John get sick?” presupposes various things—​e.g., that John exists (or existed), that John got sick, and that John got sick for a reason. A complete presupposition of a question is given by a sentence that entails all and only the presuppositions of that question. Of the three examples just given, only the last is a complete presupposition of the question “Why did John get sick?” viz., (5)  John got sick for a reason.

This sentence can be transformed into the following complete answer form for the question “Why did John get sick?” (6)  The reason that John got sick is -​--​ ​-​-​-​

by dropping “for a reason” in (5) and putting the expression “the reason that” at the beginning and “is” followed by a blank at the end, to yield (6). I will now say that p is a complete content-​giving sentence with respect to a question Q if p is a content-​giving sentence with respect to Q, p is a sentence obtained from a complete answer form for Q by filling in the blank, and p is not a presupposition of Q. Finally, Q will be said to be a content-​question if and only if there is a sentence that is a complete content-​giving sentence with

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respect to Q. By these definitions, (1) is a complete content-​ giving sentence with respect to the content-​question “Why did John get sick?” If Q is a content-​question (whose indirect form is q), and p is a complete content-​giving sentence with respect to Q, then p provides an explanation of q. Thus, (1) provides an explanation of why John got sick. More generally, any explanation that is offered is, or can be transformed into, one that answers some content-​question by supplying a complete content-​giving sentence with respect to that question. With these concepts, we can provide a simple condition for the correctness of an explanation: (7) If p is a complete content-​giving sentence with respect to Q, then p provides a correct explanation of q if and only if p is true.

Since (1) is a complete content-​giving sentence with respect to the content-​question: Q:  Why did John get sick?

(1), assuming it is true, provides a correct explanation of why John got sick. Condition (7) for correctness of an explanation has more bite than it might seem. Compare (1) with: (8)  John ate contaminated fish.

Even if (8) is true, this will not guarantee that (8) provides a correct explanation of why John got sick. (He might not have gotten sick from the contaminated fish but from something

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else.) (8) is not a complete content-​giving sentence with respect to Q. By contrast, if (1) is true, then, since it is a complete content-​giving sentence with respect to Q, it provides a correct explanation of q, in accordance with condition (7). A correct explanation may not be a good one, nor a good one correct. Goodness in explanations is a broader concept than correctness, and, unlike the latter, is context dependent. Whether (1), even if true, provides a good explanation of why John got sick depends on the “appropriateness” of the answer it provides, which is determined by the knowledge and interests of those for whom the answer is provided. For John’s doctor who is inquiring simply about what if anything John did that produced the sickness, (1) may be appropriate. For a medical researcher who wants to know much more—​e.g., how contaminated fish could have produced John’s sickness—​(1) is not good enough at all. Conversely, an explanation may be a good one, even though it is incorrect. Explanations such as the Ptolemaic and Newtonian ones of the observed motions of the planets, though incorrect, may be regarded as good ones on grounds of historical importance, or of this together with their comprehensiveness, precision, and predictive successes.

6 .   AV O I D I N G C O U N T E R E X A M P L E S The definition of “correct explanation” just introduced avoids standard causal counterexamples to deductive models of explanation. Here is an intervening cause counterexample, which I  introduced many years ago.17 Suppose Alice ate a 17. Achinstein, Nature of Explanation, chap. 5.

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pound of arsenic and died within 24 hours. Consider the following argument, which satisfies Hempel’s deductive-​ nomological criteria for being a correct explanation of her death: Deductive-​Nomological (D-​N) Argument (a)  Alice ate a pound of arsenic at time t. (b)  Anyone who eats a pound of arsenic dies within 24 hours. (c)  Alice died within 24 hours of t.

This is a valid deductive argument that contains true premises (a) and (b), among which is a law (b) in Hempel’s sense. Therefore, it satisfies Hempel’s conditions for being a correct explanation of why Alice died within 24 hours of t. Suppose, however, that Alice was killed not by the arsenic but as a result of being hit by a bus before the arsenic could really have much of an effect. Then, despite Hempel, the explanation is incorrect. Another type of causal counterexample involves cases in which the cause can be deduced from the effect, but not explained by it. For example, This body is accelerating. Whenever a body accelerates there is a force being exerted on the body. Therefore, there is a force being exerted on this body.

This satisfies Hempel’s D-​N model, supposing that the two premises are true and the second is a law. But even though we can validly infer the conclusion from the premises, what the conclusion asserts—​the presence of a force being exerted

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on this body—​is not correctly explained by the fact that the body is accelerating. Rather, it is the other way around. To employ my own account for the first example, consider the content-​question: Q:  Why did Alice die within 24 hours of t?

And, with respect to Q, consider the complete content-​giving sentence: (1)  The reason Alice died within 24 hours of t is that she ate a pound of arsenic at t.

On my conception, the fact that Alice ate a pound of arsenic at t, and anyone doing so dies within 24 hours, provides a correct explanation of why Alice died within 24 hours of t if and only if (1) is true. But (1) is false, not true. Hence, the counterexample is avoided. Similarly, in the second counterexample, the fact that this body is accelerating, and that any body that is accelerating is being acted on by a force exerted on it, provides a correct explanation of why a force is being exerted on it if and only if (2)  The reason that a force is being exerted on this body is that it is accelerating

is true. Perhaps we would say that the reason it has to be the case that a force is being exerted on this body is that the body is accelerating. But construed as an explanation of why a force is being exerted on this body, (2)  is false, not true. Hence, the counterexample is avoided.

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What Hempel and other defenders of a deductive model of explanation want to avoid is using explanatory terms such as “reason,” “cause,” and “explanation” in their deductive explanations. For example, no such terms appear in the D-​N arguments given earlier. Deductivists seek to define “correct explanation” without using such explanatory terms. What I  am suggesting is that this cannot be done if causal counterexamples such as these are to be avoided. You can cite a particular condition that obtained, as the first premise in the D-​N argument does. You can cite a true law that governs such a condition, as the second premise does. And the condition and the law may together deductively entail the sentence describing the event to be explained. But without the assumption that the condition cited actually caused or is causing the event, or that the reason the event occurred or is occurring is that the condition obtained, or that the event occurred because of the condition cited, you cannot conclude that the explanation offered is correct. By contrast, if p is a complete content-​giving sentence with respect to a question Q, and p is true, then you can conclude that p provides a correct explanation of q.

7 .  I S T H I S C I R C U L A R O R T R I V I A L ? Hempel and others might claim that it is, since I  am defining “correct explanation” using terms such as “reason,” “cause,” or “explanation”—​together with “truth.” My reply is to deny this. I am defining “correct explanation” in terms of complete-​content giving sentences with respect to a question Q, which is a concept not defined using terms such as “reason,” “cause,” or “explanation.”

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To see this, consider the earlier example: (1)  The penalty for trespassing is that the person convicted will be drawn and quartered.

(1) is a complete content-​giving sentence with respect to the question “What is the penalty for trespassing?” Therefore, (1)  provides a correct explanation of the penalty—​i.e., of what the penalty is, if (1) is true. There are no explanatory terms in (1). Explanations are not confined to answering just “why” questions. They can answer questions beginning with “what,” “how,” “who,” “when,” and others. This does not mean that whenever we utter sentences such as (2)  The reason John got sick is that he ate contaminated fish,

and (1), we are “explaining.” We can be doing many different things, including reporting, describing, complaining, and so forth. All these are what J. L. Austin called “illocutionary speech acts,” which involve uttering words with the intention of producing a certain type of effect on an actual or potential audience.18 So, when I  say that the complete content-​ giving sentence (2)  provides a correct explanation of why John got sick, and that the complete content-​giving sentence (1) provides a correct explanation of what the penalty is for trespassing, I  mean that these sentences can (in the right circumstances) be used to correctly explain these things. The 18. J. L. Austin, How to do Things with Words (Oxford: Oxford University Press, 1962). For my own account of the speech act of explaining, see Achinstein, Nature of Explanation, chap. 2.

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general definition of a “correct explanation” does not invoke terms such as “reason” or “explanation,” but only the terms “complete content-​giving sentence” and “true.”

8 .   A -​E V I D E N C E A N D E V I D E N T I A L PA R T I C U L A R I S M The concept of A-​evidence, which utilizes the idea of “correct explanation” discussed in section 5, allows us to formulate a defense of evidential particularism. Whether this is enough, and how a holist might reply, I will take up later. Consider again the sentence: (1)  The reason John got sick is that he ate contaminated fish

and the content-​question: Q:  Why did John get sick?

Sentence (1) is a complete content-​giving sentence with respect to Q. Therefore, (1) provides a correct explanation of q if and only if (1) is true. Now, consider the hypothesis: h: John got sick

and the claim e: John ate contaminated fish.

If (1) and e are both true, then there is an explanatory connection between e and h, since e correctly explains why h

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is true. Now, suppose that given that John ate contaminated fish, it is very probable that John got sick, and, more important, it is very probable that he got sick because he ate contaminated fish. That is, given e, it is very probable that there is an explanatory connection between e and h. Since we are assuming that e is true, and since e does not entail h, in accordance with the definition of A-​evidence, it follows that: (2)  e is (potential) evidence that h.

In this case, e is evidence for hypothesis h, even though h does not entail e (nor does e entail h). Also, in this case, e is evidence for h by itself—​not for h in conjunction with other hypotheses that together with h entail e. So, using the concept of (potential) A-​evidence, together with the proposed idea of “correct explanation,” we obtain a version of evidential particularism. According to the contrasting deductive-​explanatory account of evidence, e above would be evidence that h only if h entails e. It doesn’t. In this case, we want the reverse inference from e to h. So let us exchange h and e, as follows: e′: John got sick. h′: John ate contaminated fish.

Suppose we want to claim that e′ is evidence that h′. On the deductive explanatory account of evidence, to get e′ deductively from h′, we need to add various assumptions to h′. For example: (3)  John ate fish that was unrefrigerated for 6  days and fish under these conditions accumulate lots of bacteria.

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(4) Whenever one eats fish on which lots of bacteria have accumulated for 6  days, the fish becomes contaminated and one who eats it gets sick.

Proposition e′ is entailed by h′ together with (3) and (4), not by h′ alone. So, on the deductive-​explanatory view, e′ is not evidence for h′ by itself, but for the “system” of hypotheses consisting of h′ and (3) and (4). It is this system, not h′ by itself, that entails e′. On the account of evidence and explanation I  have proposed, whether e′ is evidence that h′ depends on whether, given e′, it is probable that there is an explanatory connection between h′ and e′. This would be satisfied if, given e′, it is probable that the reason John got sick is that he ate contaminated fish. The claim that it is probable is an empirical one, not an a priori one. And, like any empirical claim, evidential or otherwise, it can be defended by appeal to other empirical claims—​e.g., by appeal to claims such as (3)  and (4). The justificatory claims (3) and (4), however, do not need to be considered part of the empirical claim that e′ is evidence that h′. On the deductive-​explanatory account of evidence, however, they must be so considered, since e′ is not deductively entailed by h′ alone. So e′ cannot be considered evidence for h′ alone. In view of the difficulties with a deductive-​explanatory view of evidence, which are avoided by my own explanatory view, I prefer the latter, which supports evidential particularism. The holist, however, will not agree that I  have eliminated holism simply by a definition, whatever its advantages. The holist will say that I have simply shifted the problem to one of justification. To this I now turn.

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9 .   J U S T I F I C AT O R Y H O L I S M A N D E S -​E V I D E N C E A holist might allow me to use my preferred definition of evidence, which yields particularism for evidential statements of the form “e is evidence that h.” But he might insist that holism is still lurking, since the justification for any claim, whether or not that claim is an evidential one, is holistic. We might call this view “justificatory holism.” Consider my set of beliefs at a given time. If I want to justify or defend a claim, I  will do so by reference to this set. (Certainly I don’t want to defend a claim by invoking beliefs I don’t have.) Now, a justificatory holist might concede, how I defend a claim depends upon how and why it is being challenged, which can vary from one context to another. In one case, I may appeal to some parts of my set of beliefs; in other cases, to other parts. But here we are talking about the illocutionary speech-​act “defending a claim,” which involves uttering certain words in a given context with a certain intention. If challenged by you to defend my evidential claim (1) The fact that John got sick is evidence that he ate contaminated fish,

I may appeal to (3) and (4) in the previous section. When offering defenses of claims in actual practice, we are not holists. We do not invoke our entire belief set in such a defense. We take into account the context of the real or imagined request for a defense, including what the requester knows and wants to know.

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But now, the justificatory holist will urge, let us consider justification in a more abstract way, one that is not relativized to any particular context. We ask whether a claim such as (1) is justified—​not for any particular challenge or challenger—​but in general, irrespective of context. Yes, we do need to relativize justification to some set of beliefs in virtue of which a belief in claim (1) is justified. “How else can justification be understood?,” a justificatory holist will ask. We need to determine whether anyone holding the totality of beliefs in this set would be justified in believing (1). But we don’t need to relativize justification to any actual or potential challenger or defender, since we are not thinking of justification as a speech-​act. We don’t need to know what parts of a set of beliefs a defender of (1) might invoke in defending particular challenges. Such defenses may vary, but whether one is justified in believing (1) in virtue of a set of beliefs does not vary. That depends only on the set of beliefs. Such a view can be expressed using my concept of ES-​ (epistemic situation) evidence, introduced in ­chapter 1. An epistemic situation ES contains a set of beliefs of an actual or potential believer.19 There may or may not be any actual person in a given epistemic situation. On the account I presented in c­ hapter 1, e is ES-​evidence that h (with respect to an epistemic situation ES) if and only if e is true and anyone in such a situation would be justified in believing that e is veridical evidence that h. “Veridical evidence,” whose definition I gave in c­ hapter 1, is defined in terms of 19.  See Achinstein, Book of Evidence, chap.  2. The concept I  introduce in that book is more complex, but for present purposes we can use the simpler one.

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“potential evidence”: for e to be veridical evidence that h, it is necessary and sufficient that e be potential evidence that h, and that there be an explanatory connection between h and e. Finally, whether e is ES-​evidence that h, with respect to a particular ES, and hence whether anyone in epistemic situation ES is justified in believing that e is veridical evidence that h (and hence that h is true), depends just on the beliefs in ES. Suppose we grant the holist that there is a sense of “justified evidential claim” that is abstracted from different possible challenges to an evidential claim and different contexts in which those challenges might be made. And suppose it is true that one can be justified in believing an evidential claim in virtue of the set of the beliefs comprising one’s epistemic situation, independent of different possible challenges to the claim that might be made in different contexts. This can be admitted, an opponent of holism might say, without a commitment to holism. It may be that, if one is in an epistemic situation ES, one is justified in believing an evidential claim of the form (2)  e is (veridical) evidence that h,

without its being the case that every belief in ES contributes to, or is part of, that justification. It may be that one who is in an epistemic situation ES is justified in believing (2) because of some but not all of the beliefs in ES. Yes, we might say, anyone in ES is justified in believing (2), but this is so because ES contains a subset (perhaps a very small one) which is such that anyone who holds the beliefs in this subset is justified in believing (2). This would be incompatible with justificatory holism as I am characterizing it. It doesn’t adequately reflect

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the “holistic” essence of holism—​the idea that it is an entire system of beliefs that one has or might have that provides a justificatory basis for an evidential claim. So, let’s see how a justificatory holist could strengthen the view.

