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Everything you always wanted to know about structural realism but were afraid to ask

Abstract

A structuralist perspective is one that sees the investigation of the structural features of a domain of interest as the primary goal of enquiry. This vision has shaped research programmes in fields as diverse as linguistics, literary criticism, aesthetics, sociology, anthropology, psychology, and various branches of philosophy. The focus of this paper is structuralism in the philosophy of science, and in particular those movements that have endeavoured to articulate a structural version of scientific realism, now commonly referred to as structural realism (SR). The paper provides a critical survey of the debates raging over structural realism: it provides explicit statements of the different positions as well as the arguments put forward to support them, clarifies how the different positions relate to one another, draws attention to hitherto neglected arguments, and evaluates criticisms launched against different strands of SR. Attention to the history of the field is paid in as far as this is essential to understanding the contemporary scene, but documenting the long and intricate development of SR is beyond the scope of this paper. We begin by introducing the set theoretic conception of structure on which many of the positions that we are concerned with rely (Section 2). In Section 3 we introduce the two main strands of epistemic structural realism, discuss the central objections levelled against them, most notably Newman’s objection, and present the Ramsey sentence formulation. Section 4 is dedicated to a discussion of ontic structural realism. In Section 5 we offer some concluding remarks.

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Notes

  1. 1.

    For a discussion of structural thinking in science see Rickart (1995), and for a detailed presentation of the structures used in fundamental physical theories see Muller (1998). Resnik (1997) and Shapiro (1997, 2000) advocate a structuralist position in the philosophy of mathematics. For a discussion of the relation between structuralism in mathematics and science see Brading and Landry (2006). Surveys of structuralist approaches in the humanities can be found in Caws (2000) and Williams (2005).

  2. 2.

    For accounts of the history of certain strands of structuralism in the philosophy of science see Gower (2000), Votsis (2004, Ch. 2) Daston and Galison (2007, Ch. 5), and the relevant sections in Demopoulos and Friedman (1985), Solomon (1989), van Fraassen (1997, 2006), and French and Ladyman (2011).

  3. 3.

    Two remarks regarding this definition of structures are in order. First, sometimes structures are defined such that they also involve an indexed set O of operations on U as a third ingredient. Although it is convenient in certain contexts to list operations separately, they are ultimately unnecessary because they can be reduced to relations (see Boolos and Jeffrey 1989, 98-99; Shapiro 1991, 63). Second, Logicians often regard a set of symbols denoting the elements of < U, R > as part of the structure; see for instance Hodges (1997, 2).

  4. 4.

    Russell (1919, 59–62) provides a detailed discussion of this aspect of structures; see also Newman (1928, 139) and Redhead (2001a, 74–75).

  5. 5.

    There is, of course, a question of how to understand the ontological status of such structures. For a discussion of this point see Hellman (1989, 1996, 2001), Resnik (1997) Shapiro (1983, 1997, 2000).

  6. 6.

    A graph (in this sense) is a mathematical structure whose specification requires two types of things: edges and nodes. Intuitively we may think of nodes as objects and edges as relations. Structural realists like Ladyman are interested in so-called ‘unlabelled’ graphs because in such graphs different nodes are indistinguishable, i.e. no additional information is given about the nodes (no labelling or intension) other than potentially the edges that link them to other nodes. Leitgeb and Ladyman utilise graph theory to show that even weak versions of the principle of identity of indiscernibles can be violated.

  7. 7.

    The term ‘structural realism’ was coined by Grover Maxwell (1968). Our distinction between DESR and IESR corresponds roughly to Ainsworth’s (2009) distinction between ‘weak ESR’ and ‘strong ESR’. We prefer ‘DESR’ and ‘IESR’ to ‘weak ESR’ and ‘strong ESR’ because DESR sanctions some claims that are stronger than claims sanctioned by IESR. For instance, DESR accepts that we can have knowledge of relations between entities that have no perceptual analogue, something that IESR denies.

  8. 8.

    Maxwell (1971 18–19) summarises this position as the claim that we cannot know the first order properties of physical objects and that we can only know their second or higher order properties. This way of stating the position is misleading in two ways. First, it is important to notice that this use of ‘first order’ and ‘second order’ bears no connection with the distinction between first and second order logic, which will become important later on. Second, and more importantly, if our knowledge is limited to structural features, then even first order properties can be known, albeit of course only structurally.

