1. Scientific realism (or at least one version of it) can be characterized as the conjunction of three theses, which, following Stathis Psillos (2000), I shall call the metaphysical, the semantic and the epistemological theses. The metaphysical thesis (or, as it is often referred to, metaphysical realism) is the thesis that the world is (largely) independent from our way of representing or describing it. The semantic thesis is that our scientific theories are literal descriptions of the world and are capable of being true or false. The epistemological thesis is that we are epistemically justified in believing that our best scientific theories are (approximately) true.1Scientific antirealism, on the other hand, is the denial of at least one of the above theses.

Whereas scientific antirealists in the past often rejected the metaphysical or the semantic theses, in the last few decades, the debate between scientific realists and antirealists has mostly focused on the epistemological thesis. This development can be largely attributed to the influence that Bas van Fraassen’s constructive empiricism has exerted on the debate since the publication of The Scientific Image in 1980. Constructive empiricism has since represented a moderate and sensible alternative to scientific realism, which challenged scientific realists mostly on the epistemological ground, while making substantial concessions on the metaphysical and the semantic grounds by essentially accepting the metaphysical and the semantic theses.

This unusual consensus, however, may not be destined to last. Most philosophers of science today seem to have come to reject the ‘descriptive’ picture of science on which the semantic thesis relied in favour of a ‘representational’ picture. Whereas on the descriptive picture theories are collections of sentences or propositions that relate to the world directly by describing it, on the representational picture, theories relate to the world indirectly through their models, which represent aspects or portions of the world.

As one of the most prominent advocates of the so-called semantic view of scientific theories, van Fraassen has played a key role in establishing (or, perhaps, as he suggests (van Fraassen 2008, Ch.8), re-establishing) the representational picture, but this seems to be somewhat in tension with his acceptance of the semantic thesis. On the one hand, the semantic thesis entails that scientific theories are capable of being true or false; on the other hand, the semantic view seems to imply that, since models are not capable of being true or false and scientific theories are just collections of models, theories are not capable of being true or false either.

The tension between these two views might strike one as rather superficial and it is tempting to think that it can be resolved simply by reformulating the semantic thesis so as to make it compatible with the semantic view. This exercise, however, may not be as trivial as it initially appears. Van Fraassen, who has never been oblivious to the tension between these two views, has tried on numerous occasions to reconcile them by sketching something along the lines of what he now calls ‘empiricist structuralism’. However, it is only in Scientific Representation: Paradoxes of Perspectives that empiricist structuralism is fully developed and defended. And, as it turns out, the result is far from being a mere reformulation of constructive empiricism. Empiricist structuralism is, I shall argue, a far more radical form of scientific antirealism, which rejects not only scientific realism’s semantic and epistemological theses, but also its metaphysical thesis.

2. But how can the solution to what could seem to be a relatively minor problem turn out to have such momentous philosophical consequences? Like other supporters of the semantic view, van Fraassen thinks of scientific models as abstract mathematical structures and thinks of representation as a formal relation – a morphism – between structures. However, if one thinks of models and representation in this way, a problem seems to arise. Since morphisms are functions between (the domains of) set-theoretic structures and since the aspects and portions of the world that the models are used to represent (their real-world targets) are not set-theoretic structures, it would seem that models cannot relate to the world by dint of some morphism holding between them and their real-world targets. As van Fraassen puts it is: ‘If the target [of the representation] is not a mathematical object then we do not have a well-defined range for the function, so how can we speak of an embedding or isomorphism or homomorphism or whatever between that target and some mathematical object?’ (241).2

Let me call this problem the bridging problem – the problem of how to bridge the gap between models and the world. One popular attempt at solving it is what I shall call the ‘layer-cake’ approach, which consists in claiming that theoretical models do not represent their real-world targets directly, but do so only indirectly by representing data models for those targets, where a data model is a ‘cleaned-up’ ‘smoothed-out’ version of the data gathered from the target system and, as such, is an abstract mathematical structure itself (see, e.g. Suppes 1962). One problem with the layer-cake approach is that we seem to be able to use models to represent real-world systems even when no data models for those systems are available (a case in point is the example I shall discuss below). A much more serious problem, however, is that by introducing a new layer in the cake one can only postpone the problem, not solve it. If the theoretical model cannot represent the real-world target directly because the former is an abstract structure and the latter is not as van Fraassen seems to think, how can the data model represent the real-world target directly if the data model is itself an abstract structure?

