To expand my understanding, I wrote an example to work through.
"Any law professor possesses a Yale Law School degree unless their scholarship is worthy."
- If your scholarship is worthy, having a YLS JD is no longer a requirement for being a law professor.
- Any professor of law is either a YLS alumn or has worthy scholarship.
- ~(Law Professor YLS JD) Worthy Scholarship
- Law Professor YLS JD or Worthy Scholarship
Assume Law Professor then,
- ~YLS JD Worthy Scholarship
- ~Worthy Scholarship YLS JD
The "unless" condition does not logically force a "but not both" condition. For the law professors example, one can have both worthy scholarship and a JD from Yale.
The "unless" breaks the conditional such that the necessary statement of the initial conditional is lessened in its logical force. The "unless" operates as a logical override.
Perhaps this is also why we can extend your ice cream translation to law professors.
- If someone is not a law professor then either they do not have a Yale Law degree or else they have worthy scholarship.
Or can we? Intuitively, it seems like it should translate to "If someone is not a law professor then either they do not have a Yale Law degree or else they do not have worthy scholarship."
Ahh I think switched the terms. It should be:
"If someone does not have a JD from Yale, then either they are not a law professor or they have worthy scholarship."
- ~Yale JD Not a Law Professor OR Worthy Scholarship
This seems like it really means "OR law professor with worthy scholarship"
So this implies that if they are a law professor and do not have a JD from yale, then they must have worthy scholarship.
- (~Yale JD + Law Professor) Worthy Scholarship