Synthese (2010) 175:241–253 DOI 10.1007/s11229-009-9500-5

Melia and Saatsi on structural realism Zanja Yudell

Received: 28 October 2008 / Accepted: 10 March 2009 / Published online: 25 March 2009 © Springer Science+Business Media B.V. 2009

Abstract Newman’s objection is sometimes taken to be a fatal objection to structural realism (SR). However, ambiguity in the definition of “structure” allows for versions that do not succumb to Newman’s objection. In this paper, I consider some versions of SR that maintain an abstract notion of structure yet avoid Newman’s objection. In particular, I consider versions suggested by Melia and Saatsi. They reject a solution that restricts the domain of the second-order quantifiers, and argue in favor of buttressing the language with intensional operators such as “it is physically necessary that…”. I argue that their favored solution effectively requires the former suggestion that they reject. This argument suggests that a notion of natural properties may be indispensable to SR. Keywords Structuralism · Structural realism · Melia · Saatsi · Newman’s objection · Scientific realism 1 Introduction Structural realism (SR)1 proposes that, at best, scientific theories can characterize the structure of reality, but no more. However, this claim can mean different things depending on what is meant by “structure”. The most abstract notion of structure 1 SR is commonly sub-divided into two separate positions, Epistemic structural realism (ESR) and Ontic structural realism (OSR) (Ladyman 1998; Chakravartty 2004). The former is a claim merely about what we can know, and has no ontological implications, whereas the latter is a stronger claim that there can be no more to reality than structure. What I have to say here should be relevant to both versions of SR that employ the notions of structure I discuss. However, my attentions are directed primarily at ESR, which is the more widely held view.

Z. Yudell (B) California State University, Chico, USA e-mail: [email protected]

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available identifies structure with those features of a model that are preserved under isomorphism. A version of SR with this notion of structure denies that we can have knowledge of particular objects or the properties and relations they bear. The most we can hope for is knowledge of the second-order properties and relations born by the properties and relations. This “abstract” form of structural realism was famously attacked by Newman (1928) in a paper that argued that SR (this was not the name for the position at the time) is empty: the assertion that a given theory’s structure is true of the world is trivially true, as long as there is a model of the theory with the same cardinality as the domain of the world. I take this argument to be successful. Nonetheless, there are ways to understand SR that preserve a more or less abstract notion of structure yet avoid Newman’s objection. One compelling way to do so, as advocated by Melia and Saatsi (2006) is to supplement the language with modal operators such as “it is physically necessary that…”. I will argue that this solution does not work unless one also restricts the second order quantifiers in the Ramsey sentence to range over some subset of the power-set of the domain. Melia and Saatsi reject this kind of move, so their solution does not work by their own lights. I will then discuss the appropriate reaction to this state of affairs, and I will suggest that a notion of natural properties is indispensable to SR. 2 Varieties of structural realism One way to formulate SR, owing to Maxwell (1970), is by appeal to Ramsey sentences. Imagine your favorite scientific theory formulated as a grand conjunction in an interpreted first-order language. Call that conjunction the theory statement. SR requires that our epistemic commitment to the theory involves no more than a commitment to a Ramsified version of that grand conjunction. As Psillos (2001, p. S19) has noted (although he does not refer to the Ramsey sentence formulation of SR), SR can be understood to limit our knowledge at one of various levels of abstraction. He identifies three levels of abstraction in particular, which we can characterize in terms of the austerity of the Ramsey sentence of a theory. From less abstract to more, the levels he identifies are: (1) The particular names of the objects are removed from the theory statement and replaced by distinct variables that are bound by existential quantifiers; (2) Particular names and one-place predicates2 are removed from the theory statement and replaced by variables that are existentially quantified (relations of two-places and more are allowed to remain interpreted); (3) Particular names and all predicates are removed from the theory statement and replaced by variables that are existentially quantified. Each of these three levels of abstraction can be taken to be different versions of SR, which we can call SR1, SR2 and SR3. Note that SR2 and SR3 both require that the Ramsey sentence of a theory be formulated in at least a second-order language, if expressed in a formal language. SR3 is the most abstract formulation of SR in that, of the three, it denudes theory statements of the most possible content. There is some debate over whether or not there are versions of SR that cannot be expressed by appeal to Ramsey sentences (Cruse 2005). One might, for example, 2 I will use the term “predicate” to include both one-place predicates and many-place relations.

