I'm reading Jech/Hrbacek's: Introduction to Set Theory.
Notice that the definition of the constant $\emptyset$ is justified by the Axiom of Existence and Lemma $3.1$
Intuitively, sets are collections of objects sharing some common property, so we expect to have axioms expressing this fact. But, as demonstrated by the paradoxes in Section $1$, not every property describes a set; properties "$X\not\in X$" or "$X=X$" are typical examples
In both cases, the problem seems to be that in order to collect all objects having such a property into a set, we already have to be able to perceive all sets. The difficulty is avoided if we postulate the existence of a set of all objects with a given property only if there already exists some set to which they belong.
The Axiom Schema of Comprehension: Let $\textbf P(x)$ be a property of $x$. For any set $A$, there is a set $B$ such that $x\in B$ if and only if $x \in A$ and $\textbf P(x)$.
What does the author mean by the part in italics? My guess is that "perceive all sets" mean having all sets at hand which in the course of the abstraction doesn't really matter, while doing the suggested fix, we can think: If such and such happens, then something happens. (I guess in this case, we don't need to be sure that the set exist in question exists). Is this it?