Construct · 3 fields · 3 citations
One name. Different field. Different construct. One map.
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In model theory a model of a theory is a structure, a domain of objects together with interpretations of the theory's symbols, in which every one of the theory's axioms comes out true. Tarski's account of truth in a structure, in The Semantic Conception of Truth (1944), makes the notion precise: a sentence is satisfied by a structure or it is not, and a model is a structure that satisfies the lot. The referent is a mathematical structure, and the direction matters. The theory is given first, and the model is whatever answers to it by making its sentences true. This is close to the opposite of the scientific meaning, where the world is given first and the model is built to answer to it.[1]
In statistics and machine learning a model is a mathematical function fitted to data, its parameters estimated from a sample, used to predict new cases or to summarize how variables relate. Box's Science and Statistics (1976) argued for parsimonious but effective models and for worrying selectively about their inadequacies: the model is an approximation kept for what it does, not for being true. The referent is a fitted function, and the data come first. The model answers to the data, not to a set of axioms, and it is judged by fit and by how well it predicts cases it was not fitted on. A trained model and a logician's model share the word and almost nothing else, since one is prized for being useful though wrong and the other is true by construction.[2]
In the philosophy of science a model is a representation of a target system that scientists reason with in place of the system itself, such as the billiard-ball model of a gas, the Bohr model of the atom, or a predator-prey model of a population. Frigg and Hartmann's Models in Science (2020) treat such models as idealized stand-ins that resemble their targets in some respects and depart from them in others. The referent is a representation, and the world is given first: the model answers to the world by standing in for it. This is why the arrow runs the opposite way from the logical meaning. There the theory is given and the model satisfies it; here the system is given and the model represents it.[3]
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