5. Differential Importability and Abstractionism About Scientific Models

If the abstractionist account of scientific models is true, there seem to arise difficulties in accounting for the phenomenon of differential importability. In the abstractionist view, model-systems are abstract structures. Given that models are abstract structures, the abstractionist proceeds to characterize “similarity” between such structures and the reality they model in terms of “formal” relations like isomorphism. Hence, different degrees of similarity between model and reality are accordingly interpreted as different configurations of these formal relations. So far, things remain unproblematic. The question now arises: “What justifies the employment, in science, of one abstract model “at the expense” of some other abstract model?” Saying that they have different degrees of similarity to the target domain is to say, simply, that they are distinct models. But that difference was granted, to begin with. Hence, relations of resemblance, in whatever formal sense, that an abstract model has to really seem, in and of themselves, to provide inadequate explanation for our choosing that model instead of other models. While it is granted that similarity between model and reality is responsible for representation, our question is about what makes a representation more acceptable than others. Under what conditions would we be justified in importing more about reality from a model A than from some other model B? The actual test, it seems, of the importability of models in the sciences concerns the nature of predictions that result from the act of importing. The Newtonian model, as it stands, may be said to have adequate importability because importing from it has resulted in reasonably successful and accurate predictions. This seems to imply that predictions induced by a model are “wholly” responsible for its degree of importability. If importability can be accounted for by predictive strength, what, then, is the role of similarity in representation, and why bother about representation? Why require a model’s representation of reality for surrogating model-knowledge as knowledge of reality when predictive yield itself seems to justify this surrogacy? In response, the abstractionist can rhetorically ask, ‘Is one still not obliged to make the models “about” reality?” The rhetoric fails, however, to make its point because it is not obvious that models must be about reality. That lack of obviousness is what paves the way for instrumentalism about models. Since abstractionists posit that models represent reality, they are obliged, it seems, to combat such instrumentalism. Perhaps a more constructive response from the abstractionist would involve deflating “representation” by rendering representation a matter merely of “definition”. For an abstract model to represent reality, then, is for the model to be defined “as” reality, keeping its predictive profile in sight. That is, it is stipulated that the model “is”, for the purposes of science, the relevant portion of reality. So, in model-talk, the abstractionist would contend, scientists talk about abstract structures defined “as” the portion of reality that we want to know “scientifically”. By doing this, the abstractionist earnestly hopes to carve out a place for a model’s representation of reality. But, on this stipulative account, models are not even related to reality “intrinsically”, but are made “extrinsically” to be so. In this context, note that the similarity of the model to reality does not “obtain”, but is “manufactured”. Hence, this “stipulative” tack strongly induces an instrumentalist mood in scientific discourses because models and the theories they are described by seem to be mere black boxes, which, for reasons unknown to us, get things right about reality whenever we stipulate that models “are” some portion of reality. But this seemingly leads to more severe problems since the practice of defining abstract models as “concrete” chunks of reality seems to trespass key definitions in metaphysics and well-entrenched laws of logic. The only reply that appears to be available at this point to the abstractionist is that her definition is to be taken with a pinch of salt—that is, as mere make-believe and in an instrumental spirit. This, however, takes the abstractionist position too close to that of the direct fictionalist who views “model-talk” to involve acts of make-believe (albeit not necessarily in any instrumental sense). Hence, the abstractionist view of models seemingly struggles with making sense of model-importabilities and ipso facto, with making sense of “differential importability”.

