 A good translation of (1) into a first-order language is (1′). But the analogous translation of (2) would yield (2′), which is inadequate. A good translation for (2) would be (2″) but it is unclear why. We might convert ‘\(\neg \exists\)’ to the equivalent ‘\(\forall \neg\)’ but then we must also inexplicably push the negation into the consequent of the embedded conditional.