Читать книгу Judgments of Beauty in Theory Evaluation - Devon Brickhouse-Bryson - Страница 8

Introduction

Truth is the first virtue of systems of thought, as justice is of social institutions. Any system of thought, no matter how elegant, must be rejected if it is not true.¹ When we ask questions, philosophical or otherwise, we want answers and we want those answers to be true. But answers to philosophical, scientific, and complex questions of every kind must provide an explanation. “Does justice require arranging social and economic inequalities such that they are to the benefit of the least advantaged group?” “Does knowledge have any conditions beyond justified true belief?” “Do judgments of beauty refer to any principles?” “Does God exist?” “Do heavier objects fall faster than lighter objects?” “Do the planets move according to Copernicus’ model of the solar system?” “Is there such a thing as absolute rest?” “Was there a conspiracy to fake the moon landing?” “Did Colonel Mustard kill Mr. Boddy?” These questions, and the infinite others like them, cannot be satisfactorily answered with a mere “yes” or “no,” even if that “yes” or “no” were true. Instead, they must be answered with a system of thought—a theory.² Such a system of thought, a theory, is meant to provide an explanation of the phenomenon our question refers to. Only such an explanation of the phenomenon will satisfy our questioning. And the first virtue of such answers, explanations, and theories is truth, or at least some kind of epistemic value (probability of truth, predictiveness, constructive usefulness, power to promote understanding, and so on).³ No matter what other qualities explanations and theories have, they must be epistemically good if they are to be good explanations and theories. A theory, no matter how elegant, must be rejected if it is not epistemically good. But how do we figure out which theories are true, or epistemically good, and which are not?

Let’s work through some of the examples above in more detail. Rawls thought that justice does require arranging social and economic inequalities such that they are to the benefit of the least advantaged group. This is the difference principle—one part of one of Rawls’ two fundamental principles of justice. But clearly Rawls cannot simply insist that the difference principle is a true principle of justice. Nor can he simply put the principle to us and ask us to simply “see” its truth in isolation. To vindicate the difference principle, he must offer a theory of justice, which is of course exactly what he does. A system of thought must be constructed, refined, and deployed to answer our question “Does justice require arranging social and economic inequalities such that they are to the benefit of the least advantaged group?” Rawls’ theory of justice is such a system of thought. To answer our question about social and economic inequalities, we’ve been forced to explain the nature of justice itself. Now of course we want to know whether this system of thought—this theory of justice, which explains justice and in turn answers our question—is true.

The question of the truth of Rawls’ theory of justice is made more pointed by noticing that it is not the only theory of justice on offer. And the other competing theories of justice will issue different verdicts about the difference principle by means of a different explanation of justice. The libertarian theory of justice will deny that justice can ever countenance infringing on people’s economic activity and thus that justice must be silent about any social and economic inequalities. From the opposite extreme, a radical egalitarian theory of justice will deny that justice can ever countenance inequalities of any kind and thus that justice will not permit any social or economic inequalities, even if they are to the benefit of the least advantaged group. Less extreme, but still differing from Rawls’ theory, the utilitarian theory of justice would allow for justice to regulate social and economic inequalities but would do so with an eye to maximizing utility instead of benefiting the least advantaged group. Each of these is a theory of justice—an explanation of justice by means of a system of thought about justice. Each in turn will issue a different answer to and explanation of our question about social and economic inequalities. The first virtue of theories, systems of thought, is truth or some other kind of epistemic goodness. Which of these competing theories is true or epistemically good?