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attempt to express the structure of a theory directly using the semantic view of theories. However, for the purposes of this essay, we will only consider versions of SR that characterize the content of theories with Ramsey sentences. The reader will have to decide whether anything important is missed by this narrowing of scope. 3 Newman’s objection Newman addresses his complaint to Russell’s “Causal Theory of Perception”, which is at the very least analogous to SR3. Newman, although he does not put it this way, in effect points out that any satisfiable Ramsey sentence of the third type will be trivially true of any appropriately sized collection of objects, as long as the second-order variables range over all predicates extensionally-defined relative to the collection. This result straightforwardly follows from the semantic rules for formal second-order languages. Consequently, SR3 becomes a nearly empty position. It asserts that the only scientific statements we can claim to know are Ramsey-sentences of type 3, but knowing such statements only amounts to knowing the cardinality of the world, since such statements are true of any set of objects of the appropriate cardinality. Now a claim about the cardinality of the world is probably not completely trivial, as one cannot deduce from pure logic how many things there are. Indeed, I think there are deep issues surrounding the issue of what it is to know how many things there are in the world. On the other hand, one might think that there is no fact about the number of objects in the universe, so that SR3 becomes completely trivial. But in any event, it is clear that if SR3 allows of science, even if only of physics, merely claims to the numbers of objects that exist, then something is wrong with SR3. Even the most ardent anti-realist would expect more from scientific theories than that. Whatever the motivations behind a particular allegiance to structural realism, the position is a form of realism, and it must allow scientific theories to tell us something substantial about the world. 4 Responding to Newman’s objection: partial interpretation structural realism The problem, it seems, with SR3, is the fact that it allows too wide a scope for its second order quantifiers. The structural realist wants to assert that a particular structure is true of the world, but such a claim is trivial if any classification of objects can count as elements of a structure. For the assertion to have meaning, it must rule out many ways the world could be beyond merely having a different number of objects. One obvious way of responding to this problem is to abandon SR3 in favor of one of the less abstract forms of SR, such as SR1 and SR2. These views will not succumb to Newman’s objection, because they do not allow any collection of objects of the right size to make true the Ramsey-sentence of a theory. At least some of the predicates of SR1 and SR2 are interpreted, and so the Ramsey-sentence will only in general be true if there are objects in the world that truly have properties or bear the relations to which the predicates refer. However, this way of saving SR sacrifices much of what makes SR attractive in the first place. For the realist, the whole point of SR is to find an epistemically “safe” position that does not commit the realist to believing too much

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beyond what we can experience or to believing falsehoods that will fall away under the march of the pessimistic meta-induction (Psillos 2001, p. S18). The more interpreted content is let into one’s theories of the world, the less likely they are to satisfy these goals. So one might desire a version of SR that is more abstract than SR1 and SR2 but that avoids the problems of Newman’s objection. Melia and Saatsi (2006) consider the obvious response to Newman’s objection, namely to allow some of the predicates of the language to be interpreted and not replaced by second order variables bound by existential quantifiers. Typically, such interpreted predicates belong to the “observation language” and are the means by which the Ramsified theory “makes contact” with observation. Call such a view partial interpretation structural realism (PISR). Ketland (2004) has attempted to extend Newman’s objection to PISR by showing how any theory that is Ramsified in such a manner will turn out true as long as the domain of the actual world has the right cardinality and the Ramsified theory is empirically adequate, i.e. is such that all its observational statements are true. Obviously, such a result threatens PISR with a triviality nearly as bad as the one that results for SR3. Although PISR does not make Ramsified theories true for just any domain of the right size, it is effectively an anti-realism—the only non-observational content such a theory has is a claim about the cardinality of the unobservable domain. Melia and Saatsi respond to Ketland by pointing out that, though his argument is formally correct, it depends upon the structural realist Ramsifying every predicate in a theory that applies to unobservable entities. However, they argue, it not obligatory for a structural realist to do so. Many predicates, like “has mass”, apply to both observable and unobservables. According to Melia and Saatsi the structural realist need not replace those predicates with variables bound by existential quantifiers. Hence, she may demand that the truth of a theory depends not just on whether its claims about the observable are true, but also whether some of its claims about the unobservable are as well. PISR, so construed, does not collapse into anti-realism. I am not convinced that it is acceptable to the “spirit of structural realism” to allow a theory to make such robust claims about the unobservable, but for the purposes of this essay, I am willing to accept a “big-tent” PISR as structural realism.

