I always enjoyed philosophy, but I never thought to ask this question when I was still taking philosophy classes. So, I thought this was a good way to see what "philosophy" people think of this.
When you spend time trying to define terms in philosophy, what are you doing exactly?
Examples: In ethics: what is good? what is right? In aesthetics: what is art? what is beauty? In epistemology: what is knowledge? In social/political philosophy: what is justice?
In these cases, and others I'm sure you can think of easily, what is the goal exactly? To say what the term "should" mean? To say what the term "does" mean, in the sense of how it is used by people? I realize I'm verging on philosophy of language territory here. But I really want to know what people engaged in trying to pin down terms like this think they are doing?
In mathematics, you simply define terms however you want, and the definitions are good or bad depending on what you can do with them, is that the idea? If you just want to know how the terms are used, it seems like that isn't inherently philosophical, more empirical. I would appreciate any perspectives on this!