Methods of Theory Evaluation

Once we realize that we cannot simply divine which of these competing theories is true by direct assessment, it is clear that we need methods for evaluating theories. This is an important lesson at the root of all theorizing: the first virtue of theories is truth, yes, but given that we do not have direct, unmediated access to the truth of theories, we need some medium, some indirect means for assessing the truth of theories. Methods of theory evaluation are precisely such indirect means of truth assessment. Now, this can be fairly straightforward. Perhaps, the principal method of theory evaluation we have at our disposal is fit with the data or fit with other truths. This method says that we can assess the truth of theories by how well they fit with other things we know to be true. An example above illustrates this well, the question: “Did Colonel Mustard kill Mr. Boddy?” We want to know the answer to this question; to fully satisfy our questioning, we’ll need an explanation of the death of Mr. Boddy, which would be provided by a theory of the death. Let’s stipulate that we have several pieces of data. We know that it is true that: (1) Mr. Boddy was found, dead, in the library. (2) Colonel Mustard was found in the library holding a bloody candlestick. And (3) Colonel Mustard stands to inherit Mr. Boddy’s estate. Now we can ask: What is the answer to our question, what explains the death of Mr. Boddy? The following theory obviously stands out as the best theory, the true theory: “Colonel Mustard did kill Mr. Boddy. He killed him in the library with a candlestick in order to inherit the estate.” This theory answers our question and we know it is the true theory because it obviously fits best with the data. There are competing theories: “Colonel Mustard did not kill Mr. Boddy. Instead, Professor Plum killed Mr. Boddy in the drawing room with a wrench in a fit of rage over a failed business deal.” This theory is an answer to and explanation of our question, it is a competitor with the theory that says Colonel Mustard did it. It is possible that this latter theory is the true theory of the death of Mr. Boddy. But this theory is obviously weaker than the Colonel Mustard theory; we have every reason to believe that the Colonel Mustard theory is the true theory because it succeeds so much on the rubric of fit with the data. Notice then that the method which looks for fit with the data is still an indirect means for evaluating the truth of theories. We get at the truth of the theory in question by looking to another property—another property besides truth—that this theory possesses. For this method, the property is how well the theory fits with other truths. Truth is still bound up in this method, but it is not a method for direct assessment of the truth of theories.

There is another straightforward method of theory evaluation closely related to truth: the principle of noncontradiction. We know that contradictions are false. Thus, we have another tool for evaluating the truth of theories: if the theory includes or entails a contradiction, then we know that that theory is false. Another of the examples above illustrates this well, the question: “Do heavier objects fall faster than lighter objects?” We can answer this question by means of the fit with data method of theory evaluation. We can explain, “No, heavier objects do not fall faster than lighter objects because the principle that says that they do does not fit with observed truths, namely, the observed fact that two objects of different weights fall at the same speed.” Galileo, of course, famously conducted such experiments. But Galileo also saw that we don’t even need to do such experiments to explain our answer to the question. We can use the method of noncontradiction to answer our question in the negative. To do this, we must see that the positive answer (“Heavier objects do fall faster”) entails a contradiction. Why? Run this thought-experiment: Object A is heavier than Object B. By the theory in question (“Heavier objects do fall faster”), Object A will fall faster than Object B. Now join together Object A and Object B by a rope to form the composite Object C. Object C weighs the sum of Object A and Object B (plus the weight of the rope) and so is heaviest and should fall fastest of all. But we also said that Object B falls slower than Object A, so Object B should act as a drag on Object A and thus make Object C fall slower than the unencumbered Object A. Thus, Object C falls both faster and slower than Object A. This is a contradiction. Contradictions are necessarily false. Thus, the theory that entails the contradiction is also false. Thus, we’ve discovered something about the truth status of the theories in question. Specifically, we’ve discovered that one of the two competing theories to answer our question is false. And since there are only two competing theories, which exhaust logical space, we can conclude that the other theory (“Heavier objects do not fall faster”) is true. Thus, we’ve discovered the truth of a theory, which was our goal.

This can seem closer to a means of direct assessment of the truth of a theory, but it is not. This is still a method, a mediated means for evaluating the truth of theories. We do not directly assess the truth of the theories in question, rather we assess a modal property of that theory—impossibility. We know that this modal property is connected to a truth property and thus we can assess the truth of a theory by means of this modal property. But we are still evaluating the truth of the theory by means of another property of that theory. And in the case of the method of theory evaluation that uses the principle of noncontradiction, there is another way in which it is indirect. This method is purely negative: the modal property of impossibility is connected with the truth value falsity. We of course don’t just want to know which theories are false, we want to know which theories are true. In the falling object case above, this worked because there were only two theories that exhausted logical space. Finding that one was false was sufficient to find the other true. But this will not always be the case. If there are multiple competing theories, more than one of which does not entail a contradiction, then the method of theory evaluation which uses the principle of noncontradiction will not be sufficient to evaluate the truth of the competing theories.