5 A version of Newman’s objection for PISR So PISR may not be trivial or anti-realist, but is it still structural realism? The worry is not that one mentioned at the end of the last section, that PISR allows more of a commitment to the content of a theory than a structural realist would accept. The problem is that PISR may succumb to yet another version of Newman’s objection that applies to those aspects of the unobservable that are distinctive of the unobservable. In particular, the worry is that PISR doesn’t allow theories to say anything about the mere structure of the unobservable. Melia and Saatsi do not frame this worry in quite this way, but I believe this is the same worry that they express in Sect. 4, “The model theoretic argument bites back”. There they give a toy theory, +, that, though it seems to make claims about unobservable objects, is such that its Ramsey sentence only entails that certain macroscopic entities (“rays”) have microscopic parts. The Ramsey sentence of + does not entail anything else about the microscopic entities.

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They claim that “the physical content of the Ramseyfied theory is still too weak” and that “Ramsey sentences should require more of the theoretical world” (p. 572). I think we can make this worry more general and more precise by mimicking Ketland’s formulation of Newman’s objection. Ketland’s formulation makes use of the notions of empirical adequacy and T-cardinality correctness, and distinguishes between observable predicates (predicates that are true only of observables), theoretical predicates (predicates that are true only of unobservables) and mixed predicates (predicates that are true of observables and unobservables) . Let us distinguish instead between only two kinds of predicates: non-theoretical predicates and theoretical predicates. Non-theoretical predicates are predicates that are true of at least one observable and theoretical predicates are predicates that are true only of unobservables. A theory θ then has a model M = D, N , T , where D is a domain of objects, N is a function from non-theoretical predicates to subsets of D n , which specifies the extensions of the non-theoretical predicates, and T is a function from theoretical predicates to subsets of D n , which specifies the extensions of the theoretical predicates. Rather than empirical adequacy, let us speak of non-theoretical adequacy. Roughly, the idea is that a theory is non-theoretically adequate if it accurately characterizes all facts that concern the kinds of properties and relations born by observables, whether or not those facts involve observables. More precisely, a theory is non-theoretically adequate if and only if it has a model M such that for every non-theoretical predicate Ni , a1 , . . ., an  is in the extension of Ni if and only if the objects a1 . . .an truly bear the relation referred to by Ni . Call the set of all such objects to which at least one of θ ’s non-theoretical predicates applies D N θ . It follows from the definition of non-theoretical adequacy that if M is non-theoretically adequate, D N θ is a subset of D. Non-theoretical adequacy is stronger than empirical adequacy in the sense that every non-theoretically adequate theory is empirically adequate but not vice versa. Finally, let us say that a theory is cardinality correct if it has a model with a domain the same cardinality as the set of actual objects.3 The problem can then be stated as follows: the Ramsey sentence of a theory θ is true if θ is non-theoretically adequate and θ is cardinality correct. Proof: Assume θ is nontheoretically adequate and cardinality correct. Then there is a model M = D, N , T  of θ such that (1) D N θ is a subset of D, (2) for every n-place predicate Ni and objects a1 . . .an such that a1 , . . ., an  is in the extension of Ni in M, Ni a1 . . .an is true, and (3) D has the same cardinality as E, the domain of real objects. By (3) there is a 1-1 function f from D onto E. Because D N θ is a subset of both D and E, we can assume that f maps every member of D N θ to itself. Let ‘ f (X )’ be shorthand for the composition of f and X , extended in the obvious way if X ’s range contains subsets of the members of f ’s domain, rather than the members themselves. Then the model M ∗ = ( f (D), f (N ), f (T )) = (E, N , f (T )) is isomorphic to M. As such, M ∗ is also a model of θ . Let ∃X i θ Xi|T i be the Ramsey sentence of θ that results from replacing each theoretical predicate Ti with a variable Xi and existentially quantifying over that variable. So by the rules of satisfaction for second-order quantifiers, E, N  satisfies 3 This statement assumes that there is a fact about the cardinality of the objects of the world. I am not so sure that this is true, but it is a common enough assumption. Relaxing it would only make the Newman objections stronger.

