Planck directs himself primarily against Mach, but it is in Boltzmann's more moderate and less philosophical writings that we see the story better. Boltzmann presents his own point of view as deriving mainly from Maxwell and Hertz, two of the heroes of recent achievements in electromagnetism. Maxwell's writings are not exactly nambiguous. In fact he is for the main part taken as believing in the reality of the ether and of the electromagnetic waves in the ether, while sometimes despairing of any purely mechanical theory of their character. However, as Boltzmann emphasizes, Maxwell speaks of the envisaged mechanisms as merely analogies, partial analogies, that allow us to get an imaginative grasp on the equations. The equations must on the one hand fit the observed magnetic, electrical, and optical phenomena, and on the other hand allow of some understanding of  the theory as a description of a physical process. But on that second point we receive mainly analogies with other forms of material propagation, diffusion, and interaction -- with gases, fluids, and heat. Maxwell himself cautions us against thinking of this as a true description of reality behind the phenomena: By a judicious use of this analogy [between Fourier's equations of heat conduction and the equations of the electrostatic field] ... the progress of physics has been greatly assisted. In order to avoid the dangers of crude hypotheses we must study the true nature of analogies of this kind. We must not conclude from the partial similarity of some of the relations of the phenomena of heat and electricity that here is any real similarity between the causes of these phenomena. The similarity is a similarity between relations, not a similarity between things related. Then, as Boltzmann sees it, Hertz makes a virtue of necessity and asserts this as a way to understand the scientific enterprise as a whole. Thus Hertz writes and Boltzmann cites: scientific accuracy requires of us that we should in no wise confuse the simple and homely figure, as it is presented to us by nature, with the gay garment which we use to clothe it.  Indeed, with Hertz we begin to have such an emphasis on the representations and their adequacy to the experimental facts as sole anchor, that we can quite understand Planck's sense that the represented world is mostly counted as well-lost for love of theory: We form for ourselves inner pictures or symbols of external objects; and the form which we give them is such that the necessary consequences of the pictures in thought are always the pictures of the necessary consequences in nature of the things pictured .... The pictures which we here speak of are our conceptions of things. With the things themselves they are in conformity in one important respect, namely in satisfying the above  requirement. For our purpose it is not necessary that they should be in conformity with the things in any other respect whatever. Boltzmann, lecturing on this in 1899, expressed the philosophical point of view most trenchantly: We know how ... to obtain a useful picture of the world of appearance. What the real cause for the fact that the world of appearance runs its course in just this way may be; what may be hidden behind the world of appearance, propelling it, as it were -- such investigations we do not consider to be of the task of natural science. Finally, we may note Mach's reaction to Planck's criticisms of this heretical train of thought. Just as Boltzmann does in this last passage, so Mach atttibutes those realist misgivings to metaphysical dreams by which philosophers have infected physicists from time to time: In any case, physicists have nothing to seek "beyond the appearances". Whether philosophers will always find it necessary to affirm something real ... whose relations may only be recognized in the wholly abstract form of equations, may be left entirely for the philosophers to decide. [...] Hopefully, physicists of the 20th century will not let their investigations be disturbed by such meddling! So, as we see here, Planck and Mach each depict the other as having strayed from the true concerns of natural science into a mistaken philosophical conception of their common enterprise. These passages are revealing, but they are more polemical than instructive. We need to see precisely what options were coming into play. 

