1. Introduction

At least since the writings of Karl Popper and Thomas Kuhn made their impact on the philosophy of science it has become commonplace to regard observation and experiment in science to be theory-dependent in some significant respect. Any dependence of the use of instruments in science on the theory governing their operation is a special case of this thesis, and this issue is the concern of this paper. The theory-dependence thesis can be seen as opening the way to extreme sceptical or relativist appraisals of science. The results of observation and experiment become as fallible as the theories they presuppose. Not only are theories underdetermined by the evidence, but the evidence itself is underdetermined. Thus, added to the problem of locating the source of a faulty prediction in the maze of assumptions that yielded it is the possibility that it is the observations involved in the counter instance that are at fault. If we cannot step outside of theory to access theory-neutral data against which to test it, we seem to be forced towards a relativist view according to which proponents of rival theories are responding to different worlds (Kuhn Reference Kuhn1973, 111) or we are trapped in the “experimenter's regress”(Collins Reference Collins1985, 83–89).

There are good grounds for suspecting that the theory-dependence and fallibility of observation and experiment in science have been overplayed. For instance, novel experimental effects can be experimentally demonstrated in a way that leaves no room to doubt their reality. Michael Faraday in the early 1820s and Heinrich Hertz in the 1880s both worked in situations where fundamental electromagnetic theories were contested, but their rivals had no option but to accept the reality of the electric motor and radio waves once they had been effectively demonstrated. Jean Perrin's measurements of the motion of Brownian particles enabled him to establish beyond any reasonable doubt, with arguments that Deborah Mayo (Reference Mayo1996, 228–229) has described as “statistical overkill”, that their motion is random. Ian Hacking has argued that the appearance of dark bodies in blood cells in exactly the same positions on the slide when viewed with the electron microscope and then with a fluorescence microscope, microscopes working on quite different physical principles, leaves no doubt that the dark bodies are really there in the cells.

My own emerging doubts about the force of the arguments for the necessary fallibility of observation in science were shared by my colleague Nicolas Rasmussen (Reference Rasmussen1997, Reference Rasmussen, Chalmers, Buchwald and Warwick2001). He exploited his work on the history of the electron microscope in biology to make a case against what he saw as the “theory-dominant” tendency in contemporary philosophy of science. In particular, he produced detailed historical examples designed to show that use of the electron microscope in biology does not require appeal to a theory of that instrument and its interaction with specimens under investigation in the way that philosophers of science typically imagine. Rasmussen found that a common response to his argument was that, whilst it might apply to biology, it did not apply to physics. As a result, he brought me into the picture and pointed me towards an example of an early use of the electron microscope in physics to see to what extent his case held up there. Since I was in my anti-theory-dependence phase I was quite prepared to be able to contribute to Rasmussen's pragmatic, anti-theory dominant thesis about the electron microscope. However, as we shall see below, this was not quite how it turned out. I found that whilst some of the arguments sidestepped any appeal to the theory of the electron microscope most did not. Novel and speculative theories of the electron microscope were involved in a justification of some of the key data, but not in a way that will give any comfort to the sceptic or relativist. The use of instruments in physics can be theory-dependent in a deep sense, but this does not prevent the data collected with their aid supporting theory, even the theory involved in their use.

2. Kosso on the Theory-Dependence of Instruments

Peter Kosso has developed a view on the theory-dependence of scientific instruments that is a useful point of departure for our discussion. Kosso's case is relevant for two reasons. Firstly, it represents a clear characterisation of the view which I will attempt to improve upon and secondly, he illustrates his argument by drawing on examples involving the electron microscope, thereby facilitating the comparison of our respective positions. Kosso maintains that observation in science is indeed theory-dependent and that this poses a problem and a threat of circularity:

There is no doubt that problematic circularities occur. This is illustrated by the following anecdote. In the two years that separated my life as a physicist from my life as a philosopher I taught physics at school level. I remember being troubled by an experiment I was obliged to have a senior class conduct. It involved measuring the deflection of a coil suspended between the poles of a magnet as a function of the current passing through it. What troubled me was that I knew what was inside the ammeter being used to measure the current, namely, a coil suspended between the poles of a magnet. In this experiment the deflection would be proportional to the current readings whatever the relationship between current and deflection provided only that both coils were governed by the same relation. Theory-dependence of instruments can be a problem, but, as we shall see, it need not be.

