HOW SHOULD SPECULATIONS BE EVALUATED? MAXWELL’S SPECULATIVE STRATEGIES

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.

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.

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,”^[45] 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.^[46]

Maxwell does not claim that the assumptions he makes are true or close to it. His aim in this paper is to see whether

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.

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 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.

b. Physical Speculation

In 1875, fifteen years after the publication of his first ki­netic theory paper, Maxwell published “On the Dynamical Evidence of the Molecular Constitution of Bodies.”^[47] 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.^[48]

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.

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 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.^[49]

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 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.^[50]

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 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.^[51]

c. Physical Analogy

Finally, I turn to a truth-irrelevant speculation. In 1855, Maxwell published a paper, “On Faraday's Lines of Force,”^[52] 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 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 analogy between molecules in a gas and bees in a swarm: they are similar in some of their motions. This involves a truth­relevant 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 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 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.^[53]

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.^[54]

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