Is Turing machine a scientific theory in CS? The English Wikipedia article about Turing machine opens with:


  A Turing machine is a mathematical model of computation that defines
  an abstract machine,[1]


As a Hebrew speaker, I read a similar explanation in Hebrew Wikipedia:


  מכונת טיורינג היא מודל חישובי מתמטי אשר
  באמצעותו ניתן לתאר באופן מופשט את פעולתו של מחשב (כולל מחשב מודרני).


My problem

I understand this term as reflecting a scientific theory in CS or Math, but interestingly, none of the two opening sentences presented this concept as a scientific theory in either CS or Math.

By scientific theory I meant:


  An idea or set of ideas that can be falsified by principle
  (falsifiability as a condition for it to be real) and that one or more
  reinforcements can make it somewhat more plausible in reality.


But;

If it's a theory in Math, maybe my approach is wrong, because, as far as I understand, in Math the paradigm is different so something is either true or false (i.e, not true).

My question

Is Turing machine a scientific theory in CS?



Update

In comment section, Yuval Filmus said (minor paraphrase):


  Turing machines are a mathematical abstraction.
  They're neither a scientific theory nor a practical engineering idea;
  Actual computers are much better modeled using a different abstraction → RAM machines;
  The relevant scientific theory is the Church-Turing thesis.


This made me wonder "what is the difference between a mathematical model and a mathematical abstraction and does the former or the latter or both, can be based in a "scientific theory"?

This isn't the main question, but you are welcome to explain this in an answer as I think it's relevant.
No, as Yuval Filmus explained, a Turing machine is not a scientific theory.

Furthermore, something can be both a mathematical model and a mathematical abstraction; for example, if the model is an abstraction.

Types of scientific theories

In the physical sciences, a scientific theory is a set of rules or models that makes testable predictions that could potentially be falsified. A Turing machine just isn't any of those.

In mathematics, the word "theory" may be used to describe a framework for reasoning where we have axioms, definitions, and inference rules for making deductions that follow from those axioms and definitions.  A Turing machine isn't that, either.

Personal opinion

I don't think it's a good use of time to devote a lot of energy to these kinds of questions. Instead, I would suggest that you learn the basic material in textbooks on Turing machines and computability and decidability, and don't worry too much about how to categorize or classify it or what words can be applied to it.  From a computer science perspective, it's more useful to focus on the mathematics without trying to put it into a philosophical framework or trying to come up with definitions of these broad, vague concepts (abstraction, theory, model).