1 0 .   S T R E N G T H E N E D J U S T I F I C AT O R Y   H O L I S M The strengthened view needs to be (a) justificatory, (b) holistic, and (c)  abstract in the sense that justification is not tied to particular contexts in which particular challenges are made. The idea is that while a particularist claim of the form “e is evidence that h” may be true even if neither e nor h is “holistic,” a justification for that claim must satisfy (a)–​(c). Can there be such a thing? I will discuss a very strong proposal, with the idea that if this doesn’t yield justificatory holism, then perhaps nothing will. The proposal is that for a system of beliefs ES to adequately justify an evidential claim of the form (1)  e is (veridical) evidence that h,

one who is in ES needs to be able to meet not just some particular challenge to (1)  but all possible ones. And for this purpose, since possible challenges to (1)  are so numerous and varied, all parts of ES will need to be invoked to meet them all. True, some particular challenges to (1) may be met by appeal to particular parts of ES. But all possible challenges require the entire system ES. And anyone in ES who cannot meet all possible challenges to (1) by appealing to ES is not justified in believing (1).

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Even if this were to yield justificatory holism (which, I  will argue, it doesn’t), it is an impossible standard of justification! To be sure, there are possible challenges to (1) that can be met by appeal to the set of beliefs in a particular ES. But there will always be possible challenges that cannot be met—​challenges based on information not available to those in ES. For example, on the present proposal, the epistemic situation ES of wave theorists of light in the mid-​nineteenth century would not justify the evidential claim that (2)  Diffraction and interference phenomena constitute veridical evidence that the wave theory is correct.

This is because, although it was not available to mid-​ nineteenth-​century wave theorists in their ES, one of the “possible challenges” (which became actual at the end of the nineteenth century) derives from the results of the Michaelson-​ Morley experiments, demonstrating the absence of an ether drag. Of course, had mid-​nineteenth-​ century ether theorists known about and accepted the results of these experiments, their epistemic situation would have changed. But, given the holist claim I am considering, in the mid-​nineteenth century, they could not have known about these experiments, and if they had, they would not have been able to defend claim (2)  by reference to their original epistemic situation. The present holistic proposal leads to an interesting form of skepticism. Assume, as in the case above, that someone in a given epistemic situation ES at a time t cannot know about future experiments and observations that will be made well after t that may yield results that refute or at least challenge

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beliefs in ES. There will be possible challenges to an evidential claim such as (2) that one in ES cannot meet by appeal to ES. If so, then on the present version of holism, no matter what one’s epistemic situation, since one will be unable to meet all such challenges, one will not be justified in believing such evidential claims. I say that this is an interesting form of skepticism, because even though it may be true that e is veridical evidence that h, and even though one may come to know that e is true, one can never be justified in believing that e is veridical evidence that h. I  take it that on an evidential view of “knowing that h,” it is required that one be justified in believing that there is some e that is veridical evidence that h. But this is precluded by the present version of justificatory holism. Most important, for present purposes, even if we were to grant that justification requires a belief set ES that can meet  all challenges, we still would not get justificatory holism. All we get is that an evidential claim of form (1) is justified, relative to an ES, only if all possible challenges to (1) can be met by reference to the beliefs in ES. But this doesn’t require holism rather than particularism. It would be satisfied if each possible challenge to the evidential claim can be met by reference to one or more beliefs in ES. Perhaps some challenges will require most of the beliefs in ES, others fewer. Just because all the beliefs in ES may be needed to justify all the possible challenges, it doesn’t follow that all of them are necessary to justify each challenge. It doesn’t follow that each possible challenge needs to be met by appeal to all the beliefs in ES. If not, then justification is not holistic. What I have just said applies also to weaker versions of justificatory holism that say not that one who is in ES needs to be able to meet  all possible challenges to an evidential

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claim by appeal to the beliefs in ES but only some possible challenges of certain designated types. As with the stronger version, even if all the beliefs in ES were required to justify all the challenges in this restricted set of challenges, it doesn’t follow that all the beliefs in ES are needed to justify each challenge. Again, we do not get justificatory holism. Finally, as noted earlier, the justificatory holist wants: (a) justification, (b) holism, and (c) abstraction from particular contexts and challenges. With justificatory particularism, using my concepts of evidence, one can get (a) and (c). As far as (a)  is concerned, if e is ES-​evidence that h, then anyone in ES is justified in believing that e is veridical evidence that h, and hence that h is true. As far as (c) is concerned, if e is potential or veridical evidence that h, then e is a good reason to believe h, independent of any particular contexts or challenges. What the particularist will not give the holist is what the latter most wants—​viz. (b), holism. He will not say that something can be evidence only for an entire system of hypotheses, and he will not say that an evidential claim is justified only by reference to an entire system of beliefs but not to particular beliefs in that system.

1 1 .  D O V E R I F I E D C O N S E Q U E N C E S PROV I DE A BASI S F OR HOL I SM ? A particularist, such as Mill, wants to say that there is evidence for a theory consisting of a set of laws (evidence that provides a good reason for believing the theory) if and only if there is evidence for each law in the theory, and consequences derived from and explained by the theory are verified. How is the second condition to be understood? Do the verified

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consequences of the theory provide evidence for the theory? If the particularist says that they do, then since they are derived and explained by a combination of assumptions in the theory, perhaps even all of them, the holist will accuse the particularist of creeping holism. If these verified consequences are derived using all the assumptions of the theory, then they provide evidence for the whole theory, not for parts of it. There are several replies a particularist like Mill will make. First, verified consequences are frequently derived from some, but not all, of the assumptions of a theory. Second, the fact that a consequence of a theory has been derived and verified is not by itself necessarily evidence for the theory. The basic assumptions of the theory may have no causal-​inductive support, and if not, the idea that verified consequences provide support is subject to the competing hypothesis objection (in its acceptable version).20 Third, and most important, before accepting the charge of creeping holism, Mill will say, you need to look at the verified consequences to see what, if anything, they do support. Let me explain by reference again to the wave theory. During the 1840s, when Mill and Whewell were debating, the wave theory included basic assumptions such as these: light is a wave motion, not a stream of particles emanating from luminescent bodies; the wave motion exists in a highly elastic substance called the ether; the waves move in a direction perpendicular to the wave front; they can interfere constructively or destructively, depending on whether their phases coincide 20.  The “unacceptable” version, the one attacked by Newton, is invoked when the original theory has causal-​inductive support but the imagined competitor does not. The “acceptable” version is invoked when neither theory has causal-​inductive support.

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or cancel; and so on. One of the established consequences of the wave theory, which is explained by that theory, is that light moves in straight lines. But, Mill would insist, contrary to holism, it is explained by the theory by appeal not to the entire theory but only to a part of it that claims that light waves in the ether move in a direction perpendicular to the wave front. More important, however, Mill would ask, “Does the established fact that light moves in straight lines constitute evidence even for the theoretical assumption that light waves in the ether move in a direction perpendicular to the wave front?” Mill would say that it could if there were causal and inductive support for the assumption that there exists an ether in which the putative waves wave. You can’t have waves without some substance waving—​at least that is a basic idea behind the wave theory in the mid-​nineteenth century. So at best, the fact that light travels in straight lines, or that there are interference effects of the sort observed by Young and Fresnel, constitute evidence only for the conditional: if light consists of waves in the ether, then these waves travel in a direction perpendicular to the wave front, they interfere constructively and destructively, etc. Mill would give the same response to Maxwell’s 1860 kinetic-​molecular theory of gases. For example, the fact that a malodorous gas such as hydrogen sulfide introduced at one end of the room takes some time to be detected at the other end was taken as evidence that gas molecules do not move freely from one end of the room to the other but collide with other molecules. Mill would say:  “this observed phenomenon is not evidence that moving molecules collide, but only that if moving molecules exist then they collide.” Indeed, Maxwell himself suggests as much when in 1859 he writes to Stokes, admitting his theory is a “speculation” and saying

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Now do you think that there is any so complete a refutation of this theory of gases as would make it absurd to investigate it further so as to found arguments upon measurements of strictly “molecular” quantities before we know whether there be any molecules?21

In the next section, I will formulate this idea more generally (an idea that I think Mill as well as Maxwell regard as important, and justly so).

1 2 .   E V I D E N C E F O R   C O N D I T I O N A L EXISTENCE CLAIMS Suppose that a theory postulates the existence of a certain type of entity A (the ether, molecules, strings) and attributes a certain property P to As. Mill is saying that there may be evidence for conditional statements of the form: (1) If As exist, then they have P (e.g., if light waves in the ether exist, then they travel in a direction perpendicular to the wave front)

without there being evidence for the claim that: (2)  As, all of which have P, exist. (Light waves in the ether, which travel in a direction perpendicular to the wave front, exist.)

21. Garber, Brush, and Everitt, Maxwell on Molecules and Gases, 279. This passage follows right after the one I quoted in chap. 1, note 49.

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Now, many of the claims in theories of the sort Mill is concerned with have the form: (3)  As have P (light waves in the ether travel in a direction perpendicular to the wave front),

where this is supposed to be understood as being elliptical for, or presupposing, (2). They are not to be understood as making just a claim of form (1). When the wave theory makes the claim that it does in (3), it is claiming not just that if light waves in the ether exist, then they move in this manner but that light waves in the ether, and the ether itself, exist, and that light waves move in a direction perpendicular to the wave front. However, what is often presented as evidence for a claim of form (3) is really evidence for a weaker conditional claim of form (1). Thus, Mill wants to say, even if the established fact that light moves in straight lines is evidence for the conditional claim (1), it is not evidence for the unconditional claim about light waves and the ether in (2). And the latter is one of the fundamental assumptions of the wave theory. So, for Mill, even if there is evidence for various assumptions of the wave theory, provided that those assumptions are construed conditionally on the ether and light waves existing, they are not evidence for unconditional versions of those assumptions. Yes, Mill will agree, the conditional assumptions are part of the theory, and yes, there can be evidence for them. But so are their unconditional versions. And unless there is evidence for them, the theory as a whole is a speculation. That is why Mill focuses on the lack of evidence for the existence of the ether. Without this,

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at best you can have evidence for conditional claims in the wave theory, but not the unconditional ones. And it is the latter that wave theorists most want to assert. For Mill, the most you can say is that there is evidence that the theory is a possibility, that it might be true, that it is worth exploring—​which is exactly what Mill does say about the wave theory of light. More generally, in considering the wave theory, he writes: It is perfectly consistent with the spirit of the [deductive] method, to assume in this provisional manner not only an hypothesis respecting the law of what we already know to be the cause but an hypothesis respecting the cause itself. It is allowable, useful, and often even necessary, to begin by asking ourselves what cause may have produced the effect, in order that we may know in what direction to look for evidence to determine whether it actually did.22

Newton, who held a methodological view (“analysis and synthesis”) similar to Mill’s, is also a particularist who demands that for a theory to be proved, each of its claims needs to be established by causal-​inductive reasoning or by deduction from other claims so established. (For Newton, you can’t establish the law of gravity simply by showing that if gravitational forces exist that obey the law of gravity, then these forces produce known planetary motion. You have to show by causal-​ inductive reasoning that gravitational forces obeying his law do exist, and do in fact produce the motions in question.) Newton, at least in his official methodology, is even stricter than Mill. For Newton, if a theory is

22. Reprinted in Achinstein, Science Rules, 222.

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not so established, then it is what he calls a “hypothesis,” and “hypotheses have no place in experimental philosophy.”23

1 3 .   T H E O R Y E VA L UAT I O N :   E I T H E R /​ O R - ​I S M V S . P R A G M AT I S M There is an important assumption made by Newton and Mill, as particularists, as well as by Whewell, as a holist, concerning how theories are to be evaluated. It is an assumption for which no evidence is offered and which, I will argue, is unjustified both historically and conceptually. In evaluating a theory, both sides focus entirely on epistemic virtues. Even there, the main focus is on the question:  Has the theory as a whole been “proved,” or at least has evidence sufficient to believe the theory been supplied? Newton, Mill, and Whewell all seem to assume that epistemic evaluations are the only ones that are important, and that among such evaluations, the ones to focus on are those that tell us whether there is evidence sufficient to prove or demonstrate the high probability of the theory as a whole. This is an assumption underlying Newton’s four rules, Mill’s “deductive method,” and Whewell’s ideas of consilience and coherence. To be sure, Mill and Whewell, at least, allow the additional epistemic question: Has enough information been provided to make it reasonable to conclude that the theory is a possibility worth considering?24 Newton does not seem 23.  “Unofficially,” as I  noted in ­chapter  1, Newton violates this official methodology in his Opticks, as well as in the Principia. 24.  Mill suggests that this is so in the case of the wave theory, since it satisfies the “ratiocination” and “verification” conditions of his “deductive

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to have even that question in his “official” epistemic repertoire. The important epistemic question pertains to proof or demonstration. With regard to epistemic evaluations, Mill, Newton, and Whewell are “either/​or” theorists. “Proved” and “unproved” are the central categories. For Mill and Newton, to show that there is evidence sufficient to believe a theory, you show that there is (causal-​inductive) evidence sufficient to believe each assumption in the theory. If you don’t show this, then the theory as a whole is unproved and a speculation. For Mill, you can regard a speculative theory as a “possibility” (the cause invoked—​e.g., the ether—​“may exist and may produce the effect”). Mill seems to view such possibilities simply as ones logically consistent with the evidence, no more. For Newton, at least in his official methodology, you can’t even do that much. For both, the either/​or is the same: either provide evidence sufficient to believe each assumption, or recognize that you are speculating. For Whewell, just change “each assumption” in the previous sentence to “the set of assumptions.” That is, either provide evidence (satisfying consilience and coherence) sufficient to believe the set of assumptions; or recognize that you are speculating (in which case, for Whewell, you may have done something “of service to science,” but you have not provided “proof ”). To be sure, for Whewell, by contrast with Mill and Newton, you do not and cannot provide evidence sufficient to believe each assumption—​only evidence sufficient to believe the theory as a whole. But with regard to method,” but not the “inductive” condition. Whewell says that if a theory in its early development stage explains and predicts phenomena but doesn’t yet satisfy consilience and coherence, it can still be of value.

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this disjunction, both sides agree: either you come up with evidence sufficient to believe the whole theory or you have a speculation. And, they agree, this is by far the most important type of theory evaluation to make. There is a better alternative, I  believe. It rejects the idea of focusing exclusively on epistemic evaluations, and even within the latter, focusing exclusively or primarily on either/​or evaluations (“proved or unproved,” “possible or impossible”). Theory evaluation is much broader than that, a claim to which I now turn. In ­chapter 1, I argued that a speculative theory such as Maxwell’s kinetic-​molecular theory of gases can be evaluated from different perspectives. Which perspective(s) to use in an evaluation is a pragmatic matter that depends on the knowledge, aims, and interests of the speculator and the evaluator. One such perspective, a completely historical one, is non-​epistemic. From such a perspective, Maxwell’s theory gets high marks, since it set the stage for mathematically rigorous molecular investigations and it introduced statistical considerations in generating the Maxwell distribution law. As the historians of science Garber, Brush, and Everitt note, when Maxwell died in 1879, his contemporaries regarded his work on kinetic theory as more important than his work on electricity and magnetism (a view later reversed during the twentieth century.) But, these historians add, “we should take these nineteenth-​century assessments seriously if we are to judge the role of kinetic theory and Maxwell in the development of modern physics.”25 Even if we confine our evaluations to epistemic ones, in practice such evaluations are often more complex than 25. Garber, Brush, and Everitt, Maxwell on Molecules and Gases, 1.

