Axiom:Axiom of Abstraction/Historical Note

Historical Note on Comprehension Principle
It was first noticed that the comprehension principle led to paradoxes at around $1900$ (see, for example, Russell's Paradox).

These arise from the semantic looseness of the qualifier "in some way or other".

For a rigorous approach to set theory, it is necessary to specify exactly what the rules are by which one may build sets.

There are different techniques for doing this, the best known perhaps being the Zermelo-Fraenkel axioms.