On The Meaning Of Maxwell's Equations 

As focus I will take Poincaré's verdict on classical electromagnetism: Maxwell's theory is [just] Maxwell's Equations. This verdict was also a sort of capitulation. Maxwell himself had attempted to prove the existence of models of his equation in mechanics. The theory of the ether was a sustained attempt to provide them with a concrete mechanical underpinning. When Maxwell had his theory fully worked out, he discarded the earlier rather primitive ether models but tried to subsume his theory under the generalized dynamics of Lagrange, which deals with mechanical systems whose internal constitution is not fully specified.² In Poincaré's verdict we recognize a definitive goodbye to the interrelation of matter and ether as a live topic in physics. Poincaré's views on science were generally tending toward what Planck considers the great heresy, though stated with caution and diplomacy. In the spirit of Hertz he speaks of "images we substituted for the real objects which Nature will hide for ever from our eyes. The true relations between these real objects are the only reality we can attain ...." Of the principle of conservation of energy, for example, he writes that if we try to enunciate it in full generality, "we see it vanish, so to speak, and nothing is left but this -- there is something which remains constant...."  But Poincaré's verdict was paradoxical and provocative. If science describes nature, Maxwell's Equations must form a theory about what something is like. Mustn't the theory also say what that something is? 

reification and structuralism

If Maxwell's Equations are statements, the question is what they say. If they are not statements, the question is how they can amount to a theory at all. If we leave aside the more instrumentalist (non-statement) options, we detect here two not very well distinguished alternatives. The first is that yes, it is the electromagnetic field itself, which is a thing, and not the shape or form of something else. Today that is an often expressed view, perhaps not always clearly distinguished from rejection of the classical ether: "Fields in empty space have physical reality; the medium  that supports them does not". There is no puzzle, just a new ontology, some new and previously inconceivable furniture for the world. I'll call this alternative reification. The second alternative is a little more agnostic. It could be expressed like this: The Equations only describe a form or structure -- if that is the form or structure of something, that is an unknown entity. The field is first of all an abstract entity (mathematical: e.g. a function assigning values to points in space), though we can of course also give the name "field" to whatever it is -- if anything -- that bears this structure. That unknown bearer might well have other properties, just as ordinary things have properties beside their shape. But the theory does not describe those. Science abstracts, it presents us with the structural skeleton of nature only. To begin this sounds rather reactionary, just when we have discarded the ether and its frustratingly elusive qualities. But there is an often mentioned bit of support. Important equations tend to recur in many places. They tend to identify recurrent patterns in nature, found not once but many times. Often a new process is first described in analogy to an old one, with the equations transposed or reinterpreted. Heat diffusion and gas diffusion are analogous, the harmonic oscillator crops up everywhere.... So the equations omit the distinguishing characteristics. As a reason for structuralism, this observation does not show much at all. For whenever we see the same equations describing two scientific subjects, we also see science describing the differentiating characteristics. If we didn't, we wouldn't have an example to give! The point that such equations describe at once many different processes needs serious reflection, but it is not much of an argument for anything here. So there must be other reasons why both scientists and philosophers have kept returning to this sort of view. It has taken various forms: moderate structuralism: the theory describes only the structure of a bearer, which has also non-structural features (though science is said not to describe those) radical structuralism: "structure is all there is"  in-between structuralism: the structure described by science does have a bearer, but that bearer has no other features at all. What I presented initially is therefore the moderate form. The radical form, to which we will pay special attention below, will not be all that easy to grasp. Finally, I simply interpolated the intermediate form between them; I have not seen this discussed in philosophy of science, but only in more purely metaphysical disquisitions. The currently fashionable term, which still covers various versions, is structural realism. To speak of all the varieties at once I'll say structuralism [about science].

Planck's diagnosis contested 

When Planck reflected on how the great heresy could have taken hold among his colleagues, he diagnosed it as the counsel of despair. They turned toward anti-realism and empiricism only after classical physics had run into severe difficulties, and the physics community had gone through a slough of despond. As I will now try to show, that is not so. The very same philosophical options can be seen to emerge much earlier. Indeed, they emerge very naturally when science proves itself too complex for philosophical naiveté. We see a clear tendency to reify whatever theories invoke in their representation of nature. But conceptual difficulties and the increasingly mathematical character of science foster the structuralist impulse. As interpretations then threaten to become lost in "a bloodless ballet of categories", however, weariness sets in, and the pendulum swings back to reification. Eventually we must find some point of stable equilibrium! 