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those whose principal evaluative categories are “proved,” “unproved,” and “possible.” This is particularly so when the theory is a “work in progress” and is evaluated as such. It is not my claim that the evaluations in question are always “correct” or justified. In general, evaluations, whether epistemic or non-​epistemic, can be questioned and are subject to defense. My claim is that evaluations—​epistemic or otherwise—​are in general much more nuanced and informative than those offered by the holists and particularists I have been considering. As I noted in ­chapter 1, in his 1875 paper, “Evidence for a Dynamical Theory of Gases,” Maxwell presents a largely epistemic evaluation of a theory he himself calls a “physical speculation.” He assesses his theory, and the various assumptions within it, by referring to the epistemic reasons he has for them at the time in question. Some of these reasons, he claims, are strong enough to rise to the level of evidence sufficient to believe some assumptions (e.g., the existence of experiments which he thinks establish that heat is a form of motion of “parts too small to be observed separately”). Some epistemic reasons he offers for certain assumptions are weaker and plausible, but not sufficiently compelling to believe those assumptions (e.g., weak inductive reasons arguing from the success of mechanical theories in astronomy and electricity to their success in molecular-​kinetic theory, and hence to the claim that molecules satisfy mechanical Newtonian laws26). And some reasons are “explanatory” ones showing how, if 26. In ­chapter 1, I said that these don’t constitute what I call explanatory evidence. But they can still count as reasons for belief. Following what I took earlier to be Mill’s claim about the wave theory of light, a plausible way to interpret Maxwell’s epistemic claim here is as a conditional one: If

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true, the assumptions could explain various phenomena. The latter by themselves don’t count as evidence for the truth of the assumptions of the theory. But in showing how, if true, the theory could explain various phenomena, Maxwell is showing that the theory is epistemically possible—​i.e., possible given what is known. For some assumptions, no epistemic reasons at all are given, only ones such as simplicity of calculation (e.g., that the coordinates of molecular velocity vectors are independent). In addition, there are what he calls “unconquered difficulties.” The latter include consequences of the theory that are incompatible with observations (e.g., specific heat ratios of gases), as well as the inability of the theory to explain various properties of gases (transparency, electrical conductivity). Maxwell writes: But while I think it is right to point out the hitherto unconquered difficulties of this molecular theory, I must not forget to remind you of the numerous facts which it satisfactorily explains. We have already mentioned the gaseous laws, as they are called, which express the relations between volume, pressure, and temperature, and Gay-​Lussac’s very important law of equivalent volume. The explanation of these may be regarded as complete. The law of molecular specific heats is less accurately verified by experiment, and its full explanation depends on a more perfect knowledge of the internal structure of a molecule as we yet possess. But the most important result molecules exist, then, given that mechanical theories have been successful in astronomy and electricity, it is reasonable to believe that they are subject to mechanical laws. The success of mechanical theories does not, of course, provide a reason to believe that molecules do exist, or that they satisfy the particular mechanical assumptions introduced pertaining to their shapes, motions, and forces exerted.

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of these inquiries is a more distinct conception of thermal phenomena.27

From an epistemic perspective, the theory is doing reasonably well so far, Maxwell is saying, even though there are problems with it and further development will be required. The epistemic reasons offered vary considerably in their strength. Even if Maxwell is right in claiming that some are sufficiently strong to rise to the level of “experimental proof,” this is not so for the theory as a whole or for each assumption of the theory. But some of the reasons, while not strong enough, or of the right sort, to count as evidence for, or “proof ” of, unconditional (or even conditional) assumptions of the theory, do carry some epistemic weight. Maxwell obviously regarded the theory as a whole as unproved, since he classified it as a speculation. But “proved,” “not proved” (“possible” and “not possible”) are not the only informative categories of epistemic evaluation for the theory, or for parts of it, even if the theory as a whole and some of its parts are “not proved” or “not possible.” Other examples of such more varied and nuanced epistemic evaluation are ones given of the wave and particle theories of light by John Herschel in 1827, by Baden Powell in 1833, and by Humphrey Lloyd in 1835.28 These involve showing how each theory explains various known optical phenomena, giving the advantages and disadvantages of each. For example, Powell constructs a chart in which he evaluates wave and particle accounts 27. Niven, ed., Scientific Papers of James Clerk Maxwell, 2:436. 28.  See Geoffrey Cantor, Optics After Newton (Manchester:  Manchester University Press, 1983), chap. 8; and Achinstein, Particles and Waves,  22–​24.

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by comparing how well, if at all, each explains twenty-​one different optical phenomena, including, to mention just five, reflection, refraction, dispersion, the Poisson spot, and polarization. He rates these explanations using three evaluative categories:  perfect explanation, imperfect, and none at all. The wave theory does come out better on the whole than the particle theory. But, as with Maxwell, the theories involved are regarded as “works in progress,” for which the evaluative categories “proved” or “not proved”—​especially as applied to the theory as a whole—​are not particularly informative. I am not claiming that all epistemic theory evaluations have to be “Maxwellian” (or “Powellian”), only that they needn’t all be assessments from a “proved/​not proved,” or “sufficient/​insufficient evidence,” or “possible/​not possible” perspective. They can be ones that indicate what level of support the theory and its individual assumptions have, whether or not this rises to the level of “proof,” and why this does or doesn’t rise to that level. Evidence may be presented for some but not all individual hypotheses, and defenses of evidential claims may be offered that don’t appeal to the entire set of beliefs in a scientist’s epistemic situation. Moreover, individual hypotheses of a theory may be evaluated from the viewpoint of the theorizer and his epistemic situation, or from the viewpoint of the evaluator and his epistemic situation. If we offer an epistemic evaluation of the mid-​ nineteenth-​century wave theory from our perspective today, we will obtain a very different result from those of Herschel, Powell, and Lloyd. Accordingly, evidential particularists are correct in claiming that individual hypotheses can be evaluated epistemically, and holists are correct in claiming that the theory as a whole can be evaluated epistemically. But holists are

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mistaken in their claim that only the theory as a whole, not particular parts, can be evaluated. And both are mistaken in assuming that the only or at least the most important epistemic evaluation of a theory is one given from the standpoint of proof using categories such as “proved,” “unproved,” and “possible.” There are more varied and fine-​grained epistemic criteria, and these can be used to generate evaluations of the sort given by Maxwell and the three light-​theory evaluators above—​ones that are detailed and informative. How many details to supply, and which ones, is a pragmatic matter, not one that is dictated by universal standards of evaluation of the sort required by Newton’s rules, Mill’s deductive method, or Whewell’s ideas about consilience and coherence. To be sure, one could ask whether, or even to what extent, such standards have been satisfied by a given theory, but in theory evaluation one could, and often should, ask more. Finally, no matter whether the evaluation is detailed and nuanced or more global, scientists can and do use assumptions of a theory to explain, predict, and calculate, even if the theory as a whole is not “proved,” even if some or many of the assumptions are not either—​indeed, even if no support for any of the assumptions has been offered. Scientists do not, and should not, wait for evidence that provides “holistic” proof of the assumptions or particularist proof of each assumption in order to proceed to provide explanations, predictions, and calculations. That would stifle inquiry. It doesn’t follow, of course, that the explanations, predictions, and calculations offered are correct or fully warranted. They, like the assumptions of the theory, are subject to a range of evaluations.

5

✦ THE ULTIMATE SPECULATION A “Theory of Everything” (What Is It, and Why Should We Want One?) . . . such stuff as dreams are made on. —​P r o s p e r o , The Tempest

HOW WONDERFUL IT WOULD BE to have a “Theory of

Everything.” So say string theorists in physics who believe they may have found one to unify the four basic forces of nature. (They use the abbreviation TOE to refer to any such theory. I  will, too, whether or not it is string theory.) So thought physicists beginning in the seventeenth century who espoused the “mechanical philosophy” of nature. So more recently say two prominent philosophers, Thomas Nagel1 and David Chalmers.2 Nagel has in mind a panpsychist teleological theory that will unify the mental and the physical. Chalmers’ “aim is to specify the structure of the world in

1. Nagel, Mind and Cosmos. 2.  Chalmers, Constructing the World (Oxford:  Oxford University Press, 2012).

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the form of certain basic truths from which all truths can be derived.”3 Although those who want a TOE have somewhat different ideas in mind, there is a common, if rather neb­ ulous, core idea:  science should aim to produce a grand, unifying theory that can explain everything on the basis of fundamental laws and constituents in the universe—​i.e., laws that have no further explanation and constituents that are not analyzable into anything else. What exactly are seekers of a TOE trying to find (e.g., what counts as “everything?”)? Why would it be wonderful to find such a theory? And why suppose that there is or even could be such a thing? Proponents of the idea of a TOE offer very general empirical, or a priori, or methodological reasons for supposing that a TOE exists, or at least that it would be a good thing if it did, whether or not that theory is the one they are attempting to develop. Their claim is that some TOE does exist, or at least that it would be a good thing if it did. My main concern in what follows is with the very general reasons they offer for such a claim. These will be examined in sections 4 to 7. In section 1, I begin with some particular theories or programs that, defenders believe (or once believed), if developed in appropriate ways, would be or become TOEs. In

3. Chalmers, Constructing the World, xiii. Chalmers is attempting to extend Carnap’s ideas in the Aufbau (The Logical Structure of the World). This is related to the “unity of science” program started in the 1930s and later defended by Paul Oppenheim and Hilary Putnam (“Unity of Science as a Working Hypothesis,” in Minnesota Studies in the Philosophy of Science, vol. 2 [Minneapolis:  University of Minnesota Press, 1958]), and Robert Causey, Unity of Science (Dordrecht: D. Reidel, 1977).

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section 2, I consider, more generally, what basic constraints a TOE is supposed to satisfy. In section 3, I ask whether any of the theories or programs cited in section 1 is a TOE. In the remainder of the chapter, I discuss the very general reasons offered for seeking such a theory and I argue that they are not compelling. The idea that there exists a TOE, and if so, that scientists should discover it, is a speculation—​indeed, a very grand one. So far, no such theory has been found and, I  will argue, the reasons offered for supposing that one exists do not rise to the level of evidence sufficient to believe such a supposition (in anything other than a subjective sense of evidence). That’s what makes it a speculation (in a nonsubjective sense). But, as I have claimed in earlier chapters, a speculation can be evaluated by considering (objective) epistemic as well as non-​epistemic reasons for it that are supportive, even if not strong enough to establish it or count as evidence sufficient to believe it. TOE enthusiasts—​ both scientists and philosophers—​ attempt to do at least that much, while some, denying that it is a speculation, give what they take to be much stronger evidential reasons for thinking that a theory of everything exists. There are also TOE theorists who suggest reasons for supposing that it would be a good thing if a TOE does exist and should be found. My purpose here is to examine all these reasons, and reject them. It is also to argue that science can and should proceed very well without a TOE and without presupposing that there is one. TOE theorists speculate about the existence, as well as the value, of a TOE, but their speculations are without merit.

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1 .  S O M E ( P O T E N T I A L ) T H E O R I E S O F   E V E RY T H I N G a. String  Theory I begin with string theory, one of the examples of a speculation I noted in c­ hapter 1. Its proponents are enthusiastic and believe it is or will be developed into a TOE.4 Lee Smolin, a theoretical physicist who is admittedly a critic of the theory, characterizes its aim as one of solving what he calls “the five great problems in theoretical physics.”5 They are:



1. Combine general relativity and quantum theory into a single theory that can claim to be the complete theory of nature. This is called the “problem of quantum gravity.” 2. Resolve the problems in the foundations of quantum mechanics, either by making sense of the theory as

4. Brian Greene, a defender, writes: For the first time in the history of physics we therefore have a framework with the capacity to explain every fundamental feature upon which the universe is constructed. For this reason string theory is possibly described as being the “theory of everything” (TOE) or the “ultimate” or “final” theory. These grandiose descriptive terms are meant to signify the deepest possible theory of physics—​a theory that underlies all others, one that does not require or even allow for a deeper explanatory base.” (Greene, Elegant Universe, 16) 5. Lee Smolin, The Trouble with Physics (Boston: Houghton Mifflin, 2006), chap. 1.

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it stands or by inventing a new theory that does make sense. 3. Determine whether or not the various particles and forces can be unified in a theory that explains them all as a manifestation of a single, fundamental entity. 4. Explain how the values of the free constants in the standard model of particle physics are chosen in nature. 5. Explain dark matter and dark energy.

String theory, which seeks to solve these problems, postulates that all the particles and forces of nature arise from strings that vibrate in 10-​dimensional spacetime and are subject to a set of simple laws specified in the theory. The strings, which can be open with endpoints or closed loops, vibrate in different patterns, giving rise to particles such as electrons and quarks. The equations governing the interactions of forces and particles are to be derived from the basic idea that the vibrations of strings are propagated so as to minimize the area of propagation in spacetime. What counts as “everything” on this theory? The most straightforward answer is that the theory attempts to explain issues of the sort mentioned in Smolin’s “five problems.” No doubt there are other problems physicists would cite, and as the theory is further worked out, new problems will arise that call for explanations. But these are ones that would normally be treated by physicists, not by experts in other sciences. As Brian Greene notes, however, string theorists tend to have reductionist ideals and would like to be able to use the theory to explain a lot more, or at least believe that the theory could “in principle” explain a lot more, including psychological phenomena such as joy and sorrow, as well as complex physical

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phenomena such as tornados.6 The matter is controversial, and not all string theorists have such vaulting ambitions.

b. Seventeenth-​C entury Mechanical Philosophy Its defenders had a different physics in mind, but it is also quite general.7 The greatest of the mechanical philosophers, of course, was Isaac Newton. In his introduction to the first edition of the Principia, he writes: our present work sets forth mathematical principles of natural philosophy. For the basic problem of philosophy seems to be to discover the forces of nature from the phenomena of motions and then to demonstrate the other phenomena from these forces.8

Newton goes on to develop his three laws of motion mathematically, and finally, using these, together with theorems 6. Greene, Elegant Universe, 16–​17. Greene writes: “A staunch reductionist would claim . . . that absolutely everything from the big bang to daydreams can be described in terms of underlying microscopic physical processes involving the fundamental constituents of matter. If you understand everything about the ingredients, the reductionist argues, you understand everything” (16). On February 27, 2014, Greene gave a lecture on the current status of string theory at Johns Hopkins University. In response to a question by the present author, Greene informed the audience that he is indeed a “staunch reductionist.” Smolin writes:  “Any claim for a final theory must be a complete theory of nature. It must encompass all we know” (Trouble with Physics, 5). 7. The term “mechanical philosophy” was introduced by Robert Boyle as a program to reduce all physical phenomena to (inert) matter and motion. But as this philosophy developed, other “principles” were added, including forces and tendencies to motion. 8. Newton, Principia, 382.

