In science we often use formal models (by which I mean a mathematical structure composed of assumptions, variables, and equations, which might be solved/simulated to derive analytical insights and/or testable hypotheses). If the objective is to explain a certain phenomenon, one would proceed by (i) looking at data for relevant (to the modeller) stylised facts, (ii) set up a formal model that can capture those facts, and (iii) take the model to the data to test hypotheses derived from the model. This way, is often said, one is providing "support for a model".
Now, it makes perfect sense to build a model based on key insights from the world. But if that is the case, what is the real value of deriving hypotheses in order to "test the model"? I mean, by definition, WYPIIWYGO (what you put in is what you get out). Put good things, and you will get good things. So from an epistemological point of view, what is the actual benefit of a model? Is there real value added in using them?
I know this topic is probably huge in philosophy of science. There is a snippet about it in the Standford Encyclopedia of Philosophy. The answer there is however deeply unsatisfactory (at least to me). In particular, take this paragraph:
We begin by establishing a representation relation (‘denotation’) between the model and the target. Then we investigate the features of the model in order to demonstrate certain theoretical claims about its internal constitution or mechanism; i.e. we learn about the model (‘demonstration’). Finally, these findings have to be converted into claims about the target system; Hughes refers to this step as ‘interpretation’.
Once the model is built, we do not learn about its properties by looking at it; we have to use and manipulate the model in order to elicit its secrets.
This seems to me to be the key. A model has secrets. That's the value they add. But why is this? Is it always the case? And going back to my central question: since WYPIIWYGO, what's the merit of a model anyway? These seem not to be discussed in the link.
PS: references to great articles covering this (without needing to get into a full course of philosophy of science [not yet, at least]), are more than welcome.