Out of Context: On Models (Definitions)

"A material model is the representation of a complex system by a system which is assumed simpler and which is also assumed to have some properties similar to those selected for study in the original complex system. A formal model is a symbolic assertion in logical terms of an idealised relatively simple situation sharing the structural properties of the original factual system." (Arturo Rosenblueth & Norbert Wiener, "The Role of Models in Science", Philosophy of Science Vol. 12 (4), 1945)

"By a model is meant a mathematical construct which, with the addition of certain verbal interpretations, describes observed phenomena." (John Von Neumann, "Method in the Physical Sciences", 1955)

"A model is essentially a calculating engine designed to produce some output for a given input." (Richard C Lewontin, "Models, Mathematics and Metaphors", Synthese, Vol. 15, No. 2, 1963)

"A model is an abstract description of the real world. It is a simple representation of more complex forms, processes and functions of physical phenomena and ideas." (Moshe F Rubinstein & Iris R Firstenberg, "Patterns of Problem Solving", 1975)

"A model is an attempt to represent some segment of reality and explain, in a simplified manner, the way the segment operates." (E Frank Harrison, "The managerial decision-making process", 1975)

"A mathematical model is any complete and consistent set of mathematical equations which are designed to correspond to some other entity, its prototype."  (Rutherford Aris, "Mathematical Modelling", 1978)

"A model […] is a story with a specified structure: to explain this catch phrase is to explain what a model is." (Allan Gibbard & Hal R. Varian, "Economic Models", The Journal of Philosophy, Vol. 75, No. 11, 1978)

"The model is only a suggestive metaphor, a fiction about the messy and unwieldy observations of the real world." (Edward Beltrami, "Mathematics for Dynamic Modeling", 1987)

"[…] a model is the picture of the real - a short form of the whole. Hence, a model is an abstraction or simplification of a system. It is a technique by which aspects of reality can be 'artificially' represented or 'simulated' and at the same time simplified to facilitate comprehension." (Laxmi K Patnaik, "Model Building in Political Science", The Indian Journal of Political Science, Vol. 50, No. 2, 1989) 

"A model is generally more believable if it can predict what will happen, rather than 'explain' something that has already occurred." (James R Thompson, "Empirical Model Building", 1989)

"A model represents reality for the given purpose; the model is an abstraction of reality in the sense that it cannot represent all aspects of reality." (Jeff Rothenberg, "The Nature of Modeling. In: Artificial Intelligence, Simulation, and Modeling", 1989)

"A model is a deliberately simplified representation of a much more complicated situation." (Robert M Solow, "How Did Economics Get That Way and What Way Did It Get?", Daedalus, Vol. 126, No. 1, 1997)

"A model is an external and explicit representation of part of reality as seen by the people who wish to use that model to understand, to change, to manage, and to control that part of reality in some way or other." (Michael Pidd, "Just Modeling through: A Rough Guide to Modeling", Interfaces, Vol. 29, No. 2, 1999)

"A model is an imitation of reality and a mathematical model is a particular form of representation." (Ian T Cameron & Katalin Hangos, "Process Modelling and Model Analysis", 2001)

"A model is a simplification or approximation of reality and hence will not reflect all of reality." (Kenneth P Burnham & David R Anderson, "Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach" 2nd Ed., 2005)

"A model is a representation in that it (or its properties) is chosen to stand for some other entity (or its properties), known as the target system. A model is a tool in that it is used in the service of particular goals or purposes; typically these purposes involve answering some limited range of questions about the target system." (Wendy S Parker, "Confirmation and Adequacy-for-Purpose in Climate Modelling", Proceedings of the Aristotelian Society, Supplementary Volumes, Vol. 83, 2009)

"A theory is a set of deductively closed propositions that explain and predict empirical phenomena, and a model is a theory that is idealized." (Jay Odenbaugh, "True Lies: Realism, Robustness, and Models", Philosophy of Science, Vol. 78, No. 5, 2011)

"A mathematical model is never a completely accurate representation of a physical situation - it is an idealization." (James Stewart, "Calculus: Early Transcedentals" 8th Ed., 2016)

"A mathematical model is a mathematical description (often by means of a function or an equation) of a real-world phenomenon such as the size of a population, the demand for a product, the speed of a falling object, the concentration of a product in a chemical reaction, the life expectancy of a person at birth, or the cost of emission reductions. [...] A mathematical model is never a completely accurate representation of a physical situation - it is an idealization." (James Stewart, "Calculus: Early Transcedentals" 8th Ed., 2016)