As far as use of the electron microscope is concerned, the perceived threat looms large for Kosso. According to him, the way that the output of the microscope is related to the specimen under investigation is by way of a deductive chain of inferences that traces the causal path from the specimen via the microscope to the observable output, the theory of the microscope and its interaction with the specimen being necessarily involved in the deduction. So, in a very strong sense, observation with an electron microscope is theory-dependent. However, argues Kosso, this need not be the threat to objectivity that it appears to be. The threat is much lessened if the theory about the object under investigation is distinct from and does not include the theory of the microscope and its interaction with the specimen. Kosso contrasts the use of the electron microscope to observe DNA molecules with its use by physicists to form images of single atoms. In both cases an appeal has to be made to theories of electromagnetism, electron scattering, etc. But the first case is unproblematic in the way that the second is not because the theories about DNA under test (e.g. that the molecules form closed loops) are independent of the theory of the workings of the electron microscope whereas in the case of the imaging of single atoms this is not the case. So we have Kosso's ‘declaration of independence’, the use of an instrument provides objective evidence for a theory provided that theory is independent of those involved in understanding the workings of the instrument. Kosso refers to the violation of this condition as nepotism.

So, according to Kosso, (i) use of the electron microscope necessarily involves an appeal to the theory of the microscope and its interaction with the specimen, and (ii) that theory should be independent of the theory under test, a violation of which amounts to nepotism.

Hacking's argument from coincidence referred to above illustrates the kind of way in which (i) can be contested. Neil Thomason (Reference Thomason1994, Reference Thomason and Riggs1996) gives related arguments showing, for instance, how Galileo was able to justify his appeal to observations with his telescope without appealing to a theory of how it worked while the idea that observation always needs to be validated by theory of the observing process can be seen as far fetched when we consider observation with the naked eye. Do we need a theory of optics and perception to validate naked eye observations of an accelerating stone as Kosso (Reference Kosso1989, 254) seems to suggest? To insist that we do seems to lead to the paradoxical conclusion that science cannot get off the ground until we have a theory of how the eye works! These arguments against the claim that the use of instruments is necessarily theory-dependent certainly have some force. The case-study described in the next section shows how early uses of the electron microscope in physics involved arguments that sidestepped the need for a theoretical account of the workings of that instrument or relied on only a rough understanding of its operation. Nevertheless, there were other key arguments involved in the electron microscope's use that did rely on novel theories of its workings and its interaction with the specimen under study. These reveal ways of overcoming problems associated with the theory-dependence of instruments that differ from the one described by Kosso. There were arguments from coincidence that were used to support speculative theories of the electron microscope and its interaction with specimens by data whose interpretation relied on those same theories.

3. Dislocations in Crystals Observed with an Electron Microscope

Physical properties of crystalline solids, such as their tensile strength and ductility, differ widely from what is to be expected on the assumption that their crystalline structure is perfectly regular. In the 1930s a detailed theory was worked out that attributed these discrepancies to various kinds of imperfections in the crystal structure that came to be known as dislocations. The theory was borne out to some extent by the match between the predictions of the theory and observable features of crystals, but for a couple of decades there was no direct evidence of the existence of dislocations, a fact which apparently led metallurgists, if not physicists, to be unwilling to believe in them. The following study investigates some features of the first “direct” observations of dislocations using the electron microscope in 1956.

The first production of images of dislocations on the microfilms of an electron microscope were produced by James Menter (Reference Menter1956) working in an industrial research laboratory in Cambridge, England. It is significant that when I look at the images reproduced in that article I cannot discern with confidence what features of the images correspond to the dislocations. It is clear that these images are meant to constitute evidence, indeed the first direct evidence, for the theory of dislocations. The main thrust of Mentor's case in the article is to establish that the images do indeed represent crystal lattices and their dislocations, and he achieved his aim in a masterful way by a number of arguments some of them involving appeal to theory, including theory of the instrument, some of it well known and some of it novel. What is more, he was also able to appeal to the data as confirmation of his novel theory in a way that is quite legitimate. Let us look at some of the details of the way he achieved this.

