Structure: Its Shadow and Substance

Structural realism as developed by John Worrall and others can claim philosophical roots as far back as the late 19th century, though the discussion at that time does not unambiguously favor the contemporary form, or even its realism. After a critical examination of some aspects of the historical background some severe critical challenges to both Worrall’s and Ladyman’s versions are highlighted, and an alternative empiricist structuralism proposed. Support for this empiricist version is provided in part by the different way in which we can do justice to Worrall’s original demands and in part by the viewpoint it provides (in contrast to e.g. Michael Friedman’s) on the stability maintained through scientific theory change. 1 Planck against the heretics 1.1 Poincaré on the meaning of Maxwell’s equations 1.2 Two responses: reification and structuralism 2 On the road to structuralism 2.1 The microscope 2.2 Mathematization of the world picture 2.3 The 18th–20th century 3 The new structural realism 3.1 From scientific realism to structuralism 3.2 The Ladyman variant: objectivity and invariance 3.3 How is structural realism supported? 4 An empiricist structuralism 4.1 Royal succession in science 4.2 Defence of the empiricist version 4.3 Structure: an empiricist view Views of science and of nature change hand in hand. In the 17th century the new sciences inspired a hard-line ascetic metaphysics. Theorizing, the new scientists stripped the world of its appearances, its qualitative riches, leaving res extensa as the sole reality of nature, veiled before the mind in its sensory illusions. New instruments such as the microscope promised to confirm the The Author (2006). Published by Oxford University Press on behalf of British Society for the Philosophy of Science. All rights reserved. doi:10.1093/bjps/axl002 For Permissions, please email: [email protected] Advance Access published on March 17, 2006 at Prceton U niersity on Feruary 5, 2015 http://bjpordjournals.org/ D ow nladed from theories directly, and the newly schooled mathematical imagination promised to represent reality as fully intelligible to the mind. But as science moved on to new conceptions of nature, its self-image changed as well. Here I shall try to follow two lines of retrenchment as physical theory lent itself increasingly less to naı̈ve realism: reification and structuralism. Within these, I will focus specifically on the new structural realism, which recently tried to position itself between scientific realism and instrumentalism. After examining its difficulties, I will offer an empiricist view in response to the same ambition. 1 Planck against the heretics On December 9, 1908 Max Planck addressed the Student Corps of the Faculty of Natural Sciences of the University of Leiden. His announced topic was The Unity of the Physical World-Picture, but the real intent was a polemic against a whole bevy of famous scientists who had turned against realism in the preceding fifty years. These misguided heretics included Maxwell, Boltzmann, Hertz, and most of all Ernst Mach, who was to be Planck’s main target in this lecture. In Planck’s eyes they had forsaken the faith of their fathers. He speaks against them with passion: When the great masters of exact research contributed their ideas to science: when Nicolaus Copernicus tore the earth from the center of the universe, when Johannes Kepler formulated the laws named after him, when Isaac Newton discovered general gravitation, when your great countryman Christian Huygens put forward the wave theory of light, and when Michael Faraday created the foundations of electro-dynamics . . . [Mach’s] economical point of view was surely the very last thing which steeled the resolve of these men in their battle against traditional views and towering authorities. Nein! . . . it was their rock-solid belief in the reality of their world picture. (Planck [1909/1992], p. 131) But there is some irony in this episode. Planck had not exactly been unaffected by the heresy he is attacking. Both in this passage, in his title, and indeed throughout his lecture, he speaks of physical theories as pictures and of the product of science as a whole as a world-picture. This language of ‘science as representation’ was the common coin of his opponents, and indeed, the notion and name of world-picture is attributed to Hertz (cf. Blackmore [1992]). When Planck says that this heresy ‘enjoys great popularity, particularly in circles of natural scientists’ (ibid., p. 129) he bows to it in his own choice of language, while arguing against it. For Planck considered this heresy to be a mistaken if understandable response to the ‘unavoidable disillusionment’ when the mechanical world view began to disintegrate. 276 Bas C. van Fraassen at Prceton U niersity on Feruary 5, 2015 http://bjpordjournals.org/ D ow nladed from So what was that popular philosophy? 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 unambiguous. 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 there is any real similarity between the causes of these phenomena. The similarity is a similarity between relations, not a similarity between things related. (Maxwell [1881], pp. 51–2) 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. (Hertz [1893/1962], p. 28) 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, Structure: Its Shadow and Substance 277 at Prceton U niersity on Feruary 5, 2015 http://bjpordjournals.org/ D ow nladed from 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. (Hertz [1894/1956], pp. 1–2; see also p. 177) 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. (Boltzmann [1905a], p. 252) 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 attributes 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! (Mach [1910/1992], p. 124–5) 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. 1.1 Poincaré 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 equations in mechanics. The theory of the ether was a sustained attempt to provide them with a concrete mechanical underpinning (cf. Stein [1989], pp. 61–2). 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. In Poincaré’s 1 When Poincaré later says that Maxwell had shown that there must exist mechanical models of electromagnetism, he presumably thought that this subsumption under the generalized Lagrangian mechanics was successful. As we shall note below, this already derives its sense at best from several successive weakenings of what can count as a mechanical model. 278 Bas C. van Fraassen at Prceton U niersity on Feruary 5, 2015 http://bjpordjournals.org/ D ow nladed from 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 . . . .’ (Poincaré [1905/1952], p. 161) 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. . . .’ (ibid., p. 132). 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? 1.2 Two responses: 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’ (Mermin [1998], p. 753). 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. 2 Note however the vagaries of linguistic change in science. Stein ([1989], p. 57) makes a good case for holding that the retention of the word ’atom’ and discarding of ‘ether’ was historically arbitrary: ‘our own physics teaches us that there is nothing that has all the properties posited by 19th century physicists for the ether or for atoms; but that, on the other hand, in both instances rather important parts of the 19th century theories are correct.’ Structure: Its Shadow and Substance 279 at Prceton U niersity on Feruary 5, 2015 http://bjpordjournals.org/ D ow nladed from 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