  9. 9.

    As Demopoulos and Friedman (1985, 625–627) point out, Russell’s position has close affinities with other work done at the time, in particular by Schlick and Carnap. For further discussions of these positions see Creath (1998), Psillos (1999, Ch. 3; 2000a, 2000b, 2006b) and Salmon (1994).

  10. 10.

    Many readers familiar with Russell’s sceptical attitude towards causation in The Problems of Philosophy (1912) and in Mysticism and Logic (1918) may find his endorsement of causation here puzzling. In spite of his scepticism, it is well known among Russell scholars that a deflated notion of causation played a central role in his philosophy.

  11. 11.

    Psillos (2001a) suggested this name for the principle on the basis of Helmholtz’s and Weyl’s appeal to it. It is worth noting that Russell sometimes uses the principle in its contrapositive (but equivalent) form, namely as the claim that same causes imply same effects. Quine independently endorses a modified version of the HW principle focussing on similarity rather than sameness (1998, 19). The principle in one form or another has also been independently endorsed by Locke in An Essay Concerning Human Understanding ([1690] 1975, Book II, Ch. XXXII, §15), Hume in the Treatise ([1739] 1975, Book II, Part III, §1), Descartes in the 6th Meditation ([1641] 1993) and Mill in A System of Logic ([1874] 2008, p.423).

  12. 12.

    Stimuli, according to Russell, are ‘the events just outside the sense-organ’ (1927, 227). They are thus classified as physical events.

  13. 13.

    See also (ibid., 251, 253, 254, 263–4, 270–1; 1919, 59–62; 1912, 32, 34). Although Russell uses different terminology, his definition of structure (see, for example, (1927, 250)) is equivalent to the definition of structure given earlier. For more on this issue see Solomon (1990).

  14. 14.

    Maxwell also credits Poincaré, Schlick, and Wittgenstein, as well as Beloff, Mandelbaum, Aune and Pepper with having developed versions of ESR (see his 1968 for references).

  15. 15.

    This understanding of these terms, of course, conflicts with the prevalent understanding in the scientific realism debate. Seemingly paradoxically, Maxwell is best known among philosophers of science for his critique of the observable/unobservable distinction; see his (1962). The apparent tension is dissolved once we realise that in the context of his discussion of ESR the entire external world is unobservable, and that therefore the distinction he criticised in his (1962) is of an altogether different kind.

  16. 16.

    It is important to emphasise that this does not mean that structural differences in perceptions have no corresponding structural differences between external world causes. This kind of correspondence is in fact required by HW.

  17. 17.

    Indeed, MR entails HW but not vice versa.

  18. 18.

    A structure S 1  = <U 1 , R 1 > is embedded into a structure S 2  = <U 2 , R 2 > iff there exists a injective mapping f: U 1  → U 2 such that f preserves the system of relations of S 1 in the following sense: for all relations r 1 R 1 and r 2 R 2 , if the elements a 1 , …, a n of U 1 satisfy the relation r 1 then the corresponding elements b 1  = f(a 1 ), …, b n  = f(a n ) in U 2 satisfy r 2 , where r 1 is the relation in R 1 corresponding to r 2 in R 2 (i.e. have the same index in the indexed sets R 1 and R 2 ). We typically speak of embeddings when the cardinality of U 2 is greater than the cardinality of U 1 . In those cases, an embedding is just an isomorphism between S 1 and a part—a ‘substructure’ as it is sometimes called—of S 2 .

  19. 19.

    How much variance can be afforded before the reliability of perception breaks down is not an easy question to answer.

  20. 20.

    Psillos raises another objection in that paper. He claims that the structural realist cannot account for the possibility that the unobservable world may have extra structure not manifested in the perceptual world. This claim is incorrect. Russellian ESR just requires that all, or at least most, perceptual structures have corresponding external world structures, not vice-versa.

  21. 21.

