CLAIMS ABOUT SIMPLICITY

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.

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”^[58] 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.

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.^

“Empirically adequate” is van Fraassen's expression.^{[59] [60] He uses it to mean that the theory is compatible not just with observed phenomena but with all observable phenomena.[61] 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.[62] 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, 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.^[63] 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.

For Einstein, you cannot “extract” the “axiomatic foun­dation of theoretical physics” from experience alone. You need to invoke simplicity. And, on the present interpretation, 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 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 epi- stemic 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.^[64]

Einstein and Infeld write: “Without the belief in the inner har­mony [and simplicity] of our world there could be no science.”^[65]

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.^{[66] [67]}

To be sure, there are factors in addition to simplicity demanded by these scientists. For both, the theoretical 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 of hitherto disparate phenomena, and most of all explana­tory.

g. A Pragmatic Claim

Simplicity is a pragmatic virtue.

decries 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 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.