Empirical Adequacy and RamsificationJeffrey KetlandAbstractStructural realism has been proposed as an epistemological position interpolatingbetween realism and sceptical anti-realism about scientific theories. The structuralrealist who accepts a scientific theory Θ thinks that Θ is empirically correct, andfurthermore is a realist about the ‘structural content’ of Θ. But what exactly is‘structural content’? One proposal is that the ‘structural content’ of a scientific theorymay be associated with its Ramsey sentence ℜ(Θ). However, Demopoulos andFriedman argued, using ideas drawn from Newman’s earlier criticism of Russell’sstructuralism, that this move fails to achieve an interesting intermediate positionbetween realism and anti-realism. Rather, ℜ(Θ) adds little content beyond theinstrumentalistically acceptable claim that the theory Θ is empirically adequate. Here,we formulate carefully the crucial claim of Demopoulos and Friedman, and show thatthe Ramsey sentence ℜ(Θ) is true just in case Θ possesses a full model which isempirically correct and satisfies a certain cardinality condition on its theoreticaldomain. This suggests that structural realism is not a position significantly differentfrom the anti-realism it attempts to distinguish itself from.1.Introduction2.Technical Framework3.Ramsification4.Empirical Adequacy5.Ramsification ≈ Empirical Adequacy + Cardinality Constraint6. Conclusion1. IntroductionFrank Ramsey ([1929]) proposed a method of formalizing our scientific theories ofthe world as follows. The Ramsey sentence ℜ(Θ) of a given (finitely axiomatized)theory Θ is obtained by eliminating theoretical predicates, replacing them uniformlywith predicate (i.e., second-order) variables and prefixing the result with existentialsecond-order quantifiers.1 The epistemological significance of this technicalconstruction it that it perhaps offers the possibility of defending a plausibleintermediary or ‘third way’ position between realism and anti-realism (underwhatever guise: positivism, empiricism or instrumentalism). This position has come tobe termed ‘structural realism’ (see Worrall [1989] and Zahar [2001]).One canonical version of sceptical anti-realism about theoretical science isconstructive empiricism (van Fraassen [1980]). This anti-realist position holds that theaim of science is to construct empirically adequate theories and the maximal 1 Carnap ([1966], Chapter 26 ‘The Ramsey Sentence’) contains a detailed discussion of ramsificationand its philosophical significance.epistemic attitude to take towards a well-corroborated, explanatory, predictivelysuccessful, etc., theory is to believe that the theory is empirically adequate. This isweaker than the realist’s commitment to the approximate truth of the suitably certifiedtheorythe theory conforms to reality, at a certain level of approximation.2Attempting to delineate the structural realist’s middle way, Worrall ([1989]) proposedthat, at least in certain cases, we can defend a commitment to more than the empiricaladequacy of the theory in question, but less than the approximate truth of the theory.We can sometimes defend a commitment to a theory’s empirical adequacy plus its‘structural content’, an aspect of transempirical content which is preserved under evenradical theory change. However, the required notion of ‘structural content’ of ascientific theory is notoriously unclear. One proposal, endorsed by Worrall and Zahar([2001]), is that the structural content of a theory Θ is given by its Ramsey sentenceℜ(Θ). More exactly, the structural content of a theory Θ is what ℜ(Θ) ‘adds’ beyondthe empirical adequacy claim for Θ.Having briefly sketched the epistemological background, we now face thefollowing problem. Given a theory Θ, can we clarify the relationship between theclaim that ℜ(Θ) is true and the claim that Θ is empirically adequate? If I am correct,there is an intimate relation between these claims. We show that, at least on theconventional understanding of second-order logic, the adoption of ‘ramsification’ as acorrect representation of structural content fails to achieve the requisite intermediateposition between realism and sceptical anti-realism. Rather, as Demopoulos andFriedman ([1985]) pointed out, drawing on Newman’s critical review (Newman[1928]) of a version of structuralism advocated by Russell ([1927]), the ramsificationprocedure yields a claim which is, roughly speaking, equivalent to the claim that thetheory is empirically adequate. Actually, it is more complicated than this, as we showbelow.2. Technical FrameworkTo investigate this matter more closely3, we shall consider theories formulated inan interpreted, two-sorted, second-order language, denoted L2(<Oi>, <Mi>, <Ti>). Theextra-logical predicates of this language are interpreted by three sequences of real-world relations: <Oi> = (O1, O2, ...) (the ‘observational’ relations), <Mi> = (M1, M2,...) (the ‘mixed’ relations) and <Ti> = (T1, T2, ...) (the ‘theoretical’ relations).4 For easeof notation, we shall henceforth write ‘O’, ‘M’, etc. instead of ‘<Oi>’, ‘<Mi>’, etc., for 2 Psillos ([1999]) has become a canonical defence of scientific realism. See Sokal and Bricmont([2001]) for an important discussion of the sense in which mature scientific theories in physicsapproximate theoretical structure of the world (in particular, what they call the ‘Renormalization Groupview’ of ontology).3 The technical framework described herean interpreted language whose intended semantics is‘carved up’ according to the epistemic status (i.e., observability) of the entities and relations it referstois riddled with further problems. It is the best analysis I can give of the framework of the anti-realist opponent, and the primary aim here is to show that this anti-realist framework (at least, as Iunderstand it) doesn’t achieve its intended goal.4 The omission of functions (which we use to represent most physical quantities) is no problem, sincefunctions may be reduced to many-one relations in well-known ways. A simpler but defectivepossibility is to consider a one-sorted second-order language L2(O, T) which contains no mixedrelations. A further possibility is to consider a 3-sorted notation, with variable sorts for observableentities (chairs, bar magnets, etc.), theoretical entities (say, space-time points/events, or point particles)and for