No, that wouldn't be strict use of the term idiot, because it's no longer a clinical term. That would be a loose, or at best anachronistic use. The pejorative use has completely supplanted any other modern use of the word, and there is other clinical terminology used to describe someone with an IQ of 50.
Kind of like the word "macaroni". Three hundred years ago "macaroni" meant something like a stylish, affected Englishman.
So according to your convenient criteria, if I order some macaroni and cheese, I'm using the term macaroni "loosely", just like the term "cool" would be "loose" when applied to someone stylish. But if I call that stylish person a macaroni, then hey, I'm being strict.
Bloody brilliant, Ken.
I had not realized that "idiot" was no longer technically used to denote those below a certain IQ. But that really doesn't matter, does it. Suppose it still were so used. Then my point would be intact.
The word, "cool" when used in that way is not being used loosely. It just is being used with an entirely different meaning. The same is true of "macaroni".
There is a difference between a word being used loosely, and being used to mean something different.
For instance, I may use the term "bank" (financial institution) to designate a place in my house where I keep my money. That would be a loose use of the term, "bank". But if I used the term "bank" also to designate the side of a river (a river bank) that would be a different use of the term, "bank".
But we are really off-track concerning Godel's theorem. But you do see that it is just nonsense to say that Godel proved we cannot prove any theorem. I can prove theorems in the propositional calculus all day long by the truth table method. It is just very tedious. That is why we can program computers to do it (if we wish). Actually the proofs are too trivial to bother with.
But what Godel showed is that for some theorems no machines can be programmed to prove. Which is why brains (which can prove them) are useful.