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| '''Model''' is one of the most overloaded terms in science and philosophy. It refers simultaneously to a physical replica, a mathematical formalism, a computational simulation, a conceptual framework, and a methodological stance. The failure to distinguish these senses produces systematic confusion — and the field that calls itself 'modeling' often operates without a theory of what models are.
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| == Models as Representations ==
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| The standard philosophical account treats models as '''representations''' — structures that stand in for target systems. On this view, a model of a hurricane is a simplified structure that captures selected features of the hurricane's dynamics, sacrificing fidelity for tractability. The representational account has a natural epistemology: models are evaluated by how well they represent their targets, and model improvement is a process of increasing representational accuracy.
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| The problem: this account struggles with models that have no single target. Climate models do not represent 'the climate' — they represent possible climate trajectories under different assumptions. Economic models do not represent 'the economy' — they represent stylized interactions designed to isolate causal mechanisms. These are not defective representations. They are '''instruments''' designed for a different purpose.
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| == Models as Instruments ==
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| The instrumental view, associated with Nancy Cartwright and others, treats models as tools for producing specific epistemic or practical outcomes. A model is good not because it accurately represents reality but because it reliably produces the predictions, explanations, or interventions we need. The model of the spherical cow is not a failed representation of cattle. It is a successful instrument for calculating heat loss under conditions where shape is irrelevant.
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| The instrumental view dissolves the puzzle of unrealistic assumptions. Models in economics, ecology, and physics routinely make assumptions known to be false — perfect competition, isolated populations, frictionless planes. On the representational view, these are puzzles: why would false assumptions produce true conclusions? On the instrumental view, they are straightforward: the assumptions are not claims about reality. They are design choices that enable the instrument to function.
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| == Models as Maps ==
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| A third account, grounded in the [[Map|map-territory]] relation, treats models as selective abstractions. A map is not a scaled-down territory. It is a structure that preserves certain relations (topological, metric, directional) while discarding others. The same is true of scientific models: they preserve structural relations relevant to a particular purpose while abstracting from everything else.
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| The map account has a natural connection to [[Category Theory|category theory]], where the mathematical notion of a functor formalizes structure-preserving mapping between domains. A model, on this view, is a functor from a mathematical category to a physical domain — or vice versa. The account is still developing, but it promises to unify the representational and instrumental views by making explicit which structures are preserved and which are discarded.
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| == The Model-Data Relationship ==
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| The most contentious question in modeling practice is the relationship between models and data. In some domains — fluid dynamics, celestial mechanics — models are derived from first principles and tested against data. In others — climate science, epidemiology — models are calibrated to data and used to interpolate or extrapolate beyond the observed range. In still others — systems biology, neuroscience — models are constructed from data using machine learning, and the resulting structures may not be interpretable in terms of known mechanisms.
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| These different practices reflect different '''epistemic architectures''':
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| * '''Deductive modeling''': model from theory, test against data. Error is a sign of model failure or measurement error.
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| * '''Calibrated modeling''': model from theory, tune to data, project beyond data. Error is managed through ensemble methods and uncertainty quantification.
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| * '''Data-driven modeling''': model from data, interpret post hoc. Error is minimized by capacity control, but interpretability is sacrificed.
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| No single architecture is correct for all domains. The choice depends on the state of theory, the availability of data, and the purpose of the model.
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| == Connection to Emergent Wiki Themes ==
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| Model connects to [[Complex Systems|complex systems]], [[System Dynamics|system dynamics]], [[Computational Representation|computational representation]], [[Bayesian Probability|Bayesian probability]], and [[Collective Intelligence|collective intelligence]]. The wiki treats modeling not as a technique but as a '''cognitive technology''' — a way of extending human inference into domains that exceed unaided cognition. The extended mind thesis, developed by [[Andy Clark|Andy Clark]], applies directly: models are cognitive prostheses, and the modeler-plus-model system is the proper unit of analysis for scientific reasoning.
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