We can overcome this negative problem by pointing to yet a third method of theory evaluation, the inverse of the principle of noncontradiction: the principle of necessity. We know that things that are necessary are true, and thus to find that a theory is necessary (or entailed by something necessary) will be to find that it is true. This has been attempted in the history of philosophy and is well illustrated by another of the example questions above: “Does God exist?” Traditional arguments for God’s existence have often tried to show that God’s existence is necessary or that it follows from something necessary. If this is successful, this would indeed be a method for evaluating as true the theory that explains that God exists. But note that this is still an indirect method for evaluating the truth of the “God exists” theory, in the same modal way as with the principle of noncontradiction: we find that that theory has a modal property—necessity—and we know that that modal property is connected to the truth value true. Thus, discovering necessity in a theory is a good method for evaluating the truth of that theory. The trick of course is that necessity is a difficult concept and all the pudding is in figuring out whether God’s existence is necessary or is entailed by something necessary. The person who thinks the “God exists” theory is false does not deny that looking for necessity is a good method for evaluating the truth of theories; this person denies that the theory exhibits such necessity. This method thus still involves an indirectness: it evaluates the truth of a theory by looking to whether that theory possesses another property: necessity. So, both the methods that use the principle of noncontradiction and the principle of necessity are still indirect methods of evaluating the truth of a theory: they do not directly assess the truth of a theory, rather they assess a modal property which we know to be connected to a truth property. In the case of the principle of non-contraction, there is also the indirectness of moving from a negative (falsity) to a positive (truth). The principle of necessity does not have this particular indirectness, but, as if to compensate, it is much more difficult to use: it is much easier to show that something is a contradiction than it is to show that something is necessary. Thus, even when using these methods, tightly connected to truth as they are, discovering whether a theory is true is always a matter of discovering whether that theory has some other property.

This of course is not somehow a necessary feature of truth discovery. We can imagine a being, God perhaps, who could simply directly assess the truth or falsity of claims, explanations, and theories. But we are not like such beings. To find the truth, we must use methods that connect truth to some other property and then work to discover that property. Methods of evaluating the truth of theories are mediated by a middle term: something we can discover in theories and which is connected to truth. So far, we have found three such middle terms: fit with other truths (which is connected to truth), contradictoriness (which is connected to falsity), and necessity (which is connected to truth). To admit that we need indirect means of truth evaluation for theories is not to undercut the importance of truth or other epistemic value to our theory evaluation. It is instead to be cognizant of our limitations when it comes to evaluating theories for their truth. Assessing the truth or other epistemic value of theories is difficult. Beings like us must utilize different tools—methods that mediate a connection between truth and theories—in our endeavor to evaluate theories.

These relatively straightforward methods will probably be enough to help us in the case above of Rawls’ theory and its competitors. Recall: Rawls’ theory, the libertarian theory, the radical egalitarian theory, and the utilitarian theory are all competing explanations of justice. Using the methods we’ve sketched above, we can work to discover which theory is true or at least which theory we are most justified in believing to be true. It’s unlikely that we’ll discover necessity at the heart of any of these theories or that these theories are entailed by any necessity, so that method is perhaps not helpful. But the method of noncontradiction may be helpful. For instance, one might argue that the libertarian theory has a contradiction at its heart: to give unlimited liberty to any is ipso facto to restrict other people’s liberty (because unlimited liberty includes the liberty to trample on others), and thus the theory which says that justice can countenance no restrictions on liberty whatsoever is contradictory and thus false. If this argument is successful (this of course is just a sketch; a serious attempt to use this method would have to argue in more detail that there is a contradiction here), then we’ve knocked one of the competitors out of the running for being the true theory. There may be an analogous but opposite contradiction at the heart of the radical egalitarian theory, so perhaps we can use the same method to knock that theory out of the running as well. But when it comes to Rawls’ theory and the utilitarian theory, it seems that the method of noncontradiction has given out. We still want to know which of those theories we should think is true, but it doesn’t seem as though either theory involves a contradiction. We thus need a further method if we are to continue to winnow down the competitors until we arrive at the true theory. Fit with other truths is a method that can step in at this point. We know that it is true that justice forbids slavery. But the utilitarian theory allows that slavery can sometimes be compatible with justice (where the program of slavery maximized utility), whereas Rawls’ theory rules out slavery in principle (it’s in violation of both principles of justice and the deeper spirit of Rawls’ theory on which society is to be a fair system of cooperation among free equals). Thus, Rawls’ theory of justice fits better with other things we know to be true about justice and is thus a better theory—an epistemically better theory or a better candidate for being true.⁴