As far as I understand it, van Fraassen’s answer to this question is that the sense in which we talk of data models as representing real-world systems is different from the sense in which we talk of theoretical models as representing data models. Data models do not represent real-world systems in virtue of some morphism holding between them and the systems in question. If a data model ‘represents’ a certain real-world system, it does so in virtue of the fact that the data model is the output of a process whose input are the raw contents of the outcomes of measurements performed on that system. In this process, however, the input (i.e. the raw data from the system) does not determine the output (i.e. the data model). As van Fraassen puts it, ‘[What the phenomenon is like taken by itself] does not determine which structures are data models for it – that depends on our selective attention to the phenomenon, and our decisions in attending to certain aspects, to represent them in certain ways and to a certain extent’ (254).

But what does this mean concretely? The most radical implications of van Frassen's position are most evident in his crucial discussion of a simple example, to which I turn in the next section.

3. In the example (which I modify slightly here), Professor Deerstalker is presenting to an audience in a town-hall meeting in Red Deer, Alberta his theory about which factors affect the growth of the deer population in the area. In the process, Deerstalker displays a graph of the growth of the deer population in the area over a certain period of time (that’s his data model). At the end of the presentation, a member of the audience, Ms Nitpicker, concedes that Deerstalker’s theory ‘fits’ the graph well but asks whether it ‘fits’ equally well the actual growth of the deer population. Deerstalker proceeds to explain how he arrived at the graph by measuring diligently the values of various parameters over time, but Nitpicker is not satisfied by his answer. Her worry is not so much about the procedure that led to the construction of the graph as about whether or not the graph accurately represents the growth of the deer population in the area over time (as van Fraassen puts it, the point she is making is about metaphysics not epistemology).

At this point van Fraassen claims: ‘Although [Deerstalker] can see the logical leeway on which [Ms Nitpicker] trades there is no leeway for [him] in this context, short of withdrawing [his] graph altogether. Since this is [his] representation of the deer population growth, there is for [him] no difference between the question whether [the theory] fits the graph and the question whether [it] fits the deer population growth’ (256, emphasis in the original). Van Fraassen then goes on to suggest that ‘if [Deerstalker] were to opt for a denial or even a doubt, [his response] would be as paradoxical as any of Moore’s Paradox forms, like ‘It isn’t so, but I believe it is’ […]’ (256) and that ‘In fact, [he] would become incoherent if [he] let [such a] challenge to lead [him] into any such concession’ (256).

As, I think, van Fraassen’s revealing discussion of this example suggests, his solution to the bridging problem seems to come at a hefty philosophical price – that of rejecting metaphysical realism. In particular, I shall argue that, unless van Fraassen denies that there is a fact of the matter as to how many deer live in that area at every time during that period independently of Deerstalker’s attempts at estimating that number, there seems to be no good reason for him to think that Deerstalker has no options other than either standing by his graph or withdrawing it altogether. Nor does there seem to be any good reason to think that even doubting the accuracy of the graph would put Deerstalker in a paradoxical situation. And I cannot see any way for van Fraassen to deny that there is a fact of the matter as to how many deer live in a certain area at a certain time (independently of one's attempts at estimating that number) without rejecting metaphysical realism.

Suppose that van Fraassen is not denying that there is a fact of the matter as to how many deer live in that area at every time during a certain period independently of Deerstalker’s attempts at estimating that number. Then he (and Deerstalker) would presumably have to concede that not all estimates of that number are equally good and that some estimates are closer to the actual number than others. Moreover, presumably, not all methods for estimating the number of deer that live in the area at a certain time are equally reliable. Some methods for estimating the size of the deer population at a time, when applied correctly, are more likely than others to give as a result a number that is close to the actual number of deer in the area at that time.3 So Deerstalker’s confidence in the accuracy of his graph should largely depend on the method employed to carry out each count on which his graph is based (as well as on the frequency and timing of the counts).