Menter was certainly aware of the theory of dislocations and of speculations about the limits of the resolving power of electron microscopes, which suggested that there was a chance of using them to observe the regular arrays of molecules in a crystal. But the path that led Menter to attempt to observe them with his microscope was much more pragmatic. He was using the electron microscope to observe tiny cracks in glass (the company for which he worked was involved in the development of television tubes) and his instrument was able to resolve one of the smaller ones rather better than Menter had anticipated. Indeed, knowing the magnification of his electron microscope, established by a method to be discussed in Section 4, Menter deduced that at its thinner end the width of the crack was of the order of ten Angstroms (that is, one ten millionth of a centimeter). He realized that this was of the order of the spacing of layers of molecules in crystals, as measured, indirectly, by X-ray diffraction. This led him to investigate crystals of platinum phthalocyanine, chosen because of the relatively large spacing of the platinum atoms in them, in his electron microscope. He was indeed successful in producing the images mentioned above, which were interpreted as showing regular molecular planes undergoing the abrupt changes in direction corresponding to dislocations. Using the known magnification of his microscope he was able to calculate the spacing of the molecular layers and found it to be 12.0 ± 0.2 Angstroms, which compared favorably with the value of 11.92 Angstroms measured by X-ray diffraction. This correspondence itself constituted an argument that the images were indeed images of molecular lattices, for how else could the close correspondence of these independent measurements be explained? But this was by no means the end of Mentor's case. An appreciation of these additional arguments will require a little physics.

There is an important distinction between a diffraction pattern and an image which is best explained by considering an optical diffraction grating. If a grating is illuminated perpendicularly with a parallel beam of monochromatic light, then the light emerging from the grating will be diffracted, so that a screen placed so as to receive the light will be illuminated over a larger area than it would have been had the parallel beam been undeflected. The parallel transparent lines on the grating will give rise to bright and dark bands on the screen because of the interference of light from each of the lines on the grating. But the pattern of bands on the screen is not an image of the grating. Light from each and every transparent line on the grating contributes to each and every bright band on the screen. Should one of the lines on the grating be distorted this will not show up as a distortion of one of the bands on the screen but will result in a slight blurring of the overall pattern. Although the diffraction pattern is not an image of the grating, such an image can be formed simply by placing a suitable lens between the grating and the screen. As we have observed, X-rays are diffracted by regular arrays of atoms in a crystal, with these arrays playing the role of the grating in the optical case, so that information about crystal structure can be deduced from the diffraction patterns. However, since there is no way of focusing X-rays, one cannot convert the diffraction pattern into an image. Electron beams, like light, can be both diffracted and focused, so we have the possibility of diffraction patterns and images, a possibility fully exploited by Menter.

With his electron microscope set up to produce diffraction patterns, Menter identified the regions of his sample crystal that, when illuminated by the electron beam, led to patterns characteristic of diffraction from lattice planes in the crystal designated as the (201) planes, indicating that in those regions the crystal was suitably aligned. This was to some extent verified by direct inspection of the orientation of the observable crystal structure. Then, adjusting the microscope to image-forming mode, Menter found that images were formed when, and only when, those regions of the crystal that had produced the diffraction patterns were illuminated. This argument from coincidence could be combined with the previous one because the lattice spacing deduced from the images corresponds to the measurements using X-ray diffraction as we have seen. For Menter (Reference Menter1956, 123), at least, “the fact that a crystal showing the (201) reflection in the diffraction pattern also shows the lines [in the image] 11.9 A apart, together with the crystal habit data… , was taken as conclusive evidence that the line structure is associated with the (201) planes.”

