For example say: If I went out, then I went to the movies.
Is the negation: If I went out, I didn’t go to the movies?
This negation goes a bit too far. A better statement is “If I went out, then I may or may not have gone to the movies.”
By negating a conditional statement, we don’t jump to the polar opposite. We simply rewrite the statement in such a way that the antecedent no longer implies the consequent.
“Some of the museum’s employees are not paid significantly more than the minimum wage.”
The negation of “some” is “none,” which leads us to “None of the employees are not paid significantly more than the minimum wage.” However, this reads horribly due to the double negative (“none” and “not”). So let’s take that out: “All of the employees are paid significantly more than the minimum wage.” Now that’s something we can work with.
“An ideal bureaucracy will never be permanently without complaints about problems that are not covered by that bureaucracy’s regulations.”
The negation of “never” is usually “sometimes.” But in this case, “sometimes” makes no sense (sometimes permanently?). What we need to negate is the idea that the bureaucracy will never be without complaints permanently. In other words, we want to convey that it is possible for the bureaucracy to permanently run out of complaints. To do this, I’ll use “could potentially be” in our negation: “An ideal bureaucracy could potentially be permanently without complaints about problems that are not covered by that bureaucracy’s regulations.”