    This problem is most acute in the case of percepts since it is possible that in light of the same set of stimuli different perceivers attribute different structures to their perceptions. The epistemic structural realist may be able to bite the bullet here so long as divergent attributions of structure are the exception rather than the rule.

  22. 22.

    Russell (1948, 485–6) and Carnap (1928, §16) make similar remarks about the intransmissibility of everything but structure.

  23. 23.

    Against this view it has been objected that one can communicate, for example, a feeling of sadness by reporting it or by using specific facial expressions. Although we agree that someone can communicate in this way that they have a sad feeling, this does not imply that the person can communicate their particular sensory experience of sadness.

  24. 24.

    In this context, the notion of transmission is broader. For more on Quine’s structuralism see his (1969) and (1992); for a discussion of his position see Rosner (1996).

  25. 25.

    This argument could mutatis mutandis also be put forward in support of DESR.

  26. 26.

    Poincaré is often thought of as a conventionalist anti-realist, not only with regard to geometry but also physics. However, Maxwell (1968), Giedymin (1982), Worrall (1982; 1989; 1994), Zahar (1996; 2001), Stump (1989), Psillos (1995; 1999), Gower (2000), and Redhead (2001a) argued, in our view convincingly, that Poincaré is an ESRist. Some have also argued that Duhem ([1914]1991), another alleged conventionalist, actually held an ESR position very similar to Poincaré’s (Worrall 1989; Chakravartty 1998; Gower 2000; and Zahar 2001).

  27. 27.

    For a discussion see Laudan (1981).

  28. 28.

    Poincaré’s second historical example is the fact that some of the equations describing Carnot’s heat engines survived when the conception of heat as a material fluid (called ‘caloric’), on which Carnot’s theory was based, was abandoned (1905, 165).

  29. 29.

    A line of argument very similar to Worrall’s is developed in Zahar (1994; 2001, Ch. 2; 2004). Zahar adopts a notion of observability that is very similar to that of Russell, a move which likens his position to IESR. Worrall has recently also flirted with a Russellian notion of observability, although he has not sanctioned this notion in print.

  30. 30.

    Worrall (personal communication) now endorses a different, and rather deflationary, understanding of PMI. In its original formulation the argument assumes that scientific revolutions bring about substantive changes. Worrall now denies this and thinks that what was thrown overboard in scientific revolutions such as the shift from Fresnel’s to Maxwell’s theory was mere ‘metaphorical puff’, which may have been of some heuristic value but had no cognitive import.

  31. 31.

    See Boyd (1985), Musgrave (1988) and Psillos (1999) for a statement and defence of NMA. Critical discussions can be found in Howson (2000) and Magnus and Callender (2004).

  32. 32.

    The central equations of a theory need not encode the entire structure of the theory; all mathematically definable relations in the theory, for instance measurement scales, contribute to the theory’s structure. For a discussion of this point see Redhead (2001a).

  33. 33.

    This premise should not be taken to refer only to those parts of a theory which are explicitly mathematised but also to those that can be given a mathematical formulation.

  34. 34.

    The introduction of the class of approximately false statements is motivated by the fact that some statements assert things about the world that are neither utterly false nor approximately true. It goes without saying that any successful defence of realism will need to provide an adequate account of both the notion of approximate truth and the notion of approximate falsity.

  35. 35.

    Although this may sound like an implicit endorsement of the syntactic view of theories, it is not. At least some structural realists, most notably Worrall (1984), believe that syntactic and semantic formulations of scientific theories are intertranslatable without loss.

  36. 36.

    For an in-depth discussion and reformulation of this argument that aims to address these and other objections see Votsis (2011a). Among other things, Votsis points out that it is normal to expect that not all structures get preserved through theory change since some of them enjoy no genuine predictive success. Votsis (2011c) points out that theory parts should not be considered either (approximately) true or empirically successful because they survive; rather they should be regarded as both (approximately) true and (hopefully) surviving because they are empirically successful.

  37. 37.

    The point is mentioned already in Worrall (1989, 120–123); it is more fully developed in his (2007, 135–6, 142–4).

  38. 38.