Moreover, since the most reliable methods are extremely resource-intensive, Deerstalker would probably have to concede that the methods that were actually employed in the gathering of the data used to produce his graph were not completely reliable. Ideally, for a wildlife population that is subject to hunting, the population should be counted by a complete count three times a year (once before the mating season, once after the new ones are born and once after the hunting season). Due to a number of practical constraints, however, this is rarely the case – populations are more likely to be counted only once a year and usually not by a ‘complete’ count.

But, if Deerstalker were to concede all of the above (and van Fraassen has given us no good reason to suggest he should not), then he (and van Fraassen with him) would either have to concede that there is a fact of the matter as to how accurately his graph represents the number of deer living in the area during the period of interest or would have to deny that there is a fact of the matter as to how many deer live in the area at each time independently of his attempts at estimating their number. Of course, Deerstalker could stand by the accuracy of his graph and claim that it is a completely faithful representation of the growth of the population (or, at least, a sufficiently faithful representation for the purpose at hand). However, there seems to be no good reason to think that it would be incoherent or paradoxical for Deerstalker to concede that the graph does not represent the growth of the deer population as faithfully as it could (or even should) and maybe even mention which aspects of the growth of the deer population he has reasons to think are represented somewhat inaccurately. In fact, Deerstalker may even concede that the graph is a very crude representation of the growth of the deer population in the area, but, since it is still the best one available, one has no choice but to make do with that until a more accurate one becomes available.

If van Fraassen (and Deerstalker) conceded that there is a fact of the matter as to how accurately the graph represents the deer population growth, then he would also seem to have to concede that there is a difference between asking how well the theory fits the data and how well it fits the world. And what I said seems to suggest that Deerstalker may well have reasons to answer those two questions differently. But, if this is so, then it would seem that the only good reason for van Fraassen to deny that the second question can be legitimately distinguished from the first is to deny that there is a fact of the matter as to how many deer live in the area at a certain time independently of one’s attempts at estimating that number, a denial which, as far as I can see, is incompatible with metaphysical realism.

To see how much more radical van Fraassen’s views have become since his early constructive empiricist days, it may be instructive to compare his take on the above scenario with what I take would be a constructive empiricist’s take. As far as I can see, a constructive empiricist would have no qualms conceding that there is a fact of the matter as to how faithfully Deerstalker’s graph represents the actual growth of the population, for she neither denies that there are deer nor that, at every time, there is a definite number of them in a certain well-defined area. And anyone who concedes this much would also have to admit that there is a fact of the matter as to how faithfully Deerstalker’s graph represents the growth of the deer population in that area.4 An empiricist structuralist, on the other hand, would seem to deny that there is such a fact of the matter, for, if she did not, she would have to concede that there is a difference between the theory fitting the graph and the theory fitting the world.

4. So far, I have argued that empiricist structuralism rejects both the semantic and metaphysical component of scientific realism and that, as such, it is a much more radical form of scientific antirealism than constructive empiricism. What might seem peculiar is that van Fraassen seems to take such a momentous step in an attempt to solve a semantic problem – the bridging problem. However, I don’t think this is the case – the bridging problem is a problem only insofar as one already rejects metaphysical realism. To see why, consider one of my favourite examples.

Suppose that my daughters want to go down a hill on their toboggan and that I want to make sure they won’t go too fast. One thing I could do is to use a simple model from classical mechanics – the inclined plane model. In the model, a box sits still at the top of an inclined, frictionless plane, where its potential energy, Ui, is equal to mgh (where m is the mass of the box, g is its gravitational acceleration, and h is the height of the plane) and its kinetic energy, KEi, is zero (Ei = KEi + Ui = 0 + mgh). When we let go of the box, it will slide down the plane until, at the bottom of the slope, all of its initial potential energy will have turned into kinetic energy (Ef = KEf + Uf = 1/2mvf2 + 0 = mgh). At that point its velocity, vf, is going to be (2gh)1/2. Now suppose that the tobogganing hill is 5 m high and that I plug in 9.8 m/s2 for g and 5 m for h. The maximum velocity of the box will be (2gh)1/2 = (2 × 9.8 × 5)1/2 ≈ 9.9 m/s. From this, I infer that my daughters will reach at most a velocity of approximately 9.9 m/s.

