I'm trying to write about the differences between models and theories for academic writing (with no greek letters). I wonder if you agree with my text.
The differences between theories and models are several:
- Differences in representation
- Differences in usage
- Differences of notation
Theories are sets of statements that can be infinite and thus don’t represent reality. A model, on the other hand, is a representation of reality. A model is used to understand reality while theories are about what is true and false. The model is used to understand the theory.
A theory could be a mathematical relationship for mechanics whereas the term model is used for representing or approximating a theory. In this sense, the difference between a model and a theory is not always large.
I can not find a source for that a theory can be infinite. Do you agree?
You're correct that a theory is a set of statements, and that a theory can be infinite. However, the question of "reality" is an iffy one in logic - for example, models can also be infinite.
Theories can be thought of as "descriptions"; they list facts. A model is a structure - or, put a little more sensationally, a universe. A model is a thing in which facts can be true or false.
For example, the structure of the natural numbers with the usual operations $+$ and $\cdot$ are a model. The number $2$, for example, is in this model. The corresponding theory is the set of true things that can be said about this structure. $2$ is not in the theory, because it isn't a sentence. But the sentence "$2$ is prime" is in the theory, because it's a true fact. The sentence "$2$ is not prime" isn't in the theory, because it isn't true.
I've answered this under the assumption that the "logic" tag is accurate. Importantly, you may be talking about a different sort of "theory" and "model". For example, we can talk about the "theory of gravitation" and about a "model of population growth". These are very different from the concepts in logic, and you should make sure that you understand which one you're trying to write about.