Please name any other complex subject that does not need to do same thing. Precision in language is essential to communication and the discovery of truth. The world we live in demands that the complex, the simple, the important and the mundane, all must be described in using the same words in the language. Therefore distinctions in definition are mandatory.
Mathematics. Does “homomorphism” have heavy colloquial baggage? Hypotenuse? Countably infinite? Topology?
I’m not arguing against defining terms. I’m arguing against using deliberately misleading terms, or concepts that are colloquially held to be synonymous but asserted to be different without a justification.
For example, I’ve never heard an instance of this happening in mathematics:
Mathematician A: Hey, we’ve got a theorem that doesn’t make mathematical sense but we’re required to believe it anyway!
Mathematician B: What are we going to do?
Mathematician A: I don’t know!
Mathematician B: Well, the new theorem is related to countability, right?
Mathematician A: Yes, sort of. But it contradicts things we
have already proven about countability.
Mathematician B: Well then, lets make a
new thing called numberability.
Mathematician A: But that sounds like the same thing as countability, how will it help us?
Mathematician B: Oho! Numberability is
not the same thing as countability, its very similar, but it has features that resolve the conflicts with this theorem we need to save for some reason!
Mathematician A: Great! What features are those?
Mathematician B: How should I know? Look, when you’re talking about this theorem, just pretend that numberability and countability are the same thing, right up until someone points out that there is a conflict with some other proof. When that happens, just say that our theorem was about numberability while the other proof is about countability and so there is no conflict.
Mathematician A: But what do we do if they see through this and point out that we’re just using our numerability concept as a get-out-of-jail-free card?
Mathematician B: Accuse them of being bad at math!