    Although not a structural realist himself, Schurz (2009) provides a structural correspondence theorem that may prove useful for the structural realists. As one referee pointed out there may not be a need for a general account of structural continuity through theory change. Case-by-case demonstrations may be sufficient so long as one can show that what is preserved tells us something about the structure of the unobservables.

  39. 39.

    For more details on this case, see Saatsi (2005).

  40. 40.

    Furthermore, as a referee has pointed out, the preservation of non-structural elements through one revolution is not enough to undermine ESR; only persistent preservation through many revolutions is a reliable guide to truth. We are in general agreement with this point and would like to add that this holds also for structural elements, i.e. their survival through one revolution is no guarantee of their (approximate) truth.

  41. 41.

    And indeed it is: we have come across defences of ESR along these lines in discussions on various occasions. However, Votsis (2004, ch. 6) provides the only such defence in print.

  42. 42.

    When refraining from saying that mathematical objects are the only adequate tools for representation, the structural realist is committed to the view that non-structural representations can always be mathematised without loss of content.

  43. 43.

    The Ramsey sentence originates in Ramsey (1931). For general discussions see Carnap (1966, Ch. 26), Cei and French (2006), Cruse (2004), Demopoulos (2003), Díez (2005), Lewis (1970), Psillos (2000a, 2000b, 2006b) and Sneed (1971).

  44. 44.

    We use the somewhat cumbersome locution ‘non-observation predicate’ rather than the more common ‘theoretical predicate’ to avoid confusion. Non-observation predicates are taken to refer to properties in the unobservable domain. There are well known arguments for the conclusion that no bifurcation between observation and non-observation predicates is possible; see for instance Putnam (1962) and Maxwell (1962). At least for the sake of the argument we assume that some division between ‘benign’ and ‘problematic’ terms can be drawn.

  45. 45.

    See English (1973, 458–462), Ketland (2004, 293–294) and Psillos (2006b, Sec. 4).

  46. 46.

    Having said this, one can give different interpretations to what the existentially bound variables range over. Carnap thought they ranged over mathematical entities. For more on this see Friedman (2011).

  47. 47.

    We omit some technical subtleties here. For details see Ketland (2004). In particular, his definition of a Henkin structure also involves some collection Rel of classes and relations on the total domain of S satisfying the comprehension scheme. In what follows we assume that Rel contains all relations, i.e. S is ‘full’, which allows us to omit Rel. The results reached are then valid for full models.

  48. 48.

    This marks a slight departure from the way RS has been introduced above, where we use a one-sorted language (i.e. one with only one type of variable). However, this shift is purely technical in nature and does not affect the main ideas behind the Ramsey sentence. For a discussion of the same issues using a one-sorted logic see Ketland (2009).

  49. 49.

    A similar argument can be given on the supposition that T R is approximately true in a suitably qualified sense.

  50. 50.

    As Demopoulos and Friedman (1985, 633–635) point out, this problem parallels Putnam’s (1978) so-called model theoretic argument.

  51. 51.

    For further discussions see Demopoulos (2003, 2008). CT is based on a model theoretic notion of empirical adequacy, which is essentially van Fraassen’s (1980, 12). Demopoulos and Friedman seem to phrase their argument in terms of a different notion of empirical adequacy, namely that a theory is empirically adequate iff all consequences of the theory which are couched in a purely observational language are true (1985, 635). As Ketland (2004, 295–6) points out, the latter notion of empirical adequacy is strictly weaker than the former in that the former implies the latter but not vice versa; for this reason he calls the latter ‘weak empirical adequacy’. CT does not hold if empirical adequacy is replaced by weak empirical adequacy. In fact, a theory may be weakly empirically adequate and have a u-cardinality correct model, and yet the theory’s RS may be false. Although this problem arises only when T has an infinite model, it is serious problem since most theories involving numbers have infinite models. (Thanks to Jeff Ketland for pointing this out to us.) Demopoulos (2008, 380) agrees, but argues that the model theoretic notion of empirical adequacy was what he and Friedman were referring to in their (1985).

  52. 52.

    A note about terminology is in order. The Cardinality theorem is often referred to as ‘Newman’s theorem’, ‘Newman’s result’ or ‘Newman’s objection’. At least from a historical point of view this is incorrect. Newman’s theorem (both as stated here and as presented by Newman himself) does not involve RS, nor does Russell’s (1927) theory against which Newman’s original argument is directed. We turn to the Russell-Newman discussion below.

