But it covers only what it is able to say. Thus any attempt to be more expressive breaks it.
edit: actually the theory works just fine. It isn’t even broken but it is a different theory. If I would had said that this was a theory of “amounts” this would have been clearly progress that should be welcomed. But what if in my pretheoretic sense I equivocate “integers” and “amounts” (as could be assumed if I can’t fraction). Thus when wanting a better theory it’s ambigous whether I want or don’t want it to cover that kind of scenario.
Exactly. If it acts like integers, then use integers. The above example, you tried to use integers despite the underlying phenomenon not acting like integers. That broke it.
No, you just broke your model by doing something not covered by it.
But it covers only what it is able to say. Thus any attempt to be more expressive breaks it.
edit: actually the theory works just fine. It isn’t even broken but it is a different theory. If I would had said that this was a theory of “amounts” this would have been clearly progress that should be welcomed. But what if in my pretheoretic sense I equivocate “integers” and “amounts” (as could be assumed if I can’t fraction). Thus when wanting a better theory it’s ambigous whether I want or don’t want it to cover that kind of scenario.
Exactly. If it acts like integers, then use integers. The above example, you tried to use integers despite the underlying phenomenon not acting like integers. That broke it.