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The philosophy of models and representation is the branch of philosophy of science that asks what scientific models are, what they do, and how—or whether—they represent the world. It is not primarily about the practical craft of building models, nor about the psychology of scientific creativity. Its central concern is the relationship between the abstract, simplified, often mathematical things scientists call models and the complex, concrete systems those models are meant to illuminate. The field sits at the intersection of epistemology (what we can know), ontology (what exists), and semantics (how symbols acquire meaning), and it has become one of the most active areas in contemporary philosophy of science.
Scientific models are everywhere. Physicists model the atom as a miniature solar system, climate scientists model the Earth's atmosphere as a system of coupled differential equations, economists model markets as equilibria of rational agents, and biologists model population dynamics with logistic curves. These models are not the phenomena themselves, nor are they straightforwardly true descriptions of them. A model of a pendulum that ignores air resistance is not a literal picture of any real pendulum; a climate model that divides the ocean into grid cells of one degree does not describe any actual ocean. Yet scientists routinely learn from such models, make predictions with them, and treat them as providing genuine understanding.
This raises a cluster of questions. What kind of thing is a model? Is it a set of equations, a physical object, a fictional story, a set of rules, or something else entirely? What makes a model good? Is it accuracy, predictive success, explanatory power, or something more pragmatic? And most fundamentally: in what sense does a model represent its target? A photograph represents by resemblance, a map by convention, a sentence by truth conditions. Models seem to represent in some other way—partly by being similar to their targets, partly by being useful fictions, partly by being tools for inference. The philosophy of models and representation is the sustained attempt to answer these questions.
The stakes are not merely academic. If models are our primary means of understanding complex systems, then the nature of that understanding depends on how models work. If models represent by idealization and abstraction, then the distortions they introduce are not defects but features—yet this raises the question of how we can trust conclusions drawn from deliberately false premises. The field also bears on debates about scientific realism: if our best theories are built from models that are known to be false in various respects, what grounds do we have for believing those theories describe the world?
The modern field emerged from a longer history of thinking about how science relates to its objects. In the nineteenth century, scientists and philosophers debated whether scientific theories were literally true descriptions of hidden mechanisms or merely useful instruments for organizing observations. This debate—often framed as realism versus instrumentalism—set the stage, but it did not yet treat models as a distinct topic. Theories were the unit of analysis, and models were seen either as provisional stepping stones toward theories or as pedagogical aids.
A significant shift came in the mid-twentieth century with the rise of the "syntactic" view of theories, associated with logical empiricism. On this view, a scientific theory is a formal axiomatic system: a set of sentences in a logical language, with theoretical terms partially defined by correspondence rules that connect them to observation. Models, in this framework, were secondary. A model was simply an interpretation of the theory's formal language—a set-theoretic structure that made the axioms true. This made models logically tidy but philosophically thin. The model of a theory was just one of many possible interpretations, and the interesting questions were about the theory itself.
The syntactic view came under sustained attack in the 1960s and 1970s, most influentially by Patrick Suppes, Bas van Fraassen, and Frederick Suppe, who developed what became known as the "semantic" view of theories. On this view, a theory is not a set of sentences but a family of models—mathematical structures that satisfy the theory's laws. The theory is identified with its class of models, and the models are the primary representational vehicles. This reorientation had profound consequences. It made models central rather than peripheral, it accommodated the fact that scientists often work with models without a fully axiomatized theory, and it provided a natural way to think about theories that are not fully formalized. The semantic view became the dominant framework in the philosophy of science for several decades, and it remains influential, though it has itself been criticized and modified.
A third major development, beginning in the 1980s and accelerating through the 1990s, was the turn toward scientific practice. Philosophers such as Nancy Cartwright, Ian Hacking, and Margaret Morrison argued that the semantic view was still too abstract and too focused on the logical structure of finished theories. Real science, they pointed out, is full of models that are not neatly derived from theories, that are constructed ad hoc for specific problems, that combine incompatible assumptions, and that are often more useful than the theories they supposedly instantiate. This "practice turn" drew on detailed case studies from physics, biology, and economics, and it shifted attention from the logical relationship between models and theories to the concrete activities of building, manipulating, and using models. It also opened the door to a more pluralistic understanding of what models are and how they work.
