As it turns out, all of the qualifications introduced so far are not sufficient to answer the historical challenges. That is to say, further examples have come forward which apparently stand as firm counterexamples to the position we have reached: that given novel predictive success we should infer the (approximate) truth of the working parts of the scientific theory enjoying such success. Or, better, we have counterexamples to nearly every interpretation of this claim—dependent, in particular, on how one understands ‘working parts’.
To start with, there are cases which apparently show that novel predictive success cannot possibly be enough to motivate a realist commitment. Vickers (2013a) discusses the case of Velikovsky, and in particular his successful prediction that the surface of Venus must be ‘hot’. As Vickers writes (p. 195f.), “Given just how fantastic Velikovsky’s ideas were, the realist has no chance of arguing that the ‘working parts’ of Velikovsky’s theory were approximately true.” So the success-to-truth inference fails for this case, if we think the success is sufficient. But intuitively the success is not sufficient, even though it is undoubtedly a case of novel predictive success (given how ‘novel predictive success’ is defined in the literature). It is not sufficient, because the prediction is so vague—Velikovsky says nothing more specific than that the surface temperature of Venus will be ‘hot’. This is, certainly, a falsifiable prediction, but it is not a very risky prediction precisely because it is so vague, and thus compatible with a very large number of possible observations. The lesson seems to be that the realist needs to include in her success-to-truth inference some clause concerning (e.g.) ‘sufficient degree of risk’ of a novel prediction.Footnote 9
And yet even with such a clause in place, there are still highly problematic cases. Saatsi and Vickers (2011) discuss the case of Kirchhoff’s theory of diffraction. Here the predictions are quantitative (very specific and hence very risky) and highly accurate, and yet (the authors argue) at least some of the working parts of Kirchhoff’s theory are definitely not approximately true (see especially Sect. 4.2). Another example is discussed in Vickers (2012): the case of Sommerfeld’s prediction of the frequencies of the hydrogen fine structure spectral lines. Again, the predictions are exceptionally accurate, but Sommerfeld drew heavily on a theory of the hydrogen atom involving relativistically adjusted elliptical orbits of the electron. These orbits lie at the heart of Sommerfeld’s theory, such that it is not at all feasible to describe them as ‘idle wheels’. And in addition it does not seem at all feasible to describe these features of Sommerfeld’s theory as approximately true. A final example concerns Dirac’s prediction of the positron, as discussed in Pashby (2012). Again, we have a very impressive (risky) prediction which—Pashby argues—issues from hypotheses which cannot feasibly be described as ‘approximately true’.
This list will certainly be extended: new cases are coming forward all the time.Footnote 10 This leads to the worry that the realist cannot respond by merely inserting the word ‘probably’ into her success-to-truth inference. And one may well start to worry that it is getting harder to see how else the realist can modify her success-to-truth inference without including ad hoc adjustments which are designed merely to preserve a degenerating project.
One option is to adopt a very narrow view on which parts of a theory are truly ‘working’. As noted above, Worrall makes the distinction in terms of the ‘content’ of a theoretical claim, which is idle, and the ‘structure’ of a theoretical claim, which is working and thus merits our doxastic commitment.Footnote 11 In other words, we should not believe what our best current scientific theories say, but instead we should believe that they have the ‘structure’ of the world right (or approximately right). What should be meant by ‘structure’ has been a topic of much debate, and a lot hangs on it. But whatever the answer, our commitments become highly abstract, and are best expressed using some combination of logic and mathematics as opposed to the natural language of science.
This move has polarised the realist community. Many realists have taken issue with structural realism on the grounds that there are purely theoretical scientific claims (claims concerning unobservables), which are not purely structural claims, and which warrant realist commitment if anything does. Psillos (1999, Chap. 7) argues in this vein, focusing on Fresnel’s theory of light and the transition to Maxwell’s electromagnetic theory. For Psillos, two such examples are (a) Fresnel’s claim that the energy associated with a light wave is a function of the square of the wave’s amplitude, and (b) the principle of conservation of energy.Footnote 12 However, Votsis (2011b) dismisses Psillos’s claims here with two strategies central to defending structural realism: (i) to claim that what appears to be non-structural is actually structural, or has a ‘structural analogue’, and (ii) to claim that what appears to be purely theoretical (unobservable), is actually observable (with observability construed sufficiently broadly). Psillos’s example (a) is dealt with by Votsis via a combination of both (i) and (ii), with Votsis claiming that it reduces to a purely mathematical relation combined with a variable ‘the amplitude of light’, which, for Votsis, is “a broadly construed observable quantity” because “it is the kind of quantity that can be measured” (Votsis 2011b, Sect. 5, fn. 11). And Psillos’s example (b) is dealt with by Votsis in a similar way, reducing the principle of conservation of energy to “a mathematical relation between masses and velocities, two measureable and hence broadly construed observable quantities.” (ibid.).