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he derives from them and six observed phenomena pertaining to the motions of the planets and their satellites, he proves the law of gravity. He uses the latter to “demonstrate” other celestial and terrestrial phenomena.9 Newton does not claim that all phenomena can be so demonstrated. But the class of physical phenomena he intends is quite broad. The central idea is that physical phenomena are explainable by reference to bodies (a basic ontological category) that are in motion and are subject to forces governed by fundamental laws. The mechanical philosophy extended well into the nineteenth century, when James Clerk Maxwell, e.g., attempted to provide mechanical explanations for heat, light, electricity, and magnetism. He claimed that no more basic explanation of physical phenomena can be given.10 There are those who thought that the program of the mechanical philosophy, whether expressed in terms of Newton’s laws or later variations or additions (e.g., Maxwell’s electromagnetic laws and the concept of a field), could be extended to areas well beyond those mentioned, such as chemistry, biology, and

9. In ­chapter 3, I discussed Newton’s derivation and offered a new interpretation of his four methodological rules. 10. I repeat the passage from Maxwell on mechanical explanations given in ­chapter 1: When a physical phenomenon can be completely described as a change in the configuration and motion of a material system, the dynamical explanation of that phenomenon is said to be complete. We cannot conceive any further explanation to be either necessary, desirable, or possible, for as soon as we know what is meant by the words configuration, motion, mass, and force, we see that the ideas which they represent are so elementary that they cannot be explained by means of anything else. (Niven, ed., The Scientific Papers of James Clerk Maxwell, 2:418)

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even psychology.11 But neither Newton nor Maxwell had such ambitions. “Explaining everything” for Newton and Maxwell meant explaining physical phenomena of a sort they described in their works and other physical phenomena that may come to be discovered. But neither scientist had the ambition to apply the theories they produced beyond the physical sciences.12

c. Thomas Nagel’s Grand Unification Nagel writes: This, then, is what a theory of everything has to explain: not only the emergence from a lifeless universe of reproducing organisms and their development by evolution to greater and greater functional complexity; not only the consciousness of some of those organisms and its central role in their lives; but also the development of consciousness into an instrument of transcendence that can grasp objective reality and objective value.13

Nagel does not produce an actual theory of this sort, though he does make an outline of the kind of theory he has in mind. It will contain non-​ teleological, non-​ deterministic laws of physics “governing the ultimate elements of the universe, whatever they are.” It will also contain teleological laws 11.  For a discussion of extensions into chemistry and biology, see R. S. Westfall, The Construction of Modern Science (New  York:  John Wiley, 1971), chaps. 4–​5. 12. Later I will consider in more detail whether Newton and Maxwell in fact subscribed to all the most central ideas I associate with a TOE. 13. Nagel, Mind and Cosmos, 85.

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governing states of the universe that assign certain successor states higher probabilities than those assigned by the laws of physics. These teleological laws ascribe to the ultimate elements of the universe basic (“panpsychic”) tendencies to achieve certain outcomes or “end-​states,” including mental ones. Nagel says it is up to scientists to provide the actual “theory of everything.” His job is to state the direction that should be taken and the problems to be solved.14 What does Nagel have in mind by “everything”? He certainly wants a theory to explain all the phenomena explained by physics and biology. But he also wants that theory to explain “mental” phenomena, including consciousness, cognition, and value, since he believes that physics and biology are incapable of doing so.

d. Chalmers’ “Construction of the World” David Chalmers defends the idea that there is a small class of basic truths from which all the other truths of the world can be determined. He calls this idea a “scrutability thesis”: It says that the world is in a certain sense comprehensible, at least given a certain class of basic truths about the world. In particular it says that all truths about the world are scrutable from some basic truths.15

Unlike string theorists, mechanical philosophers, and Nagel, however, Chalmers is not out to present, or even point in the direction of, a particular scientific theory that explains, or 14. Mind and Cosmos, 92ff. 15. Chalmers, Constructing the World, xiii.

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can explain, everything. On his view, there are various types of “scrutability bases” and various senses that can be given to the “scrutability” relation. His aim is to characterize these different types, and tell us what general type he personally prefers and why. He seeks to provide a general framework for any TOE, not to construct a particular one. I classify him as a “theorist of everything” because he believes that there is a class of basic truths from which all others are “scrutable,” and he believes that this makes the world comprehensible. The “scrutability” relation Chalmers favors is “a priori entailment,” rather than some sort of empirical-​inductive relationship. And his favored class of basic truths “includes both truths of physics and phenomenal truths, as well as certain indexical truths.” The class of physical truths, he writes, will include microphysical truths (truths about fundamental physical entities in the language of a completed fundamental physics) and macrophysical truths (truths about any entities, including macroscopic entities, in the language of classical physics).16

There will also be “phenomenal” truths about phenomenal properties (what it is like to see red or feel pain), and indexical truths of the form “I am X” and “now is Y.” Chalmers claims that “all ordinary macroscopic truths are a priori entailed” by such a class.17 Although he does not use the expression “theory of everything,” he really does seem to mean “everything.” All truths whatever are to be either in the class of basic truths or are to be derivable from such a class. 16. Chalmers, Constructing the World, 110. 17. Chalmers, Constructing the World, 22.

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In what follows I will not focus on the details of any of these theories or programs but only on some general ideas they share and the basis for them.

2 .  Y O U R B A S I C   T O E The term “theory” (like “explanation” and “proof ”) can be used to refer to something that exists, if it does, whether or not it is ever constructed. It can also be used (in a “constructivist” sense) to refer to something that exists, if it does, only when it is constructed.18 So two questions are possible: Does a “Theory of Everything” exist, whether or not it is ever constructed? Will such a theory ever be constructed? (TOE theorists tend to speak in both ways. Those who do so believe that one exists, even if it is never constructed, and that it is possible to construct one or at least get closer and closer.) To answer these questions, we need to consider what constraints we should and should not impose on a TOE if we are to do justice at least to the main ideas of those advocating the search for one. Unfortunately, TOE theorists are not altogether clear or in agreement about this, so decisions about what constraints to make are somewhat open. In what follows 18. I am not here taking sides on the question of whether theories exist independently of us, or whether we construct them. I want to formulate what I  say so that both “constructivists” and “realists” about theory-existence can put aside their differences in order to deal with the questions I  am raising. Constructivists might understand the question “Does a theory of everything exist?” modally as “Is a theory of everything constructible?” Nor will I take a position on the ontological status of theories—​e.g., whether they are to be construed as ordered sets of propositions, or as sets of structures, or something else. The TOE theorists I am concerned with offer no views on this issue.

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I suggest constraints that will, I hope, reflect some basic ones shared by TOE theorists. First, a search for a TOE is a search for a theory that not only purports to explain everything (perhaps some theological theories do) but also is true—​one that offers correct explanations.19 I  will consider such a theory to consist not just in its central and distinctive assumptions but also, since it is supposed to explain everything, in the explanations it offers. Shall we include definitions it introduces, methods of computation, experimental results, and so forth? If so, which ones? In what follows I do not make any stipulations about this. The important requirement is that the theoretical assumptions plus explanations must be correct, though for a theory to be a TOE, I  will not require that it actually be experimentally established as correct or even shown to be probable. Following what I take to be the views of TOE theorists in section 1, I  will suppose:  (1) that a TOE is to correctly explain by appeal to a set of laws for which no further explanation exists—​ “fundamental” laws—​ not just ones for which no further explanation has been or will be discovered; (2) that, according to a TOE, there are (“fundamental”) objects (e.g., strings, or Nagel’s panpsychic “atoms,” or fundamental physical and phenomenal entities in Chalmers’ “scrutability” base, or some fundamental forces or fields or other ontological beings) that are not further analyzable and 19.  Scientific anti-​realists can understand this truth or correctness constraint as one requiring that the theory offer explanations that “save the phenomena.” TOE theorists tend to be scientific realists, or at least speak as if they are. For my own empirical defense of scientific realism, see Achinstein, “Is there a Valid Experimental Argument for Scientific Realism?” Journal of Philosophy 99 (2002): 470–​95.

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that are governed by the laws in the “fundamental” set; and (3) that “everything” that happens is correctly explained by the properties and states of these basic objects and the laws that govern them. What sorts of laws and explanations in suppositions (1)–​ (3) are allowed by TOE theorists? Must the laws be universal, or can they be probabilistic? If the latter are permitted, must a TOE explanation make what is explained highly probable (as Nagel, who seems to be following Hempel’s “inductive-​ statistical” model of explanation, requires)? Or, in accordance with models of explanation proposed by Railton20 and Salmon,21 does it suffice that the fundamental laws give what is to be explained a probability that may be high or low? Or, as Chalmers seems to do, shall we require that a TOE explanation deductively entail the phenomenon explained? Different TOE theorists have different views on these issues (or none at all). The discussion that follows should not be affected by which, if any, of the models of explanation a TOE theorist favors or further conditions a TOE theorist seeks to impose, so long as, according to these different views, suppositions (1)–​(3) are to be satisfied by a TOE. There is another idea invoked by some TOE theorists, viz. “finality.” This may simply involve the thought that no further (deeper, more comprehensive) explanation exists than one provided by a TOE. If so, then the idea is captured by suppositions (1)–​(3). But perhaps there is more to it than that. For example, Steven Weinberg writes that a TOE 20.  Peter Railton, “A Deductive-​ Nomological Model of Probabilistic Explanation,” Philosophy of Science 45 (1978): 206–​26. 21.  Wesley Salmon, Statistical Explanation and Statistical Relevance (Pittsburgh: University of Pittsburgh Press, 1971).

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would declare that things are the way they are because they have to be that way. Any and all variations, no matter how small, lead to a theory that—​like the phrase “This sentence is a lie”—​sows the seeds of its own destruction.22

A “final” theory should not just say what the fundamental laws and entities of the world are in terms of which “everything” can be explained; it should also make a claim to the effect that the world must be such as to contain these entities subject to these laws. (And since we are requiring truth for a TOE, the world must indeed contain these entities and laws.) What sort of “must” is this? If the Liar paradox analogy is to be taken seriously, is it a logical “must?” Or, by analogy with Kant’s defense of Newton’s laws of motion plus gravity,23 is it a metaphysical one? Or is it perhaps an epistemic “must” to the effect that all the evidence known at a given moment should strongly support the theory in question and disconfirm any contrary, or perhaps any known contrary? Weinberg does not elaborate.24 In any case, not all TOE theorists appeal to “finality,” or if they do, it is not clear that they mean more

22. Steven Weinberg, Dreams of a Final Theory: The Scientist’s Search for the Ultimate Laws of Nature (London:  Vintage Books, Random House, 1994), 283. 23. Immanuel Kant, Metaphysical Foundations of Natural Science, ed. and trans. Michael Friedman (Cambridge: Cambridge University Press, 2013). 24.  Richard Dawid (String Theory and Scientific Method [Cambridge: Cambridge University Press, 2013], 130), in a very interesting philosophical discussion of string theory, says that a necessary condition for a final theory is that it “does not have any possible rivals that provide more concise or universal predictions of empirical data.” Here, there is a question about “possible” that is similar to the one I raise about Weinberg’s “must.”

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than is conveyed by suppositions (1)–​(3).25 In what follows, I will simply understand “finality” in the latter sense, without the requirement of logical, metaphysical, or epistemic necessity. This means that a TOE, if one exists, satisfies (1)–​(3) in our world, though not in all logically, metaphysically, or epistemically possible worlds. TOE theorists who want more than this at least want this. For the present discussion it may be “finality” enough. What does “everything” encompass? We cannot impose the constraint that a TOE must provide a correct answer to literally every question that might be asked about anything at all, since according to TOE advocates, the fundamental laws governing fundamental objects have no explanation; they are simply fundamental. But given this exception, there is a lot of leeway. String theorists and mechanical philosophers do not have to claim that “everything” includes facts about mental phenomena, even though Nagel and Chalmers impose such a constraint on a TOE of the sort they want. Still, “everything” should be construed quite broadly, perhaps to include all facts about physical phenomena, or mental phenomena, or both, assuming they are nonfundamental, rather than narrowly to include just facts about certain types of physical or mental phenomena. A TOE of the sort string theorists seek will explain physical micro-​phenomena covered by quantum mechanics, as well as physical macro-​phenomena covered by general relativity. The broader the better, but we don’t have to take “everything” to include all nonfundamental facts about

25. Chalmers, e.g., allows different “scrutability” bases, so for him whether laws and entities cited are “final” depends on which base is selected. Greene (Elegant Universe, 16) is somewhat vague on this issue, saying that a TOE is a “theory that underlies all others, one that does not require or even allow for a deeper explanatory base.”

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all phenomena, even if some TOE advocates seem to (including Nagel, Chalmers, and some string theorists). TOE theorists emphasize that a TOE provides “unification,” although they do not attempt to define this idea. From the examples they offer, one may infer that at least part of what they mean is that a TOE unifies because it correctly explains a remarkably large and diverse range of phenomena (a unification of phenomena—​an idea related to William Whewell’s concept of “consilience”). But there seems to be more to their idea than this. A TOE should unify ontologically by reducing more complex objects to simpler ones governed by a set of laws; and it should explain phenomena at the more complex level by appeal to these simpler objects and laws (ontological reduction). Finally, although this is a bit fuzzier, perhaps TOE theorists will say that the assumptions of a TOE should themselves be unified:  they should “hang together” (unification of assumptions—​an idea quite similar to Whewell’s concept of “coherence”). They should not just be a set each member of which explains something different, but one whose members together explain the phenomena they do. Newton’s gravitational theory of mechanics might be said to unify in all three ways. It unifies celestial and terrestrial phenomena. It unifies ontologically by reducing the various postulated forces of gravity for each planet to just one, the universal force of gravity. And it does these things using a set of laws, viz. Newton’s three laws of motion, plus gravity, that “hang together.”

3 .  I S T H E R E A T O E O N THE HORIZON? No such theory has actually been constructed, or at least no constructed theory is yet established to be a TOE. How

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successful string theory has been in unifying the basic forces of nature is controversial among physicists themselves. Even its proponents recognize its limitations and that it is still a work in progress.26 Smolin, a critic, claims that of the five basic problems of physics cited earlier, string theory has solved, or pointed in the direction of, only two (the unification of particles and forces, and the problem of quantum gravity). He writes: At the present time, string theory does not solve any of the three remaining problems. It appears incapable of explaining the parameters of the standard models of physics and cosmology. It provides a list of possible candidates for the dark matter and energy but doesn’t uniquely predict or explain anything about them. And so far, string theory has nothing to say about the greatest mystery of all, which is the meaning of quantum theory.27

Even if string theory is (or could be developed into) a TOE, there are no experiments showing that the postulated strings and 10-​dimensional spacetime exist and satisfy the claims of the theory.28 (The energies required to produce string effects are too great for current experiments.) Moreover, even its 26. See Greene, Elegant Universe,  15–​20. 27. Smolin, Trouble with Physics, 192–​93. 28. Weinberg’s initial ardor for string theory has cooled a bit. In 2013, he wrote: “I have been a fan of string theory, but it is disappointing that no one so far has succeeded in find a solution that corresponds to the world we observe” (“Physics: What We Do and Don’t Know,” New York Review of Books, September 7, 2013). And in 2015, in his book To Explain the World, he expresses even more cooling. (See the passage quoted in ­chapter  1, p. 6, above.) While he may not be as optimistic about string theory as he once was, I will assume that he is just as passionate about finding a TOE of some sort.