 To Structuralism 

Let's begin with the disparity the scientific image and the manifest image in the17th century. You can easily see how structuralism could have been a first response. Perhaps, Galileo's contemporaries might have said, the scientific image represents only some aspects of the real and manifest world, leaving many other real aspects out of account. Then, later on, if that idea were accepted, one could add: the aspects represented by science together constitute the structure or form of the world, while all the rest is the 'matter' or content. That reaction, which would not sound all that radical, would thus be to say: fine, science abstracts,  it ignores everything else -- it will be useful to find the structural patterns and ignore the rest for a while. We are reminded here of Cardinal Bellarmini's advice to Galileo of how to view the Copernican system. One imagines that Bellarmini would wish Galileo to think no better of his 'new sciences' in general. Galileo himself, and the mechanical philosophers generally, were more radical. They rejected any such moderate structuralism in favor of reification of their world image. They said, No, THIS is all there is to it. Atomism would supply the resources to extend mechanics into a comprehensive, complete, universal physics. Colour, smell, sound, all perceptual qualities would be reduced to combinations of primary qualities in the things and sense organs. We should place this more radical metaphysical view in contrast to a methodological point that everyone can agree upon. Galileo's restriction of science to primary qualities was a much needed disciplinary move. Aristotelian scientists had felt free to multiply theoretical terms for so-called occult properties. These were a thing's properties that can't be explained on the basis of its composition. Galileo's discipline was to determine beforehand a small set of properties and restrict scientific descriptions to those. Not coincidentally, of course, they were the properties representable by geometry and arithmetic: number, size, shape .... The contrasting metaphysical thesis was extremely speculative, but for a while it looked as if the path to reduction would be pretty short. The microscope especially raised great hopes. Atoms would soon be visible, and the reduction of sensible qualities to mechanical affections would be observable. Color did seem more of an illusion when everything looked just black, white, and gray through those lenses -- the argument is not exactly airtight, to say the least, but lent some plausibility to that supposedly really real world of colorless atoms.