Now let me put aside the question of whether I should trust what the model tells me or how faithful a representation of the system the model is, for I take it that these are not what is at issue here. The problem seems to be that I used an abstract entity (the model) to represent a concrete one (the system). In van Fraassen’s own words, the question is: ‘How can an abstract entity, such as a mathematical structure, represent something that is not abstract, something in nature?’ (240).

However, even admitting that the inclined plane model is an abstract entity, I cannot see how things would have been relevantly different, from a representational point of view, if, instead of an abstract entity, I had used a concrete one to represent my daughters tobogganing down the hill. Suppose that, for example, instead of using the inclined plane model, I had decided to use a hockey puck sliding down a ramp covered with ice and to measure the final velocity of the puck and suppose that, on the basis of this concrete model, I would also have inferred that the maximum velocity of the toboggan would be approximately 9.9 m/s. I cannot see exactly why the fact that the objects in one case are supposedly abstract while in the other case they are concrete should make a difference in how they can be used to represent my daughters tobogganing down the hill. In both cases, I seem to be doing exactly the same thing – I seem to be adopting an interpretation of the model in terms of the system, which, in these two cases, roughly amounts to my taking certain objects in the model (in one case the ‘abstract’ inclined plane and the ‘abstract’ box and in the other the concrete ramp and the concrete puck) to stand for certain objects in the system (the hill and my daughters on the toboggan) and certain properties of objects in the model (e.g. the velocity of the box and that of the puck) to stand for certain properties of objects in the system (e.g. the velocity of the toboggan).5

Van Fraassen’s real worry however does not seem so much to have to do with the abstractness of the vehicle of the representation (i.e. the model) but with the fact that this ‘offhand’ response presupposes that the target of the representation (i.e. the real-world system) comes already ‘carved up’ into entities, their properties and relations (e.g. my daughters, the toboggan, its velocity) independently of how we represent the target (241–44). But, as far as I can see this ‘presupposition’ stands or falls with metaphysical realism. So, it is not so much that one needs to reject metaphysical realism to solve the bridging problem, but that the bridging problem becomes a serious problem only once one has rejected metaphysical realism.

Now, I must confess that I am inclined to believe that there are such things as my daughters and the toboggan, and that there is a fact of the matter as to how fast the toboggan is going at a certain time and that this is so even when no one is trying to measure its velocity and no data model for that system is available. But, if I wasn’t making any such assumption, I wouldn’t seem to have any reason to use the model to represent the system in the first place. If I use the model to make sure my daughters will be safe, it is because I am assuming that I have two daughters and that they have a toboggan and that, if they were to go down this hill on their toboggan too fast, they could hurt themselves. So, even if it may be true that there are other ways of ‘carving up’ the system (and possibly even other ways of carving it up ‘at its joints’ by carving it up more ‘coarsely’ or ‘finely’), the carving-up of the system is not a product of my attempting to use the model to represent it. Rather, in attempting to use the model to represent the system for some purpose or other, one is usually already presupposing that the system is ‘carved up’ in some way (whether this way of carving up the system carves it up ‘at its joints’, of course, is a totally different issue).

One may worry that this only applies to those ‘humdrum’ cases in which a model is used to represent a real-world system for some practical purpose and not to the ‘interesting’ cases, in which we have little or no idea of how the system should be carved up and, therefore, the use of the model does not presuppose that the user makes any assumption about how the system should be carved up. But this does not seem to be the case. Even if, in some cases, it may well be true that no specific assumptions about how to carve up the system are presupposed by one’s attempt to construct a model of it and it is only in the process of constructing the model that we make a hypothesis about how the system should be carved up, the very attempt to construct a model that represents the system faithfully (and not just faithfully enough for some specific purpose) seems to presuppose that, of all the ways one can carve up the system, only some carve it up at its joints and that therefore there are some such joints. Of course, our model may well happen to be one that does not to carve up the system at its joints but, if there is any point in one’s trying to figure out how the system is to be carved up at its joints, one needs to assume, contra metaphysical antirealism, that there are such joints.