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proponents admit that the exact equations of the theory are not yet known.29 The other potential TOEs mentioned earlier fare even worse. The seventeenth-​century mechanical philosophy has been abandoned. Nagel provides only a bare outline of the kind of TOE he seeks. And Chalmers presents very general ideas on how a TOE should be constructed, without even beginning the construction of one. This, however, will not discourage TOE theorists. What they believe is: (i) that such a theory exists, whether or not it is ever constructed; (ii) that constructing such a theory is an “ideal” toward which science and scientists should aim; and (iii) that it is “in principle” possible to construct such a theory. Given (i)–​(iii), they assert that searching for a Theory of Everything is a good and reasonable thing to do. What does “in principle” mean in (iii)? At least that it is not a logical contradiction to assert that such a theory will be constructed. Possibly, it is supposed to mean more, viz. that the construction of such a theory (and hence its existence) is not incompatible with established scientific laws, or with any laws that govern the universe, whether established or not. Or perhaps it is supposed to mean something epistemic, viz. that on the basis of all the evidence we now have, there is no reason for us to believe that such a theory will not be constructed. That it is not a logical, or nomological, or epistemic contradiction to assert that a TOE will be constructed is no reason to think that one will be. Nor, more important, is the fact that it is not a logical, nomological, or epistemic contradiction to assert that such a theory exists any reason to think that one does. (To borrow an example used by Daniel Dennett in discussions

29. See Smolin, Trouble with Physics, and Weinberg, To Explain the World.

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about God, that there is a teacup on Mars is not a logical, physical, or epistemic impossibility, but is no reason to think there is one.) Without asking about evidence for any particular theory that claims to be a TOE, is there any reason to believe the gen­ eral claim that the search for a TOE will not be in vain? In the next two sections, I  consider some very general arguments. Each focuses on one or more aspects of what a TOE is supposed to provide. If none by itself provides evidence for the existence or constructability of a TOE, perhaps together they do so, and thereby demonstrate that it is not a speculation. Or, for those such as the present author who consider the idea of a TOE to be a speculation, perhaps the arguments show at least that it is a good speculation—​ one worth pursuing. The arguments I consider are not ones for believing that some particular TOE exists and can be constructed, such as string theory or Nagel’s panpsychic theory. They do not purport to show, e.g., that strings or panpsychic “atoms” exist. Rather, they are supposed to provide at least some reason to think that some TOE or other exists and can be constructed, or at least that scientists must presuppose that this is so.30

4 .   H I S T O R I C A L A N D PRESUPPOSITION ARGUMENTS FOR THE EXISTENCE OF A TOE One line of thought is that the sciences, particularly physics, chemistry, and biology, have historically gone in a direction 30.  Accordingly, these arguments presuppose a (“non-​ constructivist”) view of theories according to which theories exist whether or not they can be constructed by us. See note 18, this chapter.

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from macro systems to micro systems that comprise them (e.g., from gases, to molecules, to atoms, to nuclei, to protons, to quarks, to strings); and from a set of laws governing one system to more fundamental laws governing the more fundamental system. Such efforts have met with success. Hence, it seems reasonable to expect a “final” micro-​theory as an endpoint in this process. Steven Weinberg writes: If history is any guide at all, it seems to me to suggest that there is a final theory.  .  .  . Our deepest principles, although not yet final, have become steadily more simple and economical. . . . It is very difficult to conceive of a regression of more and more fundamental theories becoming simpler and more unified, without the arrows of explanation having to converge somewhere.31

Weinberg makes it clear that this final theory will contain fundamental principles that govern “elementary” particles.32 One problem with this is that there are examples of scientific progressions in the opposite direction (e.g., going from macro-​laws governing gases to even broader macro-​ generalizations in classical thermodynamics governing 31. Weinberg, Dreams of a Final Theory, 231–​32. This is also one of the arguments for the “unity of science” program presented by Oppenheim and Putnam, “Unity of Science.” They speak of the direction from the macro to the micro as a “basic trend within science,” that has had many successes. And they speak of this trend as involving five levels:  social groups, multicellular living things, cells, molecules, atoms, and elementary particles (see 4, 9, 27–​28). See also Causey, Unity of Science. 32. In his discussion of “three contextual arguments” that string theorists use in favor of their theory, Dawid (String Theory, 35–​37) cites a similar “meta-​inductive” argument from the success of the so-​called standard model in physics to string theory as a “natural continuation of the successful particle physics research program.”

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thermodynamic systems generally; or, as noted in the previous chapters on simplicity, going from simple theories about the number of elements to complex ones). But let us accept the idea that the history of science does contain (some) progressions from macro to micro, and some from complex to simple. Historically, when physicists have postulated some entity and claimed it to be simple, fundamental, and unanalyzable (whether molecules, atoms, nuclei, protons, or quarks), they have later postulated even simpler ones (now strings) of which it is composed. And when physicists have formulated laws and claimed them to be fundamental (whether at the micro or macro level), often new phenomena have been discovered showing that the laws are not fundamental, or not even true, or at best approximately true or of limited applicability, or special cases of more fundamental ones (as happened with Newtonian mechanics). The history of physics by itself offers little if any reason to suppose that a correct and constructible fundamental theory exists. Indeed, if anything, it seems to provide support for the claim that one does not exist.33 Whatever support Weinberg’s historical argument provides for the existence of fundamental objects and laws, it does not constitute what in ­chapter 1 I called “explanatory evidence” that such objects and laws exist. Given that there 33. In c­ hapter 3, when considering a historical argument in favor of simplicity, I noted Larry Laudan’s “pessimistic induction” from the history of science. In a PBS interview on NOVA, Weinberg rejects the pessimistic induction:  “Sometimes you’ll hear people say that surely there’s no final theory because, after all, every time we’ve made a step toward unification or toward simplification we always find more and more complexity there. That just means we haven’t found it yet.” Weinberg’s final sentence here I would call an “optimistic counterinduction.”

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are some historical tendencies in science toward simpler and more fundamental theories, it is not probable that there is an explanatory connection between such tendencies and the fact, if it is one, that there are fundamental “atoms” (whatever they might be) and fundamental laws (whatever they might be). Perhaps the historical tendency of (some) physicists to proceed in a micro direction to simpler and more fundamental theories suggests the idea, and produces the hope, that a “final” TOE will be found. Perhaps it makes it probable that (some) physicists will continue to search for one. But this does not provide evidence for the claim that there is one, or that if there is they will find it. Finally, a proponent of a “historical argument” for the existence of a TOE has to show more than just that there is a theory describing fundamental entities subject to fundamental laws. He must also show that such a theory is a “Theory of Everything,” that it can unify and explain “everything.” But the history of science is full of examples in which a new theory, more fundamental and unifying than any previous one, does not, its proponent admits, explain everything, even phenomena the theorizer would like to explain that are supposed to come under the rubric of the theory. Maxwell points out that his molecular theory does not explain the known specific heat ratios of gases or their electrical conductivity. Newton points out that his mechanical theory does not explain why the planets move in the same direction on the same plane (see ­chapter 1). And, as I will note later, some physicists argue that there are certain physical systems so complex that no theory has or even could explain them.34 34. R. B. Laughlin and David Pines, “The Theory of Everything,” Proceedings of the National Academy of Sciences 97(1): 28–​31.

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A second argument, or at least claim, I will mention here is due to Thomas Nagel. The claim is not that a TOE exists but that its existence must be presupposed by science. Here are two passages from Nagel: Science is driven by the assumption that the world is intelligible. That is, the world in which we find ourselves, and about which experience gives us some information, can be not only described but understood. It seems to me that one cannot really understand the scientific world view unless one assumes that the intelligibility of the world, as described by the laws that science has uncovered, is itself part of the deepest explanation of why things are as they are.35

Nagel’s idea is that scientific inquiry itself (“the scientific worldview”) presupposes the “intelligibility of the world.”36 And, he goes on to argue, a necessary condition for the latter is that there is a TOE that explains everything at the most fundamental level.

35. Nagel, Mind and Cosmos, 16, 17. 36.  The second passage quoted here is a complex one that says at least this. But the way it is worded suggests something in addition: the scientific worldview presupposes that part of the deepest explanation of why things are as they are is that the world is intelligible. The latter I find puzzling. Does it imply, e.g., that part of the deepest explanation of why electrons exist and have negative charge is that the world is intelligible? How does intelligibility explain or partly explain that? Or is the claim supposed to mean that the scientific worldview presupposes that part of the deepest explanation of why the world is the way it is that the world is intelligible. It seems to me that it should be the other way around: part of the deepest explanation of why the world is intelligible is that the world is the way it is (subject to laws, etc.).

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This obviously does not establish, or give an epistemic reason for believing, that a TOE exists, only a pragmatic reason for presupposing that one does:  you can’t do science without presupposing this. But is it even true, as Nagel supposes, that scientists themselves generally assume or presuppose that the world is intelligible in the way that he imagines (intelligible in terms of fundamental “atoms” and laws)—​even with respect to phenomena of a sort that fall within the scope of their inquiries? As noted earlier, Newton believed that certain physical properties of the planets, e.g., the fact that they revolve around the sun in the same direction and on the same plane, cannot be explained mechanically at any level, even an “atomic” one, but require God’s intervention (not bodies subject to forces). Vitalists in biology, such as the early twentieth-​century zoologist Hans Driesch, believed that biological processes, such as ones involving a two-​celled egg forming a larva, cannot be explained in terms of the physical and chemical constituents of the process. These scientists rejected the idea that scientific inquiry presupposes the existence of a correct explanation of a sort Nagel requires. There are sympathetic supporters of string theory who remain agnostic about whether string theory, or any other candidate with laws and “atoms” that are claimed to be fundamental, can explain mental phenomena or even all physical ones. There are physicists who raise the skeptical possibility that certain physical facts—​e.g., the fundamental constants of nature having the values they do—​are matters of “happenstance” and have no explanation of the sort Nagel has in mind. Is Nagel assuming that all scientists in fact subscribe to a worldview that presupposes what he says? Such an assumption is refuted by the history of science. Is he claiming that even if

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there are scientists who don’t presuppose that the world is intelligible in a sense requiring a TOE, scientists must presuppose this to do science at all? That claim is again refuted by the history of science, unless we want to say scientists who engage in what we regard as scientific activities, but do not believe that everything is explainable by a TOE, aren’t really engaging in activities that are scientific. Finally, perhaps Nagel is saying that it would be a very good thing for scientists to assume Nagelian “intelligibility”—​good enough to be a requirement for doing good science. This claim is an important one, and I will discuss it in section 7.

5 .  T H E U N I F I C AT I O N A R G U M E N T Smolin puts this argument for a TOE as follows: The mind calls out for a third theory [beyond general relativity and quantum theory] to unify all of physics. And for a simple reason. Nature is in an obvious sense “unified.” The universe we find ourselves in is interconnected, in that everything interacts with everything else. There is no way we can have two theories of nature covering different phenomena, as if one had nothing to do with the other. Any claim for a final theory must be a complete theory of nature. It must encompass all we know.37

Smolin has in mind the fact that the four basic forces in physics interact (electromagnetic, gravitational, and strong and weak nuclear forces). Nagel, who has a similar idea, focuses on the fact that the mind interacts with the body. 37. Smolin, Trouble with Physics,  4–​5.

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One way to construe the interaction claims in Smolin’s quote is simply as suggesting a motivation for searching for a TOE:  since everything interacts with everything else, it would be desirable if a TOE could be discovered to explain these interactions. This claim, I will consider in section 7. In the present section I  will construe the quote as containing an argument for the existence of a TOE (one that makes the mind “call out” for a TOE). The argument, whether construed as providing evidence sufficient to believe the conclusion (so that it is not a speculation), or just as providing some supporting reason for a speculative conclusion, makes two claims: (i) if entities subject to certain laws interact (e.g., electromagnetic and nuclear forces, the mind and the body), there must be, or there probably is, some more basic set of unifying entities and laws that govern such interactions; (ii) therefore, since everything interacts with everything else there cannot be separate, unrelated theories of nature governing all phenomena. There can only be one, a TOE, and it will unify all interactions. It is not completely clear how broadly or narrowly TOE theorists want to construe the idea of an “interaction,” and therefore whether the claim that everything interacts with everything else is true. Nor, even if everything does interact with everything else, does (ii) follow from (i)—​that is, that there exists some fundamental TOE that unifies and explains all these interactions. Each interaction could be explained by some deeper unifying theory without its being the case that all interactions are unified and explained by the same theory. But putting these issues aside, I  want to focus here on the weaker but important claim (i). What sort of unification do TOE theorists have in mind here? In section 2, I  distinguished three ways a theory

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might unify. It might explain a range of different phenomena (Whewellian “consilience”); it might unify ontologically by reducing a more complex system to a simpler or more basic one; it might contain unified assumptions (Whewellian “coherence”). TOE theorists, I think, have in mind all three. But it is the second idea, ontological reduction, that is particularly important here in order to understand what TOE theorists are aiming for in presenting the “unification argument.” To see what such ontological unification by reduction might involve, let us contrast two cases in classical physics, both involving interacting forces. In the first case, consider the forces acting on each planet by the sun and by all the other planets. Newton’s theory unified these forces ontologically by arguing that what may appear to be various forces of gravity (or “heaviness”) exerted on and by the planets are not many different types of force, but one, subject to one law—​the universal law of gravity. Contrast this case with that of a parachutist falling who is subject to interacting forces of gravity and air resistance. These opposing forces combine to produce a much smaller acceleration (if any) than gravity alone. This type of combining of forces, even if we know how to compute it, is not what TOE theorists have in mind (or at least it is not all they have in mind). It is not ontological unification, since there are still distinct forces acting. Ontologically unifying these forces in such a case (if that were possible) would mean explaining both gravity and air resistance in terms of a single force (as in the case of Newton’s universal gravity), or explaining these forces by invoking some more basic system, different states of which give rise to the two forces (as in the case of Maxwell’s

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unification of electricity and magnetism by a set of equations governing the electromagnetic field).38 Suppose that the four fundamental forces admitted by current physics, subject to laws governing each, interact on certain occasions to produce a given result. What string theorists have in mind is a TOE that unifies these forces ontologically. As I am construing claim (i) of the present interaction argument, from the fact that the forces interact, we may infer that there is a deeper law or theory unifying the forces by showing them to be manifestations of a single force or by showing that they are produced by some more basic system, different states of which give rise to these forces. Similarly, from the fact that physical and mental states interact to produce certain behavior, we may infer the existence of some more basic state that has or gives rise to both mental and physical properties. Why should this be so? What general reason might be offered for inferring such ontological unification from interaction? Perhaps an appeal can be made to the “common cause principle,” first introduced by Reichenbach,39 according to which if two types of events or states of affairs are correlated, then, assuming they are not identical, either one causes the other or there is a common cause. So in physics, if two or more forces are found to operate together (say, electromagnetic 38. The Maxwell unification is one that TOE proponents (and opponents) often cite. But whether this is a genuine ontological unification, as they claim, is an interesting question. For an argument that it is not, see Robert Rynasiewicz, “Field Unification in the Maxwell-​ Lorentz Theory with Absolute Space,” Philosophy of Science 70 (2003): 1063–​72. 39.  Hans Reichenbach, The Direction of Time (Berkeley:  University of California Press, 1956).