In a way, it was the mathematization -- rather than mechanization -- of the world picture was the glory of 17th century physics. Descartes' physics could leap forward because he created analytic geometry. Newton's could, because he created the calculus. So you would not expect any of them to complain of too much mathematics. But they do. They remember Bellarmini and other Aristotelians charging astronomy with mere mathematical recasting of the phenomena, and with failure to provide true physical content. But now the Cartesians repeat that charge, mutatis mutandis, against Newton. To see their complaint we must remember that the Cartesians were true adherents of the mechanical philosophy, to which the English still paid verbal tribute. We see the primal form of that view of nature most clearly in Descartes' posthumous treatise The World, or Theory of Light. This magnificently ambitious work initiated the entire Faustian project of modern  theoretical science. To begin, Descartes says disingenuously that he wishes to set aside all real physical and empirical questions. He only wants to attempt the mental construction of a world entirely intelligible to the human mind. The result will be precisely the world God would have created if it was going to be a world entirely transparent to human reason, with no mystery in it at all. This World we can clearly understand, for its image, here provided, is the mind's own product. Of course, a little later in the treatise Descartes announces that this constructed World of his matches everything we have found out about the real world. That is precisely the scientific success he aimed for. And finally he adds the reification of his image -- this perfectly intelligible World, he says, is the real world. In all this we may see a lasting, paradigmatic project for theoretical science. Construct a world entirely transparent to the human mind; then show that all known phenomena fit therein. But of course, Descartes' own version had belonged to his own time. Most specifically he counts only clockwork mechanism as entirely intelligible. The World must be a pushme-pullyou machine, if we are to understand it completely. But now comes Newton, whose success is much greater by the same general standard; but who has introduced non-mechanical elements, namely forces which act at a distance, instantaneously. For with Newton, despite much lip service, the early mechanical philosophy bit the dust. The introduction of these forces is a major innovation. The world is no longer a clockwork, in which everything proceeds by push and pull. For Newton himself, this was serious; he was reared in the mechanical philosophy and did not at all see himself as overturning it. He felt very deeply the Cartesian charge that his masses, absolute velocities and forces acting instantaneously over any distance, holding the universe together in a curiously harmonious symphonic whole, reintroduced the occult properties that his own scientific heroes had just banished. Thus Newton defended his own achievement in words which indicate that he hopes for a truly mechanical explanation of gravity. But over the next century, the victorious Newtonians discarded those scruples, and began to think of Newton's own models as the fulfilment of the mechanical philosophy's aspirations. What do the Cartesians think of Newton's success? What they see is the replacement of a humanly intelligible, concrete description of nature by mathematical abstractions. Except that they themselves are eclipsed during the next century, what they see stands out ever more clearly.  The Newtonian paradigm tells scientist to describe patterns of motion, velocity, acceleration, by the new techniques of the calculus, and to add an assignment of masses and forces which turns this pattern into something that satisfies Newton's laws. Very soon they constrain themselves to assign central forces and to conservation laws -- under these constraints, success is not trivial. But the success is a triumph of mathematics, and mechanical action by contact is most definitely not among the constraints. Thus the reification of the World constituted entirely of entities characterized solely by 'mechanical' parameters sounds more and more like a hollow addition to the mathematics -- a vanilla story, as we call that now. The gap between the manifest and scientific images had certainly widened -- and had become salient by the end of the 17th century. That is why we see a general disillusionment with the microscope early in the eighteenth. Newton distinguished carefully the apparent motions described by our measurement results and observations from the reality he postulated. Berkeley and Locke then point out that instruments won't help with the question of principle, and will certainly not reveal a reality behind the appearances. Later scientific realists seem not to recall this insight of Locke and Berkeley. But it remains crucial to appreciate their point if we are to understand the continuing dialectic. By means of instruments we create new phenomena. Whatever will become visible through optical or any other instruments will still be only those apparent motions Newton described as observable -- not the forces, masses or other explanatory characteristics behind those appearances. The new appearances experienced by the inquiring and phenomenon-creating scientist must also be saved - but do not reveal the hidden theoretical underpinnings directly. All we will ever get are appearances, all we ever get are more and novel observable phenomena to save, even if conjured up by previously unimagined instruments. How are those appearances saved? By fitting them into the postulated theoretical world. In Newton we see a constant vacillation between our two main options. When in a triumphant mood, he asserts his law of gravity to describe a new, real cause -- satisfying his vera causa Rule. When pressed and conscious of the Cartesian complaints, he says instead that he will frame no hypotheses, and that it is no mean achievement to have discovered a general form or pattern for planetary and projectile motions. This is just the opposition with which I began, between reification and structuralism.  