But Menter had not finished yet. The novel part of his theoretical treatment was to apply the Abbé theory of optical microscopes to the electron microscope. An appreciation of what he achieved here will require a basic knowledge of Abbé diffraction. When light passes through a narrow slit it is diffracted into what would have been the shadow region were the wave to be undiffracted. The intensity of the diffracted light varies with the angle of diffraction. There is a peak in intensity in the straight-through direction and a number of subsidiary peaks, the first order, second order peaks and so on with diminishing intensity from peak to peak. The angle at which these peaks in intensity occur is a function of the width of the slit and the wavelength of the light. If the diffracted light is to be focussed into an image then, ideally, all the diffracted light distributed across the peaks of various orders should be integrated into the image, otherwise information is lost. A minimum condition for the formation of an image is the inclusion of the first peak. If that and higher order peaks are excluded no image results. Menter transferred this account to his experiment with the electron microscope, treating the electron beam as a wave and the lattice spacings as the slits.

Routine tests showed that Menter's application of Abbé theory was appropriate. Using an aperture to restrict the entry of diffracted electrons into the imaging system, Menter found that with that aperture set to prevent acceptance of the first peak no image was formed. As soon as it was opened to allow access to that peak the image of the crystal lattices duly appeared. Note that this argument, insofar as it is used to confirm Menter's theory, does so by taking for granted that the images are indeed the images of the lattice spacings. But Menter had another move up his sleeve to add further support to that assumption. It was yet another argument from coincidence and one that Menter himself found most convincing of all. Menter performed experiments on a purposely bent crystal so that some regions of the crystal would be appropriately aligned for diffraction and others not. The first stage in the experiment was carried out with the aperture set to exclude the first diffraction peak. Under these circumstances regions of the crystal that are suitable orientated for diffraction will show up on the screen as dark bands, because electrons from the first and higher order peaks are lost from the beam. Other regions of the crystal will show up as bright because there is no coordinated diffraction of this kind. In the second stage the aperture was opened enough to admit the first peak but not the second or higher order peaks. Because these higher order peaks are excluded there will still be dark bands on the screen although not as pronounced as before, because electrons in the first peak are getting through. However, because the first peak is indeed getting through, we now have the conditions for forming an image of those regions of the crystal that are suitable aligned. The images duly appeared on the screen, right in the dark regions where the theory would have them appear. “This experiment proves conclusively that it is only when the crystal is in a suitable orientation for Bragg reflection to occur that the closely spaced lines are seen” wrote Menter (Reference Menter1956, 129) with the implication that the lines are indeed images of the lattices responsible for the diffraction. What we have seen in the above is a series of interconnected arguments, mainly arguments from co-incidence, that show, both that Menter's theoretical interpretation of his experiment is correct and that his interpretation of the data is correct. This is exactly how a commentator at the conference at which Menter first reported his results saw it (Chalice Reference Chalice1957, 268–269). He referred to Menter's “work on the direct observation of crystal lattices and their imperfections” noting that “imperfections in the lattices were demonstrated in the micrographs,” but also noting, with respect to Menter's account of image formation that ‘experiment has justified in general terms the validity of his approach.” There is an appeal to theory to justify the interpretation of the observations, and observations confirm that same theory, a clear case of nepotism but a persuasive argument nevertheless.

A second successful experiment to resolve dislocations with the electron microscope was submitted for publication just three months after Menter's. This involved dislocations in metals, where the lattice planes are considerably closer together than in Menter's crystals of platinum phthalocyanine. These experiments were conducted by a group working at the Cavendish Laboratory under P.B. Hirsch. The kinds of arguments they used to conclude that their images did indeed represent dislocations included a range of arguments from coincidence similar to Menter's. A particularly striking confirmation was provided by the observation of the motion of the dislocations. Motion of dislocations along lattice planes was a key part of dislocation theory, being necessary for the explanation of such things as the plasticity and ductility of metals, since the forces between adjacent layers of molecules are much too strong to permit relative motion of the layers. The Hirsch group were able to witness the dislocations move in precisely the way predicted by the theory. As Hirsch and his co-authors put it, “behaviour of these moving lines is identical with that expected of dislocation lines” so these observations “leave little doubt that the lines represent single dislocation lines” whilst at the same time this feature of the experiment “represents direct proof of the Mott-Frank screw dislocation mechanism in cross slip” (Hirsch et al. Reference Hirsch Peter and Whelan1956, 679 and 682). So, again, the coincidence between observation and predictions from theory is used to support both the observations and the theory, where the theory in question here is that which ascribes properties of crystalline solids to dislocations in there crystalline structure, rather than the theory of the electron microscope. Hirsch even made a movie of the motions and showed it at the 1956 conference mentioned above. As one commentator observed, “even metallurgists were forced to believe in dislocations now” (Braun Reference Braun, Hoddeson, Braun, Teichmann and Weart1992, 348).

