Analyzing "and/or"

As someone with a somewhat logical mind who does a lot of editing, here is a question I've always wondered about.  (Warning:  this one is seriously geeky.)  How, exactly, is the formation "and/or" supposed to work?  I've always thought that it has two possible interpretations.  But, I've never seen this addressed anywhere, so perhaps I'm the only one on earth who reads it this way.

As an example, look at this sentence:

That assumption of yours is wrong and/or unfounded."

"Unfounded" meaning you do not have any evidence or reason to make the assumption, "wrong" of course meaning it is actually incorrect.  What exactly does the "and/or" mean?  The possibilities, it seems to me, are:

1. The assumption is (wrong and unfounded) OR (wrong OR unfounded). 
   
2. The assumption is ("wrong and unfounded") OR it's ("unfounded").
   

MEANING #1:  Under this looser interpretation of "and/or" it does not matter in what order the two terms appear, because either one may apply.  It might be rewritten as "the assumption is wrong and unfounded, or it is wrong, or it is unfounded."  There are 3 possible states

MEANING #2:  This meaning is how I've always interpreted the expression.   It might be rewritten as "the assumption is (wrong and) or unfounded."  There are only 2 possible states.  It could also be rewritten as, "the assumption is unfounded, and perhaps also wrong."  Here the order of the two terms matters a lot, because the second expression ("unfounded" in my example) must always be true, while the first one ("wrong") may or may not be.  Under this interpretation it would be incorrect to reverse the terms and say "the assumption is unfounded and/or wrong," since an assumption can be accused of being unfounded but not wrong -- but a person who assets that an assumption is wrong, cannot but also assert that it is unfounded.  In other words, you would never say it's wrong without also saying it's unfounded.

Somebody oughta clarify what it means. Who?  Who knows.  Maybe me.  Okay, I hereby declare that the proper meaning is #2 and that #1 represents nothing but muddy-headed, sloppy thinking.

Okay maybe nobody has a clue what I'm trying to say here, but mark my words, this is the kind of thing that the fate of empires hinges upon! 

Comments

[Turvene]

This is some serious navel gazing and/or a timely piece of critical thinking by an important scholar!