Gideon Rosen and David Lewis
So far, Lewis has granted that true predications do after all have truthmakers. But he does not yet accept the Truthmaker Principle in full generality, because he still doubts that true negative existentials have truthmakers. But if Lewis's proposal to take qua-versions of things as truthmakers will work at all - in other words, if we are entitled to take ordinary things as truthmakers by supposing that they make propositions true relative to the peculiar counterpart relations that are evoked by peculiar names for those ordinary things - then his proposal can be extended to the case of negative existentials.
We should not take cat Long qua unaccompanied by unicorns as a truthmaker for the truth that there are no unicorns. That was indeed a cheap trick, for the reason Lewis said: the requisite 'peculiar counterpart relation' is no genuine counterpart relation at all, being founded on an unimportant and unduly extrinsic respect of similarity. But if we take a qua-version of a better-chosen thing, we can use a much more satisfactory counterpart relation.
Begin with an easy case: restricted negative existentials, such as the truth that there are no unicorns in this room. (In this room now, but let that restriction remain tacit.) Let this room+ consist of this room together with everything in it: the air, the furniture, the unicorns if any, … . This room+ qua including no unicorns is a truthmaker for the truth that there are no unicorns in this room. This time, the peculiar counterpart relation evoked is founded on an entirely intrinsic and salient respect of similarity. But we could instead have used this room qua containing no unicorns; the counterpart relation is still satisfactory, being founded on intrinsic similarity not between the counterparts themselves - the rooms - but between more inclusive things - rooms+ - that are saliently related to the counterpart rooms.
Likewise, mutatis mutandis, for the less restricted negative existential truth that there are no unicorns on this planet; or even the truth that there are no unicorns in this galaxy; or even the truth that there are no unicorns in this galaxy throughout its history.
For unrestricted negative existentials, such as the truth that there are no unicorns anywhere, ever, we can take as truthmaker a qua-version of the entire world: the totality of everything there actually is. That way, our counterpart relation can again be founded on intrinsic similarity.