Models vs Theory

“A theory is just a mathematical model to describe the observations.” (Karl Popper)

"A theory is a purely mental image of how something should be." (Adrian Bejan)

“I am of the opinion that the task of the theory consists in constructing a picture of the external world that exists purely internally and must be our guiding star in all thought and experiment.” (Ludwig E Boltzmann)

"[...] we and our models are both part of the universe we are describing. Thus a physical theory is self referencing, like in Gödel’s theorem. One might therefore expect it to be either inconsistent or incomplete. The theories we have so far are both inconsistent and incomplete." (Stephen Hawking, “Godel and the End of the Universe”) [Link]

“With each theory or model, our concepts of reality and of the fundamental constituents of the universe have changed.” (Stephen Hawking & Leonard Mlodinow, “The Grand Design”, 2010)

"A theory has only the alternative of being right or wrong. A model has a third possibility: it may be right, but irrelevant." (Manfred Eigen, 1973)

“Model is used as a theory. It becomes theory when the purpose of building a model is to understand the mechanisms involved in the developmental process. Hence as theory, model does not carve up or change the world, but it explains how change takes place and in what way or manner. This leads to build change in the structures.” (Laxmi Kanta Patnaik, “Model Building in Political Science”, The Indian Journal of Political Science, Vol. 50, No. 2, 1989) [Link]

“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) [Link]

“A theory is a good theory if it satisfies two requirements: it must accurately describe a large class of observations on the basis of a model that contains only a few arbitrary elements, and it must make definite predictions about the results of future observations.” (Stephen Hawking, “A Brief History of Time: From Big Bang To Black Holes”, 1988)