Neither Menter nor Hirsch had provided a theoretical derivation that traced the causal chain from specimen to the images on the micrographs conforming to Kosso's requirement. They had not given a detailed account of how images of dislocations are formed. Within a few months of their experiment the Hirsch group had rectified this deficiency, and published a quantum mechanical account of the image formation (Whelan and Hirsch Reference Whelan and Hirsch1956). With the aid of this theory they were able to detect detail in the micrograph images that they would not otherwise have appreciated. As they put it themselves in a subsequent publication (Howie and Whelan Reference Howie and Whelan1962, 206), “much of the available information must inevitably be lost … unless a sufficiently good theory exists by which the observed and often complex image contrast effects can be interpreted,” and they proceeded to demonstrate the match between their theoretical analysis and its fit with the newly interpreted data. Whelan and Hirsch (Reference Whelan and Hirsch1956, 1303) explicitly make the point that the match between theory, which here is a novel and hence previously untested theory about the interaction of specimen and instrument, and appropriate interpretations of the images on the micrographs serve both to confirm the theory and the interpretation of the data. “The general agreement obtained between theory and experiment confirms that the images are due to stacking faults and that the theory developed… is basically correct.” This conforms as closely as one might wish with what Kosso condemns as “nepotism”, and yet the argument has force. What is more, I suggest, it is precisely the kind of argument one might expect to be utilized when novel instruments are applied in new areas.

My study of these early uses of the electron microscope in physics has an interesting sequel. Because my physics was a bit rusty I was anxious to check the details of my reconstruction with someone more knowledgeable and up to date. I was referred to Peter Hawkes, an authority on the electron microscope and co-author of a standard text on the subject who works at the CNRS Laboratory of Electron Optics in Toulouse, France. Whilst I was seeking his comments on my physics, it turned out that he had been a young researcher with the Hirsch group at the very time of the work I have reported here, so he was able to act as a good judge of my history too. I was relieved to learn that both my physics and history were free of obvious errors. Hawkes was able to comment on subsequent developments of the theory and use of the electron microscope as its resolving power has been increased well beyond what Menter and Hirsch were capable of achieving. In his letter to me Hawkes makes the point that theory becomes increasingly important as an instrument is pushed towards its limits, and observes that even a theory of the unaided eye becomes important for an appreciation of the limits of that “instrument”. With respect to the electron microscope he writes , “There was a very instructive polemic a few years ago concerning the reality or not of certain butterfly-like patterns, and the theory was able to demonstrate that such patterns would be expected if the illuminating beam was tilted (accidentally or deliberately). The point of this example is that observation unassisted by theory was positively misleading and it was an application in which the e. m. was the only tool that could provide information.” The use of instruments in science can be theory-dependent all right, but not in a way that need threaten the notion that their output can be used to confirm the very theories on which they depend.

