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Newman’s Objection and the No Miracles Argument


Structural realists claim that we should endorse only what our scientific theories say about the structure of the unobservable world. But according to Newman’s Objection, the structural realist’s claims about unobservables are trivially true. In recent years, several theorists have offered responses to Newman’s Objection. But a common complaint is that these responses “give up the spirit” of the structural realist position. In this paper, I will argue that the simplest way to respond to Newman’s Objection is to return to one of the standard motivations for adopting structural realism in the first place: the No Miracles Argument. Far from betraying the spirit of structural realism, the solution I present is available to any theorist who endorses this argument.

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  1. See Ladyman (1998).

  2. I discuss alternatives to the Ramsey approach in Sect. 2.2.

  3. See, e.g., Ladyman (1998).

  4. See Frigg and Votsis (2011, Sects. 2 and 3.4.2) for discussion.

  5. For discussion, see Suppe (1974).

  6. See Ladyman (1998, 416–418).

  7. In fact, there are many versions of OSR (see Frigg and Votsis (2011, 4.1)), and not all proponents would endorse the characterization just given. But this intuitive characterization will suffice for the purposes of this paper.

  8. See French and Ladyman (2003, 33–34).

  9. Some theorists, such as French and Ladyman (2003, 33), have argued that moving to the models approach is itself a response to Newman’s Objection. But Ainsworth (2009, 150–152) and Frigg and Votsis (2011, 255–256) argue that versions of the objection arise for either approach.

  10. See, e.g., Psillos (1999, 65), Ainsworth (2009, 161–162), and Frigg and Votsis (2011, 251–254).

  11. See, e.g., Ainsworth (2009, 162) and Frigg and Votsis (2011, 252).

  12. See Lange (2009). If one is worried by this assumption, the optics, relativity, and quantum mechanics examples in the subsequent paragraphs do not require it.

  13. Thanks to an anonymous referee for offering this suggestion.

  14. For discussion of the limitations of Fresnel’s equations, see Wright (manuscript).

  15. Since Melia and Saatsi only provide details on \(\text {L}_{\text {P}}\), I may not interpret the other operators in exactly the way they intended. But regardless, this discussion will show that intensional claims have often been discarded across theory change.

  16. See Maudlin (2011, ch. 5) for discussion.

  17. N.b.: the current objection does not apply to all versions of structural realism since, e.g., some structural realists are not motivated by concerns about the interpreted content of our theories (thanks to an anonymous referee for this observation). Will this objection arise for any structural realist who endorses the Ramsey approach? This remains to be seen; I consider a second version of the Ramsey approach in Sect. 3.2.

  18. Thanks to an anonymous referee for this suggestion.

  19. To be clear: when I speak of natural properties, I am speaking of the type of fundamental, non-disjunctive properties discussed by Lewis (1983), not about natural kinds (though there may be important connections between them). I consider other conceptions of natural properties below.

  20. See, e.g., Psillos (1999, 66), Ainsworth (2009, 168–169), and Frigg and Votsis (2011, 253).

  21. Thanks to two anonymous referees for this observation.

  22. A second alternative is Ladyman and Ross’s (2007, ch. 4) account of real patterns. Roughly speaking, a pattern is real if it (1) is projectible on some physically possible perspective and (2) encodes information about worldly structure with a certain efficiency. Because the reality of a pattern depends on what is physically possible, this proposal is prima facie threatened by the fact that claims about physical possibility have been discarded across theory change (see 3.1). But this issue is complex; I think Ladyman and Ross’s account deserves further consideration.

  23. Thanks to an anonymous referee for this suggestion.

  24. What about other ways of conceiving of natural properties? Schaffer’s scientific conception also seems to violate the grounding constraint: it would be illicit for the structural realist to restrict the domain to those properties invoked in our scientific understanding of the world, given that the structural realist denies that we have grounds for endorsing the properties identified by our scientific theories. It is more difficult to assess whether Ladyman and Ross’s real patterns proposal (see footnote 22) satisfies the grounding constraint; this question deserves further discussion.

  25. In notes (vii) and (viii) of 4.2, I discuss further what it means for a relation to be supported by the NMA and discuss further why trivially-instantiated relations are not supported by the NMA.

  26. For simplicity of presentation, I am assuming an account of objective chance according to which objective chances are defined relative to some reference class or other; on such an account, objective chances need not be time-dependent. See, for example, Hoefer (2007). This choice has no bearing on my arguments; it merely allows me to present the theory with shorter sentences.

  27. The Ramsey sentence formed from (1) to (3) will be: \(\exists X_{1}\exists X_{2}\exists X_{3}\exists X_{4}(\forall a\forall b\forall c\forall p\forall q\forall s\forall t\{(Pabc\wedge X_{1}ap\wedge X_{2}aq\wedge X_{1}bs\wedge X_{2}bt)\rightarrow [(Ch(X_{1}cp)=0.5)\wedge (\lnot X_{1}cp\rightarrow X_{1}cq)\wedge (Ch(X_{2}cs)=0.5)\wedge (\lnot X_{2}cs\rightarrow X_{2}ct)]\}\wedge \forall x\forall y\forall z[(X_{1}xy\wedge X_{2}xz\wedge (X_{3}y\vee X_{3}z))\rightarrow Ax]\wedge \forall x\forall y\forall z[(X_{1}xy\wedge X_{2}xz\wedge X_{4}y\wedge X_{4}z))\rightarrow Bx])\).