6. Differential Importability and Indirect Fictionalism About Scientific Models

Indirect fictionalists about scientific models have problems with characterizing the legitimacy of the very act of importing model-knowledge as scientific knowledge of reality. For indirect fictionalists, models in science are entitive fictions that “represent” reality by being, in some sense, similar to the latter. How do we spell out this notion of similarity? What makes model-earth similar, as it were, to actual earth? In light of our previous discussions, we first discern whether the similarity is a matter of stipulation or not. Stipulation will again invite the same worries that apparently mar any case for abstractionism. One way in which indirect fictionalists seem able to evade the stipulation-worry is by not requiring that models be “abstract” counterparts of a concrete reality. Entitative fictions, as mere possibilia, could well exist concretely, were they to exist actually. Their status as mere possibilia can even be concrete in that they may exist concretely, i.e., not as mere abstracta, in some merely possible world. Hence, defining, for purposes of science, entitive fictions “as” actual entities does not invite metaphysical or logical illegitimacy. However, other worries remain about instrumentally stipulating entitive fictions as actual realities. Now, one way in which indirect fictionalists seem able to comprehensively evade stipulation-worries is by holding that entitive entities, unlike abstracta, can resemble actual concreta just like any two actual concrete objects may be said to resemble each other. So, merely possible John may differ from actual John only in owning exactly one more Rolex than the latter. Merely possible John and actual John are similar modulo the number of Rolex timepieces owned. Indirect fictionalists, thereby, have the resources to straightforwardly contend that models-qua-fictions resemble targeted domains of reality and, in that sense, represent the latter. However, the fact that the importability of fictional models seems, given the actual practices of science, to be located in the predictions afforded by “use” of such models seems to counteract this relative advantage of indirect fictionalism over abstractionist views. The indirect fictionalist can, perhaps, say that whereas predictive strength of models determines and explains the importability of models, insofar as representing reality is concerned, entitively fictional models can represent reality by being similar to it. This proposal, however, introduces a dilemma. In situations where we have entitively fictional models A and B of some targeted domain T, such that A is more similar to T than is B, but B predicts phenomena in T far better than A does; which one of the models do we choose, and why? Choosing B, but not A, will undermine the “value”, as it were, of similarity and thereby, of representation, whereas choosing A, but not B, will undermine the value of predictive strength. The actual practices of scientists suggest that B will be chosen, for it yields better predictive outcomes. Hence, representativeness of models seems, in practice, to matter less than their importability. This again paves the way for instrumentalist conceptions of models because their representing reality seems to not matter much. Even if models are described as utterly different from their target, their having an acceptable importability will save the day. This dilemma undermines the value of indirect fictionalism about models as a satisfactory explanation for both representativeness and importability of models. If the indirect fictionalist contends that she is happy to just have given an account of the representativeness of models but not of their importability, she is only pleading guilty, albeit happily, of having produced an incomplete account of scientific models. Any theory of models that posits the existence of models must attempt to make sense of, among other things, the vital phenomena of model-importability and differential importability. In seemingly failing to account for their importability, the indirect fictionalist also fails to account satisfactorily for the “differential importability” of models.

8. Solving the Problem of Differential Importability by Invoking “Holistic” Predictive Success

In the foregoing sections, I have attempted to portray how three ontological views of models—abstractionist, indirect fictionalist, and direct fictionalist—fare in mitigating the problem of differential importability. In the said portrayal, however, certain simplifying, or potentially questionable, assumptions were made regarding (A1) the full significance or “import” of the problem of differential importability, (A2) the conditions under which it is palpable and requires resolution, (A3) how generally it interacts with philosophical—as opposed to strictly ontological—views of models, and (A4) the philosophical prudence of constraining the discussion to (a possibly limited number of) de facto extensions of ontologies of models to the epistemology, or other philosophical facets, of the model-target representational relation.

Assumption (A1) implied that the problem of differential importability is “just” the infelicity of accounting for differences in model importability, given some construal of models as abstract entities or entitive fictions. Here, the claim had been that the nature of the representational link between model and target as is posited by certain defenders of abstractionism or indirect fictionalism about models turns out, in some sense, to be both insufficient and unnecessary justification for judgements of comparative, hence differential, importability of two or more models of a given target system. This claim had been argued for under the assumption that ranking models based on their representational fidelity to the target can, in principle, disagree with their ranking based on the (reliable) success of the predictions they afford about the target. This assumption itself presupposes that representation, if posited as a relation from model to target, “must” be understood in terms of “fidelity”, “accuracy”, or some minimal notion of “correspondence”, as opposed to more heuristic idioms. The assumption (A2), to be precise, had been the above-mentioned assumption about comparative fidelity-success divergence and the correspondence notion of model-target relations of representation. Assumption (A3) had been the assumption the ontology of models has some uniquely special role to play in sustaining, or resolving, the problem of differential importability. This is apparent in the conclusion that has been drawn about direct fictionalism being relatively better placed than abstractionism and indirect fictionalism in evading the problem “by virtue” of eschewing realist notions of models per se. Assumption (A4) has been the view that the three ontologies of models under discussion are inseparable from the way in which some of their de facto proponents construe model-target relations, and where the relations are deemed representations, how they construe the significance of those representations. It is assumption (A4) that, by implying certain ontologies of models are as condemnable or tenable as are their extension to the nature of representations in a philosophical sense, sustained assumption (A3). This sustenance is appreciated by noting that the bulk, if not all, of the complaints against realist views of models in the context of their interaction with the problem of differential importability were really about the “function” that (some of) the views about model-target representational links they are sometimes de facto coupled with ascribe to those links.

