Logic and logical semantics are traditionally oriented towards the analysis of extensive (referential) relations between sets of entities that form the subject area of reasoning. Thus, incompatibility, identity, intersection, inclusion (genus vs. species) are relations between the extensions of concepts, i.e. relations between the corresponding sets. In this case, the fundamental assumption is that the universe is not empty. Such an attitude is characteristic of the general attitude of European rationalism towards positive knowledge, fuelled by the cataphatic semantic picture of the world. The extension of logical analysis to modal, intensional, and epistemic contexts posed the task of clarifying the content of such ontological assumptions. Such a refinement was the development of a wide range of semantics of “possible worlds”, the apparatus of logic, free from existential (ontological) assumptions. In this paper, we consider the possibility of an “apophatic” extension of logical analysis to judgements with negative predicates, which goes back to the logic of Lewis Carroll, which makes it possible to obtain a number of non-trivial generalizations.