Not both vs Either/or

[andwer123]

I was pondering these two terms and can't quite grasp why they aren't diagrammed the same way...

I know that:
Either X, or Y is diagrammed:
~X Y
And I also know that this leaves the door open for the possibility that you have both (which is why sometimes you see "not both" included with either/or)

I know that:
Not both X and Y is diagrammed:
X ~Y
And I also know that this leaves the door open for the possibility that you have neither since the negative term is in the necessary position, i.e. having no bearing on the existence of the sufficient condition.

Most of my curiosity comes from why the negative term is placed in the necessary position in the diagrammed "Not both". These seem to achieve opposite outcomes at their extremes (neither term present or both terms present).

Thanks for the help!

[andwer123]

I figured it out.

Either/or places the negative term in the sufficient because one term must be present. If the negative term were in the necessary position it would leave the possibility of neither being present. By choosing to use either/or, the author is requiring that one of the terms to be present. It's is the exact opposite for Not both.

That was a doozie.