I was reading about how the english language has 'changed' and 'developed' over time, and this has me wonder, what makes the 'English' Language what it is? If we define a language as a set of formulas and semantic rules we find that when we add a new word, what we essentially do is define a new language to be what we refer to as 'English', we find this to be the case because when we add a new word, the 'old language' doesn't really cease to exist.
Is it paradoxical in this sense, bringing to mind the idea of the Ship of Theseus to really talk about anything as being the same numerically and different qualitatively over time, can we see the change of time simply being that we replace one thing with another? Perhaps my broom is an immutable object in so far that if I were to remove it's handle and replace it I actually have another broom, however it is convienient in all sense and purpose to call it 'the same broom' as it will act exactly the same as it's predecessor.
Perhaps when someone is the 'same person' we mean that they have the same (immutable) identity, and any other characteristics (height, personality etc) are free to be replace with others.
Especially in the case of abstract objects, once a concept exists it cannot cease to exist even if we dont want to use it for anything, or we find there are problems with it.