Problem: Lists and Epicycles

One might think that the question I raised at the outset—how to discover which theories are true—can be solved with only the tools, the methods of theory evaluation, we’ve introduced thus far. Fit with other truths in particular is a powerful method which might seem to be able to resolve all competition between theories such that we can discover which theories are true or which theories are epistemically better.⁵ But just as the method of noncontradiction gave out at a certain point—there can be competing theories, neither of which involves a contradiction—so too will the method of fit with other truths give out. There can be competing theories both of which fit equally well with the data. To see this, consider another of our example questions above: “Do the planets move according to Copernicus’ model?” Suppose we have two competing theories: first, we have Copernicus’ model which explains the motions of the planets by positing the existence of principled orbits (circles) as well as a model of the relative positions of the bodies (heliocentricism). Second, we have a “theory” which simply lists the positions of the planets in precisely the same way that Copernicus’ model predicts, but with no underlying principles or model that systematizes those movements.⁶ Now, by stipulation, both of these theories of the motions of the planets fit equally well with the data. They say precisely the same thing about where the planets will be and thus will stand and fall together with respect to fitting with our observations about the planets (Copernicus’ theory, of course, does not fit perfectly well with the data; its circular orbits commit it to significant lack of fit with the data). Both theories fit equally well with the data, but we still need a way to adjudicate between them as to which theory is true or otherwise epistemically better. Notice that we can multiply this problem to infinity: we could have another list of the positions of the planets, identical to our previous list, except that it makes a slightly different prediction about the position of Mars in 10,000 years. We can generate infinite such lists, all of which fit equally well with the data we have available to us, but which make different predictions about future planetary motions. So, we have infinite theories of the motions of the planets from which to choose; how do we evaluate which theory is best from among these? This, of course, is meant to be a silly question: among all these options, Copernicus’ model clearly stands out as the best theory. The others are ad hoc lists built on no underlying system. But this is precisely the point: Copernicus’ theory is the best theory, despite scoring equally well with respect to fit with the data. This tells us that there is some other method of theory evaluation, other than fit with the data, at play. Infinite underdetermination will always plague the method of fit with the data. We need other methods of theory evaluation to break that impasse. If fit with the data were all that were needed, a mere list of data would always be an option, and there are infinite such lists that fit with the data available to us.

What exactly is the method of theory evaluation that Copernicus’ model scores well on as compared to the lists? It’s something like a unity or a simplicity method of theory evaluation: a theory that is simpler or more unified is a better theory, a better candidate for being true. How exactly Copernicus’ theory is more unified or simpler needs spelling out, and we need to know much more about how these methods work.⁷ But for now, it’s clear enough that something like a method of simplicity gets deployed in our evaluating Copernicus’ theory as better.

But one still might think that fit with the data is still the predominant method of theory evaluation and that the simplicity method of theory evaluation only gets deployed as a tiebreaker, to resolve the underdetermination that remains after the method of fit with the data is exhausted. But further permutations on the Copernicus case show that this is incorrect. Compare Copernicus’ theory of the motions of the planets with its predecessor: Ptolemy’s theory. Copernicus’ theory holds that the sun is the center of the solar system and that the planets (including the earth) move in circular orbits around the sun. Ptolemy’s theory holds that the earth is the center of the solar system and that the planets (including the sun) move in circular orbits around the earth. But Ptolemy’s theory also held that there are epicycles—orbits upon orbits—for each of the planets. By Copernicus’ time, Ptolemy’s theory had been refined to fit the data by adding more and more epicycles, until the theory invoked hundreds upon hundreds of epicycles. But with such epicycles (ad hoc as we recognize them to be now), the theory can fit the data. Indeed, Ptolemy’s theory actually fits better with the data (or at least it could be made to be) than does Copernicus’ theory.⁸ But Ptolemy’s theory, with its hundreds of epicycles, clearly scores worse than Copernicus’ on the simplicity method that we saw above. And it is because of this success—the comparative simplicity of Copernicus’ theory—that we rightly look back at Copernicus’ theory as a momentous step forward in our theorizing about the motions of the planets, even if it does take a step backward on the rubric of fit with the data. Thus, the method of evaluating theories by their simplicity, however that method works, is not merely a tiebreaker to be deployed as an afterthought. We can see that sometimes we think we are justified in losing some fit with the data for the sake of a greater gain in simplicity.

