PRESUPPOSITION, AIM OF 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: 'I lie 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).^[100] 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 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.

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 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.^[101] Even Brian Greene, one of the staunchest supporters of string theory, takes such an attitude to be possible.

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.^[102]

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 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.^[103]

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.^[104] 'i his tension affects how one represents or explains observable facts.

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 pressures and temperatures.

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.^{[105] [106] 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 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.

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