The field today is organized less by a single dominant paradigm than by a set of overlapping approaches, each addressing a different aspect of the problem. These approaches are not mutually exclusive, and many philosophers draw on several of them.
The semantic view, in its various forms, treats models as mathematical structures. A model is a set of objects with relations and functions defined on them, and a theory is the class of all models that satisfy its laws. This approach has the virtue of clarity: it gives a precise account of what a model is and how models relate to theories. It also handles the fact that the same theory can be formulated in different ways—the models are the same even if the sentences differ.
The semantic view has been developed in two main variants. The "state-space" approach, associated with Suppes and van Fraassen, identifies a model with a set of possible states and a set of laws that constrain which states are physically possible. The "structuralist" approach, associated with Joseph Sneed and Wolfgang Stegmüller, adds a distinction between the "core" of a theory (its mathematical structure) and its "intended applications" (the real-world systems it is meant to cover). Both variants share the core claim that models are structures and that representation is a matter of structural correspondence between the model and the world.
The semantic view's great strength is its account of the relationship between models and theories. Its great weakness is its account of representation itself. Saying that a model represents its target because they share a structure raises the question of what counts as a relevant structure and why. A mathematical structure can be mapped onto the world in indefinitely many ways, and the semantic view has difficulty explaining why some mappings are representational and others are not. Critics have also argued that the view is too static: it describes models as finished structures, but scientists often learn by manipulating models, changing parameters, and exploring their behavior, which suggests that models are more like tools than like pictures.
The most intuitive answer to the question of how models represent is that they resemble their targets. A model of a bridge represents the bridge because it is similar to it in relevant respects; a model of an economy represents the economy because its equations capture relevant patterns. This "similarity" approach, most prominently defended by Ronald Giere, holds that representation is a matter of partial, selective similarity. A model does not resemble its target in every respect—it is deliberately simplified—but it resembles it in the respects that matter for the purpose at hand.
The similarity approach has the virtue of explaining why models are useful: they are useful because they are like their targets in the right ways. It also explains why there can be many different models of the same system: different purposes select different respects of similarity. But the approach faces a serious problem. Similarity is a symmetric relation—if A is similar to B, then B is similar to A—but representation is asymmetric: the model represents the target, not the other way around. Moreover, similarity is cheap: any two things are similar in some respect. The approach needs to say which respects of similarity are representational and why, and it has struggled to do so without appealing to the intentions of the modeler, which moves the problem rather than solving it.
A family of approaches, often grouped under the label "pragmatic," locates representation not in the model itself but in its use. On this view, a model represents because scientists use it to stand for something else, to draw inferences about it, or to intervene on it. The most influential version is the "inferential" account, associated with Mauricio Suárez, which holds that representation is a matter of the model's capacity to support valid inferences about its target. A model represents a system if, by manipulating the model, one can draw conclusions about the system that are reliable enough for the purposes at hand.
This approach has several advantages. It explains the asymmetry of representation: the model represents because it is used in a particular way, not because of any intrinsic property. It accommodates the fact that models can be wildly inaccurate in some respects yet still represent well for specific purposes. And it connects representation to the actual practices of scientists, who use models to calculate, predict, and explain. Its weakness is that it risks making representation too subjective: if representation is just a matter of use, then anything can represent anything if we use it that way. Defenders respond that the use must be constrained by the model's actual capacities—the model must genuinely support the inferences it is used for—but critics argue that this reintroduces a notion of correctness that the pragmatic approach cannot fully account for.
A more recent and increasingly influential approach treats models as akin to fictions. Just as a novel creates a fictional world that is not literally true but can be true "in the story," a model creates a fictional system that is not literally real but can be explored and described. This view, associated with philosophers such as Roman Frigg and Adam Toon, draws on the philosophy of fiction to explain how models work. A model of a pendulum is like a story about a pendulum: it describes a system that does not exist, but the description is internally coherent and can be explored to learn about the fictional system's properties.