The 19th/20th century Maxwell repeated Newton's philosophical quest in one sense, Poincaré in another. It is as if a great pendulum is swinging back and forth between two extremes. On the one end, appearances are illuminated by being fitted into a theoretical structure; on the other, far end of the swing that structure itself is held up as the sole reality, the substance of the world When Maxwell thought about the ether, he would have been happy to find a Newtonian 'mechanical' model. Things had gotten worse still, for no such model was forthcoming. The ether, finer than air but more resilient than steel, just would not comply. And yet we see that in this case too, the success of the new theory vanquished all scruples. The newer sense is that certainly there is a process whereby the electromagnetic waves are propagated in space -- and Maxwell's equations are what describe this process, as fully as is required. Newton and Maxwell, in their day, agonized and vacillated between reification and structuralism -- but for their heirs the question disappears. Their agony was then seen only as the aftermath of an old-fashioned world view. That is one of the main reasons why, I think, we see the structuralist reaction emerging in the 19th century. As so often happens, what is earlier seen as a failure or shortcoming becomes the glory of a new generation. When Kirchhoff, Mach, and others attempt to define mass and force, what they really want to do is say: mechanics describes only the general, mathematical structure of motion, but that is precisely the wonder of its success. Mass and force are only theoretical parameters. We know now, through the evolution of mathematics, that abstract structures of the same type should be thought of that way. (That is, we describe a structure with some parameters left undetermined, but we place constraints on those parameters; the different admissible values of those parameters identify the instantiations that can occur in nature.) By the end of the 19th-century, this view of mechanics is expressed in a much more general form for all of physics, all of science, by prominent physicists. I'll just cite here the view as expressed later by Herman Weyl: If nature were all lawfulness then every phenomenon would share the full symmetry of the universal laws of nature. [...] The mere fact that this is not so proves that contingency is an essential feature of  the world.... The truth as we see it today is this: The laws of nature do not determine uniquely the one world that actually exists, not even if one concedes that two worlds arising from one another by ... a transformation which preserves the universal laws of nature, are to be considered the same world. Knowing a great deal about Herman Weyl, we can easily detect what is in his mind. He is pre-occupied with the picture of a group having a number of non-isomorphic irreducible representations. But we can illustrate his point in a simple way. The point he is making is that not everything left invariant by the transformation group that corresponds to a law of nature is itself a matter of law. As example we can take classical mechanics, where velocities are not invariant, they are relative to frames of reference. So the mechanics really does not describe patterns of velocity, but rather of acceleration, which is invariant. Yet we cannot very well think we have to do here with only one pattern, even if we ignore all that is frame-relative. For number too is invariant, but is left entirely unspecified and unconstrained in the laws of motion. The number of bodies that make up the system is invariant, but it is not a matter of law. Kepler had indeed held that any adequate physics would have to explain why there are exactly six planets. Happily Newton left number unspecified, so that his laws are instantiated in N-body systems for every natural number N. By the end of the 19th-century the mathematization of the physical world picture was nearly complete. Is Hertz' mechanics a theory of physical systems or of mathematical structures? Hard to say. It becomes even harder to say when the theory of gravity becomes the theory of solutions of the GTR field equations, and atomic physics the theory of solutions of Schroedinger's Equation. I exaggerate of course, and I ignore momentarily what's nearest to an empiricist's heart -- experiments, observations, empirical phenomena investigated or created, enlarging the realm of experience to previously unimaginable breadth. But it is the theorists who present us with the scientific image of the world. And these theorists write the Book of Nature in the language of mathematics. Thus, by the end of our century, the whole world complains to the scientist in precisely the words of the Cartesian to the Newtonian. Are you describing nature, or just putting it into a beautiful mathematical format? The implied complaint is not about empirical adequacy. Certainly Newtonian science improved the  tables of tides as well as ballistics, predicted the flattening at the poles, the return of comets.... Twentieth-century physics gave us transistors, fission, fusion, radar and laser optics. But what happened to the promise of a World entirely, thoroughly, and completely transparent to the human mind?