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∃X i θ Xi|T i . If E, N  satisfies a sentence, then that sentence is true, given that E is the domain of real objects and the N assigns the n-tuple a1 , . . ., an  to a predicate Ni only if those objects bear the relation referred to by the predicate Ni . So ∃X i θ Xi|T i is true. I hope it is clear why the worry should trouble the structural realist. In trying to save structural realism from triviality, she may, as Melia and Saatsi suggest, allow that some of the theory’s non-structural claims be taken seriously. But in so doing, she is merely being a realist (to some degree) about the theory in question. To be a structural realist, she must maintain that there is some domain in which we should only commit to the structural claims of a theory. In other words, there must be some merely structural claims that are true. But what the above argument shows is that any merely structural claims will still be trivially true, and hence she will not have succeeded in actually saying anything about the mere structure of the world. I believe that this is the underlying worry expressed by Melia and Saatsi. 6 Two ways to answer Newman’s objection to PISR Melia and Saatsi (2006) consider two broad strategies to respond to this worry. One strategy involves limiting the domain of quantification of second-order quantifiers in the Ramsey sentence of a theory, which is a suggestion that Newman himself makes, although in slightly different language. Newman himself had suggested limiting the domain to real rather than fictitious relations, where a fictitious relation is one “whose only property is that it holds between the objects that it does hold between” (p. 145). Newman goes on to argue that this distinction cannot save SR, but the details of this argument are not particularly relevant. However, the notion of a “real” relation does suggest other ways to hold onto SR. In standard second order logic, the second order quantifiers range over all possible subsets of a model’s object-domain. However, one may instead limit the domain of quantification of the second-order quantifiers in the Ramsey sentence of a theory to those subsets of a model’s domain that instantiate various other types of properties. Melia and Saatsi suggest the following types of properties: natural properties, intrinsic properties, qualitative properties (which are much like Newman’s “real” properties), and contingent and causal properties. Let the general structural realist position that the domain of quantification should be limited in some such way be called restricted quantifier structural realism (RQSR). How does RQSR avoid the most recent incarnation of the Newman objection? For simplicity, let’s first look at how it deals with the original Newman objection to SR3, which forms the Ramsey sentence of a theory by replacing all predicates with existentially-bound variables. The problem for SR3 is that any properly-sized domain of objects can make such a Ramsey sentence true. The reason is that there will always be some subsets of the object-domain that will satisfy the Ramsey sentence (with the quantifiers removed). But SR3 combined with RQSR avoids this general problem. If there are limits on which subsets of the object-domain can be assigned to the second order variables by the satisfaction function, then there will not in general be such subsets. As an arbitrary, but simple, example, consider the following sentence: (S)∃X∃x∃y(Xx & Xy & x = y).

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The domain D = {α, β} will make (S) true under the normal truth conditions for second order logic. However, if we demand, for example, that the quantifiers must range over proper subsets of the domain (thus limiting, in this model, possible interpretations of the second order variables to the sets {α}, {β} and ∅), then (S) will be false. Hence we have a counterexample to the triviality objection. A similar result will hold for the Ramsey sentences allowed by PISR and RQSR. Indeed, (S) is presumably allowed by PISR, which merely claims permission to leave interpreted predicates in its Ramsey sentences. However, it may be instructive to see how a properly partially-interpreted Ramsey sentence can avoid triviality. So, for example, consider the following sentence and an interpretation: (U)∃X∃x∃y(Fx & Rx y & Xy & ∼ Xx) MU = D = {α, β}, F = {α, β}, R = {α, β} The sentence (U) will be true on the model MU in the standard semantics. However, if we, say, restrict the quantifiers for single-place predicate variables to non-singleton sets (effectively restricting possible interpretations to {α, β} and ∅), then (U) will be false. As with the above example, this example shows that a Ramsey sentence will not be trivially true if the range of the second order quantifiers is restricted. Admittedly, these examples are artificial, but their artificiality allows them to simply show how the triviality argument is blocked. It’s also worth noting why the argument in the previous section no longer works. That argument depended on the facts that (1) in standard second order logic any model isomorphic to a model of a sentence will also be a model of that sentence, and that (2) any model of a sentence is also a model of that sentence with predicates replaced by variables bound by existential quantifiers. But if we restrict the range of the second order quantifiers, then those two facts will not both be true. If (1) is rejected, then the limitations on the range of the second order quantifiers will also be limits on the interpretation of predicates, and if (2) is rejected the limitation is only on the rules for evaluating the truth of second order existential sentences. I think it would be a bit odd to reject (2), as that would allow that the interpretation of a predicate could not serve as an instance of a second order variable. Melia and Saatsi do not explicitly say which option they choose, but then I think not much hangs on this question. So RQSR manages to technically solve the latest version of the Newman objection, but one might still wonder whether it is a satisfactory fix for the structural realist. Melia and Saatsi examine a number of putative restrictions on the range of the second order quantifiers, and in each case conclude that the restriction is unsatisfactory as a defense of SR. I would like to mention, in particular, their rejection of natural properties to play this role. Natural properties are those properties that “cut nature at its joints”, that objectively unify the objects which bear them. As examples, Melia and Saatsi mention “having a unit charge” and “having a unit spin” as putative natural properties. One might think that the structure that SR imputes to the unobservable realm is a structure that exists among the natural properties. However, Melia and Saatsi give two reasons to reject this idea. The first is that the distinction between natural and unnatural properties is highly controversial. The second is that since science has