4. A Multiplicity of Mutually Reinforcing Argumentative Strategies

A general understanding of how electron microscopes work was available to Menter and Hirsch in 1956. It was understood that high energy electrons have wavelike properties, that beams of them are diffracted when passing through apertures of a size within a few orders of magnitude of their wavelength, that coherent beams interfere, and that they can be focused using magnetic lenses to form images. A range of experimental evidence could be drawn on to support such claims that was totally independent of the specific uses of the electron microscope by Menter and Hirsch to observe dislocations. Insofar as they appealed to or tacitly assumed this background knowledge to justify their claims about observations of dislocations, Menter and Hirsch avoided circularity in accordance with Kosso's declaration of independence. However, they used a variety of other modes of argument not covered by, and some of them not totally in keeping with, Kosso's strictures. Some arguments bypassed a theory of the instrument altogether. Others did involve novel theory of the formation of images of dislocations, but in a way that comes close to what Kosso calls nepotism. Claims about dislocations and their imaging by the electron microscope were justified by the very results those claims were used to justify, but in a way that gives no solace to the sceptic or social constructivist.

One standard way of arguing for the data obtained with an instrument is to gain independent access to that data by other means. Galileo could argue for his telescopic observation of the inscription on a distant building by showing it to be compatible with naked eye observation of that building viewed close up without any need to appeal to a theory of the telescope. Similarly, the veracity of some observations with the electron microscope could be established by reproducing them with strong light microscopes. Something of this kind was operative when Menter observed cracks in glass. These cracks could be observed with powerful light microscopes until they became too fine to be resolved by them. These same cracks could be observed by the electron microscope also, but were then seen to extend further. The method for determining the magnification of the electron microscope, and which was to lead to the crucial realization by Menter that, at their finest, the dimensions of the cracks were comparable to the spacing of molecular planes in crystals, also relied on overlap between and mutual reinforcement of light and electron microscope data. It is instructive to look at how this was done in some detail, drawing on Rasmussen (Reference Rasmussen1997, 234–239).

The “argument of the grid” proposed by Hacking (Reference Hacking1983, 202–203) shows one way in which electron microscopic data can be reinforced by optical data. A grid of equally spaced parallel lines is drawn with pen and ink, and is then optically reduced by some known factor to such an extent that the spacings cannot be resolved by a light microscope. The subsequent resolution of these by an electron microscope not only provides a case for the veracity of its images but it also enables one to calculate its magnification. There were two disadvantages of the use of these grids to measure the magnification of electron microscopes. Firstly, even the best such grids showed a variation in size of the spacings across a single grid. Secondly, to measure the magnification of an observed specimen it was necessary to replace the specimen by the grid, and this could alter the magnification through a movement of the specimen holder. A chance discovery offered a superior solution that soon became the standard technique. It was found, in 1948, that latex particles manufactured by Dow Chemicals using a reproducible technique not only possessed a uniformity of size much greater than that shown by the spacings on a grating, but that the actual size (2600 Angstroms) made these particles detectable both by electron microscopes and the most powerful optical techniques. The actual size of the particles could be measured by various means, such as interferometry, light microscopy, and ultracentrifugation. The latex particles could be sprayed onto the grid holding the sample in an electron microscope using an aerosol and provided a ready measure of scale. Menter employed this method to evaluate the spacings of the crystal lattices presumed to be responsible for the patterns discernible on his micrographs. The fact that the value obtained agreed with that measured by X-ray diffraction constituted an argument for the interpretation of the image that bypassed direct appeal to a theory of image formation.

Whilst some electron microscope data could be supported by comparison with independent data using other techniques, this clearly would not do for that data accessible only with the electron microscope, any more than observation of buildings through a telescope could help Galileo separate veridical images from artifacts when using the telescope in the astronomical domain. But our electron microscopists had another strategy that did not rely on a detailed theory of their instruments just as Galileo did. Galileo noted that the starlets he observed near Jupiter, and only near Jupiter, moved precisely as one would expect on the assumption that they were moons of Jupiter. The match between the moon assumption and the detailed observations confirmed both that assumption and the veracity of the telescopic data in question, along the lines explained by Thomason (Reference Thomason1994). How else could the detailed match between assumption and observation be explained? In like manner, the patterns observed by Menter and Hirsch conformed closely to what was predicted by the theories proposed two decades earlier that explained bulk properties of solids by dislocations in their crystal structure. The most spectacular case was the observation of the motion of dislocations along crystal planes by Hirsch. The only plausible way to explain this match between the dislocation theory and what was shown on the micrographs is to assume both that the theory is at least roughly correct and that the patterns on the micrograph are indeed images of dislocations. This mode of argument bypasses a detailed theory of the instrument. This in itself is no more remarkable than the fact that the presence of our breakfast and the veracity of our sensations of it can be confirmed by noting that it can be seen, smelt, and tasted at the same time, an inference that fortunately does not require a detailed knowledge of how the senses work and are coordinated.