  53. 53.

    For a detailed discussion of these replies see Ainsworth (2009).

  54. 54.

    After some discussion he concludes that the only way to draw the distinction between real and fictional relations is to align it with the distinction between important and trivial relations. This, however, commits one to admitting importance as an unanalysable primitive, something which, as Newman points out, is absurd.

  55. 55.

    Zahar (2001, Appendix IV) is written jointly with Worrall. However, it becomes clear from Zahar (2004) that this response is attributable only to Zahar; we discuss Worrall’s response below. A great deal of Zahar’s (2001, 2004) and also Worrall’s (2007) discussion of RS is concerned with a version of Newman’s Problem that interprets the RS as existentially quantifying not only over theoretical but also over observable terms (Zahar 2001, 238). They are, of course, right that this is absurd. However, CT as stated above does not dispense with observational predicates, and so we discuss their arguments only in as far as they address the version of Newman’s problem under discussion here.

  56. 56.

    The example is Zahar’s. Some may object that ‘density’ is a theoretical term. How this issue is resolved is inconsequential for the current discussion.

  57. 57.

    See Votsis (2011a) for details why survival through theory change is neither necessary nor sufficient for approximate truth.

  58. 58.

    Structuralist versions of the semantic view of theories are put forward, among others, by Da Costa and French (1990, 249) and van Fraassen (1980, 43, 64; 1991, 483; 1995, 6; 1997, 522, 528–9).

  59. 59.

    Candidates are, among others, partial isomorphism (French and Ladyman 1999), embedding (Redhead 2001a), and homomorphism (Mundy 1986). For the issues under discussion nothing depends on which of these one chooses.

  60. 60.

    As we will see below, French and Ladyman endorse an ontic version of structural realism. What is worth noting here is that this endorsement does not necessitate a switch to the semantic view of theories. Having said that, we know of no ontic structural realist who advocates the syntactic view of theories.

  61. 61.

    For an argument against the idea that by abandoning extensionalism we can avoid the Newman Problem see Demopoulos and Friedman (1985, 629–30).

  62. 62.

    A similar argument is put forward by Ketland (2004, 295), and Chakravartty (2001) makes a related point.

  63. 63.

    For a discussion see Votsis (2011b).

  64. 64.

    Further discussion can be found in Ladyman (1998) and van Fraassen (2006); for a rejoinder to Psillos see Elsamahi (2005) and Votsis (2007).

  65. 65.

    Stanford (2003a; 2003b) reaches a similar conclusion arguing from the point of view of confirmation theory.

  66. 66.

    Despite their professed aversion towards theory, entity realists make allowances for some, low-level, theory. Hacking, for example, appeals to ‘low-level causal properties’, which, no matter how much glazing he puts on them, are simply theoretical properties.

  67. 67.

    In this context ‘first-order’ means that a property is not a property of another property but of an object. For instance ‘red’ is first order; ‘being a colour’ is second order.

  68. 68.

    A similar position has been suggested by Dipert (1997), but he does not use the term ‘structural realism’.

  69. 69.

    This is explicit, for instance, in Ladyman and Ross (2007, 128).

  70. 70.

    In the terms introduced in Section 2 one could say that EOSR uses a concrete rather than an abstract structure as far as relations are concerned. There is a question about whether such structures are allowed to contain properties, i.e. monadic relations, or whether all relations have to be polyadic. Esfeld (2004), and Esfeld and Lam (2008) seem to suggest that monadic properties should be ruled out. For a discussion of this issue see Ainsworth (2008, 162–9).

  71. 71.

    For a general discussion of this point (not geared towards OSR) see Schaffer (2003).

  72. 72.

    The two are ‘almost’ equivalent because traditionally bundle theories focus on monadic properties, while OSR places the emphasis on polyadic properties, i.e. proper relations. However, one can have a bundle theory that rests only on polyadic properties, and that most bundle theorists don’t discuss this possibility is an accident of history and not indicative of an intrinsic limitation of that approach. For a metaphysics of relations see Mertz (2003).