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and gravitational forces producing the motions of charged bodies with mass), and if one (say, the electromagnetic) does not cause the other (gravity), then there must be a common cause of both forces and hence of the effects produced. But the common cause principle is subject to counterexamples (in quantum mechanics, electromagnetic theory, and other cases).40 There is no convincing empirical argument for the general validity of this principle. If there is a common cause in a given case, that can only be shown empirically by appeal to the facts of the case, not by appeal to the common cause principle.41 In the parachute example, there is no reason to infer that the forces of gravity and air resistance have a common cause or that they are identical from the fact that these forces interact to produce the effect. Nor does one need to infer this in order to understand the effect in this case. To be sure, depending on the circumstances, one may be motivated by a desire for unification to try to understand certain interactions by proposing an ontological unification. But neither the fact of interaction nor the desire to find a unification provides a reason to infer that such a unification exists. Smolin himself seems to recognize this. A few pages after the earlier quoted passage (which strongly suggests an inferential argument), in commenting on the question of “whether all the forces we observe in nature 40. See van Fraassen, Scientific Image, and John Earman, Bangs, Crunches, Whimpers, and Shrieks (Oxford:  Oxford University Press, 1995). There are various formulations of the common cause principle, each subject to problems. 41. In the common cause case, we are dealing with correlations rather than interactions. But the common cause principle still might be invoked, since in certain cases there is a correlation: when one force acts so does another; and one force doesn’t produce the other.

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might be manifestations of a single, fundamental force,” he writes: “There seems, as far as I can tell, no logical argument that this should be true, but it is still something that might be true.”42 Here, Smolin treats the “interaction” idea not as an evidential basis for a TOE but, rather, as a pragmatic basis for searching for one (a view I will discuss later).43 Finally, if:  (a) interaction does require, or make probable, an ontological unification (of one of the two sorts I have mentioned); and (b)  everything interacts with everything else, then there can be only one type of “fundamental” object. Suppose, in accordance with (b), two types of  objects interact, and suppose both are claimed to be “fundamental.” If they do interact, then, in accordance with (a), there is, or is likely to be, an ontological unification. This means that either these objects are of the same type (e.g., both involve bodies exerting a gravitational force) or else there are more fundamental objects responsible for the interaction. In the first case, we have only one type of object, and in the second case, we do not have “fundamental” objects. To be sure, the existence of only one type of “fundamental” object is what string theorists and Nagel seem to want. But I am not making it a condition for a TOE that it postulate only one type of “fundamental” object. Nor, as I indicated earlier, do I accept assumptions (a) and (b), which necessitate that conclusion. 42. Smolin, Trouble with Physics, 11. 43.  John Dupré, an arch anti-​reductionist, takes the fact that in biology there are “complex interdependencies at different levels of structural complexity” to show the implausibility of reductionism of the sort demanded by a  TOE (Dupré, The Disorder of Things [Cambridge, MA:  Harvard University Press, 2003], 103). My claim is weaker: interdependencies, by themselves, don’t provide any reason for (or against) believing that there is a deeper, unifying law or system.

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6 .  O T H E R P O S S I B L E A R G U M E N T S T R AT E G I E S If the previous arguments do not establish or even give some reason to believe that a TOE exists, what sort would? Various strategies might be tried, some empirical, some a priori. I begin with two empirical ones. Empirical strategy 1: (a)  Start with a potential TOE (or at least a part of one) and provide some empirical reason to think that the allegedly fundamental objects postulated exist and that the allegedly fundamental laws invoked are true; (b)  show how this potential TOE in fact explains a wide variety of phenomena in terms of the laws governing these objects; (c) argue inductively that the allegedly fundamental objects and laws are genuinely fundamental since no known objects and laws are more fundamental and since the explanations in (b) do not, and do not need to, introduce any more fundamental objects and laws to explain what they do; (d) argue, again inductively, from (a)–​(c), that probably “all” other phenomena, known and unknown, can be explained by reference to the objects and laws in question, and require no more fundamental objects and laws to be explained.44 Empirical strategy 2: (i) Start with a non-​TOE, appealing to objects, laws, and phenomena that have been discovered and 44. As I noted in c­ hapter 4, Maxwell (Niven, ed., The Scientific Papers of James Clerk Maxwell, 2:413–​38) employs an inductive argument to argue from the fact that mechanical laws explain celestial motions, and various electrical phenomena, to the claim that they may well explain the behavior of gases. He offers such reasoning to justify his application of mechanical laws to molecular motion in gases.

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are not claimed to be fundamental; (ii) argue that the particular physical characteristics of these discovered objects, laws, and phenomena constitute some reason to believe that there are underlying objects and laws that can explain the behav­ ior of the discovered objects and other phenomena as well; (iii) extend this type of reasoning until objects and laws are inferred from the evidence that explain a large range of phenomena, where no more fundamental objects and laws are known or required for the explanations; (iv) proceed inductively in the manner of (c) and (d) above to the conclusion that the objects and laws are fundamental and that “all” phenomena can be explained by reference to them. These empirical strategies do not appeal to the history of science, or to what scientists presuppose, or to the very gen­ eral idea that everything interacts with everything else. Both strategies involve the construction of a particular TOE. In the first, we start with a potential TOE and argue that it really is a TOE. In the second, we start with something that is not a TOE and argue to the existence of a particular TOE. Neither task has been accomplished by any of the TOE proponents mentioned. With respect to the first strategy, as noted in section 4, the “fundamental” objects TOE theorists have postulated (now or in the past) have not been shown to be fundamental. And in the case of strings, or Nagel’s panpsychic “atoms,” they have not even been shown to exist. Nor (in the case of Nagel and Chalmers) have laws been formulated, or if they have (as with the mechanical philosophy), they are either false (as with Newton’s law of gravity) or else not shown to be true or to have empirical support (as with string theory). Even if steps (a) and (b) of strategy 1 are somehow accomplished, some empirical reasons are

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needed in defense of the grand inductive generalizations in (c) and (d). In the case of the second strategy, (i) and (ii) are familiar moves. (For example, they are employed by Perrin in arguing from the existence of Brownian motion to the existence of molecules that explain such motion and other phenomena as well.45) It is (iii) and (iv)—​producing arguments for fundamentality and for universal explanatory power—​that have yet to be accomplished. As in the case of string theory, or molecular theory in the nineteenth century, there are (or were) known phenomena (e.g., dark matter and “arbitrary” constants in the case of string theory, electrical properties of gases for molecular theory) that resist or have resisted explanation in terms of the objects and laws postulated. What is also needed is an empirical defense for the idea that these micro-​objects and the laws governing them are fundamental (that they themselves have no further explanation) and that they can explain “everything.” It is not my claim that these defenses are impossible to mount, only that they represent very ambitious programs that have never been carried out successfully in the history of science. (Later I will claim that the reason TOE theorists give for encouraging such programs is not compelling.) A Priori Strategies: TOE enthusiasts may want to construe the claim that a TOE exists not as empirical but as a priori. One approach is to understand this claim as an a priori metaphysical one about the universe to the effect that the universe

45.  See Achinstein, “Is there an Experimental Argument for Scientific Realism?”

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must contain fundamental objects subject to fundamental laws that explain “everything.” TOE enthusiasts such as Weinberg, Greene, Nagel, and Chalmers present no reasons for supposing that this is so.46 Earlier, I  noted Weinberg’s claim that a TOE is a “final” theory in the sense that such a theory states that the world must contain the fundamental laws and objects it postulates that explain “everything.” (I then said that for the purposes of the discussion, I  would not make this a requirement for “finality.”) But even if a TOE is to state that the world must be this way, and even if the “must” is construed metaphysically, it doesn’t follow that such a (correct) TOE in fact exists and that the world must be (and hence is) that way. All that follows is that if such a TOE exists (one stating that the world must be that way), then the world must be that way. Nagel claims that scientists do, and perhaps must, assume that the world is that way. But even if Nagel were right, it doesn’t follow that the world is or must be that way. Perhaps, then, the claim that a TOE exists is supposed to reflect an a priori metaphysical truth that requires no argument because it is self-​evident. It doesn’t look self-​evident. (If it were self-​evident, why would physicists such as Weinberg and Smolin try to present arguments for it?) Indeed, various scientists have thought it is false. I have already mentioned 46. Greene, denying that it is an a priori metaphysical claim, says that it is possible that certain features of the universe are what they are by chance or divine choice. (See earlier quote in ­chapter 3, p. 135.) Weinberg (Dreams of a final Theory, 54) says that his claim that a reductive TOE exists is “a statement of the order of nature, which I think is simply true.” But he offers no defense. Chalmers doesn’t argue that a TOE must or does exist, but seems to take the line that it would be a good thing if it did (a position I examine in section 7).

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Newton, who invoked God, rather than bodies and forces, to explain certain facts about planetary motion, which he believed could not be explained in mechanical terms; and Driesch, who invoked emergent, non-​reductive vital forces to do an analogous thing in biology. Even some more recent physicists such as Prigogine47 and Laughlin and Pines48 reject the idea that all physical phenomena are reducible to “fundamental” entities and laws.49 These scientists may be importantly mistaken in their views, but if their mistake is a priori, that should be demonstrated. Appeals to a priori self-​ evidence are notoriously suspect. There is another a priori strategy. Rather than attempting to show a priori that a TOE exists, it seeks to defend an a priori evaluative claim to the effect that it would be desirable for science if one did exist, whether or not it does and whether or not scientists could discover it. I  turn to this claim next.

7 .  W H Y W O U L D I T B E G O O D I F   A “ T H E O RY O F   E V E RY T H I N G ” EXISTED? The answer I  will consider is a simple and powerful one:  it would be good because then the world would be completely intelligible, a position taken by Nagel, as well as by Weinberg, 47.  I. Prigogine and Isabelle Stengers, Order Out of Chaos (New  York: Bantam Books, 1984). 48. Laughlin and Pines, “Theory of Everything,” 28–​31. 49. Prigogine does so for certain thermodynamic states, and Laughlin and Pines do so for certain crystalline states.

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Greene, and Chalmers.50 To properly respond to this answer, we need to consider the proposition that the world is completely intelligible. There are two ways to understand it. One way is as an assumption about a “rational order” that exists in the world itself, whether or not we do or can know what this order is. Such a world is “explainable” whether or not we can discover the explanations. It might be held that such a world exists only if things that happen in the world are subject to laws, either universal or statistical. And, to add a TOE idea, the properties of and laws governing the most basic things in the universe explain (either universally or probabilistically) the properties and laws governing all other things in the universe. The world could be “intelligible” in this way whether or not we do or even can discover this “intelligibility.”51 The second way to understand the proposition that the world is completely intelligible is as saying that the world is completely intelligible to us—​that we, or scientists, can achieve, or at least get closer to and approach, a complete understanding of the world. In both cases, “intelligibility” involves an idea of “correctness.” If the world is “intelligible” 50. In the previous section, I asked what reason we have to assume that the world is completely intelligible in the way Nagel suggests. Now I am asking why it would be good if it is. 51. This, of course, is just one concept of “intelligibility” for the world. It is one espoused not only by Nagel but by Weinberg as well—​both as regards its “objectivity” and its reduction to unifying laws governing fundamental constituents. Weinberg (Dreams of a Final Theory, 54) makes it clear that he is “talking about nature itself,” not what scientists can or will discover. And Nagel, although he claims to be espousing a form of idealism, makes it clear that this is objective rather than subjective idealism (Mind and Cosmos, 17). He, too, is “talking about nature itself,” even if his concept of nature fits some idealist mold.

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in the first sense, then it is in fact subject to fundamental laws governing fundamental “atoms” correctly described by a TOE. And if it is “intelligible to us,” then we can come to know, or come closer to knowing, what these laws and “atoms” are and how everything is explained by them.52 We can come to know, or come closer to knowing, this “rational order.” (For the present, I  will suppose this is what being “intelligible to us” requires; later, when I speak about “Newtonian intelligibility,” I will question that assumption.) Why would it be a good thing if the universe were completely intelligible in the unrelativized (“rational order”) sense? It might be said that a “rationally ordered” universe—​ one correctly described by a TOE—​would be a good thing because it would have an intrinsic beauty, simplicity, and unity. It would be better than a universe that lacked these virtues. My response is to say that, even if this is admitted, from a scientific perspective—​from a perspective of what scientists and the rest of us seek from science—​the existence of such a rational order would be a good thing only if we, or scientists, could come to know and understand this order by understanding the explanations given by that TOE. Knowledge and understanding of the universe I take to be major goals of science. But suppose the fundamental laws of the TOE are too complex for us to understand.53 Or suppose they are not too complex for us to understand, but when we attempt to make a calculation from them that is needed to produce an explanation, we can’t 52. This second sense is what Chalmers seems to be concerned with when he speaks of the world as being “comprehensible” by being “scrutable from some basic truths.” 53.  Weinberg (Dreams of a Final Theory, 233, 235)  mentions this possibility:  “Perhaps there is a final theory, a simple set of principles from

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do it. Laughlin and Pines offer an example of a quantum mechanical equation relating charge and mass of electrons and atomic nuclei that covers many macro-​and micro-​bodies. In their critique of the idea of a TOE, they write: However, it is obvious  .  .  .  that the Theory of Everything is not even remotely a theory of every thing. . . . We know this equation is correct. . . . However, it cannot be solved accurately when the number of particles exceeds about 10. No computer existing, or that will ever exist, can break this barrier because it is a catastrophe of dimensions.54

Nancy Cartwright55 borrows an even simpler example from Otto Neurath, in which a thousand dollar bill is swept away by the wind and eventually falls to the ground; it is subject to forces of gravity, wind, and friction. Even if we were able to cite (macro-​) laws governing these forces, we are unable to combine them and calculate where the bill will fall, and hence explain why it fell where it did.56 Even if in some which flow all arrows of explanation, but we shall never learn what it is. For instance, it may be that humans are simply not intelligent enough to discover or to understand the final theory.” But readers should not despair, Weinberg adds, reassuringly, “my own guess is that there is a final theory, and we are capable of discovering it.” By contrast, Nagel seems to be asserting that if there is a final theory—​if the world is completely intelligible—​then it follows that we humans can discover this theory. What I am questioning here is the truth of this claim. 54. Laughlin and Pines, “Theory of Everything,” 28. 55.  Nancy Cartwright, The Dappled World (Cambridge:  Cambridge University Press, 1999), 26–​27. 56.  We might understand the forces and laws involved that determined where it landed. But I take it that this is not sufficient for (Nagelian) “complete intelligibility,” since we don’t understand how these forces combine to determine where it landed.