Truth is the first virtue of systems of thought, but I just said that we are sometimes justified in losing some fit with the data for the sake of a greater gain in simplicity. How can this be? Doesn’t losing some fit with the data for the sake of a greater gain in simplicity constitute trading some truth for something else, simplicity? This is a puzzle. But notice that theories and explanations are, by their very nature, systematic: they are systems of thought, not mere lists of thought, mere lists of truths. Now, what makes a good system? What makes a system, in virtue of being a system, a good system? The answer is implicit in our consideration of the simplicity method of theory evaluation. A mere list of data, even if it’s completely true, is not a good theory because it’s not a good system of thought. A convoluted theory with layer upon layer of ad hoc hypothesis, even if it fits perfectly with the data, is not a good theory because it’s not a good system of thought. A system is a good system if it is, for example, simpler, more unified, more economical, more coherent, more elegant, etc. In a word, a system is a good system if it is beautiful.⁹

This is a bold and striking claim, but it is one that I will argue for in this book. If it is true, then it will follow that beauty is relevant to our evaluation of theories. If beauty is what makes a system good as a system, then theories, which are systems of thought, will be better as systems if they are beautiful. That is the thesis of this book: judgments of beauty are part of how we evaluate theories—how we discover which theories are better. That is, a theory’s beauty is part of what makes it better.

There is significant dispute in contemporary philosophy of science on whether judgments of beauty do or should play any role in scientific theorizing.¹⁰ If my arguments for my thesis are successful, obviously this project will bear on that dispute. But it should be noted that I mean my thesis to be broader in scope—applying to all kinds of theorizing endeavors, including philosophy, science, and “ordinary” theorizing (such as the Colonel Mustard case). Indeed, in contrast to the debate in the philosophy of science, I will mainly focus my attention on philosophical theorizing (hence my beginning with competing theories of justice), although some examples of scientific theory evaluation will be used. Disputes in philosophy of science about the role of beauty in scientific theory evaluation are often narrow and attend to special features of scientific theorizing (e.g., the especially empiricist or mathematical methodologies of scientific theorizing). But this means that these disputes often neglect potential connections between philosophical theory evaluation and scientific theory evaluation, even though values like simplicity and coherence are relevant to both philosophical and scientific theorizing. This is made pointed by noting that attempts to theorize about the structure of scientific theory evaluation are themselves philosophical theories, not scientific theories (given that philosophy of science is a branch of philosophy, not science). If judgments of beauty are relevant to all theorizing, then philosophers of science who are concerned with judgments of beauty will also need to take a step back and consider the role of judgments of beauty in their theorizing about science. I hope this project can provide an avenue for connecting the philosophy of science dispute over judgments of beauty with larger questions about the nature of beauty and other kinds of theory evaluation, including philosophical theory evaluation.

My thesis—that judgments of beauty are relevant to theory evaluation—should not be understood to deny the important claim that I started with: that truth (or some other epistemic good) is the first virtue of systems of thought; we must reject systems of thought, no matter how beautiful, if they are not true. I will not argue that we should sometimes abandon truth for the sake of beauty in our theories. But we do not have direct access to the truth of theories. We must rely on methods of theory evaluation that point to some other property, which acts as a middle term between theories and truth. And I will argue that beauty is one such middle term, alongside familiar methods like fit with the data and the principle of noncontradiction. Truth is the first virtue of systems of thought, but we need beauty to help us discover which of all the competing theories is true.

