They feel that there are some sorts of statements ϕ for which ¬¬ϕ = ϕ is invalid. Or, more interestingly, that if we force it to be such that all statements hav

They feel that there are some sorts of statements ϕ for which ¬¬ϕ = ϕ is invalid. Or, more interestingly, that if we force it to be such that all statements have that property then we lose the ability to talk about certain interesting things where it is not available.