The definitions that you are free to introduce or change usually latch on to an otherwise motivated thing, you usually have at least some sort of informal reason to choose a particular definition. When you change a definition, you start talking about something else. If it’s not important (or a priori impossible to evaluate) what it is you will be talking about, in other words if the motivation for your definition is vague and tolerates enough arbitrariness, then it’s OK to change a definition without a clear reason to make the particular change that you do.
So I think the situation can be described as follows. There are motivations that assign typically vague priorities to objects of study, and there are definitions that typically specify more precisely what an object of study will be. These motivations are usually not themselves objects of study, so we don’t try to find more accurate definitions for describing them. But we can also take a particular motivation as an object of study, in which case we may try to find a definition that describes it. The goal is then to find a definition for a particular motivation, so you can’t pick an arbitrary definition that doesn’t actually describe that motivation (i.e. this goal is not that vague).
I expect finding a description of (“definition for”) a motivation is an epistemic task, like finding a description of a particular physical device. You are not free to “change the definition” of that physical device if the goal is to describe it. (You may describe it differently, but it’s the same thing that you’ll be describing.) In this analogy, inventing new definitions corresponds to constructing new physical devices. And if you understand the original device well enough (find a “definition” for a “motivation”), you may be able to make new ones.
The definitions that you are free to introduce or change usually latch on to an otherwise motivated thing, you usually have at least some sort of informal reason to choose a particular definition. When you change a definition, you start talking about something else. If it’s not important (or a priori impossible to evaluate) what it is you will be talking about, in other words if the motivation for your definition is vague and tolerates enough arbitrariness, then it’s OK to change a definition without a clear reason to make the particular change that you do.
So I think the situation can be described as follows. There are motivations that assign typically vague priorities to objects of study, and there are definitions that typically specify more precisely what an object of study will be. These motivations are usually not themselves objects of study, so we don’t try to find more accurate definitions for describing them. But we can also take a particular motivation as an object of study, in which case we may try to find a definition that describes it. The goal is then to find a definition for a particular motivation, so you can’t pick an arbitrary definition that doesn’t actually describe that motivation (i.e. this goal is not that vague).
I expect finding a description of (“definition for”) a motivation is an epistemic task, like finding a description of a particular physical device. You are not free to “change the definition” of that physical device if the goal is to describe it. (You may describe it differently, but it’s the same thing that you’ll be describing.) In this analogy, inventing new definitions corresponds to constructing new physical devices. And if you understand the original device well enough (find a “definition” for a “motivation”), you may be able to make new ones.