Outline of Chapters

The first step in arguing for this thesis is to immediately defuse the most common objection that philosophers and lay readers alike will tend to have: that beauty is thoroughly relative and thus utterly unsuitable for having any connection to truth, which is not relative. This objection is most commonly expressed by citing the aphorism “Beauty is in the eye of the beholder.” The objection by means of this aphorism is not as straightforward as it might seem and thus it will have to be worked out what exactly this aphorism means and whether it does generate problems for my thesis. But whatever the aphorism means, thoroughgoing relativism about beauty would indeed be a problem for my thesis and thus I will argue directly against thoroughgoing relativism about beauty. I will do this by undermining common arguments in favor of thoroughgoing relativism about beauty, by arguing that thoroughgoing relativism about beauty has deeply counterintuitive implications, and by drawing an analogy to thoroughgoing relativism about morality. I will do all this straightaway in chapter 1.

After that initial problem is dispelled, I can take positive steps toward my thesis. The first step is to give an account of the nature of judgments of beauty. I won’t make it my purpose to give a full theory of beauty in this book, I want to leave my thesis compatible with as many full theories of beauty as possible. But a key piece of my thesis, as I said above, is that beauty is the thing that makes systems good as systems. This needs explaining. By giving a mid-level account of beauty—not a full theory, but still making important claims about the nature of beauty—I will explain why judgments of beauty are the relevant kind of judgment for evaluating systems. This mid-level account of beauty will be inherited from Kant and Mary Mothersill and will hold that the distinctive nature of judgments of beauty is that they are unprincipled—made without any reference to principles—and yet can be genuine—we can nonarbitrarily distinguish good judgments of beauty from bad judgments of beauty. I will explain why this entails that judgments of beauty are the relevant kind of judgment for evaluating systems. This account of beauty will be developed in chapter 2.

Once I have this mid-level account of beauty—judgments of beauty are unprincipled, yet possible—I can begin in earnest the argument for my thesis: that beauty is relevant to theory evaluation. I will begin this argument by illuminating how this might work by examining in detail some important methods of theory evaluation. First, in chapter 3, I will examine the method of reflective equilibrium and explain how this sophisticated method works. Reflective equilibrium is closely related to fit with the data, but also importantly uses the concept of coherence to evaluate theories. I will argue that coherence is best understood as a species of beauty, given the account of beauty I will develop. This will mean that reflective equilibrium is an example of my thesis at work. Then, in chapter 4, I will examine the method of simplicity: the method that holds that simpler theories are better theories and thus that judging a theory by its simplicity is a justified means to finding better theories. The concept of simplicity needs explaining if it is to form the basis of a fully worked out method of theory evaluation. I will likewise argue that simplicity is best understood as species of beauty, given the account of beauty I will develop. Again, this will mean that the methods of simplicity is an example of my thesis at work. Examining these methods—reflective equilibrium and simplicity—and finding that judgments of beauty are part of how these methods evaluate theories will illuminate how my thesis is supposed to work—how judgments of beauty are relevant to theory evaluation. To find my thesis implicit in such powerful and widely used methods of theory evaluation will also constitute an argument in defense of my thesis, inasmuch as we take these methods of be justified methods of theory evaluation.

But this argumentative strategy—finding my thesis implicit in methods we actually use—might seem to shift the burden onto those methods themselves. Perhaps, one might argue, we should instead reject those methods rather than accept that beauty is relevant to theory evaluation. To counter this, I will provide a more direct argument for my thesis. This argument will have a transcendental structure: I will argue that my thesis is a necessary feature of the very nature of theorizing and explaining. Theories and explanations, by their very nature, are systematic. This fact, even before we develop any particular methods for evaluating theories and explanations, will entail that we will always be evaluating theories and explanations, in part, as systems. Theories and explanations are systems directed at a particular purpose: truth (or at least some other epistemic value). We will evaluate them in terms of how they achieve that purpose. But we also must evaluate them simply as systems. And this evaluation, I will argue, requires judgments of beauty. This transcendental argument will underpin my defense of the methods of reflective equilibrium and simplicity. But it will also provide a more general defense of my thesis: that beauty is relevant to theory evaluation. This transcendental argument will be developed in chapter 5.