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mistakenly identified disjunctive properties as natural in the past, the structural realist who appeals to natural properties falls victim to the pessimistic meta-induction. So, Melia and Saatsi consider a second solution to the Newman objection to PISR, which is to permit “intensional notions” into the language in which the Ramsey sentence for a theory is formed. They mention four types of intentional relations in particular that may hold between properties: counterfactual dependence, law-like correlation, independence, and explanation. Melia and Saatsi do not clearly distinguish between these four notions, presumably because of the intimate connections that obtain between them. Let’s focus on the notion of law-like correlation, which seems as likely a ground for the others as any and for which Melia and Saatsi provide the most explicit sketch of an account. The idea is, presumably, that if the Ramsey sentence of a theory is understood as asserting a law, i.e. a physical necessity, then it will no longer be the case that just any collection of theoretical objects of the right cardinality will satisfy the Ramsey sentence. The notion of law can be built directly into the Ramsey sentence by introducing a modal operator—Melia and Saatsi use “LP ” to stand for “it is physically necessary that…”. As an example of such a modal Ramsey sentence they offer “∃X L P ∀x(X x ↔ Gx)”, which they take to say “there is a property which is lawfully coextensive with G” (p. 581). Melia and Saatsi do not say much more about how this is supposed to work, but I will not attempt to fill in the missing details here, as I think this solution does not work. More precisely, I think that using intentional operators does not remove the threat of triviality unless one also restricts the range of the second order quantifiers, which Melia and Saatsi do not think justified.

7 Intensional operators alone do not answer Newman’s objection To show that intensional operators do not, by themselves, avoid the triviality objection, we will need to be a little more precise about the semantics for our intensional operators and describe a second-order modal language. There are some choices we will have to make. The first, relatively uncontroversial, choice I will make is to use Kripke models for the semantics of our modal language. For simplicity, but perhaps with more controversy, I will also assume a fixed-domain of objects rather than a varying domain. Finally, I will assume that all possible worlds are accessible to each other. I do not think that these simplifying assumptions will make a difference in the argument that follows, but I will leave that judgment up to the reader. So let our language be a standard second-order language (without names, for simplicity) supplemented with a single modal operator “LP ”. A model M for this language will consist of an ordered set W, D, R, where W is a set of worlds, D is a domain of objects, and R is a function from n-place predicates to n + 1-tuples a1 , . . ., an , w. The first n objects a1 , . . ., an in the ordered n +1-tuple are elements of D, and the final object w is an element of W . Thus R(Ri ) tells us what the extension of a predicate Ri is for each possible world. A variable assignment g is a function from the first-order variables of the language and worlds in W to the domain D of a model, and from the second-order variables and worlds in W to the powerset of D. We write that a formula ϕ is satisfied by a model M, at a world w and under a variable assignment g as follows:

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M |w ϕ[g]. Satisfaction is defined recursively for atomic formulae, the connectives, first- and second-order quantifiers, and the modal operators in the normal ways. For a sentence ϕ with no unbound variables, we can say that it is true or false at a world w in a model M(which we write M |w ϕ)iffM |w ϕ[g] for all variable assignments g. Let’s consider, to start, Melia and Saatsi’s sample sentence: (G)∃XLP ∀x(Xx ↔ Gx). Will there be any models for which (G) is false at some world in the model? The answer is no. Given any first-order modal model M = W, D, R, assignment g and world w in W , if we can come up with a variable assignment g for ‘X’ such that M |w LP ∀x(X x ↔ Gx)[g ], then (G) is true. In this case, if we start with any variable assignment g, then if for arbitrary world v in W we let g (X, v) = g(G, v) and let g be the same as g otherwise, then g will be such a variable assignment. Indeed, if we ignore the complications of PISR for the moment, we can argue that any satisfiable SR3 Ramsey sentence will turn out trivially true in any world in any model M that has a set of worlds of the appropriate cardinality and a set of objects of the appropriate cardinality. The argument is very similar to the argument given in Sect. 5. Suppose we have a satisfiable sentence of our language θ , and let M = W, D, R be a model such that M |w θ for some w in W . Now suppose that the correct frame of the universe4 is W , D . In other words, W is the set of truly possible worlds, and D is the set of real objects. What we want to show is that any extensions of the predicates R will produce a model M that will make the Ramsey sentence of θ true at the actual world, as long as the cardinality of W is the same as the cardinality of W and the cardinality of D is the same as the cardinality of D. Proof Assume that M |w θ for some w in W , and the cardinalities are correct for W and D . Then, there is a one to one function f 1 from W onto W and a one to one function f 2 from D onto D . Then consider the Ramsey sentence of θ built up in two stages. Let θk be the result of replacing all predicates R1 . . .Rk in θ with X1 . . .X k respectively5 . By assumption, M |w θ . Let g be a variable assignment such that g(Xi ) = Ri . Then M |w θk [g], since each second-order variable is interpreted exactly the same as its corresponding predicate, and, since θ is a closed sentence, the assignments to the first-order variables are irrelevant. Let g be a different variable assignment such that g (xi ) = f 2 (g(xi )) and a1 , . . ., an , v ∈ g(Xi ) if and only if  f 2 (a1 ), . . ., f 2 (an ), f 1 (v) ∈ g (Xi ). Let w be the image of w. Since M is isomorphic to M, and g assigns to the variables the images of the assignment of g, then M |w θk [g ]. Hence, by the truth conditions for the existential quantifier, M |w ∃X 1 . . .∃X k θk . Since M was chosen only so that its frame was true, the extensions of the predicates are irrelevant. Or in other words, the Ramsey sentence of 4 Just as we supposed in the non-modal case that there is a fact about what objects there are in the universe,

we will suppose that there is a fact about what objects and possible worlds there are. And as in the previous case, although I am not confident that such a supposition makes sense, I think that, if anything, the rejection of the supposition makes the Newman objection have to work harder. 5 We are assuming that there are a finite number of predicates. As long as we assume that θ is a finitely

long sentence (which seems a reasonable assumption), this is also a reasonable assumption.

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theory θ is true in any possible world, as long as the cardinality of the set of possible worlds and the cardinality of the set of objects are the same as those sets in a model that satisfies θ . For simplicity this argument was made with an SR3 Ramsey sentence, not a PISR Ramsey sentence. But I hope it is clear, without going through the details, that the same result will hold in the case of a partially interpreted Ramsey sentence as well. As long as there are existentially bound second-order variables, if the domain is of the right size, there will be a set that contributes to the truth of the sentence. This is so even if we bring possible worlds into the picture—possible worlds only really turn the n-tuples that can be assigned to second-order variables into n + 1-tuples. Ultimately, since we still allow any collection of objects to be the interpretation of a second-order variable, even if we require that one of the objects be from a different set, there is nothing to prevent the Newman objection from going through. We also made a simplifying assumption that every world was accessible to every other world. Perhaps the true modal structure of the world, if such there be, is not so simple. Can modal structural realism be saved from triviality by adding a more complex accessibility relation? The answer is no. The fact that we assumed the modal structure of S5 played no role in the argument above. To be sure, if the models of the theory θ had a richer modal structure, then there are more ways in which the true frame of the universe may fail to be isomorphic to the frame of one of the models of θ , and such an isomorphism is required for the argument to go through. After that assumption is made, the accessibility relation will only matter in the truth conditions for the modal operators, which assign truth to modal sentences on the basis of what is the case in accessible possible worlds. But because of the way g is constructed, if g assigns an extension to a predicate at a world, g assigns the isomorphic “counterpart” of that extension at the “counterpart” of the world to the variable that takes the place of the predicate. Now it is more of a demand, and hence a move away from triviality, to expect the true frame of the universe to have the modal structure of one of the models of the theory. But it is not much of a demand, and surely not enough to satisfy the structural realist. Nor is it obvious that any interesting scientific theories will make any very sophisticated demands on the modal structure of reality. I have interpreted the modal operator “LP ” as a standard box operator in modal logic, and focused a bit of attention on it to show that merely introducing an intentional operator does not do the job that Melia and Saatsi want. But one might object that the appropriate interpretation of the operator “LP ” is not as given by modal logic. Melia and Saatsi intended it to represent “It is physically necessary that…”, and this operator requires a more subtle interpretation. Well, which interpretation should we choose? Let’s consider a few more options. One of the most influential views of laws of nature is the regularity view, according to which the laws of nature are something like mere summaries of the history of the universe. In particular, David Lewis’s view is widely accepted. For Lewis (1973, p. 73), a law is not just any regularity, but only one of those regularities that is a logical consequence of the theoretical system that best combines the virtues of predictive strength and theoretical simplicity. Call any law that satisfies this require-