One might immediately worry about the broadness of Votsis’s construal of ‘observable’. For example, is the amplitude of light really observable? Well, of course, if you define ‘observable’ in the right way it counts as observable, but then the same goes for just about any theoretical property/entity one could mention! Votsis’s proposal perhaps becomes more reasonable if one is able to retain Fresnel’s success whilst swapping amplitude-talk for intensity-talk (making use of the relationship between the two), since light intensities are straight-forwardly observable. However, Votsis does want to say that the amplitudes are observable. The reason is simply that, in Votsis’s view, amplitudes merit realist commitment given their (non-idle) role within the theory. At the end of Sect. 5 of his paper Votsis lays down a challenge to the ‘traditional realist’, to identify a non-structural element which merits realist commitment (as Psillos 1999 attempts). For Votsis, the amplitudes are non-structural and do merit realist commitment, so the only way he can accommodate them is to regard them as (broadly speaking) ‘observable’.
Other structural realists would surely try to regard amplitudes as idle, and this would then allow for a less controversial definition of ‘observable’ where amplitudes do count as unobservables, but do not present a counterexample to structural realism because they do not merit realist commitment. Such a consideration exposes a problem with the overall debate here: the sheer flexibility of structural realism when it comes to avoiding counterexamples. Indeed, there is fierce debate concerning all of the key concepts: ‘structure’, ‘observable’, ‘working/idle’, etc. The word ‘structure’ itself is used in so many significantly different ways that advocates of structural realism find it hard to agree on anything at all. This is accordingly to Votsis himself!Footnote 13 A symptom of this is that even academics heavily involved in the scientific realism debate struggle to communicate with each other about ‘structural realism’. Psillos’s examples (a) and (b), above, seem to Psillos clearly non-structural, and yet for Votsis they should be interpreted structurally.
Consider another possible counterexample to structural realism, courtesy of Saatsi (2005), again focusing on the Fresnel–Maxwell theory shift. Saatsi identifies certain spatiotemporal properties of light, which in his view are clearly non-structural in their content. He writes: “[I]t should be obvious that the minimal derivation [Saatsi’s reconstruction of Fresnel’s reasoning after idle wheels are eliminated] appeals to crucial unobservable properties and theoretical principles besides formal, logico-mathematical structure” (Sect. 3.4, my emphasis). But is it obvious? No doubt Votsis would dismiss this example too on the grounds that Saatsi’s unobservable properties and theoretical principles can be substituted for ‘structural analogues’, consisting of mathematical relations between quantities which are ‘observable’ (broadly speaking). Saatsi’s unobservable properties are, after all, expressed using equations. Saatsi insists that the equations are aids for expressing non-structural theoretical hypotheses concerning the nature of light. But these examples seem no more or less structural than the examples Psillos (1999) puts forward, and which Votsis dismisses in his (2011b).Footnote 14
Why in any case would realists make such a strong claim, that in any case whatsoever all we can ever have knowledge of (concerning unobservables) is ‘structure’? Why could it not be the case that, say, often we can only acquire structural knowledge, but sometimes our knowledge can go (modestly) beyond the purely mathematical and logical? Peters (2014) takes issue with all realist accounts which insist on there only being one ‘special’ type of theoretical element which can be deserving of realist commitment, instead favouring a ‘neutral’ realism which allows for realist commitment to all different types of theoretical entity. Thus he criticises structural realism, entity realism, and phenomenological realism. Peters puts forward two main arguments (Sect. 3.3): (i) these ‘special’ realisms are usually motivated by historical cases which are cherry-picked to favour them—e.g. structural realism is usually motivated using theories which are substantially mathematical in their content, and (ii) the criteria used to argue for realist commitment to structure will (at least sometimes) also commit realists to non-structure (mutatis mutandis for other ‘special’ accounts).
No doubt structural realists would at this point bring in the ‘upward path to structural realism’ (e.g. Votsis 2005). According to this argument, structure is all we can ever hope to know on basic epistemological grounds, thinking now about the fundamental gap between the truly fundamental nature of reality and the limited perceptual capacities of the human being (the limited information which actually reaches us from that fundamental reality). However, even if this is right, the beauty of a ‘neutral’ realism is that it is consistent with our knowledge of unobservables being purely structural. It is also consistent, however, with our knowledge going beyond that; in other words it is silent on this issue. One may worry that this necessarily means that a ‘neutral’ realism is too abstract and non-committal to successfully respond to the contemporary historical challenges. But in fact—even laying structural realism to one side—the realist has some significant cards left to play.Footnote 15