This transcendental argument will conclude the argument for my thesis. My thesis is that judgments of beauty are part of how we evaluate theories; that a theory’s beauty is part of what makes it good. But there will remain several outstanding issues to be addressed. First, I will have spent some time thinking about the nature of explaining and theorizing, but there is a third related concept worth exploring: understanding. My core claim about explaining and theorizing is that they are necessarily systematic. This fits well with what is usually claimed is the nature of understanding as compared to knowledge: whereas knowledge is propositional, understanding is systematic. It will be important to speak to how my thesis relates to understanding. Second, the arguments I will develop in defense of this thesis are meant to be general and apply to theorizing of all kinds, but I will pay special attention to theorizing in philosophy. But this issue—the role of judgments of beauty in theorizing—is often specifically raised in the context of scientific theorizing. This is because scientific theorizing is supposed to be particularly empiricist or hardnosed; one might think that judgments of beauty can have utterly no place there. It will be important to speak to how my thesis relates to scientific theorizing. Third and finally, Rawls’ work—thinking about what desiderata a theory of justice must satisfy and giving a theory of justice in light of that—is an important foundation of this project. I have generalized Rawls’ attention to the methods of theorizing, including reflective equilibrium. But giving a theory of justice comes with its own special issues: a theory of justice is not merely supposed to explain something; it is supposed to provide a practicable framework for organizing society with an eye to peace, liberty, equality, and stability. It will be important to speak to how my thesis relates to these special issues in political theorizing. Each of these three topics could support a manuscript in their own right, but I will here only begin to explore them and flag them for further work. I will do this in the Coda.

Claiming that judgments of beauty are relevant to theory evaluation—that beauty is connected to truth—inevitably strikes many as wishy-washy or going soft on the hard business of discovering the truth in philosophy or science. But I will dispel that impression and argue that we must rely on our judgments of beauty when evaluating theories for truth. There is another, more ancient adage worth remembering: Pulchritudo splendor veritatis, “Beauty is the splendor of truth.”¹¹ This adage does not say that beauty is truth, nor will I. I do not deny that we should reject a theory, no matter how beautiful, if it is not true. But our task when doing philosophy or science is to figure out which theories are true or otherwise epistemically good. And we don’t have direct access to that truth, antecedent to our judgments of beauty about theories, any more than we have direct access to that truth, antecedent to our judgments about fit with the data. Instead, finding that a theory is beautiful will be an important step toward finding that it is true, in the same way that finding that it fits with the data is an important step toward finding that it is true. A theory can be beautiful and yet not be true, just as a theory can fit with the data and yet not be true. Nevertheless, beauty and fit with the data are connected to truth and we must rely on them when forming our judgments about which theories we have reason to believe are true. Discovering whether a theory is true, which is indeed our ultimate goal, requires discovering whether it has some other property. And I will argue that one such other property, a middle term between theories and truth, is beauty.

NOTES

1 This is obviously meant to echo Rawls’ famous first lines of A Theory of Justice. Although the subject matter of this book is quite different from the questions Rawls addressed in his work, it will be clear that I am deeply indebted to him. I use the word “true” here only to echo Rawls. As I will discuss shortly, I only mean that theories must be principally evaluated according to epistemic values.

2 “Theory” is sometimes a fraught term, but I will be using it here merely to mean a “system of thought that explains some phenomenon.” Note that on this usage of the term systematicity is built into the concept and the purpose of theories is specified as explanation. Notice also that no degree of uncertainty is connoted by the term.

3 There are some debates over the exact nature of the epistemic value of theories. See, for example, Cartwright and McMullin (1984) and Slater (2008). And it is, of course, possible that there is more than one epistemic value that we use to evaluate theories. There is also the classic realist/antirealist dispute about how to understand the truth value of scientific theories. I mean the central claim here—that theories are principally evaluated according to epistemic goods—to be ecumenical with respect to these debates. I will continue to use “truth” as a stand-in for the core epistemic value of theories, but keep in mind that I mean this to be neutral with respect to debates over nature of the epistemic value of theories.