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ment a Lewis-law. However, as David Lewis has noted (1983), two sets of propositions cannot be compared for simplicity without fixing on a language in which to compare the two sets—what looks extremely complex in one language can be simple in a language designed just so. In particular, one must choose a set of “natural predicates” as the basis for comparison. But now it should be clear that Melia and Saatsi cannot accept the regularity view of laws in their solution to the Newman objection. For if “LP ” is interpreted as “It is a Lewis-law that…”, then the truth value of a Ramsey-sentence with embedded “LP ”s will effectively depend on a restriction of the second-order quantifiers. I say “effectively”, because the quantifiers will be free to range over any sets of objects, but such sets will only be capable of making true a sentence prefixed with “LP ” if they are the extensions of the natural predicates. We know that Melia and Saatsi are uncomfortable with relying on “natural” properties, but that is exactly what they would have to do to be able to use Lewis-laws in their account. An account of laws that is even less likely to be satisfactory to Melia and Saatsi is the universals account of laws, as ascribed to Tooley (1977), Dretske (1977) and Armstrong (1978). On their view, a statement such as “∀x(Fx → Gx)” expresses a law (which we may call an Armstrong-law) if and only if the property F bears the relation of necessitation to the property G, which is symbolized N(F, G). Only genuine universals can stand in the relation N to each other. So, if “LP ” is interpreted as “It is an Armstrong-law that…”, then Ramsey-sentences with embedded “LP ”s will again be implicitly appealing to a restriction on the range of the second-order quantifiers. In this case, only those sets that are the extensions of genuine universals will be capable of satisfying the Ramsey-sentence. As with “Lewis-law”, using “Armstrong-law” will not enable Melia and Saatsi to avoid appealing to a preferred group of sets of objects in order to evade Newman’s objection. A more recent view of laws that may be more amenable to Melia and Saatsi is that of Lange (2000, 2009). In his most recent exposition of his view, a “Lange-law” is one of a set of true statements that possesses non-maximal non-nomic stability. A detailed discussion of this concept is not appropriate for this paper, but we can say roughly that a set of statements is non-nomically stable if every member of that set would be true under every subjunctive supposition consistent with the entire set. Whether or not a statement expresses a Lange-law will then depend on the truth of certain subjunctive claims (including counterfactuals). It is not clear to me whether Lange’s analysis depends on a prior notion of natural predicates or natural properties. Prima facie, it does not. However, as Lange emphasizes in his 2000 book, his account of laws is not meant to be reductive but to draw connections between the concept of natural law as it appears in scientific practice and various other practices, such as induction and explanation. Inevitably, he details the connections between laws and natural kinds. So his account does not draw on a prior notion of natural properties because it does not draw on a prior notion of anything6 . However, it does end up being part of a systematic picture that includes natural properties. I cannot say whether Melia and Saatsi would find Lange’s view satisfactory or not, but his view raises an important point to which we will return in the next section.

6 In his most recent work (2009), Lange appeals to counterfactuals as the primitive ground of laws.

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So to summarize this section, it seems that none of the standard accounts of “It is physically necessary that…” that we have considered will do the job that Melia and Saatsi have set for the concept of physical necessity. Namely, they will not allow RQSR to avoid ultimately appealing to preferred sets of objects in order to avoid the triviality objection.

