The noun form of "well-defined"?

Question

What’s the noun of *well-defined* (meaning that something is defined well in a mathematical sense). Also, could you show me more examples of the same structure/principle (of transforming the adjective form to noun)? I guess it is *well-definedness*, but Google tells me that no one uses it.

Answer 1

Well, I would agree with google - "well-definedness" is one of those made-up words that might get the right point across in casual conversation, but wouldn't pass a "white paper" review.

There are several general rules (or patters) we can observe and try to apply (like the ones described here - http://writingfix.com/PDFs/Writing_Tools/Adjectives_into_nouns.pdf), but I think the problem we have with "nounifying" ;-) well-defined in the mathematical context you describe is that there is no 1 single equivalent noun that gets the point across ....

I would argue you need at least 2: clarity and completeness (maybe throw in a 3rd - simplicity)

Imagine that you were trying to determine, by consensus, how well-defined something was: you might design a simple survey whereby responders would choose a 1-5 rating (5 being the best):

Clarity: 1 2 3 4 5

Completeness: 1 2 3 4 5

Simplicity: 1 2 3 4 5

And arguably, those 3 qualities would be a solid measure of how "well defined" something was ...

Hope this helps.

--Lou