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What is the difference between a scientific theory and a model?

Can someone explain the ideas with the help of a theory in physics and a model of physics?

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    physics.stackexchange.com/questions/187967/… duplicate question on physics.SE – Not_Here Apr 7 '17 at 6:35
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    See Models in Science: Models and Theory : "The separation between models and theory is a very hazy one and in the jargon of many scientists it is often difficult, if not impossible, to draw a line." – Mauro ALLEGRANZA Apr 7 '17 at 13:25
  • @MauroALLEGRANZA +1, I think the distinction is very hazy, or maybe not that relevant in practice. The theory of QM has a certain model for photons. The theory of QFT offers another model for photons. – Frank Apr 7 '17 at 14:33
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A theory is an explanation of a phenomenon in the world, which may or may not be directly experienced by our senses. For instance, children make the most fascinating theories about the things they experience.

A scientific theory is a system of consistently defined concepts and falsifiable propositions, which has the purpose of explaining a phenomenon in the world. The latter may or may not be directly experienced by our senses. Moreover, a theory has the purpose of making both reliable and valid prognostications regarding the behavior, future states or whatsoever of that phenomenon.

A model is a simplification of something. It's purpose is to make something graspable, by leaving out details, which are negligible for understanding this thing or working with it. A model may use theoretical concepts, that is, concepts defined within a scientific theory, but may also use everyday language. Moreover, a model can also consist in a visualization, like e simple diagram or a three-dimensional object--like the ones made by architects.

For example, as a layman, I would have a hard time trying to grasp the theory of relativity as formulated by A. Einstein. Luckily, physicists make models of their theories which are suited to convey at least part of their knowledge to layman. Or: The model of a building, for instance, won't have functioning washbasins, they are left aside in order to simplify.

A similarity between theories and models is: While a model is a simplification per definition, when building a theory it is advisable to follow the principle of parsimony of explanation. But that doesn't necessarily mean, that a theory must be simple. It rather means, that a theory is better than another one if it can do the same job in a simpler way.

  • Can't we say that a theory is a model for a set of phenomena? Even if you model particular phenomena separately, they need to be consistent with each other in a theory, so the union of all the models is like one giant model that is the theory, in a sense. – Frank Apr 7 '17 at 14:31
  • Well, I agree, that we can. Then, I prefer to differentiate between a theory and a model, basically so to have two distinct "tools" to work with. I also agree that many scholars don't put much weight on distinguishing sharply between the two. According to the terminology I refer to, instead of "modeling a phenomenon" I would rather say "to formulate an intensional definition of a phenomenon". If I raise claims about causal relations between two or more phenomena, then I am formulating a theory about these phenomena (or data-sources, or observations). – user26333 Apr 8 '17 at 19:30
  • Another question: is it possible to have a theory made up of several models that would be inconsistent between themselves? In the presence of such an issue, would the theory be provisional - or - is it possible that there are things in Nature that can be modeled one way, others another, incompatible, way, and it will never be possible to make the two consistent? What I'm getting at is, even if we wish for consistency, Nature might not grant us consistency. Can we have knowledge about Nature that is truthful, but inconsistent to us? – Frank Apr 8 '17 at 19:45
  • I'm afraid that my answer will not fully satisfy you, since I believe, that we use the term "model" in a different way. The theories I speak of are made out of concepts. I use a model, to convey my ideas about a theory and its concepts. Consistency within a theory is a matter of defining concepts that aren't contradictory; still referring to "theory" as a system of concepts and propositions about the relations between them. Then, if a theory cannot predict the behavior (or processes etc.) in the world properly, it's a bad theory and will soon be forgotten by the scientific community. – user26333 Apr 8 '17 at 19:57
  • I think I'm proposing a slightly more subtle situation. Say you are doing physics, and you have an extremely successful "model" or part of your theory to predict some things, but you have another extremely successful model for another domain of physics. Yet the two could contradict each other, meaning that none can claim "finality" or being the unique model that works in both domains. It's not that either model/theory is bad. They are both very good. But they could make false predictions when used on the other domain. What do you do then? – Frank Apr 8 '17 at 20:02

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