My question stems from the two different logical forms for the following sentence under Russell's analysis. One in which the word 'not' has a wide scope and one where it has a narrow scope.
The sunken city of legend does not exist.
With wide scope:
There does not exist a unique thing that is a sunken city of legend.
not ([the x: x is a sunken city of legend] x exists)
With narrow scope:
The x such that x is a sunken city of legend, is such that x does not exist.
[the x: x is a sunken city of legend] not (x exists)
I know how to express the wide scope version into predicate logic, but not the narrow scope interpretation. Can someone please help me with this?
Also, under the narrow scope interpretation the sentence would be false, so is it okay to reject this interpretation in favour of the wide scope version?