4 The arguments developed in this paragraph against the libertarian, radical egalitarian, and utilitarian theories of justice are, of course, the rudest sketches of arguments. It’s not my purpose here to seriously argue for one theory of justice over any other, we’re merely working through these sketched arguments to illustrate how the methods of theory evaluation we’ve considered work and how they can be deployed alongside one another in an attempt to get to a final answer as to which of the competitor theories is true. Rawls of course goes into much more detail in arguing for his theory. Indeed, he uses a more sophisticated method of theory evaluation—reflective equilibrium—to advance his preferred theory.

5 Fit with the data is closely related to Rawls’ method of theory evaluation, reflective equilibrium. For more on reflective equilibrium, see Brandt (1979), Brink (1987), Daniels (1979, 1980a, 1980b, 1983, 1996), DePaul (1986), Holmgren (1989), Mandle and Reidy (2013), Rawls (1971, 2001), and Sencerz (1986). Coherence is an important part of reflective equilibrium and is also sometimes discussed as method of theory evaluation unto itself. For more on coherence, see Bender (1989), DePaul (1987, 1993), Mackonis (2013), Olsson (2005), Sosa (1980, 1989), Swanton (1992), and Thagard (1993). Reflective equilibrium (and to that extent coherence) is also connected with theory underdetermination and has roots in Quine’s view of theory evaluation. For more on theory underdetermination and the Quinean roots of contemporary reflective equilibrium, see Bergstrom (1984), Boyd (1973), Earman (1993), Glymour (1971), Laudan and Leplin (1991), Quine (1960, 1969, 1975), and Stanford (2013). I will examine reflective equilibrium and coherence in detail in chapter 3.

6 I put “theory” in quotation marks because this probably doesn’t even qualify as a theory since it is not a system of thought, but is instead a mere list of claims.

7 For more on simplicity as a method of theory evaluation, see Baker (2013), Derkse (1993), Sober (1975 and 2015), Swinburne (1997), and Walsh (1979). Simplicity is also often examined in the particular context of scientific theory evaluation. For more on simplicity as it particularly relates to science, see Bunge (1963), Chandrasekhar (1987), Feuer (1957), Forster and Sober (1994), Hillman (1962), Kemeny (1953), and McAllister (1999). For more on explanatory virtues, including but not limited to simplicity and coherence, see Laudan (2004) and Schindler (2018). I will examine simplicity in detail in chapter 4. I suspect that the method of unity—preferring theories that are more unified—is a close cousin of the method of simplicity, though I leave that argument for another time.

8 Copernicus’ theory also involved epicycles and it is not clear from the historical record how many epicycles he added to his theory. But treat this as a thought experiment if you like: Imagine that Ptolemy’s theory did achieve greater fit with the data than Copernicus’, but only by postulating hundreds more epicycles. It would still be evaluated as an epistemically worse theory because of its significant lack of simplicity. I’ll explore this example in more detail in chapter 4.

9 I have focused on simplicity thus far, but this should not be read as giving a privileged place to simplicity. I am not suggesting that simplicity and beauty are identical, nor do I think that all judgments of beauty are judgments of simplicity. But I will argue (mainly in chapter 4) that simplicity is one particular species of beauty (alongside others on this list: coherence, unity, elegance, and so on). That is, simplicity is one type of how a thing can be beautiful. Some have been concerned to argue that judgments of beauty in math and science are not merely judgments of simplicity; see Inglis and Aberdein (2014) and Todd (2008). Such arguments will not be threatening to my view, since I am not identifying beauty with simplicity, but only simplicity as one type of beauty. I will also argue in detail (mainly in chapter 3) that coherence, like simplicity, is one particular species of beauty. But I am not claiming that either of these are identical with beauty: beauty will be a broader category than either of these. Obviously, making these claims will require at least a mid-level account of beauty, which I will develop in chapter 2.

10 For discussions of the role of aesthetic judgment in science, see Bigu (2014), Chandrasekhar (1987), Curtin (1982), Elgin (2017), Engler (1990), Kivy (1991), Kosso (2002), Martin (1989), McAllister (1989 and 1999), O’Loughlin and McCallum (2019), Scorzato (2016), Thagard (2005), Todd (2008), Weyl (1952), and Zemach (1986).

11 This adage is often attributed to Plato. Although is not found word-for-word in his work, it does obviously fit with his thought.