From scientific realism to structuralism

Modern science began with Galileo's and Descartes' evangelical reification of the scientific image of the world. In some of Newton's more defensive remarks we can already see a vacillation between two responses. On the one side we see that sort of realism according to which every theoretical posit -- and nothing else -- corresponds to an element of reality. On the other emerges the more moderate structuralism which attributes to science success in abstracting important patterns in nature only, and describing those. Two centuries later the structuralist impulse has become very salient and erupts in such dicta as Poincaré's about Maxwell's equations. Contemporary philosophy of science displays a similar pilgrim's progress. Scientific realism begins with the intuition that the empirical success of science cannot be just a miracle or a coincidence, but must have an explanation. This requirement for explanation is crucial to both the motivation and content of scientific realism. However, the explanations realists offer are not all the same. Here is a more or less central version of the view, as I see it: The aim of science is to provide us with a literally true story about what there is in the world, and this aim is actually achieved to a great extent, because it is pursued by effective means to serve that end. By themselves, do these contentions explain the empirical success? Certainly not! To explain the empirical success of science, something must at least be added about to what extent, and in what respect, that aim of true description is achieved. Suppose, for instance, that the extent to which that aim is achieved is only this: our theories now make true predictions about all the observable phenomena they deal with. That would  certainly be a great extent! But it would be no more than the very success which the realists require to be explained.  So what additions do the realists introduce? The standard first addition was that at least the theoretical entities postulated by science are real. Galileo was quite right that there really are atoms, though he was entirely wrong about what they are like. The truth of the atomic hypothesis supposedly explains much of scientific success since then. The drawback to this idea appears immediately when we apply it to the ether. Shouldn't the question What explains the success of this successful theory? receive the same answer in each case, once this 'standard addition' to the realist view has been made, precisely on the basis that it provides the resources to answer this question? But if so, the success of theories of light, electricity, and magnetism in the 19th-century would then be explained in part by the reality of the ether. Today we grant the empirical successes, but can hardly explain them that way! Of course, we can now provide the different explanation, that the theories happened to track certain empirical regularities, and not any reality behind them. But if that is a good explanation now, why not then also? And if it is always a good explanation, the basis for this realist addition disappears. On the other hand, if it does not count as a good explanation, then the realists have not done what they themselves demand here: to explain the success of science in general. For such examples can be multiplied, especially when we realize that the same words -- such as "atom", "electron", "field" -- will later be used for entities quite different from any they originally stood for (so that when they are retained, the reality of their later referents does not explain the success of the earlier stages of the theory). Thus scientific revolutions, and even evolutions, embarrass the standard scientific realist. The standard pattern of realist explanation of empirical success has become a historical embarrassment, for its instances are by now expected to fail. This was forcefully pointed out by John Worrall. But Worrall insisted that despite all this, we must have a realist explanation of the success of science: The main argument for scientific realism is that our present theories in science are so successful empirically that they could not have gotten that way by chance -- instead they must somehow have latched on to the blueprint of the universe. The main argument against scientific realism is that there have been enormously successful theories which were once accepted but are now regarded as false.... [T]here is [a] reasonable way to have the best of  both worlds: to give the argument from scientific revolutions its full weight and yet adopt some sort of realist attitude towards presently accepted theories in physics and elsewhere -- through structural realism, a position adopted by Poincaré, and here elaborated and defended. Worrall's solution was to say that we must make a different addition to the initial explanation schema. What science succeeds in first and foremost is not the identification of real things in nature that make up the fabric of manifest phenomena. Instead, science succeeds in discovering the structure of whatever it is in nature that bears these appearances. That je ne sais quoi underlying the phenomena becomes partially manifest in structure while remaining forever unknown in content or quality. Thus Maxwell's Equations are retained because they describe a structure which is really there, although any additional description has to be discarded. This was a new move for scientific realists in the second half of the 20th-century. It was not of course actually new in either philosophy or science. As we saw, at the beginning of the 20th century this was salient doctrine. Bertrand Russell gave a striking analogy. What do we know of the world behind the phenomena? Listen to the radio, and hear the sounds which were produced in the studio many miles away. In between are the radio waves which have none of the qualities of sound. But we infer they must have structure which encodes the structure of this sound. Thus we know a great deal about those radio waves on the basis of observation: not what qualities they have or what they are like in themselves, but their structure. And it's precisely that, and only that, which science describes (as it happens, of course, what Maxwell's Equations describe). Scientific revolutions provided the great argument against the view that science is a steadily accumulating store of knowledge. The theoretical furniture of the world is continually discarded, removed, and replaced; certainly not accumulated. But now Worrall tells us that there is after all an accumulating store of knowledge: more and more knowledge of the structure of that furniture, although ideas which go beyond structure fall to the knife at every step. A very pretty idea. It is regrettable only that the division between structure and content is never discernible beforehand. The structure discovered is identifiable only in retrospect -- it is the part retained  through scientific theory change .... The atoms are still there at some level, so that was structure. The ether is no longer there, at any level, so that was a mistake about content.... Yet the structural realist literature and the earlier structuralisms about science as well, despite their flaws, retain genuine appeal. Surely there is an accumulation of knowledge about nature in science, and surely that is the key to its success. What can we make of this?

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