The artifactual approach focuses on how conceptual, theoretical, mathematical or computational access to some system of interest is gained through the employment of diverse epistemic tools. Apart from evading the difficulties concerning representation, the artifactual approach to modeling has other important benefits. First, it is able to accommodate many modeling practices that seem epistemically inferior according to representationalist criteria. For example, abstract, highly idealized models have been subject to longstanding criticism in both the biological sciences and economics. The artifactual approach is able to provide a more flexible account of the epistemic advantages of modeling in those fields. Second, a big part of the modeling endeavor across the sciences investigates various possibilities, involving not only actual entities and processes, but also non-actual ones. The representational model-target dyad does not seem to furnish an adequate unit of analysis for models without any actual determinable targets.
The artifactual approach to modeling stands on two pillars: (i) the constrained construction of a model that is due to its intended use(s), and (ii) the representational tools used in producing a model.Footnote 3 In this section, I will discuss both of them, proceeding then to consider the question of justification as well as the modal dimension of modeling.
From the artifactual perspective, models are particular kinds of epistemic artifacts that function as erotetic devices. That is, they are artificial systems of dependencies that are constrained in view of answering a pending scientific question, motivated by theoretical and/or empirical considerations. Typically, a lot of theoretical and empirical knowledge is already built into the model, both in terms of its specific construction and the question(s) it is designed to investigate. Much of this knowledge is implicit, and can only be appreciated by competent users in the context of particular scientific practices. Given this built-in knowledge as well as the erotetic function of models, the problem of representation is not as acute as it seems: models are not isolated entities in need of connection to worldly systems by a relation of representation. The epistemological puzzle of how the representational relationship between a model and the world should be analyzed becomes that of studying how the model construction facilitates the study of pending scientific questions.
The notion of a constraint is crucial for such facilitation: in order to achieve its epistemic aims the model needs to be properly limited. The philosophical discussion of idealization has paid attention to the constrained nature of models, highlighting how models are designed to isolate some supposedly relevant features of the system of interest, disregarding and/or distorting the rest (Cartwright, 1999; Mäki, 1992; Strevens, 2008). On the other hand, other philosophers have emphasized that the use of mathematical and statistical methods entails distortion, often with considerable epistemic benefits (McMullin, 1985; Rice, 2018). While in the discussion of idealization, philosophers have tended to examine either the benefits or shortcomings of idealization, from the artifactual perspective, idealizations typically are epistemically both beneficial and detrimental (Carrillo & Knuuttila, forthcoming). They enable certain questions to be inquired while overlooking others. This epistemic two-sidedness does not just concern idealizations, but the use of representational tools more generally.
Consequently, in contrast to the representational approach that zeroes in on the relationship of representation, the artifactual approach attends to the enablings and limitations of the representational tools that scientists employ in model construction. It recognizes that in order for a model to provide access to the actual or possible aspects of the world, it needs to have a sensuously available workable dimension rendered by various representational tools. In highlighting such a concrete dimension of models, the artifactual approach follows Morrison and Morgan (1999), who called attention to how scientists learn by building and manipulating models. This constructive and interventional side of modeling is crucial for the epistemic value of models: scientists gain knowledge through investigating and articulating different relationships built into the model. There is no need to suppose that the only route to knowledge is through (at least) partially accurate reproduction of the actual state of affairs in the world. In contrast, models as artifacts allow epistemic access to many theoretical and empirical problems by enabling various inferences (Suárez, 2004), providing novel results, prompting new experiments – and, in so doing, they possess considerable modal reach (Godfrey-Smith, 2006).
Representational tools and internal vs. external representation
The representational tools used in model construction can be analyzed according to the modes and media they embody. The representational mode refers to the different symbolic or semiotic devices (pictorial, linguistic, mathematical, diagrammatic etc.) with which various meanings or contents can be expressed. Such representational modes are embedded in representational media that encompasses the material means with which representations are produced (such as ink on paper, a digital computer, biological substrata and so forth). For instance, natural language is a representational mode that can be realized by different media, either as speech or as writing (Knuuttila, 2011).Footnote 4 Materiality may play different epistemic roles depending on the type of a model in question, as shown below by the synthetic biology case. The synthetic repressilator and the electronic repressilator both instantiate the same ring oscillator design, i.e. the same representational mode, yet they are implemented in different media, enabling different kinds of inferences.
It may sound contradictory to claim that the artifactual approach tries not to invoke representation, yet addressing, at the same time, representational tools as central for the epistemic access to the world. No such contradiction is involved, however. In order to see this, two different notions of representation need to be distinguished: internal and external.