The problem of differential importability, in its full-fledged formulation, is the problem of choosing the justificatory basis for claims of the form, “M is (strictly) more/less importable than M’ in relation to T”, where M and M’ are models of some unique target T. There are at least two distinct bases to choose from: the models’ comparative pragmatic successes, including their attainment of arguably non-epistemic priorities, if any are recognized; and their representational “fidelity” to the target, assuming that the notions of representation presupposed in this comparison are adequately, mutually commensurable. Note that functional views of model-target representation that resist the affirmation of such a fidelity would be immune to the necessity of this choice. Since representation, as far as they are concerned with it—if at all they posit it—is subservient to the pragmatic success of models, functional views would be satisfied to utilize the comparative pragmatic success of the models (assuming the commensurability of the standards presupposed for this success) as justification for comparative importability claims. The problem of differential importability, then, is a problem for informational views of model-target representations, which, owing to their implication that the representation is not only not subservient to pragmatic success of models but is its very explanans, must decide whether representation and success are independent arbiters in comparing importabilities, and if so, which one ought to be privileged, and to what extent.

As may be gauged from the discussions in previous sections, the problem is quite acute when the comparative representational fidelity of models M and M’ to a common target T opposes their comparative pragmatic success. It seems plausible that the informational view, here, must respond with a satisfactory account of how, if representational fidelity explains pragmatic success, can the mentioned opposition occur. This is because, at least prima facie, it seems reasonable to suppose that if the possession of property A explains the possession of property C, then different degrees of C-possession would also be explained by different degrees of A-possession. But in the opposition between fidelity- and success-rankings under consideration, this intuitively plausible proportionality between the degree of explanans-occurrence and the degree of explanandum-occurrence is vitally missing. The informational view can however be taken to require simply that models’ representational fidelity explains the fact that they are pragmatically successful to some positive degree, without also explaining the differences in the positive degrees of that success. Now, suppose that a situation arises where model M has a greater predictive strength than has model M’, but according to some informationally construed notion of representation—say, a certain class of model-target isomorphisms—M has less fidelity to the target T than has M’. Suppose, furthermore, that the notion of representation is suitably tapered to the pragmatic uses intended for the models M and M’, so that it is the set of pragmatic purposes P commonly intended for both M and M’, that the sort of representational fidelity they are expected to have to T has been deliberately based on. Since, ex hypothesi, both M and M’ represent T—albeit to divergent degrees—in an informational sense, both are minimally pragmatically successful—albeit to divergent degrees—as already assumed. Also, note that a choice has to be made—if at all representational fidelity and predictive success are both considered at least minimally adequate guides to models’ comparative importability—between the fidelity-ranking and the success-ranking, since neither agrees with the other. But if the fidelity ranking of M and M’ here is used as a justification for claims about their comparative importability, then predictive success will be eschewed in terms of (a certain notion of) informational representation. This would seem to be all well and good if the pragmatic context P from the very beginning only required a model with a degree of predictive success less than, and of representational fidelity more than, what the model—M’—with the lesser predictive success but greater representational fidelity has managed to offer. However, the issue here is that since representation is being assumed to be discernible as coming in lesser or greater degrees, there has to be some standard for, as it were, “measuring” those degrees. In other words, the notion of representational fidelity has to be an operable, measurable one, suggesting—prima facie—that the notion of (approximate) truth, the ground of that fidelity, has also to be equally operable and measurable. And this prima facie plausibility is very likely a conceptual triviality since what is at stake is not representation per se, but representational “fidelity”—something that seems conceptually grounded in some notion of correspondence not alien to any of the standard correspondence theories of truth.