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abstract sense such a computation exists, we are unable to produce it. And if we were somehow able to succeed at this at the macro-​level, suppose we could not compute a result from fundamental laws governing the basic “atoms.” TOE champions speak of computability (or “explainability,” or “intelligibility”) in principle. But “in principle” has little significance, at least in scientific pursuits, if in a straightforward, ordinary sense scientists can’t accomplish or achieve this and don’t care that they can’t.57 What I am suggesting is that “intelligibility” of the world in the unrelativized sense would be a “good thing,” as far as science is concerned, only if it is also intelligibility in the relativized sense. Otherwise, it becomes like God telling the suffering Job that the world is intelligible, just not to him or other humans. This may be comforting to Job and to others of faith, but it should not be to scientists seeking to understand the world. What they do and should care about is making the world intelligible to them (and to us). But if we relativize intelligibility to what scientists, and perhaps the rest of us, do and should care about, then we need to consider not just what scientists and others can understand but also what they want to understand and with what depth and completeness they want to do so. In what follows, I will call this “Newtonian intelligibility.” I do so not because Newton attempted to make things intelligible in terms of bodies, motions, and forces but because he attempted to make things intelligible in a way that needs to be viewed in terms of the problems he was trying to solve and the level at which he was trying to solve them. 57.  “Constructivists” will say that an explanation (computation) “in principle” is no explanation at all. “Realists” will say that even if it is an explanation, if it is unproducible, it is not one of interest to science.

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The basic idea is that “completeness,” as far as intelligibility is concerned, is relative to context.

8 .   N E W T O N I A N I N T E L L I G I B I L I T Y: S AT I S   E S T Earlier, I  spoke of seventeenth-​century mechanical philosophy, represented by Newtonian physics, as an example of a (potential) TOE. But now we need to think more carefully about the idea of “everything” in a TOE. It is true that in his preface to Principia, Newton states his aim very boldly and generally as one of discovering the forces of nature from the motions of bodies and then of explaining celestial and other phenomena on the basis of these forces. But in fact the only force he is really concerned with is gravity (he mentions electrical forces, friction, and forces of repulsion, but doesn’t work anything out). He is uncertain as to whether there are atoms (i.e., fundamental, indivisible bodies).58 Nor, as noted earlier, does he think it is possible to determine from his theory (or from any other mechanical one) what causes the planets to orbit in the same direction on the same plane. Most important, the theory Newton presents does not answer the question “Why do bodies attract each other in accordance with the law of gravity?”—​a question Newton explicitly raises but says that he cannot answer and that he will not “feign hypotheses” to try to do so:  “It is enough” (satis est), says Newton, “that gravity really exists and acts according to the laws that we have set forth and is sufficient to explain all the motions of the heavenly bodies and of our 58. Newton, Principia, 795–​96.

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sea.”59 Newton limits his class of “everything” to a broad range of phenomena he seeks to explain in his present investigation. This is so as well for the depth of the explanation. He is not attempting to discover a complete set of fundamental laws and objects that can explain all phenomena in nature at the deepest level. Are the explanations he offers “incomplete”? There are different ways this question could be answered, since there are different ways or respects in which an explanatory task can be considered complete or incomplete. Newton’s explanations are incomplete in the sense that they don’t answer all questions that might be raised, or even ones he himself raised about the phenomena he considered (e.g., What causes gravity to be exerted between bodies?). Nor do they answer the questions they do by invoking fundamental properties and laws governing basic “atoms” in the universe. In these respects, they are not “complete.” The explanations they give are not derived from a TOE. But there is another way to judge completeness. It is one that is relativized to the Newtonian context, to the specific project Newton sets for himself in the Principia. That project is to begin with established astronomical facts about the Keplerian motions of the planets and their moons; show how these facts provide strong evidence for the law of gravity by “deducing” the latter from the astronomical facts using his three laws of motion and theorems that follow from them; and then show how the motions of celestial bodies, and other phenomena such as the tides, can be explained from the law of gravity. Does he complete this project?

59. Newton, Principia, 943.

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What does such “completion” require? If it requires that the law and explanations offered be correct, then Newton did not complete the project. If it requires only that Newton present evidence for the law and show how to give the explanations, then whether he completed the project depends on the sense of evidence in question. He did not supply veridical evidence, since the law is not true. Nor, as I have argued, did he supply ES-​evidence—​he needed more observations. He did supply subjective evidence—​observational facts he believed constituted veridical evidence for his law. And he did furnish the explanations. So, he certainly believed that he completed his project, even if, using an objective concept of evidence, he was mistaken. But when “completion” is understood using an objective concept of evidence, it is not that his project was incomplete because his explanations were not derived from a TOE that is correct and for which there is objective evidence. His project was incomplete because his explanations were not derived from a law that is correct and for which there is objective evidence. One important way to understand “intelligibility” is as relativized to a project in which one is attempting to explain a set of phenomena and to provide evidence for its correctness. If the project is completed, and an explanation of the type sought is correct, then the “intelligibility” of the phenomena is complete with respect to that project—​with respect to the questions raised, the level at which they are raised, and standards of completeness set by the project. This is what I have called “Newtonian intelligibility,” even if Newton did not himself achieve it. His aim was to do so, his attempt was monumental, and, most important for present purposes, it is the type of intelligibility that all but entrenched skeptics believe scientists can and should try to achieve. To be sure, even

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if the explanation provided is correct and meets standards set by the project, other projects may require that the sort of explanation provided be at a different level and that a different standard of completeness for intelligibility be met. But that is still “Newtonian intelligibility,” now relativized to a different project. James Clerk Maxwell is also a defender and practitioner of “Newtonian intelligibility” (despite his view noted earlier about the fundamentality of dynamical explanations). He writes: “In all scientific procedure we begin by marking out a certain region or subject as the field of our investigations. To this we must confine our attention, leaving the rest of the universe out of account till we have completed the investigation in which we are engaged.”60 This does not mean that scientific inquiry ends when “Newtonian intelligibility” has been achieved—​ when the problem at issue is solved at some contextually determined appropriate level. Other tasks usually await us. But the idea behind “Newtonian intelligibility” is that whether, or to what extent, a theory has been established that provides complete intelligibility is to be evaluated, not just by how the world is but also by specific requirements of the inquiry.61 The inquiry can change as more information is discovered, further questions are raised, and new requirements set, so that what is complete in one inquiry and context is not complete in another. If you judge completeness solely by reference to the way the world is, then you ignore what I  earlier called the “scientific perspective.” To claim that unless a TOE is 60. Niven, ed., The Scientific Papers of James Clerk Maxwell. 61. For a general defense of the importance of contextual considerations in evaluating explanations, see Achinstein, Nature of Explanation.

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produced and established the world is not completely intelligible is to do just that.

9 .   C O N C L U S I O N S Scientists who search for a TOE, or philosophers who advocate such a search, offer very general empirical or a priori reasons for thinking that one does or must exist and can be constructed (“in principle”). They also offer very general methodological reasons for their search, saying that the practice of science presupposes the existence and constructability of some TOE, or that it is or should be an aim of science to produce one, or at least it would be good if one existed, since otherwise the world would not be completely intelligible. These general reasons are the ones I  have been criticizing. They are not strong enough to show that the claims made about the existence and desirability of a TOE are anything more than speculations or, to use Weinberg’s term, “dreams.” Nor, considered even as speculations or dreams, are the reasons offered for them strong enough to show that these are good speculations—​ones worth pursuing—​or so I have argued. Some anti-​reductionists (e.g., Cartwright and Dupré) emphasize the complexity of the world as a reason, whether empirical or a priori, for rejecting the strong form of reductionism presupposed by TOE enthusiasts. My argument with TOE theorists is not that there is some good empirical or a priori reason for thinking that a TOE does not exist. (I would not accept the idea that complexity is such a reason.) My argument is that TOE theorists have presented no good general reason for thinking that a TOE does or may well exist. Nor

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have they presented any plausible reason to conclude that if one doesn’t exist, the world is not completely intelligible in a way that matters to science. This does not mean that string theory, or Nagel’s panpsychic theory, or any other purported TOE should not be pursued. My claim is that if such theories are pursued, these endeavors should not be based on very general considerations of the sort mentioned here, but on ones specific to the theory. Those who work on string theory do so, and should, on the grounds that this theory, or some variation of it, may solve various problems in physics of the sort noted by Smolin; or on the grounds that there is some empirical reason to think that strings of the sort postulated do exist. It is up to string theorists to investigate how many different phenomena such a theory might correctly explain. But the only way to determine this is to produce the problems and the explanations the theory might offer. Those who want to take up the challenge of developing Nagel’s dream theory should do the same (except, unlike string theorists, they must first tell us a lot more about what the theory says). Nor does my argument show that scientists and philosophers who (in Weinberg’s words) “dream of a final theory” should forget their dreams and pursue what is possible. Perhaps they should. But what I am arguing is that the attempt to discover a final theory should not be based on the speculation that some TOE must exist, and that if it doesn’t, the world is not completely intelligible. That speculation, typical of TOE enthusiasts, does not deserve high marks, even as a speculation. If you think there is a TOE, then find

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a potential TOE and give arguments that support the claim that it is true and that it is a TOE, even if those arguments do not provide evidence sufficient for belief. It is one thing to dream of a final theory, but it is another to pursue that dream on the basis of the very dubious, and unnecessary, speculation that one does or has to exist.

6

✦ SUMMING UP

CHAPTER 1 BEGAN WITH TWO QUOTATIONS about speculation in science—​one from Newton and one from Einstein. Newton, in his “official” methodology, tells scientists never to speculate. Einstein tells them that only “daring speculation,” not the “accumulation of facts,” can “lead us further.” What is Einstein telling scientists to do, and Newton telling them not to do? That is, what exactly is a speculation? And which, if either, of these two scientific geniuses is right about the activity of speculating? If it is a legitimate activity, is it subject to any constraints, or can one’s imagination run wild? Can scientific speculations be evaluated as speculations, or is evaluation confined only to theories that have been tested? Are there speculations not only about the objects studied by science but also about methodologies to be used in the study, and if so, how are such speculations to be evaluated? These are some of the questions for which this book has offered answers. My first concern was to define speculation in a way that could help to provide these answers. I  proposed that speculation, in the “truth-​relevant” sense, be construed as introducing assumptions, under what I  called “theorizing” conditions, without knowing that there is evidence for those assumptions. The question then becomes:  What concept of evidence should be used? Two probabilistic concepts,

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Bayesian (B-​ evidence) and my own (A-​ evidence), were introduced. My concept—​there are, in fact, different objective and subjective versions of it—​employs the idea of the probability of an explanatory connection between evidence and hypothesis. The Bayesian (increase-​in-​probability) concept does not, even if the latter is changed to require that evidence increase the probability of the hypothesis to more than one-​half. The explanatory idea, I claimed, enables us to see why certain assumptions can be regarded as made very probable by certain facts (e.g., facts about what the authorities believe), even though the assumptions are, and ought to be, regarded as speculations—​that is, ones lacking evidence. With an explanatory concept of evidence, I argued, we obtain a more plausible account of speculation than with Bayesian ones, unless the latter are changed to incorporate an explanatory idea. With an explanatory account, using potential, ES-​, or explanatory B-​evidence, we can understand why Thomas Young’s early nineteenth-​century wave theory of light, Lord Kelvin’s late nineteenth-​century molecular theory of the luminiferous ether, contemporary string theory, and even Isaac Newton’s theory of gravity (I argue) are all justifiably classified as speculations. Whether that is to praise them or damn them, or neither, is a separate question. How should that issue be addressed? My approach to speculation in science is pragmatic. It rejects rigid views that say “never do it,” or “do it with abandon, but test,” or “do it with abandon, and don’t worry about testing.” Whether to do it, when, and how depend on the context of inquiry. It depends on: (i) what you know, or at least think you know; (ii) what you are trying to explain, unify, calculate, predict, and so forth; and (iii) how you are proposing to do so. If you are Newton employing his three

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laws of motion plus theorems, attempting to explain the motions of the planets and their moons by establishing the force(s) producing these motions and the governing law(s), then speculation is not what you want to do. (Newton did it anyway, or so I claim.) If you are Maxwell attempting to see whether a mechanical explanation of known gas laws is even possible in terms of molecules in motion subject to forces, then do it by making assumptions about the motions of the molecules and forces acting on them, even if you have no evidence that molecules exist. Don’t worry about testing, since (in 1860) you can’t do it anyway. Your job is to theoretically develop such a theory, not to test it. Similarly, how to evaluate a speculation is to a considerable extent pragmatic and context dependent. A speculation can be evaluated in an epistemic way, a non-​epistemic way, or both. And within these categories there are different perspectives that can be taken—​that of the speculator and that of the evaluator—​which may be quite different. We can ask whether, given Newton’s epistemic situation, he was epistemically justified in believing that the celestial phenomena he cites constitute evidence that the law of gravity holds. We can also ask this question from a perspective that is based on our own epistemic situation. (In ­chapter 3, I do the former, arguing that he was not so justified, or only partially so; given his epistemic situation, the law was indeed a speculation.) We can also evaluate Newton’s speculation—​ the law he introduced—​ from various non-​ epistemic perspectives—​for example, in terms of its unifying power, its simplicity, or its influence. We evaluators choose the perspective of interest. It is not dictated by “nature” or by the speculation itself. Nor is it particularly useful to combine all perspectives and give an overall grade to the speculation.

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To take his rightful place among the scientific immortals, Newton never needed that! Armed with the conception of speculation I propose, and with a pragmatic attitude toward speculating, I  examined some very general claims made by scientists and philosophers about the role of simplicity in science, about whether scientific statements can be tested individually or only “holistically,” and about whether a “Theory of Everything” exists and why it would be good to have one. Despite the pronouncements made by supporters of these claims, the claims themselves are all speculations. They lack sufficient evidence to be believed. The question then becomes:  Even though they are speculations, are they good ones? Is there any reason, whether evidential or non-​evidential, to offer in favor of making them? Do they have to be made to do and understand science? Both Newton and Einstein claimed that nature is simple, and therefore, that simplicity is an epistemic virtue. The simplicity of a theory, law, or explanation is a guide to its truth. Contrary to what these and many other scientists and philosophers have urged, the simplicity claims in question are speculations. But as speculations, do they have any support in their favor? I examined attempts to provide such support by means of inductive arguments from the success of simple theories, claims about simplicity built into prior and posterior probabilities in Bayes’ theorem, claims about simplicity as an epistemic strategy, and others. None of them is successful. Simply put, simplicity is not an epistemic virtue. Despite Newton’s claims to the contrary, simplicity is not doing any epistemic work for him in his argument for the law of gravity. It cannot do so, nor is it needed to do so. Simplicity, I  argue, is a non-​ epistemic pragmatic virtue.