As we have seen, our electron microscopists did not bypass the theory of their instruments altogether. Menter extended the Abbé theory of the microscope to the electron microscope for the first time and the Hirsch group provided a theoretical account of how the images of dislocations, as opposed to regular crystal lattices, were formed. Insofar as there was independent support, for example, for Menter's assumption that electrons share the wave character of light and for the quantum mechanics used by Hirsch, the form of argument is well captured by Kosso's account. But the most telling aspects of their case involved arguments from coincidence that served to vindicate theory of the instrument and the interpretation of its output both at the same time. The interdependence of theory and data that worried Kosso can, in appropriate circumstances, be exploited in a way that confounds rather than aids the sceptic. When Menter observed images appearing in the middle of the dark bands of the Bragg fringes and only there, just as his theory of his instrument predicted, he and others rightly took this, both as a vindication of that theory and of the claim that the images represented crystal lattices and their dislocations. The quantum mechanical account of image formation led to the prediction of fine detail in the electron microscope images not previously discerned. When this detail was indeed detected the Hirsch group rightly took this as evidence both for their theory of the instrument and for the veracity of the newly interpreted data.

It is worth stressing the sense in which the data provided by the micrographs were indeed theory-dependant. With the development of the quantum mechanical account of image formation, it was theory that led to the search for detail not previously noticed, and even if it had been noticed there would have been no way of appreciating its significance. As Clerk Reference Maxwell, Campbell and GarnettMaxwell ([1856] 1884, 349) once put it “the dimmed outlines of phenomenal things all merge into one another unless we put on the focusing glass of theory.” The coincidences involved in Hirsch's predictions are more complex than those in the case of Menter described above, and in a sense are more significant for that very reason. Hirsch's prediction of the fine detail subsequently confirmed by his electron microscope images were derived from some precise assumptions about the form of the dislocations that were a central part of the two-decade old theory plus his novel quantum mechanical account of their image formation by the electron microscope. The positive result was taken as confirming the assumptions about the form of dislocations, the applicability of the theory of image formation and the interpretation of the patterns on the micrographs.

Our example illustrates the point that experimental scientists have a whole arsenal of techniques for tackling any epistemological problems posed by the fact that the use of instruments in science are theory dependant. In 1956 Menter and the Hirsch group were able to exploit them in a range of interconnected ways to establish beyond reasonable doubt that the molecular structure of crystalline solids contains dislocations and that these dislocations can be observed with the electron microscope.

5. Arguments from Coincidence

I have described arguments from coincidence which serve to vindicate both the data and the theory used to interpret that data. They are effective to the extent that the only plausible explanation of the match between theory and data is the validity of both. Experiments that do narrow down the options so that this is indeed the choice are not easily come by. The match between the thirty two straight line graphs produced by my students in the experiment described in Section 2 and the theoretical prediction of the proportionality of the deflection of a coil and the current flowing through it did not leave one with the choice of accepting the confirmation of the theory or an unlikely coincidence. Reflection on the workings of the ammeters used revealed a different option. Even Hacking's celebrated argument from coincidence mentioned in the introduction is not strong enough until the possibility is ruled out that the observed black bodies are a consequence of the interaction between the electron microscope and the specimen, subsequently observed by the fluorescence microscope. The problem cannot be straightforwardly resolved by repeating the experiment by reversing the order in which the two microscopes are used because use of the fluorescence microscope destroys the specimen, as Rasmussen reminds me. But suppose alternatives can be eliminated, as was surely the case with the arguments of Menter and Hirsch in our main example. Suppose we do have a good argument from coincidence. What exactly does such an argument establish? Some clarifications are necessary lest it be thought that these arguments provide an all too easy solution to the problem of induction.