Indeed, if metaphysical realism is false, the bridging problem would seem to be much more ubiquitous than we have assumed so far: it would affect even the most basic descriptive uses of language and therefore even the descriptive picture according to which scientific theories are collections of sentences or propositions. Even my reporting to you that my daughters are on the toboggan would seem to presuppose that the world can be carved up accordingly. This is not to deny that there can be more than one way to ‘carve up’ the world or even that there are many ways to carve it up at its joints (by carving it up more or less ‘coarsely’). Nor it is meant to deny that by adopting certain representations of the world we make some of those ways salient. What it is meant to deny is that the world has no joints whatsoever and that it is possible to make sense of even the most basic attempts at describing or representing the world without presupposing that there are some such joints.

5. Earlier I suggested that it may be possible to resolve the tension between the semantic thesis and the representational picture simply by reformulating the letter of semantic thesis in terms of models and representation without betraying its spirit. But is it really possible to do so? I would hope so and I like to think that it can be done by adopting an interpretational account of epistemic representation (Contessa 2007 and Contessa forthcoming).

The interpretational account roughly maintains that a model is an epistemic representation of a certain target for a certain user if and only if the user adopts an interpretation of the vehicle in terms of the target. In many cases, this amounts to the user taking relevant objects, properties and relations in the model to stand for relevant (putative) objects, properties and relations in the target (where the ‘standing for’ relation is analogous to the one holding between a name and its bearer).

In this framework, the constructive empiricist’s concession that theories are to be construed literally and that they can be true or false can be expressed by saying that constructive empiricists and scientific realists adopt the same interpretation of a scientific model and both believe that, in principle, under this interpretation, the model could be (though is likely not) a completely faithful epistemic representation of the system. Where they disagree is whether all this entails that we are ever epistemically justified in believing that some conclusions about the unobservable parts of the system are true.

So, for example, in the case of the Rutherford model of alpha-scattering, both a constructive empiricist and a scientific realist would adopt an interpretation of the model according to which, from the model, one can (validly) infer that the gold foil is made up of gold atoms whose nuclei are very small relative to the size of the whole atom. Moreover, they would both believe that the conclusion of this inference is either true or false. What they disagree about is whether the explanatory success of the model is a good reason to believe that the conclusion of that inference is true.

In other words, a constructive empiricist and a scientific realist do not disagree on what models ‘tell’ us. What they disagree about is the extent to which we should believe what empirically successful models ‘tell’ us. According to the scientific realist, roughly, the more empirically successful the model is the more justified we are in believing that it gives us a faithful (although, in some respects, idealized and approximate) epistemic representation of the system. According to the constructive empiricist, that empirical success speaks only in favour of the empirical adequacy of the model – i.e. its faithfulness with respect to the observable parts of the system – not for its being an overall faithful epistemic representation of the system.

6. In this paper, I have argued that, in abandoning constructive empiricism for empiricist structuralism, van Fraassen has come to reject metaphysical realism and that, insofar as this rejection is motivated by semantic considerations (and in particular by the bridging problem), it is unjustified – the bridging problem only arises in its most serious form if one already assumes the falsity of metaphysical realism and, if one does so, the bridging problem becomes ubiquitous. I have then sketched a way to interpret the disagreement between scientific realists and constructive empiricists within a representational framework. Although more work is needed to turn this sketch into a detailed picture, I hope what I said will be sufficient to show that the tension between a representational picture and the semantic thesis is not as profound as it may seem.6

1 Assuming that one cannot be at the same time epistemically justified in believing that p and in not believing that p.
2 All page numbers refer to (van Fraassen 2008).
3 For an overview of the topic, see e.g. (Davis and Winstead 1980).
4 Contrary to what one might think, nothing hinges on the fact that deer are observable. Presumably the constructive empiricist would say the same of a graph of the decline of the number of atoms in a specific sample of Polonium-210. Constructive empiricists do not deny that there are atoms of Polonium-210, nor that, if there are any, there is a definite number of them. What they do deny is that we have any conclusive reasons to think that there are Polonium-210 atoms (let alone that there is a specific number of them in a certain sample).
5 For the notion of interpretation as used here, see (Contessa 2007) and (Contessa forthcoming, Ch. 3)
6 I would like to thank Nancy Cartwright, Michel Ghins and Bas van Fraassen for their helpful comments on previous versions of this article.

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