The fiction view has several attractions. It explains why models can be false yet useful: they are not claims about the world but descriptions of fictional systems. It explains why models can be explored and manipulated: we can reason about fictional systems just as we reason about fictional characters. And it explains why models can be partial and inconsistent: fictions need not be complete or consistent. But the view faces a challenge: how does a fiction tell us about the real world? A novel about a fictional detective does not teach us about real detectives unless we draw analogies, and the same seems to hold for models. The fiction view needs an account of how fictional systems connect to real ones, and critics argue that this connection is precisely the problem of representation that the view was supposed to solve.
A broader framework, sometimes called "model-based science," treats models not as a special kind of representation but as the fundamental units of scientific understanding. On this view, science does not proceed by discovering laws and then applying them; it proceeds by constructing models and refining them. Models are the primary cognitive tools of science, and theories are best understood as families of models or as resources for building models. This approach, associated with philosophers such as Mary Morgan and Margaret Morrison, emphasizes the autonomy of models: models are not derived from theories but are constructed from a variety of sources, including analogies, metaphors, and empirical data.
This approach is less a rival to the others than a reorientation of the field. It shifts attention from the question "How do models represent?" to the question "How do models work?"—and it answers that question by examining the diverse roles models play in scientific practice. Models are used to explore possibilities, to make predictions, to explain phenomena, to guide experiments, to communicate results, and to integrate knowledge from different fields. The model-based approach is thus more pluralistic than the others: it does not expect a single account of representation to cover all cases, because models do too many different things.
The field today is characterized by productive disagreement. The semantic view remains the default framework in much of the philosophy of science, but it has been substantially modified by the practice turn. The similarity approach has been largely abandoned as a complete account of representation, but it survives as an element of more complex accounts. The pragmatic and inferential approaches have gained ground, particularly among philosophers who study modeling in the special sciences. The fiction view is the most active area of new research, though it remains controversial.
Several debates cut across these approaches. One concerns the role of idealization. All models idealize—they simplify, distort, and omit—but philosophers disagree about whether idealization is a necessary evil or a positive virtue. Some argue that idealization is a temporary expedient that should be eliminated as science progresses; others argue that idealization is essential to understanding, because the world is too complex to be grasped directly. This debate connects to questions about the aims of science: if the goal is truth, idealization is a problem; if the goal is understanding, idealization may be a solution.
Another debate concerns the relationship between models and theories. The semantic view treats models as the content of theories, but the practice turn has shown that many models are not derived from theories and may even be inconsistent with them. Some philosophers now argue that theories and models are distinct kinds of things: theories are general frameworks, while models are specific tools for specific problems. This raises the question of how theories constrain models, and whether a model can be good even if it is not derived from any theory.
A third debate concerns the ontology of models. Are models abstract objects, concrete objects, or something in between? The semantic view treats them as abstract structures; the fiction view treats them as fictional entities; some philosophers treat them as concrete things—diagrams, computer programs, physical replicas. This debate matters because it affects what we think scientists are doing when they build and manipulate models. If models are abstract, then building a model is a matter of defining a structure; if they are concrete, it is a matter of constructing an object.
The field has also expanded beyond its traditional focus on physics. Philosophers of biology, economics, and climate science have developed accounts of modeling that reflect the distinctive features of their disciplines. In biology, models are often qualitative and mechanism-based rather than mathematical; in economics, models are often highly idealized and explicitly unrealistic; in climate science, models are computational and are validated by ensemble methods rather than by direct experiment. These developments have enriched the field but have also made it harder to maintain a single unified account of representation.
The current landscape is thus pluralistic and pragmatic. Most philosophers of models and representation accept that no single account captures everything that models do, and they have largely abandoned the search for necessary and sufficient conditions for representation. The field has instead become a set of overlapping investigations into the many ways models work, the many purposes they serve, and the many relationships they bear to the world. This pluralism is not a failure of the field but a reflection of its subject matter: models are diverse tools, and a philosophy that respects their diversity is more likely to illuminate them than one that forces them into a single mold.