A good argument from coincidence of the kind in question leaves us with a choice—accept both theory and data or acknowledge a coincidence. The fact that there is the choice indicates that the theory and data are not conclusively established in a logical sense. Coincidences do occur. One of the three series of tests carried out by the Eddington eclipse expedition to investigate deflection of starlight by the sun gave a result that matched very closely the prediction of Newtonian gravitational theory. Did this match confirm Newton's theory? No it did not. There was independent evidence that this particular series of measurements could not be trusted because the telescope had become distorted by the heat of the Sun. The match between theory and data turned out to be a mere coincidence. Similarly, the conformity of the radii of planetary orbits to Bode's law turned out to be a mere coincidence in spite of the fact that the asteroid belt was discovered as a result of investigating a gap in the series. However, the case for the coincidence option becomes less compelling when arguments from coincidence are multiple and of a variety of kinds as was the case with Menter and Hirsch in our examples. The spacing of lattice planes deduced from electron microscope measurements matched those measured by X-ray diffraction, electron diffraction data was correlated with electron imaging data in the way predicted by theory, images of lattices appeared in the middle of the dark Bragg fringes and only there, just as predicted, the dislocations were observed to move just as the twenty year old theory involving dislocations theory predicted they should move, and various practical interventions produced the expected variations in the images. I suppose there is the logical possibility that this was all a coincidence, but could there be any serious doubt that the electron micrographs were showing images of dislocations? In suggesting there is not I have the physicists involved and even the originally sceptical metallurgists on my side.

Let us accept, then, that suitable arguments from coincidence can provide convincing arguments for the truth of the interpretation of data. But what of the theories with which that data agrees. Was the theory of dislocations in crystals and its explanation of physical properties of solids or Hirsch's theory of imaging by the electron microscope established by the experiments we have described? The arguments from coincidence do constitute support for those theories, but support that falls short of proof. What the experiments we have described show, for instance, is that the dislocation theory of the day got it right about the experiments in question, which showed that there are dislocations of the kind predicted by the theory which moved along lattice planes in just the way predicted by the theory. Similarly, the Hirsch theory of image formation was confirmed insofar as it got it right about a range of otherwise unexpected detail in the images. But the fact that these theories got it right about the experimental phenomena in question does not mean that they get it right about everything. (Note Hirsch's guarded remark that his experiment showed his theory to be “basically correct”.) Here is another example to illustrate this epistemological point. Perrin's brilliant experiments on Brownian motion left no room for doubt that the kinetic theory correctly predicts the basic features of that motion, as Mayo (Reference Mayo1996, chapter 7) has argued. Did this establish the kinetic theory in its generality? Well, no it did not, because that theory is false and gets it wrong about the specific heats of gases.

Arguments from coincidence of the kind in question do not establish the truth of the theories involved but they do put important constraints on future modification or replacement of those theories. The modified or replacement theories need to explain the success of the replaced theories in the arguments from coincidence in which they figured, otherwise we are left with the coincidences. Modern theory of the electron microscope has developed well beyond Hirsch's early efforts but is able to grasp the sense in which the latter's theory was “basically correct” just as he claimed. As a result, the match between Hirsch's theory and experimental results, that is, his arguments from coincidence, survive. Similarly, contemporary kinetic theory, with its quantum mechanical modifications, can cope with the specific heats of gases, but still explains Brownian motion in the same way that Perrin claimed it did. If this were not the case the modern theory would clash with Perrin's securely established experimental results. Both the experimental results and the applicability of theories involved in good arguments from coincidence, and especially multiple arguments from coincidence, survive subsequent theory change.

The above considerations suggest that experimental knowledge grows cumulatively in a way that is not threatened by the senses in which observation, experiment and the use of instruments can be legitimately regarded as theory-dependent.Footnote ¹ A range of experimental results, such as reproducible experimental effects, can be established in a way that does not involve high-level theory. In cases where experimental results are highly theory-dependent, arguments from coincidence can serve to establish them, as well as the rough applicability of the theories involved, in a way that will survive any future theory change.