Interesting that 3 professors are consistently arguing the same thing that we Catholics are.
There is a definition. You ought not deviate from this definition. If you want to be consonant with truth.
That’s subtly different than your initial claim, which is that definitions are true or false. If definitions have truth values, then there is “the” definition of a word, but the rest are mistaken.
Mathematicians merely propose “a” definition to be used for the sake of the discussion. It is fully understood that the proposed definition often doesn’t match conventional dictionary definitions. It is understood that you probably won’t “accept” such a definition in the sense of embracing it. But acceptance isn’t necessary for conventions. You need only use the definitions in that context, not accept them.
Again, there are a few good examples in my classes: “A probability is just a number assigned to a subset of a sample space which satisfies these axioms. And that’s it–you can’t argue with a definition.” “A line is just a member of a set. It needn’t be straight or be given by a formula. And that’s it–you can’t argue with a definition.”
BTW: did you tell these 3 professors that you have a problem with insisting that a particular definition is the correct one?
There seems to be a misunderstanding regarding what a convention is. Acknowledging that something is a convention doesn’t mean that it’s advisable to deviate from it. It just means that its meaning is based on an implicit understanding between the parties that use it. It isn’t necessary that the convention have universal support.
For example, driving on the right lane is a convention. Many European countries use the left lane. Clearly there is no “truth” to using the left lane over the right or vice-versa, they are just conventions. We more or less just picked one arbitrarily to avoid accidents. It would obviously be highly impractical to use a different lane than everyone else, but the choice of which a country wants to use is arbitrary, and not a matter of truth or falsity.
Such is the case for the meanings of hand gestures or slang terms. It’s not a matter of what’s true or false, but rather what the parties involved intend to convey and to whom they are doing the conveying.
Now if we can agree that choosing definitions is like choosing the lane in which one can legally drive, then that’s settled.