  28. I will explain the qualification “direct” in note (viii) of 4.2.

  29. The new Ramsey sentence will be: \(\exists X_{1}\exists X_{2}\exists X_{3}\exists X_{4}(\forall a\forall b\forall c\forall p\forall q\forall s\forall t(\{(Pabc\wedge X_{1}ap\wedge X_{2}aq\wedge X_{1}bs \wedge X_{2}bt)\rightarrow [(Ch(X_{1}cp)=0.5)\wedge (\lnot X_{1}cp\rightarrow X_{1}cq)\wedge (Ch(X_{2}cs)=0.5)\wedge (\lnot X_{2}cs\rightarrow X_{2}ct)]\}\wedge \, \mathbf {\mathcal {N}}\llbracket (\mathbf {Pabc}\wedge \mathbf {X}_{\mathbf {1}}\mathbf {ap}\wedge \mathbf {X}_{\mathbf {2}}\mathbf {aq} \wedge \mathbf {X}_{\mathbf {1}}\mathbf {bs}\wedge \mathbf {X}_{\mathbf {2}}\mathbf {bt}) {\rightarrow }[(\mathbf {Ch}(\mathbf {X}_{\mathbf {1}}\mathbf {cp})= \mathbf {0.5}){\wedge }(\lnot \mathbf {X}_{\mathbf {1}}\mathbf {cp}\rightarrow \mathbf {X}_{\mathbf {1}}\mathbf {cq})\) \(\wedge (\mathbf {Ch}(\mathbf {X}_{\mathbf {2}}\mathbf {cs})=\mathbf {0.5}) \wedge (\lnot \mathbf {X}_{\mathbf {2}}\mathbf {cs} \rightarrow \mathbf {X}_{\mathbf {2}}\mathbf {ct})]\rrbracket ) \wedge \forall x\forall y\forall z\{[(X_{1}xy\wedge X_{2}xz\wedge (X_{3} y\vee X_{3}z))\rightarrow Ax]\wedge \, \mathbf {\mathcal {N}}\llbracket (\mathbf {X}_{\mathbf {1}}\mathbf {xy}\wedge \mathbf {X}_{\mathbf {2}} \mathbf {xz}\wedge (\mathbf {X}_{\mathbf {3}}\mathbf {y}\vee \mathbf {X}_{\mathbf {3}}\mathbf {z}))\rightarrow \mathbf {Ax} \rrbracket \}\wedge \forall x\forall y\forall z\{[(X_{1}xy\wedge X_{2}xz\wedge X_{4}y\wedge X_{4}z))\rightarrow Bx]\wedge \, \mathbf {\mathcal {N}}\llbracket (\mathbf {X}_{\mathbf {1}}\mathbf {xy}\wedge \mathbf {X}_{\mathbf {2}}\mathbf {xz}\wedge \mathbf {X}_{\mathbf {4}}\mathbf {y}\wedge \mathbf {X}_{\mathbf {4}}\mathbf {z}))\rightarrow Bx\rrbracket \})\). I have bolded the added \({\mathcal {N}}\llbracket P\rrbracket \) expressions.

  30. For example, the part of the Ramsey sentence corresponding to (\(2^{\prime }\)) will say: all pea plants with a certain unobservable property are tall, and that the NMA provides evidence for the fact that all pea plants with this unobservable property are tall.

  31. Thanks to an anonymous referee for providing this example.

  32. Thanks to an anonymous referee for pressing this point.

  33. This “trivial” interpretation of the NMA is incompatible with the argument as presented in note (vii). The trivial interpretation supports the existence of many structures, since there are many ways to define relations on the unobservable domain. But in note (vii), premise 1 presupposes that T identifies a unique structure.

    This incompatibility may be enough to exclude the trivial interpretation, since the \({\mathcal {N}}\)-predicate is explicated in terms of the argument version given in note (vii). But in this note, I will further clarify the \({\mathcal {N}}\)-predicate in a way that excludes the trivial interpretation.

  34. Thanks to Matthew Kotzen for the suggestion to distinguish these two senses of evidential support in terms of their different orders of explanation.

  35. N.b.: in using the term “direct”, there is no need to assume that any specific proposition is the conclusion of the structural realist’s NMA. The important point is that the NMA’s support for \(\llbracket P\rrbracket \) in the intended interpretation is comparatively more direct than its support for \(\llbracket P\rrbracket \) in the trivial interpretation.

  36. Thanks to an anonymous referee for pressing this objection.

  37. Here, we should regard \(\hat{T}\) and the first conjunct of \(\hat{R}\) as implicitly claiming that some unobservable entity instantiates the unobservable relation in question. Otherwise, the first conjunct of \(\hat{R}\) (and \(\hat{T}\) as well) would be trivial for a completely unrelated reason: its being an empty universal generalization.

  38. One might even try to use the NMA to support these positions. For example, one might try to argue that the NMA justifies us in believing the properties posited by our theories are natural. I think the arguments from 3.2 show that this is not the case, but this is at least a possibility worth considering.

  39. See, e.g., Worrall (1989), Melia and Saatsi (2006) and Frigg and Votsis (2011, 2.1).


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Smithson, R. Newman’s Objection and the No Miracles Argument. Erkenn 82, 993–1014 (2017).

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  • Structural realism
  • Newman’s objection
  • No miracles argument
  • Pessimistic induction