Before one hastens to conceive of how the informational view can still have truth operationalized without exhausting its operational base with empirical testing of predictions, they would do well to imagine the consequence of such a partially empirical operationalization for (standard) “scientific” realism. The realist reading of the informational view would probably not construe “partially” as applying to the class of truths upheld in science, but rather, the class of operations necessary for determining whether anything is a scientific truth. That is, the realist probably cannot afford to have a subset of scientific truths that are in no way established by predictive success in empirical settings, but may allow the testing of some prediction to be only one of the operations to be used—as a matter of methodological necessity—for the discernment of something as a scientific truth. But this qualified, realist partiality is incompatible with informational representation being a desideratum independent from a rather holistic sort of predictive success. For, if informational representation is required in some context of modeling, the present qualification on the realist’s part requires the “epistemic” justification for accepting such a representation to be necessarily composed of predictive success, at least partially. Even if such a representation is discerned as a true explanatory claim, or a means of truly understanding, the target—as opposed to rendering it merely predictable—the discernment would necessitate, by the present realist requirement that truth be necessarily discerned (even if partly) by successful predictions, predictive success not only in terms of the model being predictively successful enough for the truth of the representation to have a non-negligible prior probability, but also in terms of the representation’s “content” being systematic and clear enough, for the generation of further predictions about the target “if” the prior probability of the representation is taken by the realist as enough “provisional evidence” for its (more/less approximate) truth. Hence, given that the realist does concede a necessary partial operationalization of truth in terms of predictive success, even such representational aims as the provision of understanding and explanation are ultimately accepted on the basis of how reliably successful the predictions derived from the model turn out to be.

On the other hand, understanding or explanation is itself often a desideratum in modeling, on the grounds that securing it is more likely to lead to more and clearer predictions—and the pragmatic aim of potentially more control over the target’s behavior. Note, however, that in all of this, the ultimate decider of how importable a model is, even if its representations are parsed in informational terms, are the successful predictions derived from the model, or the potential to generate more such predictions: with both the actual success and the potential for success, co-constituting a holistic metric of predictive success. Note that even though truth, in the present context, is taken to be operationalized necessarily in terms of predictive success, nothing is said for, or against, the claim that truth—thus operationalized—coherently “explains” predictive success. This is because there might exist truth as correspondence that is necessarily discerned through empirical investigations and predictions but nonetheless grounds their nature, constraints, and success. It is just that we do not seem to know what the universally valid notion of correspondence is, and whether its discernment always needs empirical investigations. But a negative take on the latter question is not something the standard realist could plausibly afford—at least with respect to scientific truths—without introducing an unnecessary transempiricism into science. The point being made so far has been that the model’s representations can still be construed in an informational sense—as grounded in (approximate) truth—while the partial operationalization of that truth in terms of predictive success is also taken to be sufficient epistemic justification for believing provisionally in that construal, at least until the belief somehow becomes infallible, and there arises to the believer’s awareness and ultimate evidence for that infallibility.

Realize that, over the argument being developed, the realist has been shown to stray so much from his epistemic confidence in non-provisionally capturing representation or truth “within science” that what was before framed as his dilemma between ranking of representational fidelity and ranking of predictive success should now only be seen as one between the ranking of “provisionally confirmed” representational fidelity and the ranking of predictive success. This entire argument runs quite analogously even if predictive success and representational fidelity never spoke against each other with respect to two or more models: that is, if it were always the case that M exceeded M’ in terms of fidelity, if M exceeded M’ in terms of success. Because even then, the ranking of fidelity would invite a need for its, and therefore truth’s, operationalization. All of this very strongly seems to show that if comparative importability is to be justified on grounds of comparative “representational fidelity” at all, the closest one might get is to justify it on grounds of provisionally empirically confirmed representational fidelity, and hence, acknowledge the centrality, indispensability, and exhaustive involvement of judgements of comparative predictive success in justifying comparative model importabilities.

The argument in this section suggests that while the realist and antirealist alike should have the same procedural idea of model importability comparisons—namely, the comparisons of measured predictive successes—they differ in terms of what they think they are “ultimately measuring”, and whether there is anything more ultimate than predictive success being measured. Plausibly, only the standard realist needs to think that there is something more ultimate being measured—albeit fallibly—namely, (more or less accurate) informational representation, or (more or less approximate) correspondence-truth. The argument has also assumed that the potential for predictive success to be subject to “underdetermination” by data is an issue at least prima facie orthogonal to the reasonableness of positing that success as an operationalization of representational fidelity or correspondence truth. This seems unproblematic because, if underdetermination plagues the importability-comparisons of incompatible, but more or less equally predictively successful, models, the realist faces the problem of discerning how a unique truth about the target can be (approximately) represented—in an informational sense—in incompatible ways. But this is not at all the problem that has been addressed in this section. The problem that has been tackled is that: if the (standard) realist both defends a unique notion of truth and intends us to take seriously his talk of “comparing” truth and informational representation, exactly what should his “procedural” understanding of comparing model-importabilities be? The answer to this question can be discerned, even if the realist’s defense of unique truth with a unique operationalization fails on separate, independent grounds.