It strikes many as obvious that negative facts—such as that Justin Trudeau is not the prime minister of Australia—are not fundamental: negative facts must ultimately be explained in terms of positive facts (for instance, that Justin Trudeau is the prime minister of Canada). I focus on a particular class of negative facts: contingent negative existentials (such as that there are no 10ft tall humans). If contingent negative existentials are not fundamental, then they must be explained. But the claim that contingent negative existentials are explained is in tension with the widely held view that any universal generalization can be explained by its instances together with a totality fact (i.e. a fact to the effect that the instances exhaust the relevant domain). This is because a totality fact is itself a negative existential, and equivalent to a universal generalization. If the explanation for any contingent negative existential must appeal to another contingent negative existential, then—unless there are no fundamental facts—not all contingent negative existentials can be non-fundamental. I argue that we should give up the age-old mantra that only positive facts can be fundamental. I show that at least some contingent negative existentials are fundamental. I first make the case for including a totality fact in the explanans for a contingent negative existential and show that alternative accounts for explaining such facts are inadequate. I then undermine the standard arguments for subscribing to the view that there are no negative facts—including negative existentials—at the fundamental level.