  73. 73.

    For a discussion of the bundle theory with a special focus on tropes see French (2001, 21–22).

  74. 74.

    For a discussion of the modal aspects of structures see Esfeld (2009).

  75. 75.

    Strictly speaking Esfeld and Lam make this argument for their version of OSR, but it is obvious that the argument applies to other versions as well.

  76. 76.

    Quantum field theory is discussed in Cao (1997, 2003a), Lyre (2004), Kantorovich (2003) and Saunders (2003a). Group theory is the focus of French (1998, 1999, 2000) and Castellani (1998). Space-time theories are discussed with a special focus on OSR in Dorato (2000), Esfeld and Lam (2008), Ladyman (2001), Pooley (2006), Stachel (2002) and Saunders (2003c, 2003d). Lorentz’s theory of electrons is discussed in Cei (2005). Tegmark (2008) argues that OSR is the only consistent way of believing the existence of the external world.

  77. 77.

    However, notice that classical particles can be regarded as indistinguishable (Saunders 2006, 52).

  78. 78.

    Sometimes Leibniz’s law is more broadly associated with the conjunction of PII and its converse, called ‘the principle of the indiscernibility of identicals’, \( \forall x\forall y\left[ {\left( {x = y} \right) \to \left( {\forall P} \right)\left( {Px \leftrightarrow Py} \right)} \right] \).

  79. 79.

    This set-up is introduced in French and Redhead (1988). French (2006a) provides a comprehensive and accessible survey of the discussion.

  80. 80.

    QM only provides probabilities for a property to obtain. So we here extend the above statement of PII to include the probabilistic case: if for all properties the probability to be instantiated in x equals the probability to be instantiated in y, then x and y are identical.

  81. 81.

    For more on how this kind of underdetermination relates to other more traditional kinds of underdetermination see French (2011).

  82. 82.

    There are cases where this form of argument has perhaps more currency. Take the question of the existence of any supernatural being. In the absence of evidence supporting such a being’s existence many people would simply eliminate it from their ontology instead of merely be agnostics about it. The question then becomes whether individuals and/or objects are similarly eliminable.

  83. 83.

    See also Ketland (2006). The claim about bosons is disputed in Muller and Seevinck (2009). Muller (2011) also argues that far from fearing the weak discernibility of elementary particles, advocates of OSR should embrace it, because, according to him, it points to a relational understanding of particles that lends credence to OSR. For further discussions of the individuality in QM see Morganti (2009a, b, e).

Abbreviations

SR:

Structural Realism

ESR:

Epistemic Structural Realism

DESR:

Direct Epistemic Structural Realism

IESR:

Indirect Epistemic Structural Realism

OSR:

Ontic Structural Realism

EOSR:

Eliminative Ontic Structural Realism

ROSR:

Radical Ontic Structural Realism

RS:

Ramsey Sentence

HW:

Hermann-Weyl Principle

MR:

Mirroring Relations Principle

NMA:

No Miracles Argument

PMI:

Pessimistic Meta Induction

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Acknowledgements

We would like to thank Peter Ainsworth, Anjan Chakravartty, Steven French, Jeff Ketland, James Ladyman, Matteo Morganti, F.A. Muller, John Worrall and two anonymous referees for helpful discussions and/or comments on earlier drafts of the paper. Roman Frigg wishes to acknowledge financial support from the Descartes Centre at the University of Utrecht, where part of the paper has been written, and of the Grant FFI2008-01580 of the Spanish Ministry of Science and Innovation. Ioannis Votsis similarly wishes to acknowledge financial support from the German Research Foundation (Deutsche Forschungsgemeinschaft) as well as from the Center for Philosophy of Science at the University of Pittsburgh, where he was a visiting fellow in the Fall term 2010.

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Frigg, R., Votsis, I. Everything you always wanted to know about structural realism but were afraid to ask. Euro Jnl Phil Sci 1, 227–276 (2011). https://doi.org/10.1007/s13194-011-0025-7

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Keywords

  • Structural realism
  • Scientific realism
  • Philosophy of science
  • Theory change
  • Ramsey sentence
  • Newman problem
  • Identity of indiscernibles