Internal representation has to do with how various kinds of sign-vehicles or representational devices are used to make meaning and convey content.Footnote 5 In talking about ‘content’ I do not want to imply that any sign-vehicle, or representational device, would carry or correspond to a stable unit of content; meaning-making always depends on the linguistic and other practices in place, as well as the context of use. By external representation, I refer to the relationship of a model to a real-world target system, the question on which the philosophical discussion has largely concentrated. To use a toy example of the differences between these two notions of representation, let us consider traffic signs. The meaning of a Dangerous Turn road sign can be understood internally in relation to the system of traffic signs (the system itself being grounded on automobile traffic, the practices of regulating it, possible forms of roads, etc.). The sign has the function of warning of the dangerous turn only when placed in an appropriate place, in which case it can be taken as an external representation of a nearby dangerous turn, whose intended use is to caution drivers of it. But, if detached from such a context, its meaning would still be understood by people knowledgeable of the system of traffic signs.
Philosophy of science has not explicitly distinguished between external and internal representation—with the exception of the discussion of fiction.Footnote 6 One may wonder whether philosophers’ strong conviction that modeling has something to do with representation is at least partially due to such conflation. Nevertheless, the fact that something may be internally represented within a model without necessarily representing the actual state of worldly affairs opens up the prospect of conceiving modeling as a practice of exploring the possible.Footnote 7
A proponent of the representational approach might be fine with all of the aforementioned aspects of the artifactual approach, but may still urge the artifactualist to account for the various inferences, new results and learning derived from models. After all, the representational relation is also expected to provide justification for model-based results – except for the deflationary pragmatists, who separate the analysis of the notion of representation from its success. The traditional representational story is neatly packaged, but comes too cheaply. From the artifactual perspective, any (external) representational relation a model might bear to some worldly target is always an accomplishment to be independently justified – instead of being a privileged relation providing a warrant for the truth or correctness of model-based results. The justification of models, and the interpretations based on them, is two-fold. It is partly built-in due to the already established theoretical, empirical and representational resources called upon and utilized in model construction (Boumans, 1999), and partly a result of the triangulation of different epistemic means: other models, experiments, observations and background theories. Such processes of triangulation are distributed in terms of epistemic labor, likely very complex and indirect, and usually inconclusive in character.
The artifactual account and the modal dimension of modeling
That modeling involves the study of different possibilities, and often only presents how-possibly explanations, has been recognized by many philosophers of science. However, only relatively recently has there been a more concerted effort to understand the modal nature of modeling. For any progress in accounting for how models enable the study of possibilities, one would first need to know what kind of possibility is at stake. Often when modelers espouse possibility claims, their function may only be apologetic, expressing the scientists’ lacking or only partial commitment to the underlying assumptions or results of the model (Gruene-Yanoff, 2019). Another trivial use of the notion of possibility is that of considering how-possibly models as incomplete how-actually models (e.g. Craver & Darden, 2013). From the modal perspective, the distinction between epistemic possibility and objective possibility seems more far-reaching (Sjölin Wirling & Gruene-Yanoff, 2021). Epistemic possibility, in the scientific context, depends on scientific knowledge of the actual state of the world. Any scientific claim that is not ruled out by scientific knowledge is epistemically possible. Consequently, there can be several epistemically possible models of a certain actual target system. In contrast, objective possibility can also concern some unactualized state of the world. (Verrault-Julien & Gruene-Yanoff, forthcoming). As a result, there can be (epistemically) possible models of actual targets and models of (objectively) possible targetsFootnote 8 (Gruene-Yanoff, 2019). Tackling the latter kinds of models seems more challenging from the representational perspective than from the artifactual perspective, since the target system is nonexistent, and only possible.
What are models then addressing, if not actual target systems? In discussing what she calls modal understanding, Le Bihan (2016) notices how the understanding of phenomena and the understanding of the actual world are often conflated. Her account of modal understanding addresses phenomena instead of the actual world, and it does so in terms of dependency structures that enable scientists “to navigate the possibility space” (122). With such “navigation” she refers to knowledge of (i) how a particular dependency structure gives rise to (some subset of) a phenomenon (ii), how the dependency structures are related to each other, and (iii), “how some general constraints apply to the entirety of the possibility space.” (118) The increasingly popular talk of “possibility spaces” is often only hypothetical, bound to a synchronic view of possibilities, and does not apply to all modal reasoning. That said, Le Bihan’s idea of modal understanding being gained from the knowledge of how different dependency structures are able to engender certain kinds of phenomena is enlightening. Such modal understanding fits the artifactual approach, which approaches models as purposefully constructed systems of interdependencies designed to answer some pending scientific questions. These scientific questions typically inquire into how certain phenomena could be generated or maintained, or how robust it is.
Obviously, the question then becomes that of whether the dependency structures studied through modeling really do capture some objective possibilities. Massimi (2019) has suggested that “physical conceivability”, either law-bounded or law-driven, could be crucial for such inferences. While invoking law-boundedness, or drivenness, does not suit many other disciplines in the same way as it does physics, the question of conceivability is crucial for modal inferences nevertheless – as the following two case studies will show. Both the economic and biological models discussed below lay out an artificial system of interdependencies able to generate certain phenomena of interest. It is difficult to point out any actual target systems for either of these models, as they instead appear to address objective possibilities.