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Theories that make fewer assumptions, postulate fewer different types of entities, and have simpler equations than other more complex theories are easier to use for explanation, prediction, calculation, and communication. Most important, as I illustrated with Maxwell’s 1860 kinetic theory, they are excellent starting points for developing ideas that, although more complex, are likely to be more reflective of reality. The simplicity of Maxwell’s early kinetic theory is not a sign of its truth, nor did Maxwell take it to be. He explicitly regarded the theory as a speculation, and he introduced simple assumptions in order to enable him to develop them more easily and see whether a mechanical theory of gases was even possible. The debate between “holists,” such as William Whewell, and “particularists,” such as J.  S. Mill, contains various speculations about what counts as evidence for a scientific theory and about how one is supposed to evaluate a theory. These speculations, which I claim are unwarranted, are made by both holists and particularists, even if the latter are somewhat less vulnerable than the former. In the mid-​nineteenth century, Whewell said that evidence for the wave theory of light—​evidence from phenomena such as diffraction and interference—​was conclusive. Whewell’s claim about such evidence was based on the idea that if your theory explains and predicts a variety of observed phenomena (“consilience”) and if, as new phenomena are discovered, this continues without the introduction of arbitrary ad hoc hypotheses (“coherence”), then these phenomena constitute evidence for the entire theory, rather than for any particular part of the theory. This is because explanation and prediction of phenomena require all the assumptions of the theory, not isolated ones. Mill, the particularist, disagrees fundamentally. The

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nineteenth-​century wave theory is based on the assumption that an ether exists in which the waves occur. But, he says, no one has yet discovered it experimentally. The most that has been established by experiments on diffraction, interference, and other optical phenomena is that if the ether exists, then light is a wave motion. Mill’s more general point is that to provide evidence for a theory—​evidence sufficient to believe the theory—​you need to provide evidence for each assumption in the theory. For this purpose, it is not sufficient to show that the theory is “consilient” and “coherent.” (You need to “find the ether.”) Who is right? Whewell’s idea is that for observational results O to constitute evidence for a theory H consisting of a set of assumptions, O must be derivable from H. Since such derivations usually require all the assumptions in H, it is the set H as a whole, rather than individual hypotheses in H, that is supported by the observed phenomena in O. Mill is saying that this is not enough for evidential support. Each assumption in H must be supported by some or all of the phenomena in O. Whewell’s underlying evidential claim here—​that in science, evidence involves only a deductive explanatory–​predictive relationship—​is a speculation. Worse, it is one subject to numerous counterexamples. The concept of evidence I have proposed (A-​evidence, in its various forms) contains the idea that evidence involves some type of explanatory relationship between evidence and hypothesis. But it is not necessarily deductive; it requires the high probability of an explanatory connection between the hypothesis and the evidence; and it allows, but does not require, that it is probable that the hypothesis correctly explain the evidence, while allowing that the reverse may be the case as well, or that something probably explains both. With this concept of evidence, we obtain

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a type of particularism and reject Whewellian holism. Is this enough to reject holism? No, because the holist can reply that scientific claims, including evidential ones, can be defended only holistically. This is yet another speculative assumption that I argue is without merit. A major problem I find with the holism–​particularism debate is that its focus is entirely epistemic. Even as a purely epistemic debate, its main focus, in the case of both Mill and Whewell, is on one evaluative question: Is there evidence sufficient to believe the theory? (For Mill, there is only if there is such evidence for each assumption. For Whewell, there is only if consilience and coherence have been satisfied.) To be sure, both writers allow the additional epistemic question: Is there information that makes it reasonable to treat the theory as a possibility worth considering? But these questions seem to exhaust their epistemic repertoire. The alternative I  propose is more pragmatic. It rejects the idea of focusing exclusively on epistemic evaluations. There are non-​epistemic ones that, depending on the context, can be quite important. And even within the epistemic evaluations, the labels “proved” or “unproved” are often insufficient to describe the epistemic status of a theory. In actual practice, as demonstrated by examples from Maxwell’s evaluation of kinetic theory and Baden Powell’s evaluation of the wave and particle theories of light, theories are often in a state in which neither of these labels applies. They are in a state somewhere in between “proved” and “unproved.” And even if one of these two labels can be used to describe some of the assumptions of a theory, there may be others, including the theory as a whole, that cannot be so described. What evaluative categories to use depends both on the status

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of the theory and the context of evaluation. If you are writing a brief history of nineteenth-​century physics, “unproved” may be the best term to use for wave and particle theories of light in 1833, and for Maxwell’s kinetic theory in 1875. If you are writing a more extensive history, or if you are Powell in 1833 or Maxwell in 1875, a more informative fine-​grained evaluation is called for. Even if not all the assumptions of a theory have been “proved,” one can still use the theory, and scientists frequently do, to explain, predict, calculate, and so on, while admitting that perhaps some but not all the assumptions used to generate the explanations, predictions, calculations, and the like have been proved or established, or are better defended than others, or even have no support at all. The same can be said about the explanations, etc. generated from those assumptions. The final speculation I consider is that there is a “Theory of Everything” (TOE) to be found and that it would be good for scientists to try to find it. Such a theory would explain everything by appeal to a set of fundamental entities (ones that have no constituent parts) and a set of fundamental laws (ones that cannot be explained by anything further). The claim or assumption that there is such a theory has been made by various scientists and philosophers, including some contemporary string theorists, seventeenth-​century mechanical philosophers, Thomas Nagel in defense of a panpsychism, and David Chalmers in his “construction of the world.” The claim or assumption is a speculation in my sense, since the supporters of this idea do not know that there is evidence to support the general idea, nor do they have evidence for any specific theory they propose as a TOE. Indeed, in the case

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of Nagel’s panpsychic theory and Chalmers’ “construction of the world,” there isn’t even a specific theory being proposed. Nevertheless, supporters of the general idea do present epistemic and non-​epistemic reasons for believing that a TOE exists and that its existence must be assumed to make science possible. I considered historical, presupposition, unification, and a priori and empirical “strategy” arguments for the existence of a TOE. None of them rises to the level of evidence (potential, ES-​or explanatory B-​) sufficient to believe that a TOE exists. Nor do they even provide reasons sufficient to take the idea seriously. I also discussed the related normative idea of TOE supporters that it would be good for science if a TOE did exist, since then the world would be completely intelligible. There are two ideas of “complete intelligibility.” One invokes an assumption of a “rational order” for everything in the universe, whether or not scientists can know what it is. The other contains the idea that the world is completely intelligible to us (or to scientists). I argue that it is this second sense that is of most interest to scientists. I also argue that with respect to this kind of intelligibility, what needs to be defended is an idea illustrated in the work of both Newton and Maxwell, which I call “Newtonian intelligibility.” An explanation can provide complete intelligibility for some group of phenomena without providing it for all phenomena. And whether it does so for the phenomena in question is most usefully judged by reference to contextually dependent standards of completeness, not to some idealized, unrelativized one. Such a judgment takes into account the scientist’s task: what he was trying to explain, how, and how well he has succeeded. In such a case in determining whether, or to what extent, the

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scientist’s explanation provides “complete intelligibility,” we ask whether or to what extent his task was completed successfully. Newton clearly believed that he had completed his task successfully. From the motions of celestial bodies, using his three laws of motion, he thought he provided sufficient evidence for a universal force law that explains celestial and terrestrial motion. He admitted that although he produced such evidence for the law, he could not explain why it holds. Yet, he said, what he accomplished was enough to complete his particular task in the Principia. Yes, there are future tasks to be completed, depending on the questions being asked and evidence that is, or will become, available. New evidence may suggest how the new task is to be accomplished, or indeed new evidence (not available to Newton) may show that the original task is based on faulty assumptions. We can understand Newton’s claims of successful completion in terms of subjective evidence. If we employ an objective concept of evidence, such as veridical or ES-​evidence, we have to conclude that Newton’s task was not complete. The evidence he supplied for the law was neither veridical (since the law is false) nor ES-​evidence (since it wasn’t sufficient). Even if we employ one of the objective concepts of evidence and regard Newton’s task as incomplete, and hence the “intelligibility” he provided for the phenomena he was attempting to explain, as incomplete or worse, the main point remains: neither Newton’s task nor intelligibility, if any is produced, needs to be regarded as complete or completed only when he or others have constructed and provided objective evidence for a TOE. Completeness does not have to be judged, if at all, on the basis of how close a theory comes

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to being able to correctly answer all questions that have been or might be raised, and doing so by appeal to fundamental “atoms” and laws. For “Newtonian intelligibility,” completeness can and should be judged on a task-​by-​task basis without the completion of all tasks, and without necessarily completing the task in question by appeal to a TOE. Satis est.

INDEX

A-​evidence, see evidence Akaike, Hirotugu, 107 Austin, J.L., 192 Bayes’ theorem, 98 Bayesian (B-​) evidence, 15, 16, 95 upgraded, 38 Brougham, Henry, 3, 23 Brush, Stephen, 52, 210 Cantor, Geoffrey, 213n Carnap, Rudolf, 102–​104, 114n Cartwright, Nancy, 136n, 253, 259 Causey, Robert, 217n Chalmers, David, 216, 224–​225, 230, 231, 249, 252n coherence, see Whewell common cause principle, 243, 244 competing hypothesis (explanation) objection, see Mill consilience, see Whewell

content-​giving sentence, 185 complete, with respect to a question, 186 correct explanation, see explanation Dawid, Richard, 35n, 73n, 229n, 235n Descartes, René on speculation, 10–​11, 48 Di Fate, Victor, 148n, 156n Duhem, Pierre, 4–​5, 63, 77, 169, 173–​174 Dupré, John, 245n, 259 Earman, John, 244n Einstein, Albert, 68 on simplicity, 72, 74, 76, 77,  86–​87 on speculation, 1, 15n empirical adequacy, 73 ES-​evidence, see evidence Everitt, C.W.F., 52n, 210

2 74   |    I ndex evidence A-​(Achinsteinian), 17–​18, 41–​42,  95–​96 from authority, 35–​39 B-​(Bayesian), 15, 16 for conditional existence claims, 205–​208 ES-​, 17, 197–​198 potential, 17 subjective, 18 veridical, 17, 197–​198 explanation completeness in, 256–​259 correct, 185–​188 deductive model and counterexamples, 189 explanatory connection, 16–​17, 184–​185 Feyerabend, Paul, 14, 49–50 Fitzpatrick, S., 118n Friedman, Michael, 229n Garber, Elizabeth, 52n, 210 Greene, Brian, 135, 219n, 220, 221n, 232n, 249 Harman, Gilbert, 87, 88 Hempel, Carl G., 181, 189, 191 Herschel, John, 213 Hertz, Heinrich, 18n holism evidential, 168 justificatory, 196–​202 and verified consequences, 202–​205 Howard, Don, 72n inductive argument for simplicity,  91–​94 inference to the best explanation, 33–34, 87

Janiak, Andrew, 72n Kant, I., 229 Kelly, Kevin, 117–​118 Kitcher, Philip, 128n Lange, Marc, 8n Laudan, Larry pessimistic induction, 39, 92, 128, 236n Laughlin, R.B., 237n, 250, 253 Lewis, David, 100n Lipton, Peter, 33–​34, 87–​88 Lloyd, Humphrey, 213 Maxwell, James Clerk, xii, 7, 50–​65, 182–​183,  222 exercise in mechanics, 51–​54, 140–​143, 204–​205 physical analogy, 58–​62 physical speculation, 54–​58 pragmatism, 60–​65, 140ff., 258 on theory construction, 211–​213 mechanical philosophy, 221–​223 meta-​inductive evidence, 34,  36–​39 Mill, John Stuart competing hypothesis (explanation) objection, 126–​130, 181–​184 particularism, 168–​172 on the wave theory of light, 177–​179, 204, 207 Morgan, Gregory, 43n Nagel, Thomas, 76, 216, 223–​224, 231, 238–​240, 249, 251n,  253n Newton, Isaac, xiii, 11, 22, 28, 126, 221 argument for gravity (simplicity based), 143–​154

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inductivism,  31–​32 Newtonian intelligibility, 254–​259 Newton’s Rules, 71–​72, 126, 144 pragmatic interpretation of Newton’s Rules, 160–​167 on simplicity, 71–72, 74–​75, 85n on speculation, 1, 10–​11, 47–​49 Norton, John, 156n only-​game-​in-​town evidence,  34–​39 Oppenheim, Paul, 217n particularism and A-​evidence, 193–​195 evidential, 168 pessimistic induction, see Laudan Pines, David, 237n, 250, 253 Popper, Karl, 12–​13, 50 potential evidence, see evidence Powell, Baden, 213 Prigogine, I., 250 probability likelihood, 98 objective epistemic, 16 posterior, 98 prior, 98 Putnam, Hilary, 217n Quine, W.V., 169, 172 Railton, Peter, 228 Reichenbach, Hans, 113–​117, 243 Roche, Michael, 108n Rynasiewicz, Robert, 243n Salmon, Wesley, 228 scientific spec, 45 simplicity “aim of science” claim, 77, 133, 135

Einstein on, 72, 74–​75 epistemological claim, 73–​75,  88–​118 as an epistemic strategy, 113–​118 globalist view, 84ff inductive argument for, 91–​94 localist view, 83ff Newton on, 71–​72, 74–​75 ontological claim, 71–​72, 80ff pragmatic, 79–​80, 139–​143 presupposition claim, 76–​77, 133–​135 scientific virtue claim, 78, 135, 138 Smolin, Lee, 219–​220, 232, 233n, 240–​241,  245 Sober, Elliott, 85n, 104–​109 Spec, 20 speculation, see spec pragmatic view (see Maxwell) scientific,  40–​46 three contrasting views (very conservative, moderate, very liberal), 10–​15,  46–​50 truth-​irrelevant,  8 truth-​relevant, 7,  19–​24 Stanford, P. Kyle, 128n Stengers, Isabelle, 250n string theory, 5–6, 219–​221 theorizing conditions, 6–​7 theory evaluation either/​or, 209–​210 nuanced, 210–​215 Theory of Everything (TOE) a priori strategies for constructing a TOE, 248–​250 empirical argument strategies, 246–​248 historical argument, 234–​237 presupposition argument, 238–​240

2 7 6   |    I ndex Theory of Everything (cont.) unification argument, 240–​245 what is a TOE?, 216–217, 226–​231 why should we want a TOE?, 250–​255 Thomson, J.J., 18n, 96–​97 Thomson, William (Lord Kelvin), 4, 63 truth-​relevant speculation, see speculation underdetermination, 75–​76, 123–​132 van Fraassen, Bas, 73, 78–​79,  244n veridical evidence, see evidence

wave theory of light, 203–204 and the ether, 176–​179 Weinberg, Steven, 6, 228–​229, 232n, 235, 236, 249, 251n, 252n Westfall, R.S., 223n Whewell, William, xii–​xiii, 12, 13, 89–​90,  169 coherence, 32, 131, 231 and the competing hypothesis objection, 182 consilience, 32, 131, 231 holism, 174–​175 hypothetico-​deductivism,  32–​33 wave Theory, 177–​179 Young, Thomas, 3