8 Laws and natural properties Now even if the above arguments are right, I suppose it’s still possible that there is some alternate semantics for the modal operator or some further view of laws that could provide a basis for answering the triviality objection without making use of preferred classes of objects. We have not seen a definitive proof that the intensionality solution requires an implicit appeal to a restricted domain of properties. However, at this point, I would presume that the obligation falls to the advocate of intensional notions to fill in the details herself. There is also good reason to doubt that it will be possible to fill in the details in the way the Melia and Saatsi want. As has been understood since Nelson Goodman’s Fact, Fiction, and Forecast (1954), there are deep connections between the concept of law of nature and the concept of natural kind. Trying to make sense of one without the other may well prove impossible. So appealing to laws in place of natural properties to avoid the triviality objection does not promise to be a successful strategy. There may of course be some intensional notion other than “it is physically necessary that” that does not bear such tight connections to the idea of naturalness and which satisfactorily combats the triviality objection. But why would one want to search so hard for such an alternative? What, after all, is SR supposed to be about? SR asserts that we can know the structure of reality. I can understand what that claim means if structure is a feature of laws, or of properties, but not of bare particulars. Yet by refusing to allow that some sets of objects are preferred over others, one is denying a role to the properties that characterize objects and letting the objects be distinguished from each other only by their mere individuality. While this is a possible metaphysics, it seems at least as controversial the distinction between natural and unnatural properties. One of Melia and Saatsi’s arguments against natural properties was that the concept is controversial, but this argument has no force if the alternative is also controversial. It is now worth returning to Melia and Saatsi’s primary objection to natural properties, namely that their use undermines SR’s ability to respond to the pessimistic meta-induction. The worry is that the natural properties at one time may turn out to be disjunctive, and hence non-natural at a later time and that the Ramsey sentence of the earlier time can then not remain true at the later time. As examples of such apparent natural properties that have since proved disjunctive or unnatural, Melia and Saatsi cite being green, being hot, and being hydrogen. But this objection only works if ‘natural property’ is identified with ‘fundamental property’, and they need not be so identified. All these considerations suggest that it will not be possible to formulate SR without committing to preferred classes of objects. In other words, it seems that any accept-

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able SR will have to be a version of RQSR. The empiricist on the “upward path” to structural realism, as described by Psillos (2001) will likely not be too happy if such a result is true, and may choose to abandon SR altogether. But I see far less reason for the realist on the “downward path” to SR to object. 9 Conclusion So, in conclusion, let me summarize the argument of this paper. I have considered the structural realist claim that science gives us, at best, mere structural knowledge of the unobservable realm. Naïve structural realism falls victim to Newman’s objection, as does the more sophisticated PISR, as Melia and Saatsi have suggested and which I have tried to generalize. Melia and Saatsi reject RQSR as a solution and attempt to solve the problem using the intensional operator “it is physically necessary that” in the Ramsification of a theory. I have tried to argue that such attempts are implicitly versions of RQSR. Finally, I have suggested that RQSR may not be as bad as Melia and Saatsi suggest, and that SR may have no other alternative response to Newman. References Armstrong, D. (1978). A theory of universals. Cambridge: Cambridge University Press. Chakravartty, A. (2004). Structural realism as a form of scientific realism. International Studies in the Philosophy of Science, 18, 151–171. doi:10.1080/0269859042000296503. Cruse, P. (2005). Ramsey sentences, structural realism and trivial realization. Studies in History and Philosophy of Science, 3, 557–576. doi:10.1016/j.shpsa.2005.07.006. Dretske, F. (1977). Laws of nature. Philosophy of Science, 44, 248–268. doi:10.1086/288741. Goodman, N. (1954). Fact, fiction and forecast, Cambridge: Harvard University Press Ketland, J. (2004). Empirical adequacy and ramsification. The British Journal for the Philosophy of Science, 55, 287–300. doi:10.1093/bjps/55.2.287. Ladyman, J. (1998). What is structural realism? Studies in History and Philosophy of Science, 29A, 409–424. doi:10.1016/S0039-3681(98)80129-5. Lange, M. (2000). Natural laws in scientific practice, Oxford: Oxford University Press. Lange, M. (2009). Laws and lawmakers: science, metaphysics and the laws of nature. Oxford: Oxford University Press. Lewis, D. (1973). Counterfactuals. Cambridge: Harvard University Press. Lewis, D. (1983). New work for a theory of universals. Australasian Journal of Philosophy, 61, 343–377. doi:10.1080/00048408312341131. Maxwell, G. (1970). Structural realism and the meaning of theoretical terms, In S. Winokur & M. Radker (Eds.), Analysis of theories and methods of physics and psychology: Minnesota studies in the philosophy of science, (Vol. IV, pp. 181–192.s). Minneapolis, MN: University of Minnesota Press. Melia, J., & Saatsi, J. (2006). Ramseyfication and theoretical content. The British Journal for the Philosophy of Science, 57, 561–585. doi:10.1093/bjps/axl020. Newman, M. H. A. (1928). Mr Russell’s causal theory of perception. Mind, 37, 137–148. doi:10.1093/ mind/XXXVII.146.137. Psillos, S. (2001). Is structural realism possible? Philosophy of Science, 68(Supplement), S13–S24. doi:10. 1086/392894. Tooley, M. (1977). The nature of laws. Canadian Journal of Philosophy, 7, 667–698.

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