Wilsonian Quantifier Trilemma: frogs and princes
In an earlier blog I referred to the “Wilsonian quantifiers”; ‘some but not all’ and ‘all or none’. These are to the ‘all’ and ‘exists’ quantifiers as ‘exclusive or’ and ‘if and only if’ are to ‘and’ and ‘or’. I have found a troika involving them.
Moe: No frogs are princes.
Larry: Some but not all frogs are princes.
Curly: All frogs are princes.
Moe, Larry and Curly all agree that frogs exist.
By 2/3 majorities each:
LK: Some frogs are princes.
ML: Some frogs are not princes.
KM: All or no frogs are princes.
The last can be read, “All frogs are equally princes.”